title: How to evaluate, how much current flows in the circuit?

text: Please take into advisement, that I'm quite a beginner in subjects of physics and especially about electricity. Lately I've decided, that I want to learn more on basics of electronics and I've started reading about it, but a few things still are unclear for me. I understand, that the voltage is the force, which pushes electrons through the wire. I also understand, that current is amount of electrons pushed by the wire in time. It's also clear for me, that power source, such as battery, has defined voltage, which it can provide. What is unclear:   1. How can I determine, how much current will flow through the circuit? Suppose, that I connect a 1.5V lightbulb to a 1.5V battery - how much current will flow through this circuit?   2. Too high voltage will fry the lightbulb (or other resistor), because voltage (being an actual electrical energy, as I understand that) will cause too much heat in the resistor. But is it possible to apply too much current to a resistor?   3. Battery capacity is expressed in mAh. Say, that the battery has 1200 mAh = 1.2 Ah = 72 Amin (ampminutes) = 4320 Asec (ampseconds). Is it actually (physically) possible to drain 4320 amps from this battery in a second? If not, what is the restriction, which prevents one from doing so? (not that I want to try :))


title: The momentum of a hole

text: I'm currently working through "A Guide to Feynman Diagrams in the Many-Body Problem" by R.D. Mattuck (self study, not a homework problem) and am stumped by the following problem: "In a system of free particles, a hole is created in the single particle state $\phi_k=\frac{1}{\sqrt{V}}e^{i\vec{k}\cdot\vec{r}}$. What is the momentum of the hole?" The answer given is $-\vec{k}$. In the above, $V$ is the normalization volume of the system, $\vec{k}$ is the wavevector and $\vec{r}$ is the position. Natural units ($\hbar=1$) are used throughout this question. If this were a particle instead of a hole, the momentum would simply be $\vec{p_e}=\vec{k}$. If the answer given in the book is correct, am I then right in thinking we must redefine the momentum operator somehow? If so what motivation do we have for doing this? In my head these ideas seem to run contrary to what I know from solid state physics: if we have an electron in the valance band and excite it to the conduction band, and if there is no input of momentum during this process, then I always thought we would be left with an electron of wavevector $\vec{k}$ and a hole with wavevector $\vec{k}$ also. My feeling is that this IS correct, but that I am falling victim to the sloppy condensed matter habit of using the terms wave-vector and momentum interchangeably. Edit: I have come to the realization that the issue is with the wording of the problem, which is not entirely transparent. It makes more sense if written: "An electron initially has momentum $\vec{k}_e$ and wavefunction $\phi_{k_{e}}=\frac{1}{\sqrt{V}}e^{i\vec{k}_e\cdot\vec{r}}$. It is removed from the system leaving behind an empty orbital. What is the momentum of the orbital? In the particle-hole picture, what is the momentum of the hole?" Answer: The orbital left vacant still has wavevector $\vec{k}_e$ which can be seen by applying the momentum operator $\hat{p}=-i\nabla$ to $\phi_{k_{e}}$. The vacant orbital is not, however, the same thing as a hole. If the system originally had zero total momentum, then we have removed some amount $\vec{k}_e$ and the total momentum of the system is now $-\vec{k}_e$. We attribute this momentum to the hole, and say that $\vec{k}_h=-\vec{k}_e$. The hole wavefunction must then be (see Heisenberg, 1931 for proof) $\phi_{k_{h}}=\phi_{-k_{e}}=\frac{1}{\sqrt{V}}e^{-i\vec{k}_e\cdot\vec{r}}$. Applying the momentum operator to this wavefunction gives the correct result. The confusion arose because, in the question given by Mattuck, it is unclear whether $\vec{k}$ is the wavevector of the empty orbital left behind by the electron or the wavevector of the hole.


title: QFT in curved space

text: Can someone exactly tell me what one gains from doing QFT in curved space, and how reliable these new results are. I want to know if it is worth while putting some man hours towards this. Please don't exaggerate any facts, just the truth.


title: Concerning Scattering Intensity and Particle Concentration

text: I am trying to determine what governs my sensor output. I have an optical sensor that emits infrared radiation on a sample volume and gives me a voltage output from the scattering of (1 to 10 micron) particles through a 90 degree scattering angle. I introduce aerosol particles of various sizes and keep track of the scattering output voltage Parallel to my sensor output I also record the Number, surface and mass concentration of my aerosol particles from a different sensor unit. I am trying to determine what governs my sensor output voltage. I know that Mie scattering depends on Mie intensity parameters, which depends on particle size, i.e. $$ I(\theta) = \frac{I_0 \lambda^2(i_1 + i_2)}{8\pi R^2} $$ where $$i_1, i_2$$ depends on the particle size. As I increase the number concentration, my signal increases, indicating a dependence on total particle surface area in the sample. I have plotted my sensor output vs number, surface and mass concentration for different particle sizes. Should I not be able to make my Sensor Output vs Number Concentration for the different sized particles collapse if I multiply the number concentration by the area of the individual particles? Or is the area dependence in Mie scattering more complicated than this?


title: What "I" should use in Rotational Energy formula $(I \omega^2)/2$

text: $\text{Rotational Energy} = \frac{1}{2} I \omega^2$. What $I$ should be used? $I$ as a inertia tensor matrix = stepRotation * inverse moment of inertia * inverse stepRotation; Or I as moment of inertia? Inertia tensor matrix gives changing energy due to rotation changes. So I don't believe its the right answer, but I'm not sure. Moment of inertia remains the same in simulation because it only represents the mass resistance to rotation in a fixed axis calculated by integration of massparticles * radius from object center.


title: Enginering question about F1 car

text: In formula F1 car, air coming infront of the car goes up with very high velocity as a result pressure difference is created which is very high from Bernoulli theorem.. The F1 car is very light so Bernoulli theorem suggest that instead of moving in the road, the car should fly out in the air.. What is wrong here ? Don't give answer like because the car is heavy. It is lightest car and its speed is nearly to the speed of some plane..


title: Are the Maxwell equations a correct description of the wave character of photons?

text: In basic quantum mechanics courses, one describes the evolution of quantum mechanics chronologically. Interference experiments with particles showed that particles should have a wave character; on the other hand, the photo-electric effect showed that electromagnetic waves should have a particle character. So there's a **particle-wave duality**. The course continues with postulating the **Schrödinger equation** , and solves the problems for the **wave character of classical particles** (e.g. with respect to harmonic oscillators to solve the UV-catastrophe in the description of blackbody radiation). On the other hand, one describes the photo-electric effect extensively with perturbation theory, as the electromagnetic wave acts as a periodical force on an electron. But the electromagnetic wave is still described with the Maxwell equations, and not by Schrödinger. _Suppose history went a little differently_ : the corpuscular character would still be the generally accepted behaviour of light (as Newton preferred), and one discovered the wave character of photons and electrons simultaneously by doing interference experiments. The laws of Maxwell, Gauss, Faraday and Ampère weren't discovered yet. Schrödinger comes up with his equation, and one describes the wave character of electrons as well as photons with this equation. Would this equation give a exhaustive description of the electromagnetic (and vector like) behaviour of photons? In other words: is the **Schrödinger theory** , in some way, **equivalent** to the **Maxwell theory** for the description of photons? Or are the Maxwell equations some kind of limit for greater dimensions (like the Newton equations for mechanics)? What is the link between these two "wave character" descriptions of photons?


title: The Molecular Hamiltonian and the avoidance of Overcounting

text: Whenever I see the total non-relativistic molecular Hamiltonian, $\hat{H}_{molecular} = \hat{T}_{e} + \hat{T}_{n} + \hat{V}_{ee} + \hat{V}_{nn} + \hat{V}_{en}$ I always notice that the sums describing the electron-electron and the nucleus-nucleus interactions respectively are corrected for overcounting (i.e. the second index is greater than the first), $\hat{V}_{ee} = \sum_{i}\sum_{j>i}\frac{1}{|\mathbf{r_{i} - r_{j}}|}$ $\hat{V}_{nn} = \sum_{I}\sum_{J>I}\frac{Z_{I}Z_{J}}{|\mathbf{R_{I} - R_{J}}|}$ whereas the sum describing electron-nucleus interactions is not corrected for overcounting: $\hat{V}_{en} = \sum_{I}\sum_{j}\frac{Z_{I}}{\mathbf{|R_{I} - r_{j}}|}$ Could anyone possibly tell me why this is? Thank-you!


title: Concerning Electrogravitics in an inertial frame

text: Listening to Feynman, He pointed out the fact that if a magnet is in an inertial frame with respect to a coil, there can be no electromotive force and hence no electricity produced. It is only when the magnet is moving with respect to the coil that there is electricity. That got me thinking, the same thing happens with time dilation. In that when an observer is in an inertial frame with the subject, they both experience the same time. But when the subject is moving time dilates or contracts. Is this just a coincidence, allegory, or are the two experiences related?


title: Majorana-like representation for mixed symmetric states?

text: Is there a generalization of the Majorana representation of pure symmetric $n$-qubit states to mixed states (made of pure symmetric $n$-qubit)? By Majorana representation I mean the decomposition of a state $$|\psi\rangle = \text{normalization} \times \sum_{perm} |\eta_1\rangle |\eta_2\rangle \cdots |\eta_n\rangle,$$ where $|\eta_k\rangle$ are uniquely determined (up to a global phase in each and the permutation) qubit states. Typically, they are presented as points on the Bloch sphere. When it comes to a desired generalization - by it I mean a unique set of invariants and covariants of $\text{SU}(2)$ assigned to each density matrix. The uniqueness (up to permutations) is crucial, otherwise one can just spectrally decompose the density matrix $$\rho = \sum_i p_i |\psi_i\rangle\langle\psi_i|$$ and apply the standard Majorana representation to each of its eigenvectors (obtaining invariants $\\{ p_i \\}_{i\in\\{1,\ldots,n\\}} $ and covariants $\\{ |\eta_{i,j}\rangle \\}_{i,j\in\\{1,\ldots,n\\},}$ ). However, for the case of the eigenvalue degeneracy it is no longer unique. A naive dimension counting $(n+1)^2-1=2n + n^2$ gives a hint that there may be $n$ covariant points plus an invariant $n\times n$ matrix. An auxiliary question is if there is a unique representation of $k$-dimensional subspaces of pure symmetric $n$-qubit states? (If there is one, then it is possible to 'fix' the mentioned approach with the spectral decomposition.)


title: No mixing in light cone perturbation theory

text: In hep-ph/0609090, _Triumvirate of Running Couplings in Small-x Evolution,_ Kovchegov et. al. calculated the running coupling correction to the Jalilian- Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (JIMWLK) equation using light cone perturbation methods. The diagrams he was calculated are of two types:   1. Bubbles which comes from (regular) gluon and goes to (regular) gluon.   2. Bubbles which comes from instanteneous gluon and goes to instanteneous gluon. However, he didn't look in the more involved case when we have some mixing between interactions. The question I would like to ask doesn't requires to read Kovchegov's paper and in terms of LCPT I can phrase it also in the following way - is there an arument why the matrix elements involving both regular and instanteneous interactions (such as $\left\langle g\left|H\right|qq\right\rangle \left\langle qq\left|H\right|0\right\rangle $ or $\left\langle qq\left|H\right|qq\right\rangle \left\langle qq\left|H\right|g\right\rangle \left\langle g\left|H\right|0\right\rangle $ for example, where $H$ denotes the interaction part of the QCD Hamiltonian) should not taken into account when calculating the wave function or any higher order corrections?


title: Coupling constant problem

text: In the scalar $φ^4$ theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}(\partial_t\phi)^2 -\frac{1}{2}\delta^{ij}\partial_i\phi\partial_j\phi - \frac{1}{2}m^2\phi^2-\frac{g}{4!}\phi^4. $$ I want to know details about the coupling strength g. How will I start? I studied some technique from Feynman diagram, that it represents the strength of a scattering. But I need to find out the value of this constant and need guideline how will I study so I can understand clearly. Is there any relationship which gives us the enough evidence for putting the coupling constant into Lagrangian.


title: How does Haldane conjecture follow from the topological $\Theta$ term

text: The one dimensional SU(2) Heisenberg quantum spin chain is known to be described by the 1+1d O(3) nonlinear $\sigma$ model with a $\Theta$ term, following the action $$S=\int\mathrm{d}^2x\frac{1}{g}(\partial_\mu n)^2+\frac{i\Theta}{8\pi}\epsilon_{\mu\nu}\epsilon_{abc}n_a\partial_\mu n_b\partial_\nu n_c,$$ where $\Theta=2\pi s$ is related to the spin $s$ on each site. On the other hand, Haldane conjectured that the integer spin chain is gapped, while the half-integer spin chain is gapless (or degenerated?) My question is how to understand the conjecture based on the topological $\Theta$ term? Or explicitly, how to calculate the ground state degeneracy and the low energy spectrum from the action given above? Is it even possible to write down the ground state wave functions for topological field theory? Is there a systematic way to analyze the low energy spectrum of a topological field theory in general?


title: Degeneracy of states  in mixed infinite square well, harmonic oscillator

text: I'm trying to determine the degeneracy of states given by $g(\epsilon)=g_{0} \epsilon$ for a system that is trapped in a quite specific potential. In two dimensions, the particle has a potential as in the infinite square well, while on the third dimension, the potential behaves as if a harmonic oscillator. The energy for a single particle is given by $$\epsilon = \frac{h^{2}}{8mL^{2}}(n_{x}^{2} + n_{y}^{2}) + hf \biggl(n_{z} - \frac{1}{2}\biggr)$$ I'm having some difficulty with this problem because of the broken symmetry. Is there any analytic way to determine the degeneracy as a function of energy?


title: Wavefunction normalization

text: How do we normalize a wavefunction that's a linear combination of sines and cosines (or of $Ae^{ikx}+Be^{-ikx}$ -- they're the same, right)? One you square it, wouldn't the integrand be oscillating through all space, and thus infinite?


title: How to construct an isomorphism between the Complexified Special Linear Lie Group and the Special Unitary Group?

text: This may be an unenlightening question, but I'm just not sure about the result and hoping someone can help me varify it. $\\\$ This question is related to these three questions. $\\\$ I want to construct the isomorphism relationship between the Lie Groups $SL(2,\mathbb{C})$ and $SU(2)$. I have the feeling that there should be some such isomorphism of groups. $\\\$ To begin, we know that as Lie Algebras $$ \mathfrak{sl}(2,\mathbb{C}) \simeq \mathfrak{so}(1,3) $$ and $$ \mathfrak{su}(2) \oplus \mathfrak{su}(2) \simeq \mathfrak{o}(4) $$ But we also know that $$ \mathfrak{so}(n) \simeq \mathfrak{o}(n) $$ so I believe that this allows us to write $$ \mathfrak{su}(2) \oplus \mathfrak{su}(2) \simeq \mathfrak{sl}(2,\mathbb{C}) $$ This makes sense anyway, since we know that the real algebra of the complexification of $\mathfrak{su}(2)$ is $\mathfrak{sl}(2,\mathbb{C})$, and in taking the real algebra of the complexified Lie algebra we get two commuting copies. So, the part that I am not yet convinced about is how to get from this relationship between algebras to a relationship between groups. I was told by someone in the department that > **Theorem** The Fundamental Theorem of lie Groups: Let $G_1$, $G_2$ be Lie > groups. Then $G_1$ and $G_2$ have isomorphic Lie algebras if and only if > they are locally isomorphic. So this is a local statement only. Moreover, he said that there is an extension of this theorem to a global statement which says that the Lie groups are globally isomorphic if they are simply connected. Now, for our two groups, $SL(2,\mathbb{C})$ and $SU(2)$, we know that they are indeed simply connected. We could prove this, or instead, recall that they are the Universal Covering Groups of $SO(1,3)\uparrow$ and $SO(3)$ respectively, and so by the definition they must be simply connected. This would solve our problem, and we could write down $$ SU(2) \times SU(2) \simeq SL(2,\mathbb{C})$$ and be done. $\\\$ However I want to try to verify that statement, as opposed to taking it in blind faith (not that I have any reason to doubt it, but rather that I'd like to 'learn it' as opposed 'to be aware of it', if that makes sense). $\\\$ I tried looking it up, and the obvious source didn't have anything on a Fundamental Theorem of Lie Groups, only a short bit on The Third Theorem of Lie. Some searching brought up these lecture notes (in .pdf format) from UCLA. It appears to be getting at what I want, but unfortunately is written in category theoretic language, which I know nothing about. $\\\$ Could anyone verify for me if this is correct, and perhaps point me to a book/ website/ lecture notes etc. where I could reference. (Our library is huge, so a book being online need not be a constraint). $\\\$


title: Violations of Dulong-Petit rule as an upper limit to heat capacity

text: Does any known substance have a heat capacity at constant volume ($C_V$) **per mole of atoms** greater than $3k_B$ ~ 24.94 J/(mol K)? In order to count, the substance must actually be made of atoms, that is, ordinary nuclei and electrons. If so, what are the extra degrees of freedom responsible for this unusually large heat capacity?


title: Please justify invoking logical positivism to causal patches and black hole interiors in quantum gravity!

text: Logical positivism is often invoked to explain why external observers can't talk about black hole interiors, or why we can't talk about what happens outside our causal patch in inflationary models. But just exactly how justified is this questionable philosophy of logical positivism? According to another philosophical tradition, scientific realism, it is meaningful to ask about what happens inside a black hole, or beyond our causal patch. Just because we can't measure something in principle doesn't mean it doesn't exist!


title: Why doesn't string theory have a mass gap?

text: Gravitons are string modes which can have arbitrarily small energies. Just make the wavelength arbitrarily large. String theory has no mass gap, but why? A classical string can only have positive energies. The string tension makes a positive contribution. The string kinetic energy also makes a positive contribution. A classical string can have an arbitrarily small mass because it can be arbitrarily small in length. But quantum strings can't shrink beyond the string scale. The lack of a mass gap can be traced to a shift factor to the string energy in the Virasoro constraint. For a single string, this shift is unconstrained and arbitrary. Without interactions, this is none other than the "string chemical potential". But we can create/annihilate strings after second quantizing them. This shift becomes physical. Modular invariance of worldsheets of genus one fixes the shift, and it turns out to be negative. String theorists explain this as the Casimir effect on the worldsheet, but this is just a name, and not an explanation. Why is this Casimir shift negative? Only a negative value can cancel the mass gap. Don't say $ζ$-function regularization, because it's purely formal and doesn't explain a thing.


title: Quantum $n$-body problem

text: Is the quantum $n$-body problem as difficult as the classical $n$-body problem? Or quantum mechanics allows to get a simpler exact solution? Suppose there are 3 particles with uniform potential field. Can their wave functions be found exactly?


title: What's is the origin of Orbital Angular Momentum of electrons in atoms?

text: Consider the Hydrogen 1s electron. We know that, in the quantum picture, the electron isn't orbiting or rotating at all, rather we simply state that the electron is spread over the entire space with the probability of finding it being maximum a radial distance $R$ (=Bohr radius) away from the nucleus. This helps explain why the electron does not radiate EM radiation while in the atom. But, with this understanding, I do not understand the source of the orbital angular momentum. Is it intrinsic like the spin?


title: rotation matrix - why am I thinking this wrong?

text: The rotation given in Question 1 part ii) doesn't match with this wikipedia link http://en.wikipedia.org/wiki/Rotation_matrix. $$ \begin{array}{lcl} x' &=& x \cos\theta - y \sin\theta \\\ y' &=& x \sin\theta + y \cos\theta \end{array}$$ What's the difference? Why are the two answers different? (I don't think it's a mistake on the previous link.)


title: Why does a $1/2$ appear in this simple capacitor equation?

text: The maximum energy stored by a capacitor is when it's (theoretically) fully charged or just before it reaches dielectric breakdown, if you will. It seems, then, that the maximum energy ($E$) $=QV$ where $Q$ is the maximum charge attained and $V$ is the maximum 'voltage'. However, the correct equation for the maximum energy according to my textbook, is $E=\frac{1}{2}QV$. PS: I know an argument can be made using integration but I'm looking for a simple, intuitive explanation because my reasoning that $E=QV$ seems sound to me. I know about Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$? but I'm looking for a reason to disprove my specific argument that $E=QV$ and not the 'Oh, it comes from integration' response.


title: Will adding cold water to a hot iron pan harm it? Why/why not?

text: Adding cold water to a aluminum pan can be harmful.   Is this same with iron pan too?   How can it be explained?


title: I'm getting weird autocorrelations when simulating an Ising model below the critical temperature

text: So I'm simulating an Ising model using Monte Carlo and the Metropolis algorithm. After letting it reach equilibrium, I try to calculate the autocorrelation of the magnetization. As long as the system is above the critical temperature (about 2.4), I get the expect results. But when it's below the critical point, I get a weird autocorrelation result: ![Ising model](http://i.stack.imgur.com/Rd8If.png) That straight line is completely bizarre. Now, at this point I am below the critical temperature, so it's supposed to be different anyway, but I'm not sure. It doesn't feel right. Is this result expected?


title: Is more energy required to magnetize based on its distance to other objects?

text: I have had this question since I was in college physics, but never could figure out how to express it. Well, now I think I have it. Let's imagine two scenarios A and B. Both scenarios start with two non- magnetized iron bars. In scenario A, the iron bars are 0.1 m apart. In scenario B, they are 0.5 m apart. In both scenarios, one bar is magnetized over time to the same strength. The question is in two parts:   1. do the potential energies due to magnetism differ in the two scenarios?   2. does the energy required to magnetize the iron bar differ in the two scenarios? The question relates to how to account for the difference in potential energy. My reasoning is that the only place it can be drawn from is the energy required to magnetize the bar. Is this reasoning correct?


title: Why are topological solitons present in some phases for lattice models?

text: Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved topological density. The reason is nontrivial homotopy. Surprisingly, in some phases, but not all phases, the analog of topological solitons, or at least what can be interpreted as them, also emerge over lattice models. Why is that? There is no nontrivial homotopy over a lattice. Why are there some phases of the XY-model with deconfined vortices and antivortices? Why are deconfined monopoles present in some 3D lattice models?


title: Dark Matter and Modified Gravity

text: Could someone please explain briefly or refer me to an article or manuscript that shows how f(R) modified gravity theories can be used to explain the problem of Dark Matter, particularly Galaxy rotation problem?


title: Trace and adjoint representation of $SU(N)$

text: In the adjoint representation of $SU(N)$, the generators $t^a_G$ are chosen as $$ (t^a_G)_{bc}=-if^{abc} $$ The following identity can be found in Taizo Muta's book "Foundations of Quantum Chromodynamics", appendix B Eq. (B.10), page 381: $$ \mathrm{tr}(t^a_Gt^b_Gt^c_Gt^d_G)=\delta^{ab}\delta^{cd}+\delta^{ad}\delta^{bc}+\frac{N}{4}(d^{abe}d^{cde}-d^{ace}d^{bde}+d^{ade}d^{bce}) $$ where $d^{abc}$ is totally symmetric in $a$, $b$ and $c$ and is defined in the fundamental representation by $$ \\{t^a_N,t^b_N\\}=\frac{1}{N}\delta^{ab}+d^{abc}t^c_N,\quad [t^a_N,t^b_N]=if^{abc}t^c_N,\quad \mathrm{tr}(t^a_Nt^b_N)=\frac{1}{2}\delta^{ab} $$ It puzzles me that how does $d^{abc}$ appear in $\mathrm{tr}(t^a_Gt^b_Gt^c_Gt^d_G)$. Could anyone provide a proof for the above identity? Many thanks in advance!


title: N=2 SSM without a Higgs

text: In arXiv:1012.5099, section III, the authors describe a supersymmetric extension to the standard model in which there is no Higgs sector at all, in the conventional sense. The up-type Higgs is a slepton in a mirror generation, and other masses come from "wrong Higgs" couplings to this particle. I'm wondering if this approach can revive the fortunes of N=2 supersymmetric extensions of the standard model, where there are three mirror generations, but which run into trouble with oblique electroweak corrections. I realize that this may be, not just a research-level question, but a question which will require original research to answer! However, if anyone has an immediately decisive argument about the viability of such a theory, now's your chance. :-)


title: Transform hamiltonian

text: I have got the following Quantum Hamiltonian: $$H=\frac{p^{2}}{2m}+k_{1}x^{2}+k_{2}x+k_{3}$$ Which transformation can I use to change this Hamiltonian into an harmonic oscillator hamiltonian? Note: $k_{1}, k_{2}$ and $k_{3}$ are constants.


title: Matlab package: graphical calculus for quantum operations including beam splitters and polarizing beam splitters

text: I need a matlab package that will make my life easier. I have quantum circuits with optical beam splitters, polarizing beam splitters and photodetectors. These circuits are getting very complicated and I am wondering if anyone knows of a matlab package that would make my life easier. A graphical package would be excellent and I suppose any software will do.


title: Origin of Laue equations?

text: The Bragg condition (by Bragg in 1913) can be derived by the Laue equations that is making use of the Miller indices and all the latice/crystal stuff (so basically it's bringing Bragg's law to more fundamental ground). But what is interesting to me: When did the "Laue way" came up? Was it only named after Max von Laue or did he himself publish a paper introducing this formalism? Neither Wikipedia nor the books I have are citing it. The Laue diffraction/condition/law is always just presented without origin. But I'd like to find it's real origin.


title: Rigorous justification for rotating wave approximation

text: Whenever I have encountered the rotating wave approximation, I have seen "the terms that we are neglecting correspond to rapid oscillations in the interaction Hamiltonian, so they will average to 0 in a reasonable time scale" as the justification for its use. However, it is not completely clear to me why does this justify that the Hamiltonian that we obtain is a good approximation of the original one, and I was wondering if there is a more rigorous version of the justification, whether it is for a particular system, or in a more general case. As an example, something that would be a satisfying answer would be a result of the form "If you consider an arbitrary state of the system and any time t large enough, and evolve the system according to the RWA Hamiltonian, we obtain with high probability a state close to the one we would obtain under evolution of the original Hamiltonian". "t large enough", "close" and "high probability" would preferably have some good quantitative description.


title: Bra-ket notation and linear operators

text: Let $H$ be a hilbert space and let $\hat{A}$ be a linear operator on $H$. My textbook states that $|\hat{A} \psi\rangle = \hat{A} |\psi\rangle$. My understanding of bra-kets is that $|\psi\rangle$ is a member of $H$ and that $\psi$ alone isn't defined to be anything, so $|\hat{A}\psi\rangle$ isn't defined. Is $|\hat{A} \psi\rangle = \hat{A} |\psi\rangle$ just a notation or is there something deeper that I am missing?


title: Causality and operationalism: from sets and functions to monads

text: When working in a laboratory, the most basic behaviour is to turn a knob or dial and then see a transformation of some data output. An example is increasing a magnetic field and seeing Zeeman splitting. We normally use this behaviour to create a function, thinking of the system as being composed of a set of states. I am interested in a program which borrows some of the assumptions of quantum gravity. Namely, I am working towards a picture where states are not fundamental, but instead processes are. This leads us to the following picture. We take the turning of the knob as a morphism and the change in the data output as another morphism. The experiment, then, is a map from an arrow to an arrow and this is just an endofunctor on the category of the apparatus. Can we then use this endofunctor to create a monad and subsequently an algebraic theory for the system under investigation?


title: $\pm$ (light-cone?) notation in supersymmetry

text: * I would like to know what is exactly meant when one writes $\theta^{\pm}, \bar{\theta}^\pm, Q_{\pm},\bar{Q}_{\pm},D_{\pm},\bar{D}_{\pm}$.  {..I typically encounter this notation in literature on $2+1$ dimensional SUSY like super-Chern-Simon's theory..}   * I guess that when one has only half the super-space (i.e only the $+$ of the above or the $-$) it is called the $(0,2)$ superspace compared to the usual $(2,2)$ superspace. In this case of $(0,2)$ SUSY I have seen the following definitions, $Q_+ = \frac{\partial}{\partial \theta^+} + i \bar{\theta}^+\left( \frac{\partial}{\partial y^0} + \frac{\partial}{\partial y^1} \right)$ $\bar{Q}_+ = -\frac{\partial}{\partial \bar{\theta}^+} - i \theta^+\left( \frac{\partial}{\partial y^0} + \frac{\partial}{\partial y^1} \right)$ which commute with, $D_+ = \frac{\partial}{\partial \theta^+} - i \bar{\theta}^+\left( \frac{\partial}{\partial y^0} + \frac{\partial}{\partial y^1} \right)$ $\bar{D}_+ = -\frac{\partial}{\partial \bar{\theta}^+} + i \theta^+\left( \frac{\partial}{\partial y^0} + \frac{\partial}{\partial y^1} \right)$   * I am guessing that there is an exactly corresponding partner to the above equations with $+$ replaced by $-$. Right?  How does the above formalism compare to the more familiar version as, $Q_\alpha = \frac{\partial}{\partial \theta^\alpha} - i\sigma^\mu_{\alpha \dot{\alpha}}\bar{\theta}^{\dot{\alpha}}\frac{\partial}{\partial x^\mu}$ $\bar{Q}_\dot{\alpha} = -\frac{\partial}{\partial \bar{\theta}^\dot{\alpha}} + i\sigma^\mu_{\alpha \dot{\alpha}}\theta^{\alpha}\frac{\partial}{\partial x^\mu}$ which commute with, $D_\alpha = \frac{\partial}{\partial \theta^\alpha} + i\sigma^\mu_{\alpha \dot{\alpha}}\bar{\theta}^{\dot{\alpha}}\frac{\partial}{\partial x^\mu}$ $\bar{D}_\dot{\alpha} = -\frac{\partial}{\partial \bar{\theta}^\dot{\alpha}} - i\sigma^\mu_{\alpha \dot{\alpha}}\theta^{\alpha}\frac{\partial}{\partial x^\mu}$ {..compared to the above conventional setting, in the $\pm$ notation among many things the most perplexing is the absence of the Pauli matrices!..why?..} I would be very grateful if someone can explain this notation. {..often it turns out that not just the Qs and the Ds but also various superfields also acquaire a $\pm$ subscript and various usual factors of Pauli matrices look missing..it would be great if someone can help clarify this..}


title: Ask an equation to solve the next location of an object?

text: ![enter image description here](http://i.stack.imgur.com/ERdpA.jpg) It is a long time that I have not learnt physics. But now I really need an equation to solve a problem. I appreciate physicists give me a little hint. Here is a object on the desk without friction. There are two forces on it with opposite forces. There is no pivot. So what kind of equation should I to calculate the next location of this object. As a human being, I think it will end up like ![enter image description here](http://i.stack.imgur.com/dbfS9.jpg)


title: How can Ohm's law be correct if superconductors have 0 resistivity

text: Ohm's law states that the relationship between current ( I ) voltage ( V ) and resistance ( R ) is $$I = \frac{V}{R}$$ However superconductors cause the resistance of a material to go to zero, and as I understand it, as $R \to 0$, $I \to \infty$. Does this present a problem for Ohm's law?


title: Infinitely many soft photons from pushing an electron?

text: I have been looking at some of the archives here and seen it quoted by Ron Maimon , that pushing an electron with a classical field means the electron will produce infinitely many soft photons should the universe be flat. Is this to be taken literally or it could be explained in more detail to me?


title: Classical 3-body problem

text: There is a formulation of the classical 3-body Newtonian problem reducing this problem to 6 equations (e.g. http://www.3bproblem.blogspot.com). I would like to know where can I find a discussion or demo of this setting. Any examples of other non-trivial frames for this problem are also welcome, i.e. others than the center of mass frame in 9 equations.


title: Solving the differential equation of a beam under moving load using green functions

text: i started working on this paper and i didnt understand one part of it , the problem is : > Solve this equation using green functions : > > $$ EI {\partial^4 y(x,t)\over\partial x^4}+\mu > {\partial^2y(x,t)\over\partial t^2}= F(x,t) :(1)$$ $$F(x,t)= P\delta(x-u)$$ > with $\int_{-\infty}^\infty\delta(x-x_0)f(x)dx = f(x_0)$ $\delta$ is the Dirac-delta function, P is the amplitude of the applied load, and $u(t)=v\, t$ the position of the load. > initial conditions : > > $${\partial^3 y(x,t)\over\partial x^3}=k_ly(x,t)$$ , > > $${\partial^2 y(x,t)\over\partial x^2}=k_t{\partial y(x,t)\over\partial x}$$ > , > > For $x=0 , l$ : > > $$y(x,t)= {\partial y(x,t)\over\partial t}=0$$ > > $l$ is the beam length and $k_t$ and $k_l$ are constants and the paper said that : > Using the dynamic Green function, the solution of Equation $(1)$ can be > written as: $$y(x,t) = G(x,u)P : (2)$$ where $G(x,u)$ is the solution of the > differential equation: $${d^4y(x)\over dx^4} - \psi ^4 y(x) = > \delta(x-u):(3) $$ in witch : $\psi ^4 = {\omega ^2 \mu \over EI}$ My question is how did they simplify it to the form $(2)$ where $G$ is solution to $(3)$ ?


title: Newtons Cannon ball problem

text: ![enter image description here](http://i.stack.imgur.com/STNEW.jpg) Let's I have a Newton's Cannon ball of 15 kg and want to fire so it will round the earth and back to me. > My query is which law can evaluate the speed that cannon ball will revolve > round the sun ? any hints or answer will be appreciated.


title: What is the $t\bar{t}$ production supposed to bring up

text: The $t\bar{t}$ production, I've read, that will somehow confirm the QCD and might bring up new physics. Why are we studying $t\bar{t}$ production from $p-p$ collisions at the LHC? What are we trying to find? What is the new physics that might bring up? What do we anticipate from this production?


title: How is a one position shift of an interferometer fringe pattern defined?

text: When Michelson and Morley conducted their 1887 interferometer experiment, they were expecting a fringe pattern shift of 0.4 (see the chart at http://en.wikipedia.org/wiki/Michelson-Morley_experiment). I understand that fringe patterns are represented as series of alternating dark and light bands, but I don't understand what exactly one fringe is. In particular, would a fringe shift of 1.0 be defined as a dark band moving (shifting) to where its adjacent dark band had previously been? To check my understanding:   * If so, then if a laser with a 532 nanometer wavelength were used as the light source in a Michelson-Morley style interferometer, would adjusting the position of the movable mirror a total of 266 nanometers (266 rather than 532 because the beam reflects back off the mirror) result in a 1.0 fringe shift as previously defined?   * Or, since light waves are sinusoidal, would the dark bands occur at every crossing of the x-axis (and the light bands at the peaks and valleys), such that the 1.0 fringe shift would occur after moving the mirror only 133 nanometers - rather than the 266 nanometers of the previous question?


title: SUSY (Supersymmetric) Quantum Mechanics

text: I have seen some books, e.g. by Fred Cooper (Supersymmetry in Quantum Mechanics), define: $A = \frac{\hbar}{\sqrt{2m}} \frac{d}{dx} + W(x)$, $A^\dagger = \frac{-\hbar}{\sqrt{2m}} \frac{d}{dx} + W(x)$, $V_1(x) = W^2(x) - \frac{\hbar}{\sqrt{2m}} W'(x)$, $V_2(x) = W^2(x) + \frac{\hbar}{\sqrt{2m}} W'(x)$. In other places, I have seen it defined: $A = \frac{\hbar}{\sqrt{2m}} \frac{d}{dx} + W'(x)$, $A^\dagger = \frac{-\hbar}{\sqrt{2m}} \frac{d}{dx} + W'(x)$ $V_1(x) = W'(x)^2 - \frac{\hbar}{\sqrt{2m}} W''(x)$, $V_2(x) = W'(x)^2 + \frac{\hbar}{\sqrt{2m}} W''(x)$. It seems like these two definitions will give you completely different Hamiltonians and partner potentials. Could someone comment on if these two conventions are equivalent, and if so, how?


title: Which quantity gives the resistance of a component?

text: In a current vs potential difference graph, we can obtain the value of the resistance of the component. There are books that say gradient-inverse is the resistance and also books that say the value of $\frac{\text{current, I}}{\text{potential difference:V}}$, which comes from the coordinates of the graph, provides the resistance. I tend to believe the second method (coordinates) provide the true value of resistance. The reason is because when we discuss gradient, we are talking about change wrt to another quantity. e.g. acceleration is change of velocity wrt time. Resistance is NOT change of potential difference wrt current. Resistance is the ratio of potential difference over current, according to Ohm's law. This is frustrating because I can find official solutions to international certified examinations also saying that the gradient method is the correct one. So can someone who is very knowledgeable in this area provides the true answer? Students need to be taught the correct methods. Update: The two ways to calculate the resistance from an I-V graph is:   1. Take the inverse of the gradient. In the diagram ,it would be $\frac{10-1}{15-5}=\frac{9}{10} \Omega$.   2. Take the ratio of $\frac{V}{I}$ which in this case will be $\frac{10}{5} = 2 \Omega$. These two methods yield different results, but both give the same dimension. Which one is the correct method? ![enter image description here](http://i.stack.imgur.com/SjP1G.png)


title: A vertical variation of modern versions of Michelson-Morley

text: For almost a year now, I have been in the uncomfortable position of having an idea. However, there is one nice thing about this idea. It makes a concrete, exact and relatively easy to test physical prediction. The idea predicts that there is a 11,187 m/s (Earth’s escape velocity) aethereal wind directly into the surface of the Earth at its surface. I believe it would be possible to test this by performing a vertical variation of modern versions of the Michelson-Morley experiment (MMX) with one arm pointed in the vertical direction. (Modern MMX) In 2003, Müller et al. performed a normal (2 horizontal orthogonal arms) modern MMX using cryogenic optical resonators that found a “possible anisotropy of the speed of light c, (of) 2.6 +/- 1.7 parts in 10^15” ( arXiv ) In a brief conversation with Holger Müller a Professor at Berkeley and the lead author of that paper, he stated that to this knowledge no one had ever performed a variation of the experiment using a vertical arm. He also mentioned that such an experiment would be complicated by the fact that gravity would slightly compress the length of the vertical bar making two equal length bars no longer equal in length. “They haven't been done as far as i know. The problem is that any interesting physics signal would be hard to tell from a large signal from stretching of the arms under their own weight.” - H. Müller I am interested in attempting to run this experiment myself. To that end, I have the following questions:   1. Given current Physics understanding, is there any reason to expect that such a vertical variation of the MMX wouldn’t return the exact same results as all other MMXs, namely that there is no anisotropy in the speed of light?   2. Given the complications mentioned by Professor Müller, are there reasonable methods available to overcome them? Especially considering the size of the effect (c + 11,187m/s vs c) is substantially larger than the accuracy obtained in his and similar modern MMXs.   3. What is the order of magnitude cost of such an experiment? If I am to fund this personally, would such a project cost \$10,000? \$100,000? \$1,000,000? more? Any insight offered on this topic will be greatly appreciated.


title: Nanotech - zero dimensional fullerene

text: Not really a physics junkie, and I think this is a chemistry question, but since there's no chemistry.stackexchange.com (yet) I think here is the best place. I was just reading up on nanotech and came across the phrase "can construct 0D fullerenes, 1D graphenes...". Flags went up at "0D fullerenes" and I can't find further information about it in many places. A fullerene is apparently any pure-carbon atomic structure, in various forms, but the zero-dimensional part is throwing me. What is a 0D fullerene?


title: Why does the coefficient of performance need to be calculated with $W + Q$?

text: > How much work must a heat pump with a COP of 2.50 do in order to extract > 1.00 MJ of thermal energy from the outdoors (the cold reservoir)? The first formula that came into my mind after reading this question is the $$COP=\frac{\lvert Q(\text{cool})\rvert}{\lvert W\rvert}$$ However, when I used the equation above, the answer that I got was 0.4 MJ instead of the answer given which is 0.67 MJ. And then I tried various other ways to try and get the 0.67 MJ and only when I used this equation that I finally get the answer 0.67 MJ. $$COP=\frac{\lvert W+Q(\text{cool})\rvert}{\lvert W\rvert}$$ What I don't understand is that why do we need to add $W$ with $Q$? Or is it not the correct way after all? Would somebody explain this to me, please?


title: What sort of thermodynamic process is this?

text: I have to calculate the work done in this thermodynamic cycle: LINK. ![enter image description here](http://i.stack.imgur.com/9l79q.jpg) But the bottom bit of the cycle is something I've never seen before. I guess the curve in $pV$ space is given by $$\left( V- \frac{V_2 -V_1}{2} \right) ^2 + \left( p-p_1 \right) ^2 = \left( \frac{V_2 -V_1}{2} \right) ^2$$ Which is physically meaningless because of units...


title: Fluid Dynamics Tsunami

text: I have been given a energy head (pressure) in meters for a given tsunami on land. My question is if the tsunami hits a wall 1 meter by 1 meter, is it possible to calculate the height it will reach. I am thinking it is due to the fact that a liquid is incompressible and therefore a given pressure will make the tsunami height rise when it hits the wall to a certain height? Any ideas?


title: When a moving body collides with a stationary body, far from its centre, how do you calculate the resulting spin

text: Imagine you had a long heavy rod in space with no significant gravity acting upon it. And a projectile is flying towards it, perpendicular to the orientation of the rod, with the impact some between the centre of mass of the rod and an end of the rod. Upon impact there is no deflection (for whatever reason the bodies fuse together). Basic preservation of momentum says the centre of mass this fused body will continue to travel in the same direction of the original projectile. But will it also be rotating? And at what rate? If there were a fixed point of rotation I would know how to calculate the rate of rotation. But since it is moving I am confused.


title: Is there a relation between the magnetic field force of the earth and the gravitational force between the earth and other bodies?

text: According to Newton's Universal Law of gravitation, we can say that a huge body of mass will attract another body of mass within a short range, however, if both bodies are for instance magnetic, wouldn't there be a repelling/attracting force between the bodies? Since both the earth and the sun are known to have their own magnetic fields why isn't this represented in the universal gravitation law?


title: SHS Interferometer and diffraction limit

text: I'm currently researching Spatial Heterodyned Spectrometers (SHS) and I'm a bit at a loss understanding the influence of the diffraction limit. I'll be measuring a diffuse visible light source with entrance/exit optics, which will would limit the images resolution on the sensor. Can I see fringe patterns smaller than this limit or are they blurred out? Any sources would be helpful, as I could not find anything on this problem (neither pro nor con).


title: What is considered 100% efficiency when talking about photovoltaic cells?

text: I was reading this article in Popular Science and figured that I actually don't know what is considered 100% efficiency. Is it when every photon that hits the cell kicks out an electron that is excited enough to become free? Not every photon in the spectrum has enough energy to do that, does it?


title: Is there any difference between massless Dirac fermions and Weyl fermions?

text: In graphene we call the low energy excitations around the Dirac point Dirac fermions, which are massless. Is this just by convention or is there any further differences between massless Dirac fermions and Weyl fermions


title: Why should any physicist know, to some degree, experimental physics?

text: I've been trying to design a list with reasons why a proper theoretical physicist should understand the methods and the difficulty of doing experimental physics. So far I've only thought of two points:   * Know how a theory can or cannot be verified;   * Be able to read papers based on experimental data; But that's pretty much what I can think of. Don't get me wrong, I think experimental physics is very hard to work on and I'm not trying to diminish it with my ridiculously short list. I truly can't think of any other reason. Can somebody help me?


title: Energy in electromagnetic radiation

text: I learned that power intensity in EM (electromagnetic) radiation is $$ I=\frac12c\varepsilon_0E_0^2 $$ This equation implies that the energy in EM radiation is frequency-independent I also learned that photon energy (quantized energy) in EM waves is $E=hf$; this equation implies that EM energy is amplitude-independent The first equation describes the wave nature of light, while the second one describes the particle nature of light, can we combine the two equations like this $$ \frac{hfN}{At}=\frac12c\epsilon_0E_0^2 $$ where $N$ is the number of photons that flow through the surface area $A$ during $t$ interval of time?


title: Point source approximation

text: I have a 0.05 mm radius sperical source of Photons, and a 10 mm X 10 mm detector aligned to be orthogonal to their distance vector. Distance is D $\approx$ mm. I want to know how good the point source approximation for my source is, given distance D. In particular, I suspect that if $D\approx 4\, mm$, the point source approximation is not very good. Characteristic lengths of the problem are Distance $D$ and radius $r$. I can calculate the solid angle $\theta$ from which the detector looks at the source, but how should I relate those quantities?


title: W + jets at NLO

text: I would like to calculate $pp \rightarrow W (\rightarrow \ell \nu)$ + n-jets (n=2, maybe also 3) at NLO, with some cuts and plot some distributions. I used MadGraph extensively for LO processes and I was wondering how reliable it is at NLO? Does anyone know any reference comparing multiple NLO codes? I have tried MCFM and I am not very experienced with it but the calculation seems to take a lot of time (obviously since it's NLO). Is there a way to make it run in parallel? I know that you can separate the real emission and virtual parts and then combine them later, but that doesn't seem to give a huge speed increase. Any help is appreciated. Thanks.


title: Transverse part of a current

text: I am reading Many particle physics (3rd edition by Mahan). On page 51, there is a current of the form $$\vec{j}(\vec{r})=\vec{J}_0e^{i\vec{k}\cdot\vec{r}}$$, the transverse part of it is: $$\vec{j}_t=-\frac{1}{k^2}\vec{k}\times(\vec{k}\times\vec{J}_0)e^{i\vec{k}\cdot\vec{r}}$$ I can easily obtain this by using the total part minus the perpendicular part, which is: $$\vec{j}_t=\vec{j}-(\vec{j}\cdot\vec{k})\vec{k}/k^2$$ However, the book gives a definition of a more general form of the transverse current: $$\vec{j}_t(\vec{r}):= \frac{1}{4\pi}\nabla\times(\nabla\times\int d^3r'\frac{\vec{j}(\vec{r}')}{|\vec{r}-\vec{r}'|})=\vec{j}(\vec{r})+\frac{1}{4\pi}\nabla(\nabla\cdot\int d^3r'\frac{\vec{j}(\vec{r}')}{|\vec{r}-\vec{r}'|})$$ In the last equal sign the definition of Dirac delta is used. I want to show the last term in third line and fourth line are equal, but I can't proceed the last term, any one please guide me how can I simplify this?


title: Does the induced charge on a conductor stay at the surface?

text: My textbook says that when a conductor is placed in an electric field, the electrons in it realign so that the net electric field inside the conductor is zero. There isn't a proof for this. It merely states that the electrons drift opposite to the applied electric field and create an opposite electric field inside the conductor canceling the external one. I imagine Gauss's Law would provide a simple proof. If we try enclose a point inside the conductor in a gaussian surface, and note that the enclosed charge is zero, so the flux through the surface is zero and so is the electric field at the surface. When I looked back at my reasoning, I realized that I had assumed that the charges induced on the conductor always stay at the surface, which I had no way of proving. How do I prove this formally?


title: Pressures in multiple hydraulic drive system circuits when driving common drive shaft

text: Assume that there are two 'idealised' and identical hydraulic drive system circuits each consisting of a connected positive displacement pump and hydraulic motor where both motors (from each independent circuit) are connected to the same drive shaft. Thus, the motor RPMs are mechanically synchronized. Assume that there is no pressure relief valves in the hydraulic circuits and they therefore have no maximum pressure. My question relates to the pressure in the two hydraulic circuits when the pumps have equal flow and thus equal motor RPM. Will the circuits always have equal pressure (i.e. supply half the output torque each) or is it possible that one circuit could reach an equilibrium where one supplies e.g. 2/3 torque and the other 1/3 torque (and hence run at different pressures)? Is there some natural feedback in a real system that would lead to a balance in torque output?


title: Resonance and Natural Vibrations in Vacuum

text: In my Physics textbook, it says that if two pendulums of the same natural frequency are placed next to each other and if one is set into vibration, the other starts resonating and when the first one gets damped due to air friction, the vibration of the second one again sets the first into vibration (resonance) and this goes on until all the energy is dissipated as sound. My Question is: If placed in vacuum, will these two complement each others' vibrations and continue vibrating in perpetual motion (because there isn't any propagation of sound in vacuum due to absence of a medium)?


title: The Nucleus of an Atom

text: We know that the protons in a nucleus are positively charged, whereas the neutrons do not possess a charge; we also know that unlike charges attract. So why does the nucleus stay intact, even though there isn't supposed to be any electrostatic force of attraction within it? Instead, why isn't there any repulsion between the protons which are like-charged?


title: How can a Photon have a "frequency"?

text: I picture light ray as a composition of photons with an energy equal to the frequency of the light ray according to $E=hf$. Is this the good way to picture this? Although I can solve elementary problems with the formulas, I've never really been comfortable with the idea of an object having or being related to a "frequency". Do I need to learn quantum field theory to _really_ understand this?


title: When a high speed neutrino just misses an old neutron star, why isn't it trapped?

text: Suppose a neutrino is seen travelling so fast that its Lorentz gamma factor is 100,000. It races past an old, no longer active neutron star, narrowly missing it. As far as the neutrino is concerned, it is the NEUTRON STAR that is moving at extreme speed, & its mass is 100,000 times larger than 2 solar masses. Therefore, from the speeding neutrino's perspective, the neutron star should appear to be a black hole definitely large enough to trap the neutrino. So how come the speeding neutrino continues its travel right past the old stellar remnant? Is there an agreed name for this question or paradox?


title: Graphene and relativistic dynamics

text: Is it possible to rewrite the **Lorentz-transformations** (for quantum particles) in terms of **effective mass m*** known from condensed matter physics? "From pencil lead to relativistic quantum physics" "A Mechanism for the effects of Relativity" Matter_waves#Four-vectors


title: Derive vector gradient in spherical coordinates from first principles

text: Trying to understand where the $\frac{1}{r sin(\theta)}$ and $1/r$ bits come in the definition of gradient. I've derived the spherical unit vectors but now I don't understand how to transform cartesian del into spherical del at all. People keep saying use the chain rule, but I don't see it! Any help?


title: stimulated and spontaneous emission

text: I have a question regarding the dependence on energy density of the probability rate of emission/absorption while studying lasers in particular. It is given that,the probability rate of absorption as well as stimulated emission depends on the energy density as well as the no. of atoms on either levels but the probability rate of spontaneous emission depend only on the no of atoms and not on the energy density.Why is it so?


title: What is precisely a Yangian symmetry?

text: The terms Yangian and Yangian symmetry appear in a list of physical problems (spin chains, Hubbard model, ABJM theory, $\mathcal{N}= 4$ super Yang-Mills in $d=4$, $\mathcal{N}= 8$ SUGRA in $d=4$), seem to be linked to (super)conformal symmetries and dual (super) conformal symmetries and Hopf algebras. So, what is precisely a Yangian symmetry, and what is the physical signification of this symmetry?


title: Dimensionality of Hilbert space

text: Simple question, but I can't seem to find the answer searching very easily. Does the dimensionality of a Hilbert space correspond to the number of possible states a system can take on? ("The system" being the one the Hilbert space describes.)


title: More about gravitation as the source of redshift of light beams

text: In the realm of physics there is no knowledge, the justification of which does not depend either upon experience or upon reason. In the light of the findings of the preconditions of knowledge made in for instance epistemology, this statement is certainly an oversimplification, but I still think it may very well serve its purpose as far as my actual two questions are concerned. In order to phrase these two questions, I have first to explain which physical theories I assume as a correct basis for phrasing them. And inasmuch as a question of mine is based on alternative mutually incompatible theories, the issue extends to also asking the answering forum to decide which of the theories that best explains the theoretical logics of physics and the empirical findings that have been made until this date. When commenting on the topic Gravitation as the source of redshift of light beams, Ted Bunn, among others, have assumed that when light is generated by a light source located at a given distance from a heavy body, and radiated radially from that body, then the _energy_ of the light rays would be decreased by an amount proportional to the difference in gravitational potential between the place where the light source is located and the potential of the place where an observer is detecting the light. Since the phrasing of my questions necessitates a correct model of the gravitational red shift of electromagnetic radiation, I now ask if this explanation of the physics of the gravitational redshift is free from contradictions. The gravitational redshift applying to the case outside of a non-rotating, uncharged mass which is spherically symmetric is described by the known exact equation, where • G is the gravitational constant, • M is the mass of the object creating the gravitational field, • R is the radial coordinate of the point of emission (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), • r is the radial coordinate of the observer (in the formula, this observer is at an infinitely large distance), and • c is the speed of light. The steady oscillation of a light-emitting source may be used as a clock. A common equation used to determine gravitational time dilation is derived from the Schwarzschild metric, which describes space-time in the vicinity of a non- rotating massive spherically symmetric object. In the known equation • t zero is the proper time between events A and B for a slow-ticking observer within the gravitational field, • t fast is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate), • G is the gravitational constant, • M is the mass of the object creating the gravitational field, • r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), • c is the speed of light, and • r zero is the Schwarzschild radius of M. • If the distance r from the center of the object M is a fixed, constant distance, we arrive at the result that the ratio between the proper time between events A and B for the slow-ticking observer (or low-frequency observer) and the coordinate time between events A and B for the fast-ticking observer (or high-frequency observer) becomes a fixed, constant ratio. Thus, the original frequency of the oscillation is not an element affecting the gravitational redshift thereof. From these gravitational red shift equations I must thus conclude that the “effective mass” of the photon is not a factor in the red shift equation. Neither is the “potential energy” of the photon in a gravitational field a factor in the red shift equation. The reasoning proposed by Ted Bunn is thus incompatible with the exact gravitational red shift equations. Ted Bunn uses the metaphor: "In Newtonian language, if you imagine the source of the light at the center of a spherically symmetric expanding spacetime, then the light travels 'uphill' in a gravitational potential all the way to the observer. The observed redshift is partially due to this redshift and partially due to the observer's motion. Conversely, if you put the observer at the center, the light 'falls downhill' all the way to the observer. This gives a different breakdown of the observed redshift into gravitational and Doppler contributions." This metaphor describes a model according to which the pace of the ticks of two different clocks put beside each other, i.e. a fast-ticking clock and slow-ticking clock, would be affected differently while traveling 'uphill' or ‘downhill’ in a gravitational field. But they are not affected differently in the way proposed by the Ted Bunn model, according to which the high-frequency and low- frequency light would be affected differently by the gravitational potential difference. Further, at one point, I find a valid reason to object to Ted Bunn's conclusion that a photon passing a particle, or a larger clump of matter, is blue shifted as it falls in and equally red shifted as it comes out, by way of which Ted Bunn concludes that there's no overall "tired-light-like" redshift due to an effect of this sort. However, wouldn’t it be plausible that the gravitational forces emanating from a light beam passing through the universe would cause a mechanism of action analogous to the mechanism of action causing the interaction between a physical object passing through the space and the surrounding objects? My suggestion that such an interaction also takes place between a beam of photons and a physical object I claim to be corroborated by the fact that the work performed by a beam of light passing very close to the Sun certainly will make the Sun go for a little ride. Had an object the size of the Sun passed the Sun, the ride would have been very much potent. But the effect of a beam of light upon the Sun’s position in space of course will be impossible to detect by way of current measurement techniques. But the work is nonetheless done. And much smaller objects than the Sun will be noticeably displaced and accelerated. According to the basic laws of physics, the energy that has been used to accomplish the work in question, is taken away from the light beam, which thus becomes red shifted. Qualitatively, it is therefore true that this type of redshift is a real redshift. But it is enough to make a rough calculation in order to establish and conclude that this red shift in our present Universe will be so insignificant that it will entirely drown in the cosmological red shift. However, in the very young Universe this type of red shift was quite a factor to be accounted for.


title: Is it possible to find the ground state of generalized Ising models?

text: Is there a general solver (or a theoretical algorithm) for obtaining the ground state configuration of the extended Ising model, which involves an arbitrary lattice, arbitrary coordination number (i.e. $n$-body interactions for arbitrary $n$), arbitrary Hamiltonian, and arbitrary spin of each particle (-1,0,1 and so forth)? Except exact enumeration, what could we do better? I know such a requirement is too stringent. But is there some research or established knowledge that aims to accomplish this?


title: Realistic calculation of heat loss for pipe

text: Good day everyone, I am new on this site and I hope to find here help, since I am not going anywhere with the literature I have found. I try to calculate realistically the heat loss of a hot, uninsulated pipe. Let's say, it is $170\,\,C$, 1 meter long, $8" (=0,203\,\,m)$ of diameter. I want to calculate the whole losses for the situation of no wind (only normal convection) and $20C$ of outside temperature. The $170C$ is the temperature at the outside surface of the pipe, the surface is known, I also know the Stefan–Boltzmann constant ($\sigma$) and I take $\alpha=5$ for the convective coefficient of air at the surface of the pipe as well as $\epsilon=0.85$ for the steel pipe emissivity. My problem is, that in literature, some parameter is always being rejected as negligible due to the fact, that most of the times the example is some kind of exercise of a heat transfer class. I want to calculate the real thing and then decide what is negligible and what is not. So my main question is: do I just add the radiation losses to the convective losses of the pipe ? $$Q_{loss} = Q_{conv}+ Q_{rad}$$ $$= (\alpha*Α*\Delta T) + \epsilon*Α*\sigma*((T_{pipe})^4-(T_{air})^4) \tag{with T in K}$$ According the above, I get $Q_{conv} = 479\,\,W$ and $Q_{rad} = 958\,\,W$. Is there any mistake in my way of thinking or is it truly that simple ? Thanks in advance. Marcus


title: How to calculate cost of AA accumulator charge?

text: I would like to calculate how much it will cost to change AA accumulator. Is it really cheaper than usage of batteries (don't consider ecology question as of now)? Let's say I have the following   1. accumulator: GP Rechargeable NiMH AA HR6 270AAHC 2700 series (2600 mAh);   2. battery charger 1: GP PowerBank Smart 2 (GPPB14, pdf)   3. battery charger 2: Technoline BC700 (pdf). In accordance with BC700 data, accumulator currently is in the following condition (?): 200 mA, 1.26V. The cost of electric power is 3.18 per K.W.H..   1. Is there any difference in terms of cost (besides time of charging) which battery charger is used and in which mode?   2. How to calculate cost of charging?   3. How to calculate possible cost of accumulator refresh (=recovery)? Believe, it will depend on number of charges and discharges.


title: Steering forces on a bicycle

text: Ok, I always notice this weird thing and try to overcome it but cant.   Ok as shown in the image when I ride the bike by just one hand and pull the handle back say from the right side so as commonly the handle should rotate towards right and the bike should turn to right but it never happen no matter what i do the handle turns to left and the bike always go to left and when i try to push it forward so that it turns to left then the handle turns to right and so the bike also turns to right. As from how much i know about laws of motion's i don't know why it happens. Please help as it is too much weird and interesting for me ![enter image description here](http://i.stack.imgur.com/OV1j6.jpg)


title: Calculate average acceleration without time?

text: I have a question about a flea jumping, for which I need to show that the average acceleration is around 1000 $ms^{-2}$. I know that to calculate average acceleration you can use $\frac{dv}{dt}$, however I only have the following information: > _At the moment the flea's leg leave the surface its body is raised 0.44 mm > and it is moving at a speed of 0.95$ms^{-1}$._ I would appreciate it if somebody could help me show the average acceleration of the flea during take off.


title: How to establish relation between flow rate and height of the water column of the tank?

text: Suppose a water tank has 1" diameter drain at the bottom and is filled with water up to one meter height above the drain. What time it will take the tank to drain out completely. Now say, the tank is filled up to two meter height above the drain then what time it will take the tank to drain out? Will it be double or less than it? Can we establish a relation between flow rate for the given height of water column?


title: Closed linear cosmology implies G M / R = c^2?

text: I have a question about a linear FRW cosmology with $k=+1$. Assuming zero cosmological constant the first Friedmann equation can be written: $$\left(\frac{\dot R}{R}\right)^2 + \frac{kc^2}{R^2}=\frac{8\pi G}{3}\rho$$ where scalar curvature $k=-1$ (open),$0$ (flat) or $+1$ (closed) and $R(t)$ is the radius of curvature of space. Now I assume a linear cosmology so that: $$R = c t.$$ Thus the Friedmann equation becomes: $$\frac{c^2}{R^2} + \frac{kc^2}{R^2}=\frac{8\pi G}{3}\rho.$$ If $k=-1$ then $\rho=0$. This is the empty Milne Universe with negative spatial curvature. If $k=0$ then we have a flat Universe with: $$\frac{c^2}{R^2} = \frac{8 \pi G}{3} \rho.$$ Because the Universe is flat I can write an expression for the total mass $M$ in a sphere of radius $R$: $$M = \frac{4}{3} \pi R^3 \rho\ \ \ \ \ \ \ \ \ \ \ \ (1)$$ so that $$\frac{GM}{R}=\frac{c^2}{2}.$$ Now I want to look at the case with $k=+1$: $$\frac{c^2}{R^2} + \frac{c^2}{R^2}=\frac{8\pi G}{3}\rho.$$ One could say that this case must have a positive spatial curvature and thus the equation (1) linking mass, density and volume of a sphere is not valid. But I can define $\rho^\prime = \rho/2$ so that I get the equation: $$\frac{c^2}{R^2} = \frac{8 \pi G}{3} \rho^\prime.$$ This is exactly the same as the flat Friedmann equation but with half the density. Therefore equation (1) is still valid. Thus a sphere of radius $R$ will have a mass $M/2$ so that, in this case, one would get the equation: $$\frac{GM}{R}=c^2.$$ Is this correct?


title: How to get general relativity from linear gravity theory?

text: I know someone had done this study. Namely the field approach to general relativity. We can easily get an linear gravity theory. But it will be very complicated when we consider the self-interaction(The final result is we will get general relativity). How can we defeat this difficulties ? Can you please show me some papers or articles about the mathematical details?


title: Why is it thought that normal physics doesn't exist inside the event horizon of a black hole?

text: A black hole is so dense that a sphere around it called the event horizon has a greater escape velocity than the speed of light, making it black. So why do astronomers think that there is anything weird (or lack of anything Inc space) inside the event horizon. Why isn't simple the limit to where light can escape and in the middle of event horizon (which physically isnt a surface) is just a hyper dense ball of the matter that's been sucked in and can't escape just like light. Why is it thought that the laws of physics don't exist in the event horizon?


title: Combined gas law in an open atmosphere

text: The question was asked about pressure vs. Volume increasing in an ideal gas as temperature is increased. My question then is this. What is the formula to determine how much volume and pressure will increase as temperature is increased? Let me frame the question this way. PV/T=P2V2/T2 this formula works for a controlled system where more than one of these values can be maintained. If we apply a known amount of heat, say n, to the atmosphere, what formula would be used to calculate volume and pressure as the temperature is increased?


title: How to calculate the force between two different magnets?

text: I'm doing an experiment and I need to calculate the force between two magnets with different stats, different sizes and flux density. I learned physics in high school so I know all the terms. In my experiment, those magnets align one above the other, but then one of them moves to the side, so if you put them on a grid, the location of one of them will be (0,0) and the other will be (5,3) for example. I've found formulae on the internet only for two identical magnets, and only if they align one above the other.


title: How to calculate how many degrees the Sun is from the horizon?

text: Given a position on earth (latitude/longitude, and maybe also height relative to sea-level) and a time, what's the algorithm to find how many degrees the Sun is from the horizon? And the same for the opposite, given a location and date, how do you calculate the time when the Sun will be such-and-such degrees from the horizon (such as to calculate astronomical dusk and dawn)?


title: Does a reference or classification standard for altitude classifications of geocentric orbits exist?

text: I'm looking for a primary reference of the altitude classifications of geocentric orbits (LEO, MEO, GEO, HEO), but I was not able to find something so far. I noticed that there is very different information about this classification scheme, for example LEO: The English Wikipedia defines LEO from 160 to 2.000 km above mean sea level; in comparison, the German Wikipedia defines LEO from 200 to 1.200 km. Does anybody know if there is an established standard for this orbit classification, e.g. at NASA, ESA or any other space agency, which can be referenced (f.i. a paper, guideline or handbook)? Thank you really much!


title: Sky-Watcher Skymax-127 (AZ) 127mm (5") f/1500 SynScan GO-TO Maksutov-Cassegrain Telescope

text: I have not purchased the above item yet but was wondering whether or not I should? Can I hook this scope up to a monitor or laptop so I can see what my scope is seeing? Is this scope is any good at viewing planets etc., Mars and Saturn in particular? Will it give clear views of nebulae etc.? Thanks for your responses.


title: Are there good resources explaining mean field approximation?

text: I am a computer science master student. In a statistical learning theory course I am taking, mean field approximation was introduced to approximately solve non-factorizable Gibbs distributions that were derived using maximum entropy inference. Our professor has a strong background in physics and often uses terms from statistical physics. Unfortunately, I lack that background. So,   1. Are there any resources explaining mean field approximations from a non-physical/computer science perspective? I couldn't find any.   2. Or alternatively, are there "crash course"-like resources that would allow me to understand one of the more physically motivated explanations without looking up tons of terms? **EDIT:** Here are some details that hopefully help to narrow it down: In this course, we are trying to sample from intractable, non-factorizable Gibbs- distributions (mainly in the context of clustering). Apparently, this cannot be done (efficiently), therefore we retreat to a mean-field approximation.


title: How can the pre-measurement be fulfilled?

text: In the decoherence program, the pre-measurement refers to the evolution in which the system and apparatus form a Schmidt state. In Maximilian Schlosshauer's review article(2005), I read "the linearity of the Schrödinger equation entails that the total system SA evolves from an initial product state to a state of Schmidt form." Why? Is it an assumption? How can this process be fulfilled?


title: How do we know Dark Matter is non baryonic?

text: It seems widely stated, but not thoroughly explained, that Dark Matter is not normal matter as we understand it. Wikipedia states _"Consistency with other observations indicates that the vast majority of dark matter in the universe cannot be baryons, and is thus not formed out of atoms."_ How can we presume to know this? Our best evidence for such dark matter is the rotational speeds of galaxies. It sounds like we can measure/approximate the gas density and stellar masses somehow, yet I don't understand how we can account for things like planets, asteroids, black holes without accretion disks, and other things that have mass but don't glow. How is it we dismiss these explanations for it, and jump right to WIMPs and other exotic explanations?


title: Moving Between Degenerate Vacua?

text: In spontaneous symmetry breaking, moving round the circular valley of Mexican hat potential doesn’t cost energy. These angular excitations are called Goldstone bosons. But doesn't the angular excitation imply that the system moves from one vacuum to the other because all points on the circular valley are degenerate vacua? If Goldstone excitations are like this then how can a symmetry remain broken?


title: Relation between Dirac spinor and its adjoint

text: I'm trying unsuccessfully to solve the following problem in Thomson's _Modern Particle Physics_ : "Starting from $(\gamma^{\mu} p_{\mu} - m) u =0, $ show that the corresponding equation for the adjoint spinor is $\bar{u} ( \gamma^{\mu} p_{\mu} - m) = 0.$ Hence, without using the explicit form for the $u$ spinors, show that the normalisation condition $u^{\dagger} u = 2E$ leads to $\bar{u} u = 2m $ and that $\bar{u} \gamma^{\mu} u = 2 p^{\mu}.$" Here, $u$ is a free-particle solution to the Dirac equation (in the basis of momentum, so here the $p^{\mu}$ are c-numbers) and $\bar{u} = u^{\dagger} \gamma^0$ is as usual its adjoint spinor. The equation for the adjoint spinor is very easy to derive by just taking Hermitian conjugates of both sides of the Dirac equation, but for the life of me I can't derive _a priori_ the latter two equations. I've tried all manner of substitutions and tricks to no avail. Could someone guide me in the right direction?


title: Are combined masses in space, such as galaxies, considered to be uniform bodies? *In addition, a related question about force

text: If we were to calculate the force that one galaxy exerted onto another, would we consider the individual masses within the galaxies, or the masses of the galaxies as a whole? Do the individual stars within one galaxy have control over the individual stars within another? Or, do we consider the galaxies to be single bodies, each with it's own mass, and the distance between them as two uniform bodies? If so, could we call galaxy clusters uniform bodies as well? And if a galaxy cluster were to all of a sudden lose a star (hypothetically), would the net force exerted onto the other galaxy cluster be the same if you counted each star individually? As another curiosity, I would like to pose this question: if a galaxy cluster were to lose one fourth of its mass, $2.0\times10^3$ light years away from the other galaxy cluster's centre of mass, how would the effect be different than if the mass was lost only $0.50\times10^3$ light years away? What I mean is, the distance would be different, so the force would be different (**(if you can address this as well please)and information would have to travel faster than light for this to occur, yet with a mass loss this great, the other cluster would be sure to notice it almost immediately).


title: Does causality alone resolve the mathematical ambiguity of expressing physical systems?

text: Newton's 2nd law of motion is most often written in the differential form $\sum F = {dp \over dt} $ but can also be expressed in an integral form $ p = \int\sum F dt $ Each form of expressing the connection between force and momentum is mathematically correct, but if we adhere to causality we are limited to the second expression (Forces lead to momentum (movement) - not vice versa). This limitation is further exemplified when one attempts to simulate the equations in a digital computer. If feedback is involved the first expression can lead to algebraic loops, while the second gracefully evolves simulated motion. Algebraic loops do not represent physical reality (even the fastest of all physical systems are limited by the speed of light!) So other than what is defined to be the independent/dependent variables, and/or the operation of either differentiation vs integration, there is nothing in the mathematics that tells us which is the 'correct' formulation of the laws of motion. The presence of differentiation in the mathematics implies prediction - knowing the future and therefore expresses the physical system in a non-causal manner. Rewriting the system in an integral form expresses the system in a causal way. The integral form in a sense reveals the roles of each factor in cause and effect. Are there perhaps other ways (missing equation(s), other types of mathematics) that can help to resolve the ambiguity that calculus can cause? Is $F = ma$ incomplete? Perhaps some expression involving entropy is required for completeness. Physical reality favors memory and shuns prediction. BTW Newton's law just served as a simple example towards my question. The ambiguity can be realized in any other mathematics involving calculus that model physical systems (including Maxwell's equations).


title: How can rheostat change the current without changing int voltage

text: NCERT science of 10th, in chapter `electricity` on page 205, there, a is line written: > a component use to regulate the current without changing the voltage source( > simply voltage ) is called variable resistance(rheostat) but according to the ohm's law voltage is directly proportional to the current then how can a variable resistance is able to change the current? do it voilates the ohm's law?


title: Is there any significance of atomic orbitals?

text: We have been taught that the atomic orbitals we read about are probability density region of finding electrons of particular energies which are designated by the various quantum numbers. Since, there is high degree of uncertainty when we talk about the position of merely the detection of an electron as well as the energy that we "observe" and which may pretty much not be the actual energy of the observed electron, what then is the significance of any atomic orbital? I am not very well read in the various techniques and theories that we have developed over time, but still I think that atomic orbitals are at best a high probability region of finding certain electrons. Since we must not be able to do that with enough certainty how then can we check the validity of the existence of orbitals? Is it possible, that the idea of atomic orbital is now outdated in terms of modern development and only used for simplistic explanations of complex electron motions and phenomenons? Overall, I am interested in learning the significance of atomic orbitals. Google provides various links explaining the theory and listing its uses in modern chemistry but I could not find anything which properly explains the significance or even tries to explain the actual presence of something like an atomic orbital other than saying that we find so and so probability regions while working with Schrödinger equations. Added after answers and comments: The answers are listing the uses of the contruct only, I tried to say that I am interested in finding out whether something like an orbital is actually there or not. Maybe an example will help, there is no boundation for an electron of certain energy to move in an orbital that is dumbled or double dumbled shaped! I agree with electrons having certain energies described by quantum numbers, but how can one definitively prove that an electron belonging to say 2p_x resides in a dumbled shaped orbital? Again, are orbitals true? Are they actually significant and not just a helpful mathematical construct? Can it be definitively proven?


title: Distribution of Kinetic energy after an Impact

text: How does the huge amount of kinetic energy of some fast object like a meteor or rocket etc. gets distributed into various kinds of energy like kinetic, sound, light etc after making an impact with another body. Is there a rule under which this happens or is it TOTALLY random, and if it is random then what kind of random process does it form?


title: Do these cars rotate on themselves?

text: I was reading about the moon rotation around earth and the tidal lock related. I found some interesting information already here and on astronomy.stackexchange.com as well. The moon is known to have a full rotation period of ~27 days. However I really can't wrap my head about this. Let's consider these vehicles going around earth: ![enter image description here](http://i.stack.imgur.com/lOm43.jpg) ✓ They always "face" the same side to the earth ✓ They found themselves on the same position after a full revolution around earth ... but are they rotating on themselves and do they have this tidal lock effect? I would have said no but after reading about the tidal lock of the moon, should I say so? The same question can be asked for planes (if the fact that these cars touch the ground is an issue).


title: The choice of pivot point in non-equilibrium scenarios

text: It is true that under equilibrium condition, no matter what pivot point one choose, the resulting net torque will always be zero. I wonder if this principle apply to non-equilibrium scenarios as well, namely, the net torque of the system being the same regardless of choice of pivot point? For example, if we put a sphere on a inclined smooth ramp, we would expect the sphere to slip down the ramp without rolling. However, if we choose the point of contact between the sphere and the surface of the ramp as the pivot point, we will have a torque due to gravity. Apparently this contradicts our assumption. What's the mistake here?


title: Can a person at a photon sphere of a black hole decide where the black hole is?

text: A person at the photon sphere of a black hole will observe the following:   * The black hole surface will cover exactly half of the visible sky (say, the left half), and cosmic horizon will cover the other half.   * Looking in any direction between these hemispheres the person will see oneself.   * The person will observe no centrifugal force however fast he moves. Any object the person thowing to the left will experience the centrifugal force pulling it further left, while any object thrown to the right also will experience the centrifugal force pulling it to the right. Approaching the black hole in such circumstances may look quite like actually escaping it to the crew.   * The space to the right as well the space to the left seemingly includes objects of any length and dimensions, the further objects are, the more they are time-dilated and length-contracted. Is there any way for a spacecraft commander to decide (by an experiment conducted in a small$^1$ amount of time) which hemisphere is the sky and which hemisphere is black hole in such circumstances? \-- $^1$ Here _small_ means small compared to characteristic time scales of the problem.


title: Why would the environmental lapse rate be slower near the ground?

text: I have data taken from over 2300 ascents through the atmosphere at various locations around the world, for every 500 meters vertically upwards I have averaged the temperature and plotted it: ![Lapse Rate](http://i.stack.imgur.com/4Bhex.png) Its quite clear the lapse rate is dropping near ground level for every location. Near ground level is supposed to be unsaturated, meaning a lapse rate of approximately -2C/1000 feet however for the data I have the average never goes more negative than -1.5C/1000 feet and drops to below -1C/1000 feet near the surface. **Can someone explain this?** An excel file with the data can be found here if you wish to look into it yourself: https://www.dropbox.com/s/0k44i1mc4nxt8pu/Cities.xlsx **Edit** : I have also updated the spreadsheet to contain differential (the gradient) of the curves.


title: On Aharonov–Bohm effect

text: Aharonov–Bohm effect in brief is due to some singularities in space. In books it's infinite solenoid most of the time, which makes some regions of space not simply connected. What intrigues me is the fact that in real experiment we can't use infinite solenoid. So even if we use one and say that locally it's good approximation it doesn't change the fact that whole space is still simply connected. But the fact is that the effect was experimentally observed. So the question arises - how one should describe this effect in more rigorous manner (or maybe not rigorous but possible in real world)?


title: is this heat calculation equation correct?

text: > If I have a line of copper wire (lets say $\textrm{1 meter}$ long, > $\textrm{1 mm}$ thick) and one end is a flattened disk of copper about the > size of a quarter, and I apply a lot of heat to it (I'm talking > $800\,^{\circ}\textrm{C}$) will the entire line be heated to the same > degree? I mean what temperature will the unheated end be after, say, a > minute? Can it too reach $800\,^{\circ}\textrm{C}$ degrees over time? I'm going to start by asking the question, what would happen if the cool end were at $400\,^{\circ}\textrm{C}$ ? In this case, the rate of heat flow from the hot to the cool end would be $$ \begin{align} \frac{k A}{l}\Delta T &= \frac{400\,\textrm{W/mK}\cdot \pi\,(0.0005\,\textrm{m})^2}{\textrm{1 m}} \cdot 400\,\textrm{K} \\\ &= 0.1257\,\textrm{W} \end{align} $$ The radiative transfer from the copper to the surroundings, which I'll call air at $20\,^{\circ}\textrm{C}$, will follow from the Stefan-Boltzmann Law. For the copper, the radiative flux is $$ \begin{align} \sigma \, T^4 &= \left( 5.67 \times 10^{-8}\,\textrm{W/m}^2 \textrm{K}^4 \right) \left(673\,\textrm{K}\right)^4 \\\ &= 11632\,\textrm{W/m}^2 \end{align} $$ For the back flux from the air (disregarding any convection), you have $ \left( 5.67 \times 10^{-8}\,\textrm{W/m}^2 \textrm{K}^4 \right) \left(293\,\textrm{K}\right)^4 = 418\,\textrm{W/m}^2, $ so if the disk has a radius of $1\,\textrm{cm}$ and is two-sided, its surface area is $ 2\,\pi \,\left(0.01 \,\textrm{m}\right)^2 = 6.28 \times 10^{-4}\,\textrm{m}^2, $ and the $\textrm{NET}$ radiative loss is about $ \left( 11214\,\textrm{W/m}^2 \right) \left( 6.28 \times 10^{-4}\,\textrm{m}^2 = 7.04\,\textrm{watts}. \right) $ Evidently the radiative loss would be a lot more than the conductive gain, so the equilibrium temperature of the "disk" end is going to be considerably lower than $400\,^{\circ}\textrm{C}$. Next I tried a formal solution, but I didn't like the result(!) so I'll just see what happens if the disk temperature is $100\,^{\circ}\textrm{C}$:Radiative loss $ = 5.67 \times 10^{-8}\cdot \left( 373^4 - 293^4 \right) = 680\,\textrm{W/m}^2 $, total of $0.427\,\textrm{watts}$. Conductive gain $ = 400\,\pi\, 0.0005{^2} \cdot 700 = 0.220\,\textrm{watts}. $ So, as a whole, if the copper wire were thicker(lets say ten times so, placing it at $1\,\textrm{cm}$), would it enable it to reach $800\,^{\circ}\textrm{C}$ as a whole?


title: How is the current for the Dirac equation derived?

text: Why is it that the derivative of the current $j^\mu$ is the difference between the Dirac equation and its adjoint?


title: General relativity in terms of differential forms

text: Is there a formulation of general relativity in terms of differential forms instead of tensors with indexs and subindexs? If yes, where can I find it and what are the advantages of each method? If not, why is it not possible?


title: Do Quantum Energy Generators really produce more energy than they consume?

text: I'm not a science expert, just someone whose interested. I was taught that you cannot produce more energy than the amount put in. I received a thing on facebook asserting that a Quantum Engery Generator can do this, so I'm naturally very cynical about the claims being made on www.collective- evolution.com. However, as someone without technical knowledge, I am unable to critically examine the claims being made. I'd be grateful if someone with more knowledge than me could take a look and let me know. Thank you.


title: Ascertaining a mathematical equality to derive a partition function

text: we have an equation like this: $$\mathcal N(x)=\sum_{q=1}^\infty (\psi(x,q) \log(q)) \qquad (1)$$ while $\psi(x)$ is the function for some oscillations (may contain complex part), $x\in \Bbb R$ and $q \in \Bbb N$. It is further ensured that: $$ \mathcal N(x) = \left\\{ \begin{array}{l l} x & \quad \text{if $x\in \Bbb N$}\\\ 0 & \quad \text{otherwise} \end{array} \right.$$ I need your help, even if it sounds simple, **whether the following equality is mathematically correct** : $$n^{-\psi^*}=\mathcal N(n)^{-\psi(n,q)}$$ with $n \in \mathbb{N}$ and $\psi^*=\psi(n,q)$. I would really appreciate your help. I need this for constructing a partition function. **If the above equality as such is not correct, how is the correct formalism?**


title: How will a particle with energy less than $V_{\rm min}$ behave?

text: Consider e.g. the finite square well: $V = -V_o$ between $x=-a$ and $x=a$, $V=0$ elsewhere Now for scattering states, $E$ must be $> 0$. For normalizable bound states, $E$ must be $< 0$ and $> V_{\rm min}$ (=$-V_o$ in example). But if a particle in a lab has Energy which $< 0$ and $<V_{\rm min}$, is it bound or will it scatter? And I don't know why I haven't thought about this before but what does it mean for a photon to have negative energy?


title: What precisely, is the string theory landscape in 10 dimensions?

text: I was reading this Physics.SE thread. The OP said, (changed the last word to type HO) > > > For D = 10, there are 5 vacua. Or maybe it's more correct to say 4, > since type I is S-dual to type HO. This lead me to the 2 closely related questions:   1. When considering the landscape of string theories in some $D$ dimensions, are the S-dual theories considered as the same theory, as suggested by the quote? What about the T-dual theories? I don't think the T-dual theories should, because in that dimension itself, they are different until and unless one dimension is compactified, when they become approximately equal.   2. When it is said that the string theory/M-theory landscape in $4$ dimensions in $10^{520}$, are the S-dual theories counted as the same? I don't think they are, because there is no classification of this landscape yet.


title: Why do electrons in graphene behave as Dirac fermions near the Dirac points?

text: I've been learning about graphene, and I recently calculated the band structure for it using a nearest-neighbor tight-binding model for the $\pi$ electrons: $$\varepsilon(\vec k)=\pm t\sqrt{3+2 \cos \left(\frac{\sqrt{3} k_x}{2}-\frac{3 k_y}{2}\right)+2 \cos \left(\frac{\sqrt{3} k_x}{2}+\frac{3 k_y}{2}\right)+2 \cos \left(\sqrt{3} k_x\right)}$$ I was told that the dispersion of graphene around the Dirac points (points in $k$-space where $\varepsilon(\vec k)=0$ -- these turn out to be the vertices of the Brillouin zone) is linear, and this linearity leads to the particle behaving like a Dirac fermion. I have partially confirmed the linearity, but I don't know where to start to verify the second part. Wikipedia mentions the following, too: > It was realized as early as 1947 by P. R. Wallace that the E–k relation is > linear for low energies near the six corners of the two-dimensional > hexagonal Brillouin zone, leading to zero effective mass for electrons and > holes. Due to this linear (or “conical") dispersion relation at low > energies, electrons and holes near these six points, two of which are > inequivalent, behave like relativistic particles described by the Dirac > equation for spin-1/2 particles. Hence, the electrons and holes are called > Dirac fermions also called graphinos, and the six corners of the Brillouin > zone are called the Dirac points. Could someone explain how a locally conical $\epsilon(\vec k)$ graph leads to a Dirac fermion? I have not yet worked with the Dirac equation myself.


title: A machine which copies any object with 100% accuracy?

text: Does physics allow for a machine that copies an object with 100% accuracy?


title: Given a slanted pipe

text: Question: I have a pipeline that is tilted. I know the length of the pipeline, and the pressure (90psi) that is felt at the very bottom. I'm trying to find out how much liquid has leaked out if the pressure at the bottom decreases to 80psi. Is the pressure felt at the very bottom directly proportional to the amount of liquid that is in the pipeline?


title: Calculate flow rate of air through a pressurized hole

text: I was wondering about this: If there is a pressurized container, like a tank of compressed air at some pressure that is greater than the ambient air pressure, and this tank of air has a hole in it, what is the velocity of the escaping air through the hole? Is there a formula for this?


title: Lepto-genesis and electroweak theory

text: Is there any term in standard electroweak theory that breaks CP-symmetry and thus explains lepto-genesis?


title: A posteriori solution to the Hamilton Jacobi equation

text: I was wondering about the following: For many simple systems it is far too cumbersome to solve the Hamilton Jacobi equation compared with the Hamilton or Lagrange formalism. Now I was wondering, whether it is possible to find the solution to the Hamilton Jacobi equation, if I know the full solution via the Lagrange or Hamilton approach. Hence, my question is: Is the fact that I already know the solution of the mechanical system of any help, if I want to do the problem via the Hamilton Jacobi way?


title: What is the reason behind the shape of the absorption curve of electron paramagnetic resonance

text: ![](http://i.stack.imgur.com/3ZHax.png) In our EPR experiment, the signal looks like the "first derivative" part of the above picture. Why is this? What does the "first derivative" mean and why is it the quantity our instruments detect in such an experiment?


title: Radiative Corrections and Bremsstrahlung

text: I am having trouble understanding why it is consistent to include "Breamsstrahlung" diagrams in computations of scattering amplitudes. For example, consider the scattering of two electrons to two electrons. According to Peskin and Schroder (I'm looking at chapter 5), it seems that in addition to including one-loop diagrams, you should also include diagrams with radiated photons in the final state. I would think however that these diagrams correspond to an _entirely different process_ , namely a process in which two electrons scatter to two electrons and a photon. Why should these diagrams be included in electron-electron scattering in which _no_ photon is produced? P&S almost seem to argue that they need to be included for the simple reason that, if they didn't include them, they would get a nonsensical (i.e. infinite) result.