title: Reversible Stirling Engine

text: So it has been asserted that a Stirling engine with proper regeneration can be made reversible. It will consist of two isothermal quasi-static processes connected by two constant-volume processes. The working gas is supposed to be heated/cooled through infinitesimal temperature differences (thus preventing the creation of entropy). I'd like to know an explanation on the working gas properties during each step of the cycle. What are the state conditions for the gas at each of the points in the cycle (including inside the regenerator)? I've been looking for a the past week and found nothing.


title: Time evolution of quantum state after an observation

text: As described in the wikipedia article on wave function collapse, the mathematical formulation of quantum mechanics postulates that wave functions change according to two processes:   1. When not being observed, a wave function will evolve (deterministically) according to some relevant differential equation, e.g., Schrödinger's equation.    2. Upon measurement, a wave function will collapse (probabilistically) to one of its component eigenfunctions.  > What I'd like to understand is how quickly after a measurement a particle's > wave function will wander away, according to (1), from whatever > eigenfunction it collapsed to. As a concrete example (I hope!), consider two Stern-Gerlach experiments set up in sequence, both arranged to measure the z component of spin, in which we feed to the second experiment only the spin up half of the beam from the first experiment. When one learns about this in an introductory QM course, it is said that the observed output from the second experiment will still be all spin up. But is this still true if the experiments are spaced really far apart? How will the time evolution in (1) affect the outcome then? (Or is there something I have missed that prevents time evolution from affecting the intermediate beam?) If the observed outcome from the second experiment does depend on the distance between the experiments, then it seems this would give a way to measure (at least in principle) how rapidly a pure eigenstate can degenerate (by measuring, for example, the distance between the two experiments needed to get an output beam from the second experiment which is 75% up, 25% down).


title: Projectile motion, canon vs cliff

text: A cannon is placed at the bottom of a cliff 85 m high. If the cannon is fired straight upward, the cannonball just the reaches the top of the cliff. a) Calculate the initial speed of the cannonball. b) Suppose a second cannon is placed at the top of the cliff and fired horizontally with the same initial speed as part (a). Prove numerically that the range of this cannon is the same as the maximum range of the cannon from the base of the cliff. My work for part A ![work](http://i.imgur.com/TQMSiZY.jpg) How do I know what the velocity of the ball is at the top of the cliff?


title: Additional mass of block on inclined plane

text: I would like some help in solving this problem. ![Height is 15 cm , base is 88 cm](http://i.stack.imgur.com/fjVLX.png) Height is 15 cm , base is 88 cm My attempt: $$(119.3 + m)(\sin(\theta)) = (88*9.8)$$ $$ 15^2 + 88^2 = 89.269^2 $$ $$ \sin^{-1} = 15/89.269 $$ $$ (119.3 + m)(9.6733) = (88*9.8) $$ $m = -30.14$ ....Am I missing something? I feel like it has something to do with the force of friction...


title: Retrocausal interpretations of quantum mechanics

text: Can retrocausality resolve the paradoxes of quantum mechanics? The Copenhagen interpretation presumes something has no property until it is measured, but retrocausal interpretations explain that away by claiming that thing has a definite property before measurement, but the choice of which property is affected by the configuration of the measuring apparatus in its future. The philosopher Huw Price has written a lot about this. Nonlocal entanglements are also explained away because entangled pairs are connected by going to the past, then back up to the future. Or going to the future, then back to the past without travelling faster than light at any time.


title: History of the use of the concept of phase space in engineering

text: Engineering textbooks constantly use the concept of 'phase space' (see e.g. http://www.cs.cmu.edu/~baraff/sigcourse/notesc.pdf). That is, they think of the state of a mechanical system as a high-dimensional geometric space. For example, for a system of particles, the phase space has $6n$ dimensions, where $n$ is the number of particles. My understanding is that the notion of phase space initially developed among theoretical physicists (possible in conjunction with quantum mechanics? or possibly before that point?). Therefore, I'm wondering when and how engineers began to adopt this terminology and concept from physicists. It might have something to do with differential equations, since the concept of representing the state of a mechanical system as a point in a space becomes obvious when you view ODE's in terms of flows on euclidean spaces. NOTE: The phase space concept was invented by theoretical physicist and mathematician Willard Gibbs.


title: Is a weak measurement the same as an unsharp measurement or POVM?

text: This is prompted by the strong claims made in Science 332, 1170 (2011) to have observed trajectories of photons, "something all of our textbooks and professors had always told us was impossible". I'm suspicious of this claim because they work entirely within quantum theory, and it seems to me that in making weak measurements at two points on what they say is a trajectory, they do nothing else than make unsharp measurements of incompatible observables, a concept that was first introduced, to my knowledge, by Busch and Lahti in Phys. Rev. D 29, 1634–1646 (1984), and that is now much used in quantum information. Certainly observables that are at time-like separation are in general incompatible, so an unsharp measurement approach would seem applicable. A brief account of the Science paper mentioned above can be found here, amongst other places, and a few quotes can be found here, but, this being Science, I couldn't find a preprint. I was first alerted to this paper by a page at the BBC. The claim highlighted by ZapperZ, "Single-particle trajectories measured in this fashion reproduce those predicted by the Bohm–de Broglie interpretation of quantum mechanics (8), although the reconstruction is in no way dependent on a choice of interpretation", seems to me particularly egregious, insofar as both their choice of what experiment to do and of what to do with their raw data seem partly driven by the form they want to present their results in. It seems entirely possible to present the data in terms of unsharp measurements and POVMs, which would give relatively less support to the de Broglie-Bohm interpretation.


title: Car parking special-relavity puzzle

text: Hi I read the following puzzle from an old text book long time ago. However it doesn't provide the answer. So what is the solution? Let's suppose a car is going to park to a garage and the garage is exactly the same size of the the static size of the car. Now the car is running in a speed that in its point of view the garage is just 1/10 of its static size. So it will consider the garage is too small to fit. On the other hand, the garage manager consider the car is only 1/10 of the garage size so it definitely fit. The question is to explain what will ACTUALLY happen if the car try to park in the garage, and what the garage manager and the driver will see.


title: Primordial Black Hole Detection

text: There's ample direct evidence for the existence of galactic and stellar mass black holes. However, there is no such direct evidence of primordial black holes, those formed after the Big Bang. A recent paper [http://arxiv.org/abs/1106.0011] describes oscillations the Sun might undergo if it encountered a primordial black hole. The theory that primordial black holes exist hasn't had experimental backing. Why should one believe they actually exist? Is this science or "guesstimating?"


title: Are the hypotheses of the Bernoulli equation satisfied for a bird or airplane wing at low Mach number?

text: A previous question by David Zaslavsky was a request for a broad, "how things work" type of explanation of the lift of an airfoil. The answers given there are enlightening, but don't address a more specific question I have. First a summary of my current understanding. There is no logical reason to assume that parcels of air take equal time to travel above and below the wing. If we did make such an assumption, Bernoulli's principle would make all kinds of incorrect predictions. "How things work" explanations (e.g., this one) often speak as though Bernoulli's principle is one effect, and then there are some other effects, such as conservation of momentum; it's implied that these effects are additive, and it's often stated that the Bernoulli effect is negligible. But in fact Bernoulli's principle is, under certain hypotheses, equivalent to conservation of energy. Conservation of energy and conservation of momentum are not effects to be added. They're two physical laws, both of which need to be obeyed. It's only under certain hypotheses that Bernoulli's principle is equivalent to conservation of energy. It requires nonviscous flow, and the version given in freshman physics textbooks also assumes incompressible flow, although there is also a version for compressible flow. The WP article on Bernoulli's principle states that it's usually valid for Mach numbers lower than about 0.3, which I guess might be valid for birds and some small planes (cruise speed for a Cessna 172 is Mach 0.25), but not passenger jets. Based on this, I can envision two logical possibilities: (1) The hypotheses of Bernoulli's principle hold for birds and some small planes. The equation gives at least an approximately correct result for the net force on the wing, but there is no obvious, simple way to know what velocities to assume. (2) The hypotheses of Bernoulli's principle fail in these cases. Which of these is correct? If #2, which hypothesis is it that fails? Is the incompressible-flow version inapplicable but the compressible-flow version OK?


title: man walking in rain:relative velocity

text: > A man walking in rain at a speed of 3kmph find rain to be falling > vertically. When he increases his speed to 6 kmph, he finds rain meeting him > at an angle of 45 deg to the vertical. What is the speed of the rain?? My approach: $ \overline{V_{\operatorname{rain}}} - \overline{V_{\operatorname{man}}} = \overline{V_{\operatorname{rain relative to man}}}$ $\Longrightarrow \overline{V_{\operatorname{rain}}} = \overline{V_{\operatorname{rain relative to man}}} + \overline{V_{\operatorname{man}}} $ Equating velocity of rain wrt ground in both cases, we get $9+ x^2 = 36+ x^2 - 12x \frac{1}{\sqrt{2}}$ where x is velocity of rain wrt to man. so x becomes $9\frac{\sqrt{2}}{4}$ but that means velocity of rain wrt ground is (according to the first case, where velocity of man is 3 kmph) : $\sqrt{9 + {(9 \frac{\sqrt{2}}{4}})^2}$ which is the wrong answer. Is it a calculation mistake?? Or is my basic idea incorrect? Please help!


title: Man in elevator, holding it, on a scale

text: ![elevator pulley system](http://i.stack.imgur.com/1bLlk.png) This is the scenario where my mass is $60 kg$, the mass of the elevator is $30kg$, and due to a malfunction, I have to hold myself and the elevator at rest. The question is, if there is a weighing scale under me, (of negligible mass), then what force will it measure (in newtons)? My approach: The total mass of the system is $90kg$ which is approximately $900 N$ for equilibrium, tension in the rope is $900N$ because I am giving a downward force of $900N$, so according to Newton's 3rd Law, upward force on me by the rope must be $900N$. This means I should go up, and the weighing scale must not show any reading. But that is not among the options to choose from. Guidance rather than a direct answer would be appreciated.


title: Quantum Cyclotron Frequency - Why is it off by a factor of 2?

text: Say you have a magnetic field $\vec{B}=(0,0,B_0)$. Then the Schrodinger Equation Hamiltonian for a spin-2 particle of charge $e$ moving in this field is: $$H = \frac{1}{2m}[\vec{p}-e\vec{A}]^2-\vec{\mu}\cdot\vec{B},$$ where $\vec{A}=(-\tfrac{1}{2}y,\tfrac{1}{2}x,0)$ is the magnetic vector potential. You can find the speed by finding this commutator: $\frac{d\vec{r}}{dt}=i[H,\vec{r}]$. When I did out this calculation, I ended up with $\frac{\vec{p}-e\vec{A}}{m}$. However, I'm told that I should have gotten $\frac{\vec{p}}{m}+\vec{\omega}_c\times\vec{r}$, where $\vec{\omega}_c$ is the cyclotron frequency. This has the value $\vec{\omega}_c=-\frac{e\vec{B}}{m}$, but if you plug that in, you get $\vec{\omega}_c\times\vec{r}=-\frac{2e\vec{A}}{m}$. Why is this off by a factor of 2?


title: Einstein action as a functional of the tetrad (first order formulation of gravity)

text: Let the Einstein-Hilbert action be rewritten as a functional of the tetrad $e$ (units shall be set to $1$) such that $S_{EH}(e)=\int \frac{1}{2}\epsilon_{IJKL}~e^I\wedge e^J\wedge F^{KL}(\omega(e))$, where $\epsilon$ is the Levi-Civta-symbol as usual, $F$ is the curvature of the spin connection $\omega$ and $I,J,K,L$ denote internal indices, indicating that the object carries a rep. of the Lorentz group. How do I get back to the usual action $S_{EH}(g)=\int~d^4x\sqrt{-g}R$? I am trying to figure it out using identities but can't finish till the end. Could anybody give a little more detailed account, please? Thank you.


title: Carousel; explanation of a certain phenomenon.

text: There are countless of hilarious youtube videos like this one here, in which you can see that the carousel causes people to be pulled outwards.   * What force is actually working on them, and why does it pull them outwards (instead of for example inwards)?   * Can you give me some other (notable) example of this force in everyday life?


title: Evolution operator for time-dependent Hamiltonian

text: When i studyed QM I'm only working with non time-dependent Hamiltonians. In this case unitary evolution operator has the form $$\hat{U}=e^{-\frac{i}{\hbar}Ht}$$ that follows from this equation $$ i\hbar\frac{d}{dt}\hat{U}=H\hat{U}. $$ And in this case Hamiltonian in Heisenberg picture ($H_{H}$) is just the same that Hamiltonian in Schrödinger picture ($H_{S}$), i.e. it commutes with $\hat{U}$. Now i have Hamiltonian that depens explicitly on time. Specifically, $$H_{S}=\frac{\hat{p}^2}{2m}+\frac{1}{2}m\omega \hat{q}^2-F_0sin(\omega_0t)\hat{q}$$. And in my problem I need to calculate $H_H$ (Hamiltonian in Heisenberg picture). I've found that differential equation for $\hat{U}$ (I've mentioned about it above.) has generally solution in the form (with $U(0)=1$) $$U(t)=1+\xi\int\limits_0^t H(t')\,dt'+ \xi^2\int\limits_0^t H(t')\,dt'\int\limits_0^t' H(t'')\,dt''+\xi^3\int\limits_0^t H(t')\,dt'\int\limits_0^t' H(t'')\,dt''\int\limits_0^t'' H(t''')\,dt'''+...$$ So my questions are:   * Is there other ways to calculate $\hat{U}$, could give a link or tell me about them?   * If you know form of the solution for my case, please tell me.   * If you know any articles or papers articles on this topice, please link them to me, too.


title: Can a balloon float into space? (+orbital velocity)

text: After watching the recent "space jump" a question arose. Why can a balloon not float into space? Can one be made/designed to do this? Next, everything in orbit is falling back to earth. It only maintains its altitude with speed, about 26,000mph give or take. This number means what, 20,000+ mph relative to what? If the shuttle or station was to stop or approach zero mph it would fall to Earth, right? The balloon was at 128,000 feet and was only traveling at the Earth's rotational velocity of 1600mph. As viewed from the ground zero mph since it came down almost in the same stop. So what happens between say 130,000 feet and space that you need to increase your speed by 24,000mph? Last if we were at a high enough orbit and "stopped", where we would not fall back to Earth, would we be able to watch the earth leave us. Could we wait there for a year for the Earth to return? How far out would this be?


title: Spring coupled platforms & conservation of momentum - can it be solved with freshman physics?

text: This question came up as an exercise in a first year undergraduate course I was a TA for. It turned out to be a lot more difficult (impossible?) than anticipated... > Two platforms of mass $M_1$ and $M_2$ ($M_1\neq M_2$) are connected by a > spring of constant $k$, and are initially at rest with the spring > unstretched, sitting on a frictionless surface. A man of mass $m$ stands on > one platform and begins to run, always with a constant speed $v$ measured > relative to the platform he is running on. What is the maximum speed reached > by the other platform, relative to the ground? My intuition is telling me that I need to know something about how the man gets from rest to his constant speed (instantaneously? very slowly? with some smooth acceleration?) to solve this, but I haven't been able to prove to myself that this is required. If this is a requirement, I think the most reasonable assumption would be that he reaches his full speed instantaneously. What I'm most interested in is whether this problem can be tackled with a typical freshman's toolbox - simple arguments around conservation of energy/momentum, no/very limited differential equations, basic calculus. I can see an easy way to get an upper bound on the maximum speed from energy/momentum considerations, but I don't see a way to check if this speed is ever reached.


title: What is the relation between the Higgs field and chirality?

text: Wikipedia states that the spontaneous breaking of chiral symmetry _"is responsible for the bulk of the mass (over 99%) of the nucleons"_. How do the nucleons gain mass from the spontaneous breaking of chiral symmetry? Why don't leptons gains mass from it? What is the role of the Higgs field in this all?


title: Potentials in Feynman path integral

text: I am trying to understand the Feynman path integral by reading the book from Leon Takhtajan. In one of the examples, there is a full explanation of the calculation of the propagator $$K(\mathbf{q'},t';\mathbf{q},t) = \frac{1}{(2\pi\hbar)^n} \int_{\mathbb{R}^n} e^{\frac{i}{\hbar}(\mathbf{p}(\mathbf{q'}-\mathbf{q})-\frac{\mathbf{p}^2}{2m}T)} d^n\mathbf{p},\quad T=t'-t.$$ in the case of a free quantum particle with Hamiltonian operator $$H_0 = \frac{\mathbf{P}^2}{2m},$$ and the solution is given by $$K(\mathbf{q'},t';\mathbf{q},t) = \left(\frac{m}{2\pi i \hbar T}\right)^{\frac{n}{2}} e^{\frac{im}{2\hbar T}(\mathbf{q}-\mathbf{q'})^2}.$$ Could you please help me to understand how to perform the calculation in the case where the Hamiltonian is given by $$H_1 = \frac{\mathbf{P}^2}{2m} + V(\mathbf{Q})$$ where $V(\mathbf{Q})$ is the potential defined by $$ V(\mathbf{Q})=\left\\{ \begin{array}{cc} \infty, & \mathbf{Q} \leq b \\\ 0, & \mathbf{Q}>b. \\\ \end{array} \right. $$ Update : I've read the article provided by Trimok, and another one found in the references, but I am still annoyed with the way the propagator is computed. I may be mistaken, but it seems that in that kind of articles, they always start the computation from the scratch, without using what they already know about path integral. I am actually trying to write something about the use of path integrals in option pricing. From Takhtajan's book, I know that for a general Hamiltonian $H=H_0 + V(q)$ where $H_0 = \frac{P^2}{2m}$, the path integral in the configuration space (or more precisely the propagator) is given by \begin{equation} \begin{array}{c} \displaystyle K(q',t';q,t) = \lim_{n\to\infty}\left(\frac{m}{2\pi\hbar i \Delta t}\right)^{\frac{n}{2}} \\\ \displaystyle \times \underset{\mathbb{R}^{n-1}}{\int \cdots\int} \exp\left\\{\frac{i}{\hbar}\sum_{k=0}^{n-1}\left(\frac{m}{2}\left(\frac{q_{k+1} - q_k}{\Delta t}\right)^2 - V(q_k)\right)\Delta t\right\\} \prod_{k=1}^{n-1} dq_k.\\\ \end{array} \end{equation} I would like to start my computation from this result, and avoid repeating once again the time slicing procedure. So du to the particular form of the potential, I think I can rewrite the previous equation as \begin{equation} \begin{array}{c} \displaystyle K(q',t';q,t) = \lim_{n\to\infty}\left(\frac{m}{2\pi\hbar i \Delta t}\right)^{\frac{n}{2}} \\\ \displaystyle \times \int_0^{+\infty} \cdots\int_0^{+\infty} \exp\left\\{\frac{i}{\hbar}\frac{m}{2}\sum_{k=0}^{n-1}\frac{(q_{k+1} - q_k)^2}{\Delta t}\right\\} \prod_{k=1}^{n-1} dq_k.\\\ \end{array} \end{equation} Then I need a trick to go back to full integrals over $\mathbb{R}$ and use what I already know on the free particle propagator. However, since the integrals are coupled, I don't find the right way to end the calculation and find the result provided by Trimok. Could you please tell me if I am right or wrong ? Thanks.


title: Is this algorithm for simulating a quantum computer accurate?

text: I'm very new to quantum mechanics. I'm thinking of writing a quantum computer simulator, would the following work?   * Each qubit is stored as a single bit,   * For each operation, the qubits involved are transformed into a complex vector of amplitudes of size 2^N. This will result in a vector containing 2^N-1 0s and one 1.   * This vector is multiplied by the unitary matrix representing the operation.   * The resulting vector is squared element-wise.   * An outcome is picked using the elements of the result as probabilities and the qubits are set according to this outcome. I'm not concerned with the running time or the memory cost of the algorithm. What I am concerned about is whether this would result in a physically accurate simulation.


title: Finding the components of the tensor for potential and kinetic energy

text: I have a rather poor understanding of what a tensor is, but enough to apply it to the biggest part of the classical mechanics I'm studying.   However, I've run into a small problem while studying "Free vibrations of a linear triatomic molecule". (We're assuming all 3 atoms are in 1 straight line and the forces they exert on each other are represented by springs with constant values for $k$). My potential energy is described as: $V=\frac{k}{2}(\eta_1^2+2\eta_2^2+\eta_3^2-2\eta_1\eta_2-2\eta_2\eta_3)$   Where $\eta$ is a coordinate relative to the equilibrium position. And 'hence' the tensor has the form: $\vec V=\begin{bmatrix} k & -k & 0\\\ -k & 2k & -k\\\ 0 & -k & k \end{bmatrix}$ How do I go from 1 to the other and vice versa?   I've tried googling terms like "Equation to tensor", "Potential energy tensor", "Absolute value of tensor" etc. but they didn't yield anything usable for me.


title: Any way to Find the Position Function of a body under gravitational force?

text: Here's the problem I am trying to find a solution to: > Consider a heavy point particle of mass $m_2$ fixed at a point (preferably > the origin) and another light point particle of mass $m_1$ at an initial > separation of $r_i$ from the fixed particle. There are no other bodies that > can interfere with their interaction. Given any time $>t$, what will be the > separation $r$ of the two particles at that time? I tried to solve this myself with the following procedure: $$E = K_E + P_E$$ where $E$ is the constant total energy, $K_E$ and $P_E$ the kinetic and potential energies of the light particle respectively. Elaborately, $$\frac{-Gm_2m_1}{r_i}=\frac{1}{2}m_1v^2-\frac{Gm_2m_1}{r}$$ Solving for $v$ gives me $$v=\sqrt{2Gm_2(\frac{r-r_i}{rr_i})}$$ after that I get to a halt when this appears $$t=\frac{1}{\sqrt{2Gm_2}}\int{\sqrt{\frac{rr_i}{r_i-r}}dr}$$ which I cannot solve further, So I post this question in Mathematics Stack Exchange, and a satisfying answer to the integral they give is $$t=r_i\sqrt{r_i}\ln\left(\sqrt{r}+\sqrt{r-r_i}\right)+\sqrt{r(r+r_i)}-\frac{r_i\sqrt{r_i}\ln\left(\sqrt{r_i}\right)}{\sqrt{2Gm_2}}-(r-r_i)^2$$ which doesn't seem correct by the way. Differentiating this again must get me back to where i started but I don't get there. Is there any other way to solve such a question or is this the best that can be achieved?


title: Is a holographic recorder able to capture a large full color picture?

text: Is it practical to attempt to build a 3D hologram generator that is full color and big enough to recreate a watermelon full size? If so, is real-time control feasible?


title: When calculating the local apparent sidereal time, which time scale should I use?

text: UT1, UTC, TAI, TDB, or what? I need to determine the time difference between a given observation and the epoch from which certain constants apply. I typically work with the J2000.0 epoch. This is to determine how much time has passed and how far motions have propagated. I recently learned that when making planetary observations, I should convert the observation time into TDB time for improved accuracy (Jean Meeus). But I also found out that we use Earth-based time for sidereal time computations, so the rule doesnt apply for sidereal time... but unfortunately which Earth-based time scale to use was not specified in my research. There are a half dozen or so. UT1, UTC, TAI to name just a few. They differ from as much as 0.00017 seconds to as much as 1 minute 6 seconds. Now, when I compute sidereal time, I am consistently in error by anywhere from 20 to 35 seconds, depending on the resource I compare to. And I cannot seem to resolve this inconsistency, no matter how complicated or detailed my math gets; I find I am getting more and more out of synch with the quoted, expected value with each new variable I factor in (exactly opposite Id expect). I LOVE exactness. This is an exercise in conceptual understanding of the variables at play and in the technicality of it all; practicality is not an issue here, Im just trying to figure it all out with as much precision as possible. Any help at finding as precise a value as possible for sidereal time would be appreciated. I have been using my local clock time and date (local civil time). Factoring out daylight savings if applicable, converting to GMT (time zone offset). I assume that my result is the time in UT or UTC (I may be wrong). While my resource (Astronomical Algorithms, Jean Meeus) assumes that UT and UTC are identical to one another, so I dont concern myself with any more details. Then I use the equations in chapter 12 and (?)22, on sidereal time and nutation. In doing this I get results that differ by as much as 35 seconds, max, from that which Im quoted on sites like WolframAlpha, other EDU and GOV (time keeping) sites, as well as iPod Touch apps that purport to display sidereal time.


title: Is there more energy in the collapse of a cavitation bubble than the energy required to create the bubble in the first place?

text: The following does not include all scientific details and parameters, only a common summary of "thoughts". What is scientifically wrong with this summary? When you take your beer and tap the top of a friends beer bottle, the beer shoots out the top as the CO2 is taken out of solution and rebounds off the bottom of the bottle. If the liquid in the bottle does not have anything in solution, the tap on the top of the bottle results in the explosion of the bottom of the bottle. This is from the cavitation that was created at the bottom of the bottle, and the pressure wave that propogates through the liquid to collapse the cavitation. When the cavitation collapses, the momentum of the water that has now been shifted down hits the bottom and blows out the bottom of the bottle. It does not seem that the energy imparted with the relatively light tap on the top is enough to violently blow out the bottom of the bottle. Is there more energy in the collapse of a cavitation than the energy required to create the cavitation in the first place? Or is it just the momentum of the liquid that blows out the bottom of the bottle? Pits and dings in metal pump blades are caused by cavitation collapse. What is and where does that power come from?


title: Two similar questions related to analytic continuation of a complex variable and its conjugate

text: 1. See the scan attached below. Brown, in his QFT book, argues a certain way to do an integral. I understand that 1.8.13 or equivalently 1.8.14 can be performed once analytic continuation is done. I also understand that under this transformation the LHS of 1.8.12 would not change when viewed as an integral over $C^2$. But, I do not understand why the value of the integral should not alter when viewed as an integral over $R^2$ as Brown claims and then uses to finish the evaluation of the integral.   2. A similar kind of argument is used while doing complex scalar field theory where we treat $\phi$ and $\phi^*$ as independent fields. For a while, I have understood it as first complexifying them such that the the two fields combined now live in $C^2$ and then solving the variational problem in the complexified space. And then in the end we identify the two fields as conjugate of each other, that is, we project them over to $C$ again. The fact that extremas in the variation in complexified space maps bijectively to extrema in the variation in the original problem looks kind of a mathematical accident to me. But, as often happens in mathematics, there is a deep reason behind such coincidences. So, I wonder if somebody can shed the light on some deep reason for the fact that we can use this kind of trick of complexification and projection. It isn't obviously clear to me why this trick can be used unless this above argument is produced which seems like some magic is happening behind the curtains.![enter image description here](http://i.stack.imgur.com/Fxl8O.jpg)


title: The Asymmetry between Real and Imaginary in the three Pauli Spin Matrices

text: The Pauli spin matrices $$ \sigma_1 ~=~ (\begin{smallmatrix} 0 & 1 \\\ 1 & 0 \end{smallmatrix}), \qquad\qquad \sigma_2 ~=~ (\begin{smallmatrix} 0 & -i \\\ i & 0 \end{smallmatrix}), \qquad\qquad \sigma_3 ~=~ (\begin{smallmatrix} 1 & 0 \\\ 0 & -1 \end{smallmatrix}),$$ are mathematically symmetric in the sense that (like $i$ and $-i$) they can be universally exchanged with each other in several ways without altering any mathematical result. However, the visual forms for these three matrices are unexpectedly diverse (e.g., only $\sigma_2$ uses $i$ and $-i$). My understanding of physics history is that Pauli (and also Dirac) developed his matrices by trial and error, rather than by applying any specific theory. Does a deeper theoretical explanation exist for why these very different visual representations of spin are nonetheless interchangeable in multiple ways?


title: In what position can a current-carrying loop of wire be located in a magnetic field so that it doesn't tend to rotate?

text: I understand that if the wire is not aligned with the magnetic field, it won't rotate, but I'm still confused on how so. Also, which direction is the current flowing?


title: How do I solve the current of this resistor using Maxwell's Current Theorem?

text: I've been trying to solve this using the method the prof. taught us, and I happen to know the answer but I can't reach it no matter how many times I've tried. The circuit in question is below: ![image](http://i.stack.imgur.com/X6wgG.jpg) I am asked to use Maxwell's circulating current theorem to find out the current at the $20 \Omega$ resistor. My method was to write out all the loop equations: $20 = 15I_1 + 10I_2$ $10 = 15I_1 + 25I_2 + 15I_3$ $10 = 15I_2 + 35I_3$ then solve by method of elimination. My answers are as follows: $I_1 = 2.44A$ $I_2 = -1.66A$ $I_3 = -0.43A$ The answer for $I_3$ is $-0.57$. Am I on the right path? If not, can someone point out where I am going wrong and why? Thanks


title: How target locking woks?

text: In many aerial war face movies they show that aircraft is locked by missile ,particularly in movie **_behind enemy line_** " F/A-18 Hornet" is locked by 2 **_SAM missile_** ,pliot try to break the lock but aircraft get shot down.   i find wikipedia have some  information about this.   i dont understand this concept ,how this locking work and how pilot break the lock?


title: Question on static friction

text: ![enter image description here](http://i.stack.imgur.com/fzIUA.png) This is the question, and the answer is given as 2). Now my basic doubt is, are they asking us the direction of the total contact force on the object by the floor? Or, are they asking the direction of the static friction on the block by the floor? What is it? Because, the normal reaction between any two surfaces in contact is ALWAYS perpendicular to the two surfaces. Please help me, and please answer this before closing it as being too specific.


title: Does entanglement have a speed or is it instantaneous

text: The phenomenon of observing one entangled particle and noticing the other take on corresponding values... Does this take a finite speed at all or is it instantaneous?


title: Collection of histories vs. collection of momentary configurations

text: For a given Hamiltonian, is the space of histories of a classical system the same as the symplectic manifold? Do I have to take care of gauge equivalences and if so, is this only an issue for fields (not for trajectories)?


title: Thermal expansion and conductivity

text: When thinking about how the lattice constant of silicon can be given up to eight decimal places without a remark for the temperature I realized that, it seems _most insulators and semiconductors seem to expand less than metals when exposed to heat._ Is there an intuitive connection between the band structure and the thermal expansion?


title: ${1 \over T} e^{-i/T}$ for Boltzmann-Gibbs distribution

text: There is a book from Tom Carter on entropy. In the Economics I application (page 111), he ingeniously computes that the distribution of fixed amount of M money over N individual tends to $$p_i = {1 \over T}\, e^{-i/T}$$ The temperature, $T = M/N$, is the average amount of money per individual. The author calls this a _Boltzmann-Gibbs distribution_. I wanted to find a plot and compare it with Pareto distribution and Planck black body radiation. The problem is however, and this is my question, Wikipedia does not have it! Actually, there is an article on Boltzmann distribution, which is also called Gibbs distribution, but I see nothing similar to $p_i = 1/T\, e^{-i/T}$ there. At least I cannot see how ${N_i \over N} = {g_i e^{-E_i/(k_BT)} \over Z(T)}$ with $N=\sum_i N_i,$ and partition function, $Z(T)=\sum_i g_i e^{-E_i/(k_BT)}$ can be reduced to it. I do not see a plot $p_i(T)$ either. Are they related?


title: Car on a frictionless banked curve

text: > _A car is on a banked curve, following a path which is part of a circle with > radius $R$. The curve is banked at angle $\theta$ with the horizontal, and > is a frictionless surface. What is the speed the car must go to accomplish > this?_ What I don't understand about this problem is why we assume there is only the normal force and the gravitational force on the vehicle. From that point onwards, I have no trouble following the solution. The way I see it, if we're considering only that there exists a normal force and a gravitational force, something the car is doing (accelerating?) must be "adding" to the normal force. Or is it possible that the car could just be coasting, and it could keep a constant height along the banked curve?


title: How can W+ boson turn an electron to a electron neutrino?

text: If you look at the Feynmann Diagram of an electron capture: ![enter image description here](http://i.stack.imgur.com/3mS4E.jpg) Whe W+ boson turns the electron into a neutrino. How is this possible? I thought the the boson carries the positive charge and converts the electrons into a positron. Why is this possible?


title: The expansion of a function in powers of a parameter

text: In the perturbation theory for non-degenerate levels, the energy $E_n(\lambda)$ of an eigenstate $|\psi_n(\lambda)\rangle$ of the hamiltonian $\mathcal{H}=\mathcal{H}_0+\lambda \mathcal{H}_1$ (where $\mathcal{H}_0$ is the unperturbed hamiltonian with eigenstates $E_n^0$ and $\lambda\mathcal{H}_1$ is the perturbation) is described by the equation $$E_n(\lambda)=E_n^0+\dfrac{\lambda\langle\phi_n|\mathcal{H}_1|\phi_n\rangle+\lambda^2\langle\phi_n|\mathcal{H}_1|\psi_n^1\rangle+\lambda^3\langle\phi_n|\mathcal{H}_1|\psi_n^2\rangle+\dots}{1+\lambda a_n^{(1)}+\lambda^2 a_n^{(2)}+\dots}.$$ Here, $|\phi_n\rangle$ is the $n$'th eigenstate of the unperturbed hamiltonian, and $a_n^{(p)}=\langle\phi_n|\psi_n^p\rangle$, with $|\psi_n^p\rangle$ being the $p$'th correction to the $n$'th eigenstate. The zeroth correction of course equals the eigenstate of the unperturbed hamiltonian: $|\psi_n^0\rangle=|\phi_n\rangle$. **My question is the following** : how does one go from the above equation to this? $$\begin{array}{r l} E_n(\lambda)&=E_n^0+\lambda\langle\phi_n|\mathcal{H}_1|\phi_n\rangle\\\ &+\lambda^2\left[\langle\phi_n|\mathcal{H}_1|\psi_n^1\rangle-\langle\phi_n|\mathcal{H}_1|\phi_n\rangle a_n^{(1)}\right]\\\ &+\lambda^3\left[\langle\phi_n|\mathcal{H}_1|\psi_n^2\rangle-\langle\phi_n|\mathcal{H}_1|\psi_n^1\rangle a_n^{(1)}-\langle\phi_n|\mathcal{H}_1|\phi_n\rangle a_n^{(2)}\right]+\dots \end{array}$$ The book I'm working with tells me this is done by _"Expanding this expression in powers of $\lambda$"_ , but I can't recognize the procedure. Of course the first term $E_n^0$ is of order $\lambda^0$, and the second term $\lambda\langle\phi_n|\mathcal{H}_1|\phi_n\rangle$ is of order $\lambda^1$, and these can be taken from the original equation right away, but I can't find out how the subtractions in the third and fourth term got there.


title: Interaction between neutrino and an anti-neutrino?

text: What happens when a neutrino and an anti-neutrino interacts together? For example, what does a muon neutrino and anti-muon neutrino produce? it says in my book that it creates "muons and antimuons". But, how? Don't the particle and the antiparticle annihilate when they interact with each other?


title: Do mirrors increase the amount of light in a room?

text: So if you have a light bulb in a room, and you had a tool to measure the amount of light that's in the room, then let's assume the amount of light only caused by the bulb is "1" If you place a mirror next to the bulb, does the amount of light in the room in crease to "2"? Can you keep going so that the light in the room in creases to 3..etc with more mirrors? How far can you take this? Also, is it actually adding light to the room, or is it simply causing the same photons to move faster (reflecting from one mirror to the next) making it seem like there is more light in the room, but there really isn't? Made me think, so I thought I ask here :)


title: Are the Maxwell's equations enough to derive the law of Coulomb?

text: Are the 8 Maxwell's equations enough to derive the formula for the electromagnetic field created by a stationary point charge, which is the same as the law of Coulomb? If I am not mistaken, due to the fact that Maxwell's equations are differential equations, their general solution must contain arbitrary constants. Aren't some boundary conditions and initial conditions needed to have a unique solution. How is it possible to say without these conditions, that a stationary point charge does not generate magnetic field, and the electric scalar potential is equal to $$\Phi(\mathbf{r})=\frac{e}{r}.$$ If the conditions are needed, what kind of conditions are they for the situation described above (the field of stationary point charge)?


title: Applications of QFT in theoretical physics

text: I would like to know which fields in physics have seen growth or benefited by applying QFT? I know that approaches to quantum gravity such as string theory use QFT, HEP and also some branches of condensed matter physics. Where is it applied in condensed matter physics exactly? And in what other areas of theoretical physics, has QFT been applied?


title: Result of increasing the radius of earth?

text: How can increasing the radius of earth may cause an impact on the solar system ? Like, would earth may start making a bigger orbit (due to increase in size and wait) or vice versa ? or else ? PS: The base of my question arises from the point of view of "Growing Population", and managing it by "artificially increasing the size of earth" (Instead of say, finding possibilities to live on other planets like Mars). So, if the radius increases, naturally the circumference of the sphere, and hence surface to live on will increase. I understand however that probably exploring newer planets might be more feasible solution. But just for curiosity I shared my query. :)


title: Special Relativistic approximation to GR

text: Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR can be achieved simply by using Special Relativity and applying a series of (infinitesimal?) Lorentz boosts to simulate acceleration/a gravitational field. In fact, I believe this is precisely the approach used by GPS system for accurate triangulation/location, as mathematically and computationally it is a somewhat simpler process than applying the Einstein field equations. So my question is: has anyone else heard of this? An explanation of how exactly this approximation works, and where/why it fails in comparison to true GR (perhaps the strong gravitational field case?) would be much appreciated.


title: Zener diodes - how do they work?

text: I was going through some of the theory behind Zener diodes. I know what they're used to work at constant voltage, but I don't know how they work. Actually, I kind of get that too, I know that voltage is constant until breakdown occurs (avalanche breakdown), but I don't get why a minimum current is needed to maintain a constant voltage, which is what the textbooks say. Why is there a _minimum_? I thought any current below the breakdown voltage was constant. I don't see why the voltage would vary through the diodes if it's below a set amount of current, yet remain constant between voltages x-y? Any help would be greatly appreciated, I can't wrap my head round exactly what's going on inside the little buggers. P.S, is there more of an appropriate question for the electronics section? As I know electronics is a natural part of physics, and I heard this kinda stuff gets studied quite a lot in physics exams.


title: Books about alternative interpretations of quantum mechanics

text: Recently I've heard that there exist alternative interpretations of quantum mechanics which, while not as widespread as the Copenhagen intepretation (or so it would seem), are equally valid in the sense that they describe all the observable effects. Wikipedia mentions a few ones, the more popular of which seems to be the many worlds interpretation. What are some books, suitable for someone with an undergraduate level knowledge of QM, that describe these alternatives? Something not too mathematical might be best for an introduction to the subject, but I'm not looking for a popular book either, of course.


title: Hamiltonian formulation of single particle in an electromagnetic field

text: Consider a charged particle in a static electromagnetic field. Suppose that the domain is simply connected so that the second law of Newton's dynamics reads: $$ m\frac{\mathrm{d}^2\vec{x}}{\mathrm{d}t^2}=-e\left(\vec{\nabla}\Phi+\frac{\mathrm{d}\vec{x}}{\mathrm{d}t}\times(\vec{\nabla}\times\vec{A})\right) $$ where:   * $m$ is the mass of the particle,   * $\vec{x}$ is position vector,   * $\Phi$ the (scalar) electric potential,   * $\vec{A}$ the (vector) magnetic potential. My question is how to derive the Hamiltonian formulation from here. The Hamiltonian is: $$ H(\vec{x},\vec{p})=\frac{1}{2m}\left\|\vec{p}-e\vec{A}\right\|+e\Phi(\vec{x}) $$ and the Hamilton equations look like: $$ \begin{cases} \frac{\mathrm{d}x_i}{\mathrm{d}t}=\frac{1}{m}(p_i-eA_i)\\\ \frac{\mathrm{d}p_i}{\mathrm{d}t}=\frac{e}{m}\sum_{j=1}^3(p_j- eA_j)\frac{\partial A_j}{\partial x^i}-e\frac{\partial\Phi}{\partial x^i} \end{cases} $$ Another question related to this one is why the magnetic potential is "included" in the "generalized" moment $\vec{p}-e\vec{A}$. I undertand why from the Lagrangian of the system but perhaps there is a physical explanation. **EDIT:** Consider a single particle in a conservative force field $F=-\vec{\nabla}V$. Then the Newton's equations are: $$ m\frac{\mathrm{d}^2\vec{x}}{\mathrm{d}t^2}=-\vec{\nabla}V $$ This is a second order differential equation, which we can transform into a system of first order differential equations, by adding a new variable which is usually the speed $v$ in mathematics but here we will take the momentum $p=mv$. The system I am talking about is: $$ \begin{cases} \frac{\mathrm{d}\vec{x}}{\mathrm{d}t}=\frac{\vec{p}}{m}\\\ \frac{\mathrm{d}\vec{p}}{\mathrm{d}t}=-\vec{\nabla}V(x) \end{cases} $$ which is just the hamiltonian form of the Newton's equations. Can we do the same kind of trick in the case of the system above?


title: Difference between normal mode methods and wavenumber integration?

text: Normal mode and wavenumber integration methods allow the evaluation of an integral transform solution. The text book that I am reading states that the normal mode method evaluates the field as a sum of residues for the poles enclosed by the integration contour. On the other hand, wavenumber integration uses direct numerical quadrature to evaluate the integral. Normal mode methods are only applicable to problems dominated by the pole contributions. My question is why the Normal mode models are considered to be only an approximation, and only applicable when pole contributions dominate. Shouldn't the integral expressed as a sum of residues be exact?


title: Is it known what causes the "knee" in the observed Cosmic Ray spectrum?

text: I've seen many versions of the figure shown below -- the famous _Swordy plot_. They tend to explicitly point out two features in the CR spectrum, the **knee** and the **ankle**. I know that the source of UHECR's above the _ankle_ is currently a mystery. But I'm having a devilish time sussing out the cause of this feature at the knee. Is it known why the slope changes? ![enter image description here](http://i.stack.imgur.com/kSBuo.png)


title: Manipulation with braket notation

text: I am still getting used to the braket notation. Is this manipulation correct? $$ \frac{-\hbar^2}{2m}\int_{-\infty}^{\infty}\frac{\partial^2\phi_n^*}{\partial z^2} \phi\,dz = \int_{-\infty}^{\infty}\phi\left(\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial z^2}\right)\phi_n^*\,dz = \int_{-\infty}^{\infty} \phi \hat{K}\phi_n^*\,dz = \left( \int_{-\infty}^{\infty} \phi^* \hat{K}\phi_n\,dz \right)^{*} = \langle\phi|\hat{K}|\phi_n\rangle^{*} $$


title: Coherent virtual photons and the vector potential

text: Does this paragraph make sense? "The vector potential emitted by a current carrying wire is a packet of coherent virtual photons, all with the same momentum traveling in the same direction. They cannot annihilate each other, for this would violate conservation of momentum. They travel to infinity. Momentum must always be conserved."


title: Tidal Forces from the Moon on the Earth's Crust

text: How do we determine how much the surface of the Earth deflects due to tidal forces from the Moon (and Sun)?


title: How is mobile communication made possible from airplanes?

text: I have heard that communication using mobile phones begins to degrade when used on a vehicle moving at speeds above 200 km/hr due to doppler effect as described here (p-22). How is this limitation overcome in airplanes. What is the specific technology used to overcome this limitation.


title: Is the effective Lagrangian the bare Lagrangian?

text: In standard (non-Wilsonian) renormalization we split the bare Lagrangian $\mathcal{L}_0$ into   * a physical Lagrangian $\mathcal{L}_p$ with measurable couplings and masses    * counterterms $\mathcal{L}_{ct}$ with divergent couplings We then calculate with the bare Lagrangian perturbatively to a cutoff $\Lambda$ adjusting the counterterms so that it's valid to take the continuum limit. In the Wilsonian theory we start with a Lagrangian $\mathcal{L}_w$ and a scale $\Lambda$. We suppose $\mathcal{L}_w$ is a small perturbation to some fixed point of the renormalization group flow. Using the renormalization group we deduce an effective Lagrangian $\mathcal{L}_{eff}$ at some scale $\mu<\Lambda$. We then take the limit $\Lambda \to \infty$. What do we calculate with in the Wilsonian theory? Is it the case that $\mathcal{L}_{eff} = \mathcal{L}_0$ from the standard renormalization theory? If so, why? **Example:** In $\phi^4$ theory we have   * $\mathcal{L}_0 = \frac{1}{2}Z_0(\partial_\mu \phi)^2-\frac{1}{2}Z_0m_0^2\phi^2+ \frac{\lambda_0Z_0^2}{4!}\phi^4$   * $\mathcal{L}_p = \frac{1}{2}(\partial_\mu\phi)^2-\frac{1}{2}m^2 \phi^2+\frac{\lambda}{4!}\phi^4$   * $\mathcal{L}_{ct} = \frac{1}{2}\delta_Z(\partial_\mu\phi)^2-\frac{1}{2}\delta_Z\delta_{m^2}\phi^2+ \frac{\delta_\lambda\delta_Z^2}{4!}\phi^4$ I have no idea what $\mathcal{L}_w$ and $\mathcal{L}_{eff}$ are though? And no book (Peskin and Schroeder, Deligne and Witten etc.) seems to explain it. My guess is as follows $\mathcal{L}_w = \frac{1}{2}(\partial_\mu\phi)^2-\frac{1}{2}m_\Lambda^2 \phi^2+\textrm{all interactions}$ and that at fixed $\mu$ we have $\mathcal{L}_{eff}\to\mathcal{L}_0$ as $\Lambda\to\infty$. I have no real reason to think this though, and still less idea how to prove it!


title: Action and reaction - not the same effect

text: If I press on something, it presses me back with the same force. if I press a pillow with my fist, l do not feel pain but if I press a rock with my fist with the same force, I do feel the pain. why? Regardless of the fact that my force gets distributed over the pillow surface, I should still get a reaction on my fist that should equal the force I applied. To be able to compare the two well, please assume that my force on the rock is also over a similar area to the pillow and not concentrated on narrow points that do not cover the whole fist area.


title: What is the definition of particle-hole symmetry in condensed matter physics?

text: People often talk about particle-hole symmetry in solid state physics. What are the exact definition and physics picture of particle-hole symmetry? How to define the density of particles and holes?


title: Does the "Energy Catalyzer" generate energy by converting Nickel to Copper?

text: From Wikipedia: > The Energy Catalyzer is an apparatus built by [...] Andrea Rossi, [and] > Sergio Focardi. The 2009 patent application claims "a method and apparatus > for carrying out nickel and hydrogen exothermal reactions," with production > of copper. Although the patent cites previous works on cold fusion, one > statement by Rossi asserted that it is not cold fusion, but rather LENR, > Low-Energy Nuclear Reaction. > > [...] > > According to Focardi, "the hydrogen is heated at a given temperature with a > simple resistor. When the ignition temperature is reached, the energy > production process starts: the hydrogen atoms penetrate into the nickel and > transform it into copper.” Are these claims true?


title: Black hole accretion of dark energy

text: Dark energy physically can be interpreted as either a fluid with _positive_ mass but pressure the negative of its density (pressure has units of energy/volume, and energy is mass), or a property of space. If it's a fluid, it should add to the mass of black holes like any form of energy (no hair), and the black hole should grow? However, if dark energy is a property of space, then this won't happen. Is my reasoning correct that we can differentiate (in theory) by looking at black hole's growth rate? Edit: There are many ways to define growth quantitativly. For example, we can put test particles in orbit and look at decreases in their proper time to orbit the hole.


title: Questions about classical and quantum scale invariance

text: This is kind of a continuation of this and this previous questions.   * Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an interacting version of that. Then what can be the constraining effects on the perturbation theory from the fact that the free theory was scale invariant? (for an example like this see this recent paper)    * Can one give a QFT example where this can happen that a non-marginal coupling flows to a non-zero fixed point and the anomalous dimension of the corresponding operator adjusts so that the coupling becomes marginal at that point? (..for the fixed point of the RG flow to be interpreted as a point of scale invariance this adjustment has to happen!..)


title: Why can't Humans run any faster?

text: If you wanted to at least semi-realistically model the key components of Human running, what are the factors that determine the top running speed of an individual? The primary things to consider would be the 'thrust' provided by the legs, with significant components in the vertical and horizontal, and also wind resistance and energy dissipated by muscles and bones during the 'landing' half of each step, before the thrust part kicks in. If a human was running in a vacuum (somehow...) would they be able to run much quicker, or is the wind resistance part negligible compared with the losses involved in the running action itself? If anyone has references great, but I'd be happy with a well reasoned back of the envelope calculation.


title: Help wanted achieving cryogenic temperatures

text: My son's science project involves liquifying air. I found the Linde process which is the way it was done first. We are trying and not getting very far so I am looking for advice. I have an air compressor good to 150psi. We are slowly ramping up the pressure in the system. We are currently testing at 80psi. We pressurize 20 feet of copper tube bent in a coil running through an ice bath. The tube exits and goes into the bottom of a thermos. The end of the tube is capped, and we allow a small leak so that pressure drops from 80psi to 1atm. We insulated the few inches between the ice bath and the thermos. We do not yet have a double walled tube, but we taped the thermos so all the air coming out is exiting through the insulation. When we run, the thermos drops from room temperature (about 68F in the basement) to our best of 45F. I'm quoting in Fahrenheit right now because the boys are very obnoxious about not wanting to use a temperature system they aren't comfortable with, and I just haven't been able to convince them that they are being unreasonable. The point is, we are not even achieving the temperature of the ice bath. Incidentally, as measured with my multimeter, the ice bath is always 3C. I'm curious about that too, but that will be a separate question. Needless to say, we are not achieving any refrigeration. The next step we will increase the leak so that the flow through the system is much higher. And we will start trying to use a Peltier cooler so we can have an intermediate stage that is 20C or so cooler than the ice bath. Obviously we can up the pressure, but I would think we should see something more than we are getting. Any suggestions? Should I take a picture of our setup?


title: Orbital mechanics and rocketry: Is it ever a good idea to intentionally lower periapsis?

text: tl;dr: Hohmann Transfer appears to be the optimal way to achieve a circular- to-circular orbit, but is it possible to lower the periapsis in order to achieve a more elliptical orbit with apoapsis at the same distance, using less delta-v than a Hohmann transfer? I've been playing an awesome game called Kerbal Space Program, which models to quite an accurate degree the spacecraft mechanics that you may encounter within a solar system. I was reading about how the Oberth effect dictates that rocket burns are much more efficient when orbital velocity is higher. I want to minimize fuel consumption, which is a noble and practical endeavor. The situation is this. A stable circular (or nearly circular) orbit has been established around a planet. The goal is to travel to a target location in orbit around the same planet that is in a much larger orbit. Being already in a circular low orbit makes it easy to adjust the inclination to match that of the target body, so I'm currently most interested in the case where I am already in a near-circular orbit in the same plane as that of my target body. It is the next step that I'm confused about. I see two approaches.   1. Fire engines in prograde direction at periapsis to gain enough energy to reach the vicinity of target body.    2. Fire engines in retrograde direction at apoapsis to lower the periapsis to the lowest point possible before entering atmosphere. (this step is "undoing" some of the work done in entering the original circular orbit; If the planet we're orbiting is the one we launched from, it is possible to angle the launch to match target inclination and produce this elliptical orbit from the beginning. But let's not assume this is possible for now.) At the new lowered periapsis, the prograde engine burn is more efficient.  I am ignoring the fact that these will have us arriving at the target at different times; going back around a few times should eventually produce a capture opportunity. So I believe what this means is that approach #2 may be preferable if it can be established that the same target distance can be reached by #2 using less total engine delta-v than with approach #1. I started out by thinking that perhaps the most mathematically simple way to attack this is by observing the rate of orbital energy change introduced by these burns. How much delta-v does it take to lower periapsis to half its current location from a circular orbit? This must be balanced with the amount of extra energy rate gained by engine burn at periapsis, but does halving the periapsis mean that the delta-v here produces 4 times as much energy because orbital speed is 4 times as high? Or is it 16 times? But then I realized that a circular orbit of radius N has a lot more orbital specific energy than a highly elliptical orbit with apoapsis N. I'm not sure I understand the proof, but the Hohmann transfer (e.g. approach #1 forms the first half of a Hohmann transfer) is apparently the most efficient way to gain a larger circular orbit. However I'm not interested in the second burn. The second burn is going to be for establishing an orbit around the target body and that should hopefully be negligible. It would not be predictable anyway. I can't really even make up my mind as to whether it's always, sometimes, or never worth it to do this! **Update:** I thought about it a little more, and it is possible that a Hohmann transfer is more or less necessary because having very low orbital speed at apoapsis for target body encounter is not conducive to establishing an orbit around it: the speed must be a close match in order to achieve gravitational capture. In this case the answer to my question would be "Probably, but your assumptions are flawed". It is possible that if we are in an orbit that is actually retrograde to your target body that this sort of high-eccentricity attack would reduce the backwards transverse motion upon arrival at apoapsis, so that's one thing I've learned (stumbled upon) today. The original question still stands, can we get our orbit to swing out farther by intentionally reducing periapsis?


title: Time-orded operator in Srednicki

text: On page 51 Srednicki states, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order operator $T$, moves all...where they annihilate...". How correct is this paragraph? **Is equation (5.14) always valid? Is equation (5.14) the reason why the time-ordering symbol $T$ appears all over the place in QFT?** The equations I'm referring to are (braket package available?): $$\langle f|i\rangle = \langle0|~a_{1'}(+\infty)a_{2'}(+\infty)a_{1}^\dagger(-\infty)a_{2}^\dagger(-\infty)~|0\rangle$$ and since time goes from right to left inside the braket we put the $T$-symbol $$\langle f|i\rangle = \langle 0|T ~a_{1'}(+\infty)a_{2'}(+\infty)a_{1}^\dagger(-\infty)a_{2}^\dagger(-\infty)~|0\rangle$$ without changing anything. After this, the $T$-symbol appears everywhere!


title: Ice bath is always 3C, why?

text: I've always learned that a mixture of ice and water should reach equilibrium at approximately 0C. I've actually tried to create that a number of times in different contexts and always fail. First, an ice bath in a plastic container. I get 3C, occasionally as low as 2C with a multimeter thermocouple. Granted those are inaccurate, so I've tried a digital thermometer from Vernier with claimed accuracy of 0.5C. I confirmed with an IR thermometer. Same story. Thinking that perhaps it is due to warming from the outside, I have put the ice bath in a thermos and chilled it a while. Same story. I am not using distilled water, so there are some minerals in the water, but if anything I thought that would lower the temperature of the ice bath.


title: Calculation of the maximum load to the bar

text: Looking for a way of calculating the maximum weight (W) to the rod with the given length (L) where the rod did not break and that only bend for (b) mm. ![enter image description here](http://i.stack.imgur.com/o5lps.jpg) Need only approximative solution (read: simple as possible :), nothing with finite-elements or integrals or so. The practical background: What rod i should to use for suspension of 100kg with L=1.5m and max bending approx. b=1cm? For what _constants_ should I looking for in the published "properties" for the different materials and different profiles? E.g. steel rod vs bamboo? :) Some URL's to helpful practical solutions (read: easy math) is very welcomed - my googling failed.


title: How is derived the relation between capacitances when a $Y-\Delta$ transformation is applied in a capacitors network?

text: A $Y-\Delta$ transformation can be applied to circuits in order to make an equivalent circuit (but simpler to put in terms of series/parallel devices). Wikipedia and other books show how to deduce the relation between resistances in a network. You can use this tool (as pointed by @Alfred_Centauri) to calculate the relation between capacitances in a capacitors network. But, How exactly is derived that relation from basic principles?


title: Advantage of doing research in theoretical high energy over other fields?

text: I am undecided about the field I want to do my PhD in, in graduate school. I am asking because the applications that I am filling ask me to write the intended field of study. I found the people who do theoretical high energy physics are the best one able to describe physics and explain it at all levels, otherwise my choices are neutral. Since I am just a student and do not know the big picture of this field and other fields in physics, I want to ask what are the advantages and disadvantages of doing a PhD in theoretical high energy physics?


title: growth condition for the potential

text: what growth conditions should the potential inside the Hamiltonian $ H=p^{2}+ V(x) $ has in order to get ALWAYS a discrete spectrum ?? for example how can we know for teh cases $ |x|^{a} $ , $ exp(b|x|) $ and so on with real parameters a,b and c how can we prove that for theses potentials we will have only a discrete set of eigenvalues ?? another question is it possible to find a potential which have the eigenvalues $ E_{n}=n^{c} $ for some positive real number 'c' , i have heard that no potential in QM could have eigenvalues bigger than $ E_{n}=n^{2} $


title: How does current flow in a irregularly shaped heterogeneous resistor?

text: The motivation for my question is understanding how electricity gets through your skin as opposed to running along it, and how the presence of things like water on the skin affect the relative deadliness of electricity, or ability of it to permeate the skin. I don't understand how to view the body as a resistor, as the skin, and all the components of the body have different resistances and thicknesses. How do I know what parts of the body carry significant current? And how much current in total?


title: Understanding a Physics Paper on Quantum Teleportation of Continuous variables

text: The paper I am trying to understand is here: http://pra.aps.org/abstract/PRA/v49/i2/p1473_1 The paper describes the quantum teleportation protocol in a general case with continuous dynamical variables (position and momenta) in contrast to what is always discussed here, the discrete case. I am very confused as to **what is being teleported** in this this scheme. I understand that in the discrete case, its its polarization state of a photon or the spin of an electron. What I understand is that you start out with an entangled pair of particles in position and momentum in the original EPR State: http://prola.aps.org/abstract/PR/v47/i10/p777_1 So if you are to try to teleport the position and momenta information of a particle, what is this exactly? Don't we need an origin point? Going on with the teleportation procedure, you interact the input particle with one of the entangled pairs, now somehow an analogous bell measurement is made on the position and momentum of the combined pair?? Now you communicate that result to the other entangled particle and you do appropriate "shifts" so that the particle is now the input particle in terms of position and momentum. Does this mean that the position and momentum distribution of one particle is teleported to another? What happens if the input particle was moving? Does this mean that after teleportation, the other particle keeps on moving too? This is extremely confusing.


title: Help me understand the first equation in Landau & Lifshitz's Quantum Mechanics

text: While I've covered a basic course in Quantum Mechanics, I'm self-studying Landau & Lifshitz's book to help me understand what's going on. Unfortunately, I'm stuck on the very first equation in the book. Landau & Lifshitz write: > The basis of the mathematical formalism of quantum mechanics lies in the > proposition that the state of a system can be described by a definite (in > general complex) function $\Psi(q)$ of the coordines so far so good... > The square of the modulus of this function determines the probability that a > measurement performed on the system will find the values of the coordinates > to be in the element $dq$ of configuration space. The function $\Psi$ is > called the **wave function** of the system again, fine... > A knowledge of the wave function allows us, in principle, to calculate the > probability of the various results of any measurement (not necessarily of > the coordinates) also. All these probabilities are determined by expressions > bilinear in $\Psi$ and $\Psi^*$. The most general form of such an expression > is > > $\int \int \Psi(q)\Psi^*(q')\phi(q,q')dq dq'$ > > where the function $\phi(q,q')$ depends on the nature and the result of the > measurement, and the integration is extended over all configuration space. > The probability $\Psi\Psi^*$ of various values of the coordinates is itself > an expression of this type. OK, there's a lot here I don't understand. I can accept most of the statements on faith, but what I don't understand is what the hell $q'$ is for. Why can't the equation just use q throughout?


title: How can I apply Conservation of Energy in electromagnetism?

text: How can I apply **C.O.E** to a system that applies magnetic & electric fields at the same time to do work, and convert energy from one form to another? Let assume we have a conductor that moves within a magnetic field(electric motor) how can **C.O.E** be applied so that input $E$ = output $E$ ? Or in general a wire that has current flowing, and the work done to do that. And the work done by the magnetic forces to move it. And in many other applications... Is there a general way to calculate it? It seems a bit difficult.


title: Forces other than the fundamental interactions, e.g. friction

text: Forgive me for the silly question, but I just don't get it. I just completed an elementary course in mechanics, and I am curious to know what I am about to ask. We have, all year, dealt with many forces like gravity, friction, normal forces, tensions etc. But only one of them is listed as a fundamental force, that is, gravity. I know that the only forces that exist in nature are the four fundamental force, and all of these are, apparently, non-contact forces. But then how do you account for, for example, friction? We know that $F_\text{frictional}=\mu N$, But how do we arrive at that? Is this experimental? I cannot see how contact forces like friction can exist, when none of the fundamental force is a contact force. Again, forgive me for my ignorance.


title: Adding matter to make galaxies bigger

text: What are the actual factors that play a role in the accretion of matter into galaxies? I read about Accretion Disks but I don't quite understand how they work yet.


title: Proof of quantum mechanical position uncertainty

text: How can you prove the uncertainty for position is: $$\Delta{x} =\sqrt{\langle x^2\rangle-\langle x\rangle^2}$$ $\Delta{x}$, taken to be the root mean square of x. $$\Delta{x} =\sqrt{\langle \left(x-\langle x\rangle\right)^2\rangle} $$ $$\Delta{x} =\sqrt{\langle \left(x-\langle x\rangle\right) \left(x-\langle{x}\rangle\right)\rangle}$$ $$\Delta{x} =\sqrt{\langle x^2-2x\langle x\rangle +\langle x \rangle^2\rangle}$$ This is the bit which I am not sure about and why I can do it (taking the outer braket and acting it on the inner x values: $$\Delta{x} =\sqrt{\langle x^2\rangle -2\langle x \rangle \langle x\rangle +\langle x \rangle^2}$$ $$\Delta{x} =\sqrt{\langle x^2\rangle -2\langle x\rangle^2 +\langle x \rangle^2}$$ $$\Delta{x} =\sqrt{\langle x^2\rangle - \langle x \rangle^2}$$


title: Theoretic Mass Energy Conversion?

text: say you had a large quantity of a heavy element such as uranium... AND you put a massive amount of energy into it, so that it began to undergo nuclear fission and transformed to a significantly smaller element(s). Would it be possible to use this energy to now begin a process of fusion, to output energy? And then once it's fused beyond a certain size, back to fission? Basically the idea is to extract back and forth as much energy as possible from the original sample.


title: How to model water flow with and without friction against other objects?

text: I am interested in modeling water flow including boundary flow (with friction) against other objects in the path of the water flow. I'm not a physicist but I am interested to learn the relevant physics (and the corresponding mathematical model) required to begin modeling a generic simulation engine. I've searched this forum using "model water flow surface friction" search string, and I've read water flow in a sink, and What is the velocity area method for estimating the flow of water?. Please suggest topics and other search strings, and advise if this is off- topic for this Physics forum. Thanks in advance. Clarification: I'm looking at   * no-slip condition (i.e. solid walls)   * with turbulence and   * introduction of another body (with mass) into model for calculating the displaced water flow around the body.


title: Is the FRW metric describing the shape of the universe or the shape of the expansion applied to the universe?

text: Is it (the output, i.e, spherical, flat, hyperbolic) describing the physical shape of the universe and its curvature at any given instance of time _or_ is it describing the shape of the expansion function applied to the universe? (i.e, the evolution of the universe spatially over time) So a cone shaped universe could have a "flat" solution applied to it and this just means it keeps expanding forever. Or a "positive" solution applied which means expansion will eventually halt and reverse, ending in a Big Crunch. The original arbitrary shape (conical) not being affected at all?


title: Pileup subtraction for event reconstruction

text: In particle physics experiments, pileup occurs when two particles hit the same detector (say a calorimeter) at roughly the same time, resulting in what looks like a single event with higher energy than either one. Naturally, this can be a pain when analyzing data, and I've heard bits and pieces about methods for subtracting off the pileup events in the final analysis. Presumably this entails identifying events that seem to have a two-peak structure and either dropping the event from the analysis (eek, systematic error) or finding a way to separate them into the two events they are. All the analysis comes after the experiment, in which pileup can be reduced by segmentation of detectors (identify separate events because they are recorded on different parts of the detector) and faster data-taking (making it easier to identify that double- peak structure). But I can't seem to find any accessible information on pileup (the only article Google seems to turn up is a fairly advanced one from the LHC, which I can't quite follow) or its reduction, and would really appreciate a brief summary of pileup subtraction techniques or a pointer to the right place to look.


title: Different kinds of S-matrices?

text: It seems to me that the notion of an "S-matrix" refers to several different objects One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in the asymptotic past and future. This means the incoming and outgoing states belong to the free theory and the S-matrix is an operator on the free theory state space (Fock space). It is the ratio between the time evolution operators of the interacting (but adiabatically "turned off") and the free theory over an infinite time span This construction already yields potentially several objects since there can be several free field limits. For example if the model admits something like S-duality then both the g -> 0 and the 1/g -> 0 limits are free. It is then possible to consider 2 kinds of S-matrices: in one we adiabatically set g -> 0, in the other 1/g -> 0 But it seems that there also should be something like a "fully interacting" S-matrix. This S-matrix should be an operator on the space $Fock(H_{discrete})$ where $H_{discrete}$ is the subspace of the full state space corresponding to the discrete part of mass spectrum Is it indeed the case there are several different S-matrices? If so, why is it "carefully hidden" in the literature? Is it possible to compute the "fully interacting" S-matrix in perturbation theory using the Bethe-Salpeter equation to extract the bound state spectrum?


title: Question from Schutz's

text: In q. 22 in page 141, I am asked to show that if $U^{\alpha}\nabla_{\alpha} V^{\beta} = W^{\beta}$, then $U^{\alpha}\nabla_{\alpha}V_{\beta}=W_{\beta}$. Here's what I have done: $V_{\beta}=g_{\beta \gamma} V^{\gamma}$ so, $U^{\alpha} \nabla_{\alpha} (g_{\beta \gamma} V^{\gamma})=U^{\alpha}(\nabla_{\alpha} g_{\beta \gamma}) V^{\gamma} + g_{\beta \gamma} (U^{\alpha} \nabla_{\alpha} V^{\gamma})$. Now, I understand that the second term is $W_{\beta}$, but how come the first term vanishes?


title: Light Deflection by a Black Hole

text: I think I've come across a paradox while studying general relativity. Wikipedia states that the deflection angle of light by a point mass is $4GM/(c^2b)$. http://en.wikipedia.org/wiki/Gravitational_lensing_formalism Where b is the impact parameter, the limit of the perpendicular distance of the light ray from the point mass as the light gets far away. By shining a light that gets pulled close to the photon sphere of a black hole I can make a photon orbit the black hole an arbitrary number of times before escaping, leading to a deflection angle much greater than 2*pi. However, to make this angle go to infinity (at the photon sphere) according to the equation, I need to make b go to zero. However, if I shine a light very close to to center, it passes the event horizon and will go into the black hole without orbiting forever. What am I missing in this analysis?


title: Is there a better approximation of drag (other than quadratic drag)?

text: This is a student inquiry sparked by sheer curiosity. Wikipedia states the drag equation, $F = 1/2v^2pC_dA_c$. (p = mass density of fluid/gas, v = velocity, c_d = drag coefficient, a_c = cross sectional area perpendicular to velocity.) Wikipedia claims that this equation is only accurate under certain conditions: > _The objects must have a blunt form factor and the fluid must have a large > enough Reynolds number to produce turbulence behind the object._ **Does there exist a more general equation that can accurately measure the drag of all objects, at all speeds/Reynolds numbers and considering all physical properties affecting the drag?**


title: What happens when electron degeneracy pressure is being overcome (right before an object turns into a black hole)?

text: I was wondering about hydrostatic equilibrium (the balance of radially inward and outward forces) in large (i.e. above the Chandrasekhar limit) stars. It is often said that when the gravitational force exceeds any outward forces or pressures, mainly the electron degeneracy pressure I'm thinking, the star collapses into a black hole. But how can this happen without the Pauli exclusion principle being violated? A similar question: Does black hole formation contradict the Pauli exclusion principle? The answer by @Siva in that question makes some sense to me, but I don't understand at what point we start our counting of states from the object being a star to a black hole. What happens in the middle? Is there a sharp change?


title: Why is it difficult to construct the Ramond-Ramond sector in Berkovits' SFT?

text: I've been trying to get familiar with string field theory (SFT) and I've stumbled upon the statement that the Ramond-Ramond (RR) sector of Nathan's SFT has not been constructed yet. Why is that?


title: Compare Dynamics of Cosmic Ray Neutron Radiation

text: Examining cosmic ray neutron radiation near ground by neutron monitors for example (http://www.nmdb.eu), different stations show similar dynamics in the signal. At one station, I like to "substract" the incoming radiation in order to obtain information about local effects. Can I take the incoming signal from another station? But signals of two stations differ:   1. ~~sometimes lags up to 10 days between similar peaks~~   2. peaks differ in amplitude   3. efficiencies differ between the detectors How to correct for such effects analytically? (like the known corrections for pressure, latitude, altitude, etc.) Or are there appropriate techniques for statistical decomposition?


title: A question about relativistic spin operator

text: The question comes from Ryder's Quantum Field Theory, 2nd edition. The author was looking for relativistic spin operator. It was concluded that it cannot be $J^2:=\mathrm{J} \cdot \mathrm{J}$, where $J_i$ is the generator for rotation in Lorentz group. p.56: > _$\ldots \Sigma$ is, of course, the matrix representative of $\mathrm{J}$, > so we conclude that the relativistic spin operator is not $\frac{1}{2} > \mathrm{J}$. This is confirmed by the fact that $\mathrm{J} \cdot > \mathrm{J}=J^2 $(c.f.(2.167)) does not commute with all the generators of > the Lorentz group. For example, $\ldots$, $[J^2,K_1] \neq 0 $._ Later Ryder found the square of the Pauli-Lubanski operator is the Casimir, but still not the relativistic spin operator. (It was refered to literature) I have a question about the logic here. Why the spin operator needs to commute with all the generators in the Lorentz group. If the spin operator commutes with the Hamiltonian, it is a conserved quantity. We can use the eigenvalue to label states (good quantum number). That is precisely $[H,J_i]=0$. Is that still insufficient, because it may be frame-dependent?


title: Roughly how many atoms thick is the layer of graphite left by a pencil writing on paper?

text: Actually I can't expand much as the question pretty much explains the query. I would be interested in the method of estimating an answer as well as a potential way to measure it experimentally. Thanks. P.s. I'm not sure what tags to include for this one - for those that can, feel free to edit them as you see fit.


title: Escape Velocity of Asteriod 243 Ida

text: I was reading about this asteroid (apparently, it has a moon, isn't that awesome?) and I started thinking about if I was on this asteroid, and I jumped, would I fall off? It's been a while since I did something like this, so I went to Wikipedia to get some formulas. There I found $$v_e = \sqrt{\frac{2GM}{r}}$$ Where   * $G$ is the gravitational constant ($6.673 × 10^{-11}\ \mathrm{m}^3\mathrm{kg}^{-1}\mathrm{s}^{-2}$)   * $M$ is mass of the body (found to be $4.2 × 10^{16}\ \mathrm{kg}$)   * $r$ distance from center of mass (found to be $53.6\ \mathrm{km}$) $$v_e = \sqrt{\frac{2(6.673\times 10^{-11})(4.2\times 10^{16})}{53600}} = \sqrt{104} = 10.22\,\frac{\mathrm{m}}{\mathrm{s}}$$ I'm a fairly fit guy, about 73kg and .6m vertical leap here on earth. I found a formula for the speed of a free falling object to be $$v = \sqrt{2gd}$$ If I assume that my speed when I hit the ground is the same as when I jump up, that means my jump speed is about 3.4 m/s, which is significantly less than the required 10.4 m/s. So it would seem I would not be able to jump off of this asteroid. Are my formulas, assumptions, and calculations correct here? Also, how would I use this information to determine how high I would jump (would it be enough to freak me out? Well I'd be jumping off an asteroid, so it would freak me out anyway... although I imagine I would be going slow enough for (my ship?) to pick me back up.)


title: How can I explain the scientific basis of the constant speed of light to a $c$-decay proponent?

text: This Phys.SE question asks why and how the speed of light is constant. I would like to ask a related, almost converse question: **Given that the speed of light is constant,** how could I explain to a young-earth-creationist who is still a proponent of the disgraced Barry Setterfield $c$-decay theory that the $c$-decay theory contradicts observed physical reality, as described and understood by all scientists, including those in the Physics and Astronomy fields? Surely a variable speed of light would throw a monkey wrench into all sorts of fundamental laws or systems in physics? Surely it would be measurable on instruments today, if there was even a **miniscule change** in the speed of light relative to a continuous cold caesium fountain atomic clock? The fact that there is no observable change in any recent trustworthy data, is the beginning, middle, and end of the scientific argument. Am I correct? My physics education ended at Grade 12. So I'm asking for a high-school level explanation. I also wonder if $c$-decay theorists are contradicting themselves, or have sawn off the branch upon which they themselves sit; For example, I wonder this; Would we have to modify our expectations of what the doppler effect (red shift) would look like, as light comes towards us from distant stars, if the speed of light is variable? Would we not have to throw all our doppler data out, and all the distances themselves, if the speed of light is variable in some undefined way, and thus unknown and unknowable? The $c$-decay theory was spawned because redshift data indicates that the stars are too far away for their light to have reached us in the mere 6000 years the universe has existed. In short, if $c$-decay theory exists to explain distant stars to young earth creationists and help them breathe a sigh of relief, wouldn't it be slightly-less-scientifically-bogus, to just dispute the doppler effect and the distance of those stars?


title: Is there a maximum number of types of elementary particles?

text: Doing a Google search i found a paper called The maximum number of elementary particles in a super symmetric extension of the standard model. It claims in the abstract that the upper bound is 84 (i don't have access to the article) My question is: Is there a max number of types of elementary particles predicted in advanced physics theories such as string theory? What are the reasons for this?Are the arguments purely mathematical?


title: Earnshaw's theorem for extended conducting bodies

text: I read on Wiki that Earnshaw's theorem has been proven for extended conducting bodies. If we consider the case of a positive charge at the centre of a symmetric metal cavity- the positive charge and the induced negative charge constitute a system which violates Earnshaw's law. Where am I wrong in thinking this way?


title: Experimental test of the non-statisticality theorem?

text: Context: The recent paper _The quantum state cannot be interpreted statistically_ by Pusey, Barrett and Rudolph (now On the reality of the quantum state, _Nature Physics_ **8** , 475–478 (2012), arXiv:1111.3328) shows under suitable assumptions that the quantum state cannot be interpreted as a probability distribution over hidden variables (go read it now). In the abstract they claim: "This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology." The claim is supported on page 3 starting with: "In a real experiment, it will be possible to establish with high condence that the probability for each measurement outcome is within $\epsilon$ of the predicted quantum probability for some small $\epsilon> 0$." Something felt like it was missing so I tried to fill in the details. Here is my attempt: First, without even considering experimental noise, any reasonable measure of error (e.g. standard squared error) on the estimation of the probabilities is going to have worst case bounded by $$ \epsilon\geq\frac{2^n}{N}, $$ (tight for the maximum likelihood estimator, in this case) where $n$ is the number of copies of the system required for the proof and $N$ is the number of measurements (we are trying to estimate a multinomial distribution with $2^n$ outcomes). Now, they show that some distance measure on epistemic states (I'm not sure if it matters what it is) satisfies $$ D \ge 1 - 2\epsilon^{1/n}. $$ The point is we want $D=1$. So if we can tolerate an error in this metric of $\delta=1-D$ (what is the operational interpretation of this?), then the number of measurements we must make is $$ N \ge \left(\frac4\delta\right)^n. $$ This looks bad. But how many copies do we really need? Note that the proof requires two non-orthogonal qubit states with overlap $|\langle \phi_0 |\phi_1\rangle|^2 = \cos^2\theta$. The number of copies required is implicitly given by $$ 2\arctan(2^{1/n}-1)\leq \theta. $$ Some back-of-the-Mathematica calculations seems to show that $n$ scales at least quadratically with the overlap of the state. Is this right? Does it require (sub?)exponentially many measurements in the system size (not suprising, I suppose) _and_ the error tolerance (bad, right?).


title: CHSH violation and entanglement of quantum states

text: How is the violation of the usual CHSH inequality by a quantum state related to the entanglement of that quantum state? Say we know that exist Hermitian and unitary operators $A_{0}$, $A_{1}$, $B_{0}$ and $B_{1}$ such that $$\mathrm{tr} ( \rho ( A_{0}\otimes B_{0} + A_{0} \otimes B_{1} + A_{1}\otimes B_{0} - A_{1} \otimes B_{1} )) = 2+ c > 2,$$ then we know that the state $\rho$ must be entangled. But what else do we know? If we know the form of the operators $A_{j}$ and $B_{j}$, then there is certainly more to be said (see e.g. http://prl.aps.org/abstract/PRL/v87/i23/e230402 ). However, what if I do not want to assume anything about the measurements performed? Can the value of $c$ be used to give a rigourous lower bound on any of the familar entanglement measures, such as log-negativity or relative entropy of entanglement? Clearly, one could argue in a slightly circular fashion and define an entanglement measure as the maximal possible CHSH violation over all possible measurements. But is there anything else one can say?


title: How often does nuclear fusion occur within the human body?

text: I'm just curious. I figure atoms fuse occasionally just by chance, like quantum tunneling or rogue waves. Is this true? If so, any idea how often?


title: Consideration of static atomic displacements in electronic structure calculations

text: I am hoping to discuss some details of electronic structure calculations. I am not an expert on this topic, so please forgive any abuse of terminology. It is my understanding that first principles electronic structure calculations are based on perfect translational symmetry of a crystalline lattice. Further, that the first round of calculations traditionally treat the atomic nuclei as fixed points due to the large disparity in nuclei and electron velocities, and after the initial electronic structure is solved, one can then turn on the nuclear motions and understand the interaction between the nuclear and electronic motions. The heart of my question is: is it possible to investigate local distortions of structures using existing techniques? By a local distortion, I mean a distortion which does not disrupt the long range crystalline periodicity, but results in a very different local atomic environment?


title: Why we call the ground state of Kitaev model a Spin Liquid?

text: Now we always talk about the so-called Kitaev spin liquid. One important property of spin liquid is **global spin rotation symmetry**. Let $\Psi$ represents a spin ground state, if $\Psi$ has global spin rotation symmetry, then it's easy to show this simple identity $< \Psi \mid S_i^xS_j^x\mid \Psi >=< \Psi \mid S_i^yS_j^y\mid \Psi >=< \Psi \mid S_i^zS_j^z\mid \Psi > $. But Baskaran's exact calculation of spin dynamics in Kitaev model shows that _only the components of spin-spin correlations(nearest neighbour sites) matching the bond type are nonzero_ , which violates the above identity, further means that the ground state of Kitaev model **does not** have global spin rotation symmetry. So why we still call the ground state of Kitaev model a _Spin Liquid_ ?


title: Fitting a circuit scheme to a simpler model

text: I have to simulate the electric field within a gas filled discharge gap generated by a radio frequency voltage generator. The circuit, provided to me by the experimenters somewhat far away, is given in the second picture below. Now the program I use expects me to feed it the time depended voltage curve and three values do describe the circuit: **R, L, C**. > How to match the more complicated real circuit to the model? In any case, > I'll have to plug in some values for the three parameters R, L, C > eventually. (Numerical values: $C1 = 22\ nF=2.2\cdot 10^{-9}, R1 = 2\ Om, L1+L2 = 8\ \mu H=8.0\cdot 10^{-6}, C2 = 3.4n\ F=3.4\cdot 10^{-9}$ [transformer parasitic capacitance]$, R2 = 100\ MOm=10^8\ Ohm, R3 = 1\ Om, L3 = 100\ nH=10^{-7}\ H.$ Moreover, it's running at 1MHz, sinusoidal, about $10kV$.) * * * **Edit.:** So computing the resistence of the "real" model, setting $R_2=\infty$, I get $$Z_\text{tot}=Z_{C_1,L_1,R_1,L_2}+\frac{1}{\frac{1}{Z_{C_2}}+\frac{1}{Z_{R_3,L_3,R_\text{Gap}}}}$$ $$=\left(R_1+i\ \omega\ (L_1+L_2)-i\frac{1}{\omega\ C_1}\right)+\frac{1}{\frac{1}{-i\frac{1}{\omega\ C_2}}+\frac{1}{R_3+R_{Gap}+i\ \omega\ L_3}}$$ $$=\left(R_1+i\ \omega\ (L_1+L_2)-i\frac{1}{\omega\ C_1}\right)+\left(R_3+R_{Gap}+i\ \omega\ L_3\right)\frac{1}{1+(i \omega\ C_2)\left(R_3+R_{Gap}+i\ \omega\ L_3\right)}$$ with $\omega\ C_2\approx 2\cdot 10^{-2}F\ Hz,$ $\omega\ L_3\approx 6.8\cdot 10^{-1}H\ Hz,$ $R_3=1\Omega$ ![enter image description here](http://i.imgur.com/4vQHuRv.png) I tried to ask this on the electrical engineering page, but with no responses. * * * I have no idea if it's of relevance, but I can post the text of the manual of the generator, which I also have, but which isn't really written in my language. I have no idea how the picture even corresponds to the question above. The letter symbols seem a little off. So if the following doesn't make any sense, then ignore it and just take the question above this at face value. ![enter image description here](http://i.imgur.com/HvQPuZL.png) _"This generator simplified block diagram is presented on Fig. 5_ *' (the third picture). _Clock signal generator, protect and control circuits are realized by using programmable logic device(PLD) Xilinx XCR32256XL. This chip configuration(and generation parameters) could be changed in-system by special JTAG (Joint Test Action Group)-programmer. Control signal are boosted by gate drivers and gone to the power switch gates. The converter is designed as half- bridge circuit using MOSFET(Metal-Oxide-Semiconductor Field Effect Transistor) switches and fed by voltage up to 400 VDC. Power oscillatory circuit, included elements C1 and high voltage step-up transformer having loss inductance L and parasitic capacitance C2, forms output voltage. In fire mode this circuit part can be simulated as two coupled oscillators; one of them consists of L and C2 and has resonance frequency about 1 MHz. As a result, output voltage will increase fast, have sinusoidal-like shape and reach breakdown level of load. After discharge gap breakdown, in limit mode, capacitance C2 is shunted by small plasma impedance and we can ignore its influence on power oscillation. Resonance of power oscillatory circuit in this mode will be defined by elements L and C1 and resonance frequency value will be less significantly than clock signal frequency(~1MHz). Output voltage will decrease a lot, its shape is changed to near triangle and power supply passes to limit mode. Powerful 1.3 kW capacitor charging module is used to feed RF converter circuit. It has galvanic isolation from mains and adjustable output voltage. Control circuits and gate drivers are fed by auxiliary AC/DC and DC/DC supplies. External synch signal is transferred by digital isolator, it has standard 50 Ohms impedance, active level is “HIGH”(+5 Vampl). Control signal is inactive if input connector is not jointed."_ I also don't actually know where the voltage they measure (which is supposed to be 10kV) is taken from in the circuit. Maybe the pictures plainly say it, but I can't read it. * * * Lastly, I want to post this, because I find it pretty amusing: _"High output voltage (up to 25 kV) and high level of electromagnetic interferences require highly experienced personnel to operate with generator. Careless use may be cause of electrical shock, health hazard, malfunction or even damage of nearby equipment."_


title: Type I' String theory as M-theory compactified on a line segment?

text: I was considering the S-dual of the Type I' String theory (the solitonic Type I string theory). That is the same as the S-dual of the T-Dual of Type I String theory. Then, that means both length scales and coupling constant are inverted. So, since inverting the length scale of the theory before inverting the coupling constant is the same as inverting the coupling constant before the length scale, I think the S-dual of the T-dual of the Type I String theory is the same as the T-dual of the S-dual of the Type I String theory. The S-dual of the Type I string theory is the Type HO String theory. The T-dual of the Type HO string theory is the Type HE String theory. Therefore, the S-dual of the Type I' String theory is the Type HE String theory. But the Type HE String theory is S-dual to M-theory compactified on a line segment. _**So does this mean that the Type I' String theory is M-theory compactified on a line segment?_** Thanks!


title: Would a cone shaped Stirling engine work?

text: A Stirling engine evidently functions by heating and cooling air, thus making the piston move up and down. What if the heated side of the cylinder were shaped as a sort of cone with a gentle slope, cut off before a point forms (I guess it would look like a trapezoid from the direct side), so that the surface that must be heated is reduced in size, lets say by half? Would that still permit the engine to run as well as it did with a large top surface?


How fast does the water travel down river when the discharge gates of a large dam are opened? Can the discharge-wave travel downstream faster than the water? Is this likely to occur for a real river and an actual sudden discharge from a large reservoir?


title: Inexact measurement and wavefunction collapse

text: As is usually said, measurement of an observable $q$ leads to collapse of wavefunction to an eigenstate of the corresponding operator $\hat q$. That is, now the wavefunction in $q$ representation is $\psi(q)=\delta(q-q_0)$ where $q_0$ is result of measurement. Now, in reality measurements are never exact, so the wavefunction should not have that sharp peak. Instead it should be broadened depending on precision of measurement. In this case, can we still introduce an operator, an eigenstate of which would the new wavefunction appear? Is it useful in any way? Or does the new wavefunction depend too much on the way it was measured so that each instrument would have its own operator? How would such opeartor look e.g. for a single-slit experiment?


title: What does the decay constant mean?

text: In my curriculum, the decay constant is "the probability of decay per unit time" To me, this seems non-sensical, as the decay constant can be greater than one, which would imply that a particle has a probability of decaying in a time span that is greater than 1. Can someone explain this?


title: Making or Demonstrating Principle of Electron Microscope

text: is it possible to either demonstrate the principle or make a SEM ( electron microscope ) at home or lab as an enthusiast?? and how can i start?


title: When traveling close to the speed of light

text: I hope this isn't a stupid question for you guys but here we go. As you travel close to the speed of light, it is to my understanding you gain mass.. does this also apply when the brain sends electrical signals to the muscles? Do the signals (that are traveling at the speed of light) cause the body to weight more? Plz help this question has been bugging me


title: Chiral edge state as topological properity of bulk state

text: As far as I know, quantum hall effect and quantum spin hall effect has chiral edge state. Chiral edge state is usually closely related with delocalization, since back scattering is forbidden. However, some topological nontrivial state does not have chiral state, such as majorana bound state in topological superconductor. I am quite interested whether the existance of chiral edge state is determined by bulk topological properity? Thanks in advance