title: How electricity, and generating electricity works on the atomic level?

text: I am trying to understand the basics physics as to how electricity works. Unfortunately it seems most online material is either complex full blown mathematical equations, or water pump analogies. I am interested in what happens at the single electron level. I guess i should start from what i think i understand. Please correct me if any of my assumptions are wrong. * * * **Energy Flow:** Different materials are made from molecules, those molecules are made from different atom types. Those atoms arrange themselves in in different configurations: ordered(called crystalline), random(amorphous), and a combination of both (Poly-crystalline). The crystal is defined by a lattice and a basis. The lattice is a mathematical representation of points in space, and the basis is a "pattern" that gets pasted on each lattice point. The "pattern" is 1 or more atoms. The crystals are bound together by different types of bonds (ionic, covalent). Since the lattice is just a representation, there is no meaning to start / end point, making the lattice have _translational symmetry_. _Auguste Bravais_ discovered there are only 14 ways you can rearrange the lattice and keep translational symmetry. Naturally crystals are formed when liquid cools down, since it happens in many locations and at different orientations, mostly poly-crystalline are formed. There are several _crystal growth_ methods to create own more perfect crystals. Each atom has an _electron configuration_ , and has several different shells / levels of energy. There can be 2n^2 electrons per level. The lower the level the higher energy needed to bump the electron to the next level (because is closer to nucleus - where the protons are). When arranging several atoms together, due to _pauli exclusion principle_ (convoluted quantum mechanical principle that states two fermions(electrons) can not have the same quantum state) the atoms can not have the electrons at exactly the same energy level, forcing them to change slightly, split and spread into _energy bands_. Conductivity determined by number of _free electrons_ in the conductor that are free to move around. (more later) The highest energy band available for material is called _valence band_. The next band is called _conduction band_. The conductivity is affected by the number occupied of electrons in valence band and the _band gap_ between the valence to the conduction band. (more now) If the valance band is half filled, there is room for the electrons to move resulting in high conductivity (metals). If the band is full, but the band gap to the conduction band is small enough so electrons can be excited to the next band where they can move and there is conductivity(semi conductors). In insulators the valance band is full and the gap is too big, and an electron cant carry enough _thermal energy_ to bump other electron through this gap. Thus, the lattice, crystal structure and atom properties affect the band distribution which affect the number of free electrons. When applying electric field on a wire, a force is applied to all the electrons, making them accelerate. _Mean free path_ and _mean free time_ represent the length & time on average before a collision happens with other atom / electron / material impurities etc. All of those collision, stopping and pushing, contribute to the net directional _drift velocity_ of the electron as it moves in the conductor. drift velocity = current. voltage drop = energy used for exciting electrons over the gap. * * * When connecting current, to a circuit, due to the voltage (potential) difference at the start to the end, electrons start to flow. If there is no resistance, enormous current (as per ohm's law) flows, resulting in _short circuit_ which burns(?) For the circuit not to short, you _must_ add resistance. By adding infinite resistance (say by cutting the wire so the medium is now air between the two) it is called _open-circuit_. Also when using resistor need to take into account _power dissipation_ using the power law. Most(?) resistors are only rated for 0.25 watt dissipation . **How is electricity generated?** Spinning a magnet with some properties of strength, physical size etc, which are summed up as _magnetic flux_ (X), around / between a coil (Y) with some properties of length, resistance, number of turns. Using _Faraday's law_ of _electromagnetic induction_ you can calculate the voltage generated in the coil. The bigger the flux, the faster you spin it, the more coil, all result in higher voltage. (lets assume eventually DC current is produced) **Q:** How long does this voltage last? Is because the more current drawn at this voltage, the _magnetic reluctance_ is increased inside the coil due to electrons movement making in harder to spin the magnet? How is chemical battery affected? **Sources:** ecee.colorado.edu/~bart/book/book/contents.htm britneyspears.ac MIT 802 (non atomic theory + equations) MIT 2.57 (atomic / quantum equations mostly, some theory). en.wikipedia.org/wiki/Classical_and_quantum_conductivity


title: Would the arms of a rotating ice skater still move outwards if there was no other object in the universe?

text: If there is no other object in the universe apart from a rotating ice skater, then nothing can be used as a reference frame. Would it make any sense to say that the skater is rotating? If so, rotating with respect to what? Would she feel an outward pull on her arms? Does rotation makes sense if there is no background reference frame?


title: Multiple source Pipe Network: Given a known outflow, can we deduce the inflows?

text: I have the following simple Y shape water pipe network: ![](https://docs.google.com/drawings/pub?id=1lnPJkaP80nkzdHSB9YfHapth_tlhInnxF- UhPFhQN3s&w=960&h=720) Given $S_{out}$ ( in $m^3/s$), can we compute $S_1$ and $S_2$? For the pipe, we know for each pipe their corresponding diameter $d$, length $L$, roughness coefficient $C$, **we also know the height for each node relative to ground, and hence I guess we do know about pressure in this case.** All the pipe properties ( such as $d$, $L$ and $C$) are assumed constant regardless of their position in the pipe layout. An additional remark here (this remark has nothing to do with my current question; but it serves to identify what the kinds of inputs I have with this question.) For a close loop pipe network, we can use the hazen william formula and hardy cross method to compute the head loss. This means that whatever that is required to be known about the pipe is already known, as long as they are used in hazen william formula and hardy cross method. My question is, **given the above information, is there anyway we can uniquely compute $S_1$ and $S_2$ for the Y shape network above**? From what I know, we have one equation but two unknowns ( the conservation of source): $$S_{out}=S_1+S_2$$ And all the pipe properties are not relevant as far as this Y Shape pipe network is concerned. My conclusion is that above network is unsolvable. But I hear the claim that it is actually solvable as long as we take into account of the aforementioned pipe properties. But I think this is not the case. What do you think? **Bonus: It would be great it one can provide a formulation for the solution of a general shape water pipe network, with or without loops.**


title: Data for binary systems

text: I am looking for binary systems data that can be used in the context of Kepler's laws. Masses, distances, periods, etc.


title: Conductivity of a crystalline solid

text: In a crystalline solid each atomic level 'splits' into _n_ levels ( _n_ = number of atoms in the system). When the number of atoms is large each level becomes replaced by a band of closely spaced levels. In a semi-conductor we have an empty "conduction band" and a fully occupied "valance band". Conductivity arises because electrons get excited to the conduction band. **Question:** Why can't electron in the valence band freely move around and therefore conduct electricity? My question also applies to metals where the conduction band is already half-filled. What's special about this conduction band that allows electron to move around freely?


title: Using the image charges method to find the electric field

text: The following is a question from a tutorial in my Physics 2 course about conductors and the Method of image charges. > We are given two infinite perpendicular and grounded plains. > > The first plain is in the $X-Z$ plain and the second one is on the $Z-Y$ > plain. > > A point charge $q$ is set at the point $(a,b)$, where $a,b>0$. > >   1. Find image charges to the problem > >   2. Find the electric field > > This question has a solution in the tutorial, the answer to the first question is given as the following image which also explains the setting of the problem: ![enter image description here](http://i.stack.imgur.com/UPsQc.png) The answer to the second question is divided into two parts, for the region $x,y>0$ and elsewhere. The solution claims that in the region $x,y>0$ the electric field is that of the four charges seen in the image, and I agree (this follows from the uniqueness theorem). However, I don't understand the last part of the solution, the solution says that the electric field in those regions $x<0$ or $y<0$ is $0$. Why is the electric field $0$ there ? I know that since we put charges there we can not use the method of image charges since we actually changed the charge density in the place we are trying to calculate the electric field at, so I don't have a method for tackling this. Since the answer doesn't justify this claim, and since the answer is $0$, I figured there must be a simple explanation, but I am not able to think of one.


title: Why does Relativity effect the melting point of mercury?

text: I know there is a related question, that references the Dirac Equation, that relies on relativity, but I've just watched this video: http://www.youtube.com/watch?v=NtnsHtYYKf0 Which seems to say there is something new on this topic? What specifically has changed in our understanding? Here is the paper he references. * * * In short, he (in the video) says that as mercury is large, it's electrons have to orbit really fast to not get sucked in. As they move much faster they approach _c_ and gain mass meaning they are less able to bond with other mercury atoms. for a start, I know that electrons fill shells and the bohr model of 'orbits' is quite naive. The abstract of the paper says : > An old problem solved: Monte Carlo simulations using the diatomic-in- > molecule method derived from accurate ground- and excited-state relativistic > calculations for Hg2 show that the melting temperature for bulk mercury is > lowered by 105 K, which is due to relativistic effects. Which doesn't tell me much. So, what new information do we have about the melting point of mercury due to relativity?


I would like to derive Euler's equations of rigid body motion from least action principle. Suppose we are in free space so we have no gravity so Lagrangian is equal to kinetic energy. $$ L = T = \int_M \rho(x)(x\cdot \Omega_B)^2 d^3x $$ where $\rho$ is density, $\Omega_B$ is angular velocity bivector in reference body frame and $M$ is the rigid body. The action principle says(if I haven't messed up something) that $$ 0 = \frac{d}{ds}\bigg|_{s=0}\int_0^T \int_M \rho(x)[x\cdot (\Omega_B(t)+s \delta \Omega(t))]^2 d^3x $$ for every $\delta \Omega$ with zero ends i.e. $\delta \Omega(0)=\delta \Omega(T) = 0$. I should get these equations: $$ I(\Omega_B) - \Omega \times I(\Omega_B)=0 $$ where $$ I(\Omega) = \int_M \rho(x) (x\wedge (x\cdot \Omega)) d^3x $$ But I can't see where I would get the time derivative of $\Omega_B$ from the action principle. Can someone tell me what I'm doing wrong? I guess there is some trouble with that $\delta \Omega$ can't be completely arbitrary.


title: Status of large-scale structure formation within cosmology today

text: Since the CMB results of the past decade, would it be fair to say that the consensus among cosmologists is that cosmic strings are no longer considered as a (major) source for density perturbations? If so, what are the leading theories to explain how the universe developed inhomogeneity from a nearly uniform early universe? What are the active areas of research for within structure formation today, besides relying upon relativistic perturbation methods? Is there a recent review for a status of the field today?


title: What Shannon channel capacity bound is associated to two coupled spins?

text: The question asked is: > What is the Shannon channel capacity $C$ that is naturally associated to the > two-spin quantum Hamiltonian $H = \boldsymbol{L\cdot S}$? This question arises with a view toward providing a well-posed and concrete instantiation of Chris Ferrie's recent question titled _Decoherence and measurement in NMR_. It is influenced too by the guiding intuition of Anil Shaji and Carlton Caves' _Qubit metrology and decoherence_ (arXiv:0705.1002) that "To make the analysis [of quantum limits] meaningful we introduce resources." And finally, it is reasonable to hope that so simple and natural a question might have a rigorous answer that is simple and natural too---but to the best of my (imperfect) knowledge, no such answer is given in the literature. ## Definitions Let Alice measure-and-control by arbitrary local operations a spin-$j_\text{S}$ particle on a local Hilbert space $\mathcal{S}$ having $\dim \mathcal{S} = 2j_\text{S}+1$, upon which spin operators $\\{S_1,S_2,S_3\\}$ are defined satisfying $[S_1,S_2] = i S_3$ as usual. Similarly let Bob measure-and-control by arbitrary local operations a spin-$j_\text{L}$ particle on local Hilbert space $\mathcal{L}$ having $\dim \mathcal{L} = 2j_\text{L}+1$ upon which spin operators $\\{L_1,L_2,L_3\\}$ are defined satisfying $[L_1,L_2] = i L_3$ as usual. Let the sole dynamical interaction between the spins -- and thus the primary resource constraint acting upon the communication channel -- be the Hamiltonian $H = \boldsymbol{L\cdot S}$ defined on the product space $\mathcal{S}\otimes \mathcal{L}$. Further allow Bob to communicate information to Alice by a classical communication channel of unbounded capacity, but let Alice have no channel of communication to Bob, other than the channel that is naturally induced by $H$. Then the question asked amounts to this: what is the maximal Shannon information rate $C(j_\text{S},j_\text{L})$ (in bits-per-second) at which Alice can communicate (classical) information to Bob over the quantum channel induced by $H$? ## Narrative In practical effect, this question asks for rigorous and preferably tight bounds on the channel capacity associated to single-spin microscopy. The sample-spin $S$ can be regarded as a sample spin that can be modulated in any desired fashion, and the receiver-spin $L$ can be regarded variously as a tuned circuit, a micromechanical resonator, or ferromagnetic resonator, as shown below: ![Alice and Bob do spin microscopy](http://i.stack.imgur.com/wXUuo.png) The analysis of the PNAS survey _Spin Microscopy's Heritage, Achievements, and Prospects_ (2009) can be readily extended to yield the following conjectured asymptotic form: $$\lim_{j_\text{S}\ll j_\text{L}} C(j_\text{S},j_\text{L})=\frac{j_\text{S}\,(j_\text{L})^{1/2}}{(2\pi)^{1/2}\log 2}$$ Note in particular that the dimensionality of Bob's receiver-spin Hilbert space $\mathcal{L}$ is $\mathcal{O}(\,j_\text{L})$; thus a Hilbert-space having exponentially large dimension is _not_ associated to Bob's receiver. However it is perfectly admissible for Alice and Bob to (for example) collaborate in squeezing their respective spin states; in particular the question is phrased such that Alice may receive real-time instruction of unbounded complexity from Bob in doing so. ## Preferred Form of the Answer A closed-form answer giving a tight bound $C(j_\text{S},j_\text{L})$ is preferred, however a demonstration that (e.g.) $\mathcal{O}(C)$ is given by some closed asymptotic expression (as above) is acceptable. It would also be very interesting, both from a fundamental physics point-of- view and from a medical research point-of-view, to have a better appreciation of whether the above conjectured capacity bound on spin imaging and spectroscopy can be substantially improved by any means whatsoever.


title: Equal mass on either end of a spring

text: I'm taking physics this term and this is the first time taking physics in 3 years. Here is my homework question (of course those variables all have values but we'll use variables for now): Consider the following macroscopic oscillator: two masses of equal mass $m$, are attached to a spring and oscillate with amplitude $A$, at a frequency $v$. Use classical physics to calculate the energy of the oscillator. This is how I did it. Can someone tell me if my solution is correct? Since the question didn't say where the masses are and under what environment, I assumed they are on either end of the spring and the environment is frictionless. Let $k$ be the spring constant. For each of the blocks, we have the differential equation $m\frac{d^2x}{dt^2}=-k(2x)$. This has the solution $x(t)=A\cos(\sqrt{\frac{2k}{m}}t)$. Therefore, the frequency is $\frac{\sqrt{\frac{2k}{m}}}{2\pi}$. Equating this to $v$, we can find the value of $k$. Hence, the energy of the oscillator is $\frac{1}{2}k(2A)^2$. Edit: My main concern is my computation of $k$. Because I tried to look for a similar question and I found http://www.uccs.edu/~rtirado/Ch14%20ISM.pdf problem 99. Their computation does not involve $2\pi$ anywhere. Can someone possibly explain that to me?


title: Is the total mass of Earth's atmosphere essentially constant in time?

text: Per a few questions and comments on this site such as Huge buildings affect earth's rotation? I wonder, is the mass of the Earth's atmosphere roughly constant? We're burning an incredible amount of fossil fuels which put a huge amount of water and $\textrm{CO}_2$ into the atmosphere. Global temperature increases are causing more water evaporation. A very stormy season can carry a huge amount of additional moisture over parts of the globe. **Is there some physical process such as the gravitational gradient between the surface of the Earth and the edge of space or something else that keeps the Earth's atmosphere roughly constant in mass? Related, is the pressure at sea-level roughly constant?** I'd expect that as we burn more fossil fuels the amount of mass in the atmosphere would increase slowly but I wonder now if there is a counterbalancing effect. An increase in the overall mass of the atmosphere would imply a tiny lengthening of a day. Has such a lengthening been measured?


title: Solving a light ray worldline with the geodesic equation

text: I'm having trouble solving the geodesic equation for a light ray. $$ {d^2 x^\mu \over d\tau^2} + \Gamma^\mu_{\alpha\beta} {dx^\alpha \over d\tau} {dx^\beta \over d\tau} = 0 $$ I apologise, but I'm a bit new to this, but I have the initial $x^\mu$ and initial $dx^\mu\over d\tau$. I'm just not sure how to use them to solve the equation for $x^\mu$. I would logically start with $$ {dx^\mu \over d\tau}_{initial} = v^\mu $$ and suppose that the initial acceleration would be $$ {d^2 x^\mu \over d\tau^2}_{initial} = - \Gamma^\mu_{\alpha\beta} v^\alpha v^\beta $$ But that doesn't really help me integrate it, since I've only got constants for the initial condition. How would I solve this for $x^\mu(\tau)$? Furthermore, I feel that this equation may not apply to light rays, as their proper time ought to be $0$, right?


title: What if EM or QCD was spontaneously broken?

text: Suppose that Standard Model Higgs mechanism broke electromagnetism, by e.g. veving the charged component of the doublet, so that the photon was massive with $m_\gamma\sim v$. Could such a Universe still have large scale structure? Atoms (i.e. stable electronic orbits)? Life? Assuming we got past those hurdles, would it have been much more difficult to have discovered special relativity? Would we have been stuck at Galilean invariance, without the invariance of the speed of light from which to build SR? I appreciate that this is speculative. And, also, the identical question but for a coloured Higgs vacuum that breaks QCD. Would broken QCD still be confining? I guess so - so we could still have nucleons and the resulting chemistry? In general I wonder how fine-tuned the spontaneous symmetry breaking pattern must be for life/structure. Without EWSB, I know that there are no stable electron orbits, and no life.


title: Advice on doing physics under the umbrella of mathematics and the converse

text: In the current scenario of research in QFT and string theory (and related mathematical topics), which of the following would an undergraduate student, like me, be advised to do and why if s/he is interested in both the foundations and pushing the frontiers of these subjects and doesn't differentiate between them or thinks that different set of skills and attitudes are required (plus the student is not so strict about mathematical rigor and even **precise** , logical, hand waving arguments suffice to convince him/her)?   1. Get into a maths department for graduate studies and work under people having similar interests and probably also take advice from people in physics department.   2. Get into a physics department for graduate studies and work under people having similar interests and probably pick up the mathematics one needs along the way. Moreover, what would such a student majoring both in mathematics and physics advised to concentrate on during his/her undergraduate education? It seems to me after reading this post and general experiences of mine that often mathematicians are more willing to accept physical ideas than physicists willing to accept mathematical ideas. Also, the number of people willing also seem to be more in mathematics, at least to me. Also, it seems that some physicists often develop a kind of hatred for mathematics and always remain skeptical that any mathematics can ever do good to physics. On the basis of this, I am inclined towards option 1. Please feel free to correct me.


title: At what speed do things stop being stable and essentially become atomic bomb?

text: I know that when things go very fast (approaching the speed of light), they tend to turn into atomic bombs. What speed can you reach (in earth's atmosphere) before nuclear fusion begins. Does this speed vary with different materials and is so how much? What about in a vacuum, it seems like air resistance could be the problem.


title: Pendulum Hits a Mass and Spring

text: I think this problem’s solution is on the web but after a few days of searching, I can not find it. Can anyone give me a reference? Thanks in advance. A mass and spring are resting on a frictionless table. A pendulum is pulled back, released, and hits the mass. The spring coils, recoils, and propels the pendulum. One of the interesting aspects of this problem is the driving force appears then disappears every now and then. How is this modeled. Thanks in advance.


title: Quantum entanglement? And quantum double slit

text: Does quantum entanglement consist only of 2 matter that are connected by each other? And what is the connection between the observer and the matter that is being fired? I'm not a physicist though but physics is starting to interest me. Especially the quantum world. :D


title: Is this the correct way to I combine multiple interdependant pressure readings?

text: I want to measure the density in different layers of a suspension. To do this I want to place pressure sensors at different heights. Let's assume that the sensors are not by orders of magnitude more exact than neccessary (because I want to detect small differences in density, like 1% over heights of 1m or smaller, and maybe I'm on a budget for the sonsors). The idea would be to place the sensors on a vertical pole with a known distance between two. The pole will be placed in the liquid and not be moved vertically during the measurements. Possibly I will use two sensors at each height. Now, I know that - labeling the sensors downward, 0 at the top - that $(p_1-p_0)+(p_2-p_1)=p_2-p_0$ Now my questions are, how do I use this fact to combine the readings into a coherent, exact picture and how do I calculate the actual error of my result? Here's my approach:   * Set up linear equations for the "true" pressures that follow the relation given above.   * find - numerically, with some equation solver - the tupel of "true" pressures that satisfy the linear equations and have the least mean square deviation from the measured pressures Is this approach basically correct? How would I calculate the error of the true pressure from the error of my sensors?


title: Thermodynamics and electromagnetic fields

text: The energy density in an electromagnetic field is given by: $u = (1/2) <\vec{E}^2 + \vec{B}^2>$ where $<,>$ denotes the average over time. In a cavity it holds that $u= u(T) = \frac{1}{V}U(T,V)$ The force acting on a surface element is given by $d\vec{F_i} = \sum_{j=1}^3 \sigma_{ij} d\vec{o_j}$ where $\vec{o_j}$ denotes the infinitesimal surface element. It also holds that $\sigma_{ij} = \frac{1}{2}(\vec{E}^2 + \vec{B}^2)\delta_{ij} - E_i E_j - B_i B_j$. Since we are in a cavity the radiation is isotropic and the tensor $\sigma$ only has values on the diagonal and it holds that $\sigma_{ij} = p \delta_{ij}$ I'm now supposed to show that the following equation holds: $p(T) = \frac{1}{3} u(T)$ This should probably be really easy but I didn't get any hints for this exercise and I just can't seem to find a way to start. If someone could just give me a hint about how I should start this problem, I'd greatly appreciate it. Cheers!


title: Determining Orbital Velocity

text: Is there any way to determine the orbital velocity of a point around another stationary point, if I don't know the mass of either of the points but know the force that gravity exerts and the distance between them. I'd like to know at what velocity I should push the non-stationary point perpendicular to the stationary point, so that it will maintain a circular orbit.


title: The vacuum light speed: Is it really constant, i.e., independent of location in space-time?

text: I am by no means an expert in this field, however something puzzles me about the speed of light and the relativity of time and space (space-time). Is is universally acknowledged that the speed of light (299,792,458 m/s) is the universal speed limit, and that nothing can travel faster than light? That is a measurement based on a man-made interpretation of time ( _hours, minutes and seconds etc. are man made...there is nothing natural dictating how long a second should be_ ). For instance, according to Einstein, time and space bend around the physical matter of the universe, so for example, time near or on the surface of a "super massive black hole" should be drastically slower, relative to that of earth. Lets say for example that for every second that passes on the black hole, 10 seconds pass on earth, so essentially time on the surface of the black hole is 10 times slower than the time on earth. Given the example above, is the speed of light at the surface of the black hole still 299,792,458 m/s, or is it 299,792,458,0 m/s?


title: The basic equation of bosonization

text: [..quoting from Page 11 of Polchinski Vol2..] Given $1+1$ conformal bosonic fields $H(z)$ one has their OPE as, $H(z)H(0) \sim -ln(z)$ Then from here how do the following identities come?   * $e^{iH(z)}e^{-iH(z)} \sim \frac{1}{z}$   * $e^{iH(z)}e^{iH(0)} = O(z) $   * $e^{-iH(z)}e^{-iH(0)} = O(z) $   * $\langle \prod_{i} e^{i\epsilon_i H(z_i)} \rangle_{S_2} = \prod_{i<j} z_{ij}^{\epsilon_i \epsilon_j}$ for $\sum_i \epsilon_i =0$ I have pretty much no clue how these are derived! (..I have done many OPE calculation earlier but this one beats me totally!..) It would be great if someone can either show the derivation or give a reference where this is explained! * * * Also I am curious if there is a generalization of this to arbitrary even dimensional complex analytic complex manifolds...


title: General Solution of Mechanics Problem

text: I had a homework problem that > Given velocity, $v^2(t)=\frac{K}{x(t)}$, where $x(t)$ is distance, find $v$ > as a function of $t$. Of course if we assume a positive root, it is easy but what if $v(t)$ assumes the positive root when $t<a$ and negative root when $t\ge a$? Is a more generalized solution possible?


title: How is a wormhole formed by spacetime surgery?

text: How is a wormhole formed by performing surgery on spacetime?


title: Many-worlds interpretation vs 'just' randomness?

text: I have this question about MWI I always wanted to ask but never dared to! It could be that I just don't know enough physics to understand the answer, or the question! Anyway, here goes: What is it that differentiates MWI from a physical theory (let's call it 'pure random') which is equivalent but where, in every instance where MWI asserts that the universe spawns/splits up (Schrödinger's cat-esque situations), this theory simply asserts that the universe flips a coin and randomly1 decides which of the possible universes should be realized. In this theory, the other forks are never realized, so there's always just one universe in one state making a bunch of random choices how to proceed. To me this theory seems less objectionable than a theory postulating an enormous amount of parallel universes that can't see each other anyway. So my question is, is there any physical reason to prefer MWI over the 'pure random' theory (and what is this 'pure random' theory called anyway)? After all, the parallel universes in MWI are inaccessible anyway, so it doesn't seem to have any consequence they exist. It's just another way of expressing randomness... and it doesn't even seem MWI can fully do away with randomness anyway. (After all, why am _I_ experiencing this particular universe, and not one the many other ones MWI asserts exists? To me it seems I'm experiencing a random one among the possible ones.) I'm wondering if my 'pure random' theory is really the same thing as what MWI- believers talk about, albeit they use a more colorful language and that's why it gets presented this way in the popular press. But on the other hand many presentations of MWI (including Wikipedia) seem to imply these multiple universes really do exist, and that Everett was of this belief. Apart from the obvious consequences to things like quantum immortality (which Everett also believed in, further underlying he believed in the existence of these parallel universes), are there other observable/measurable differences between MWI and pure random or other reasons to prefer this? * * * 1 The probability distribution would be to reflect the event in question, just as I imagine that MWI would in some situations split up several universes with various properties, and the 'concentration' of a given property reflects the probability of measuring that property... I hope it makes sense!


title: I don't understand what we really mean by voltage drop

text: This post is my best effort to seek assistance on a topic which is quite vague to me, so that I am struggling to formulate my questions. I hope that someone will be able to figure out what it is I'm trying to articulate. If we have a circuit with a resistor, we speak of the voltage drop across the resistor. I understand all of the calculations involved in voltage drop (ohm's law, parallel and series, etc.). But what I seek is to understand on a _conceptual_ level what voltage drop is. Specifically: what is the nature of the change that has taken place between a point just before the resistor and a point just after the resistor, as the electrons travel from a negatively to a positively charged terminal. Now as I understand it, "voltage" is the force caused by the imbalance of charge which causes pressure for electrons to travel from a negatively charged terminal to a positively charged terminal, and "resistance" is a force caused by a material which, due to its atomic makeup, causes electrons to collide with its atoms, thus opposing that flow of electrons, or "current". So I think I somewhat understand voltage and resistance on a conceptual level. But what is "voltage drop"? Here's what I have so far:   * Voltage drop has nothing to do with number of electrons, meaning that the number of electrons in the atoms just before entering the resistor equals the number of atoms just after   * Voltage drop also has nothing to do with the speed of the electrons: that speed is constant throughout the circuit   * Voltage drop has to do with the release of energy caused by the resistor. Maybe someone can help me understand what voltage drop is by explaining what measurable difference there is between points before the resistor and points after the resistor. Here's something that may be contributing to my confusion regarding voltage drop: if voltage is the difference in electrons between the positive terminal and the negative terminal, then shouldn't the voltage be constant at every single point between the positive terminal and the negative terminal? Obviously this is not true, but I'd like to get clarification as to why. Perhaps I can clarify what I'm trying to get at with the famous waterwheel analogy: we have a pond below, a reservoir above, a pump pumping water up from the pond to the reservoir, and on the way down from the reservoir, the water passes through a waterwheel, the waterwheel being analogous to the resistor. So if I were to stick my hand in the water on its way down from the reservoir, would I feel anything different, depending on whether I stuck my hand above or below the waterwheel? I hope that this question clarifies what it is I'm trying to understand about voltage drop. EDIT: I have read and thought about the issue more, so I'm adding what I've since learned: It seems that the energy which is caused by the voltage difference between the positive and negative terminals is used up as the electrons travel through the resistor, so apparently, it is this expenditure of energy which is referred to as the voltage drop. So it would help if someone could clarify in what tangible, empirical way could we see or measure that there has been an expenditure of energy by comparing a point on the circuit before the resistor and a point on the circuit after the resistor. EDIT # 2: I think at this point what's throwing me the most is the very term "voltage drop". I'm going to repeat the part of my question which seems to be still bothering me the most: "Here's something that may be contributing to my confusion regarding voltage drop: if voltage is the difference in electrons between the positive terminal and the negative terminal, then shouldn't the voltage be constant at every single point between the positive terminal and the negative terminal? Obviously this is not true, but I'd like to get clarification as to why." In other words, whatever takes place across the resistor, how can we call this a "voltage drop" when the voltage is a function of the difference in number of electrons between the positive terminal and negative terminal? Now I've been understanding the word drop all along as "reduction", and so I've been interpreting "voltage drop" as "reduction in voltage". Is this what the phrase means? Since I've read that voltage in all cases is a measurement between two points, then a reduction in voltage would necessarily require four different points: two points to delineate the voltage prior to the drop and two points to delineate the voltage after the drop, so which 4 points are we referring to? Perhaps a more accurate term would have been "drop in the potential energy caused by the voltage" as opposed to a drop in the voltage? EDIT # 3: I think that I've identified another point which has been a major (perhaps the major) contribution to the confusion I've been having all along, and that is what I regard as a bit of a contradiction between two essential definitions of voltage. When we speak of a 1.5V battery, even before it is hooked up to any wiring / switches / load / resistors / whatever, we are speaking of voltage as a function of nothing other than the difference in electric charge between the positive and negative terminals, i.e the difference in excess electrons between the two terminals. Since there is a difference in number of electrons only in reference to the terminals, I therefore have been finding it confusing to discuss voltage between any other two points along the circuit -- how could this be a meaningful issue, since the only points on the circuit where there is a difference in the number of electrons is at the terminals -- so how can we discuss voltage at any other points? But there is another definition of voltage, which does make perfect sense in the context of any two points along a circuit. Here we are speaking of voltage in the context of Ohm's law: current/resistance. Of course, in this sense, voltage makes sense at any two points, and since resistance can vary at various points along the circuit, so clearly voltage can vary at different points along the circuit. But, unlike the first sense of voltage, where the voltage is a result of the difference in electrons between the terminals, when we speak of voltage between two points along the circuit, say, between a point just before a resistor and a point just after the resistor, we are not saying that there any difference in number of electrons between these two points. I believe that it is this precise point which has been the main source of my confusion all along, and that's what I've been trying to get at all along. And this is what I've been struggling to ask all along: okay, in a battery, you can tell me that there is a voltage difference between the two terminals, meaning that you can show me, tangibly and empirically, that the atoms at the positive terminal have a deficit of electrons, and the atoms at the negative terminal have a surplus of electrons, and this is what we mean by the voltage between the two, then I can understand that. But in contrast, I accept that there is voltage (I/R) between a point just before a resistor and just after a resistor -- _but_ can you take those two points, the one before the resistor and the one after the resistor, and show me any measurable qualitative difference between the two? Certainly there is no difference between the number of electrons in the atoms of those two points. In point of fact, I believe that there is no measurable difference between the two points. Ah, now you'll tell me that you can show me the difference between the two points: you'll hook up a voltmeter to the two points, and that shows the voltage between them! Sure, the voltmeter is telling us that something has happened between the two points. But the voltmeter does not tell us anything inherent in the points themselves -- unlike the two terminals of a battery, where there is an inherent difference between the two points: one has more excess electrons than the other -- that is a very inherent, concrete difference. I guess what we can say is that the electrons travelling at a point just before the resistor are travelling with more energy than the electrons travelling at a point just after the resistor. But is there any way of observing the difference in energy other than a device that simply tells us that the amount of energy has dropped between the two points? Let me try another way: we could also hook up a voltmeter to the two battery terminals, and the reading would indicate that there is voltage between the two terminals. And if I would ask you yes, but what is it about those two points that is causing that voltage, you could then say, sure: look at the difference in electrons between the two points -- that is the cause for the reading of the voltmeter. In contrast, when we hook up the voltmeter to the points just before and after the resistor, and the reading indicates a voltage between the two terminals. But in this case if I would now ask you the same question: yes, but what is it about those two points that is causing the voltage, I'm not sure if you'd have an answer. I think this crucially fundamental difference between the two senses of voltage is generally lost in such discussions.


title: Preventing a block from sliding on a frictionless inclined plane

text: I want to demonstrate what force $F$ you would have to exert on an inclined plane of angle $t$, mass $M$ to prevent a block on top of it with mass $m$ from sliding up or down the ramp. I worked out an answer, but I figure it must be wrong because it doesn't factor the mass $M$ of the inclined plane into the force needed for the block on top to stay still. Here is my logic:   * The components normal to the force of gravity on the block on top are $mg \cos(t)$, $mg \sin(t)$   * In particular, the component down the ramp is $mg \sin(t)$ as can be demonstrated with a visual   * Thus, we want $F$ to have a component in the direction opposite the vector down ramp with equivalent force so that $F_{\rm ramp (net)} = 0$   * So we want it to be true that $mg \sin(t) = F \cos(t)$   * So $F = mg \tan(t)$. Intuitively, this makes some sense: A steeper slope seems like it would require more force to counteract the component of gravity acting down the ramp. However, this answer and explanation completely disregards $M$, the mass of the ramp itself. Can somebody explain where I am going wrong, or if I obtained the right answer, why it is not dependent on $M$?


title: Is there anything particularly special about sticky tape in the production of graphene?

text: Is there anything special about the properties of sticky tape that means that it can be used to peel graphene layers from graphite? Or is it simply that it's sticky?


title: Degree of Time Dilation At a Distance From the Sun where acceleration = g?

text: At higher altitudes above a body, clocks tick more slowly, and gravitational field is weaker. But what is the relationship? It is tempting for a GR newbie such as myself to think that anywhere that the gravity is equal to that of the earth's surface that time-dilation would be the same, i.e. dilation as a simple function of local gravitational acceleration. I have been assured that this is not the case. I wonder if someone can calculate the following situation, which strikes me as the simplest 2nd case to compare with earth's surface: At the surface of the Sun, gravity is roughly 28 times that at the Earth's surface. If we move out to a suitable distance, we can find a place where the gravitational acceleration is the same as the surface of the Earth - 1g - and we can hold a clock there with a rocket. What is the time dilation there with regard to a "Far away" observer? I understand to the dilation on the Earth's surface to be 0.0219 seconds per year compared with the distant observer.


title: Born Oppenheimer Approximation: Why can any molecular state be represented as a linearcombination of electronic states?

text: in the Born Oppenehimer Approximation, one expands the molecular wavefunction $\Psi(x,X)$ in terms of the electronic wavefunctions $\phi(x;X)$: $\Psi(x,X)$ = $ \sum_k(c(X)_k\phi(x;X)_k)$ (x are the electronic coordinates and X are the nucleonic coordinates) Now, since the electronic wavefunctions are eigenstates of the electronic Hamiltonian, the constitue a complete basis of the electronic space. Thus any electronic wavefunction can be expanded in termes of the eigenfunctions. But, how can we be sure that any molecelar wavefunction can be expanded in terms of the electronic wavefunctions? How can we be sure that the molecular Hilbertspace is not larger than the space which is spanned by the eigenstates of the electronic Hamiltonian?


title: What is the longest distance over which echolocation is effective?

text: Some animals, most notably bats, use echolocation in order to navigate and detect the location and size of objects and prey. This usually takes place over short distances. What are the theoretical limitations to scaling up this system for long range navigation purposes?


title: Specific heat of aluminium as a function of temperature

text: I am trying to find the curve describing the specific heat of aluminum as a function of temperature between about 50K to 300K(or room temperature) for an experiment I am doing. Ultimately I need to integrate between those bounds. Google doesn't seem to provide any useful links. I was able to find some values at specific temperatures, but not enough data to produce a curve. Any references to places that might contain this sort of data are welcome.


title: QFT in Quantum Computing and Control Theory?

text: Is QFT being applied to quantum computing and control theory? I took yesteryear a basic course on quantum computing and if I remember correctly we didn't touch on any QFT (though I think that if it were a course with prequisites of QFT, not a lot of people would have attended the course).


title: Spatial profile for a superconducting qubit's wavefunction

text: What is a spatial profile for a wavefunction of a superconducting qubit (such as say a flux qubit, charge qubit, or a transmon)? I am trying to calculate the energy shift of an superconducting qubit (say a charge qubit for the sake of discussion) coupled to a multi-mode field inside a transmission line. When dealing with a real atom, normally in order to avoid divergences, instead of treating the atom as a single point, one considers the spatial profile of its wavefunction (and then the Fourier transform of that can be used that effectively provides a natural frequency "cutoff"). For an atom it seems to make sense to take a look at a given orbital and think of the atom's "size" in terms of it. Is there any literature on the equivalent for superconducting qubits? Since we usually think of the superconducting qubit's degrees of freedom in terms of the flux/charge (or equivalently phase/Cooper-pair-number) , it is not obvious to me what the physical "size" of these wave functions would be? Most naive way might be to think about say the size of the loop (for a flux qubit) or size of the "island" (for a charge qubit), but I would like to know if anyone knows of published discussions on this topic. Thanks!


title: Where do the conservation laws come from?

text: I know the conservation of energy comes from Noether's theorem via the time- translational symmetry, and if I remember correctly, the conservation of momentum comes from space-translational symmetry. My question is: for a given system, what is the starting point of identifying conservation laws, and how do you know that there's not more that you haven't identified? Do you just start by identifying symmetries? As an example, consider a system of hard, spherical, elastically colliding billiard balls. I suppose the conserved quantities are energy, momentum, and angular momentum; for each particle these correspond to the terms $\frac{1}{2}mv^2$, $mv$, and $m\omega$. How do we know there isn't something like $kmv^3$? (I know this isn't one, but it's just to demonstrate my point). And why is the conserved quantity always a scalar? Are there cases where the conserved quantity is not calculated by summing other scalars?


title: Entropy before and after collapse of the wavefunction/ and interpretation?

text: Seems like it might be pretty rudimentary but I want to see if my thinking is on the right track as well as what the result means. The question is, is the entropy of the collapse of a wavefunction or entangled system more before the collapse? My reasoning is that as Entropy is a measure of the "unpredictability" of information content (in this context), the more we know the less entropy there is. So for example if we have N fair coin tosses in which we don't know the outcome, we would have N bits of unknown information as $ \sum_{i = 0;N} 2^N = N$ but the first we flip and once the answer is known we would have an entropy of N-1 as we don't know those N-1 states. Once all is known we have an entropy of 0. Of course we would deal with a continuous function for waves, but am I on the right track of thought? If so, then how does the second law of thermodynamics fit in in that the Universe is supposed to go to a higher state of entropy? Just an aside question, but is the wavefunction collapse the same as the collapse of an entangled system? Seems that the wavefunction itself is just a superposition of several different eigenstates, is it safe to say that these eigenstates are "entangled"? Thanks, Brian


title: n-p-n p-n-p and n-n-n heterostructure for LED

text: I was studying LED Heterostructures and I found out that my book is always giving reference to p-p-n type heterostructure. So I looked up into another book in order to find other type of heterostructures like npn, pnp, nnp etc. but that book also contained same example. Is there any specific reason behind using ppn heterostructure for LED. Can't I use nnp, npn or ppp? thanks for giving your precious time.


title: Would string theory change everything?

text: Whilst I don't know anything except the definition of String theory and I'm a beginner, I'm curious about it. What I would like to know is: does string theory change a lot in Physics? If it's not true, what else would suffocate in Physics due to String theory? It's just an assumption and not some experimental observation, right? A layman's explanation would be helpful!


title: Symmetrizing the Canonical Energy-Momentum Tensor

text: The Canonical energy momentum tensor is given by $$T_{\mu\nu} = \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$ A priori, there is no reason to believe that the EM tensor above is symmetric. To symmetrize it we do the following trick. To any EM tensor we can add the following term without changing its divergence and the conserved charges. $${\tilde T}_{\mu\nu} = T_{\mu\nu} + \partial^\beta \chi_{\beta\mu\nu} $$ where $\chi_{\beta\mu\nu} = - \chi_{\mu\beta\nu}$. The antisymmetry of $\chi$ in its $\mu\nu$ indices keeps the divergence of this new EM tensor zero. It also keeps the corresponding conserved charges the same. Now even though $T_{\mu\nu}$ is not a symmetric tensor, it is possible to choose $\chi_{\beta\mu\nu}$ in such a way so as to make ${\tilde T}_{\mu\nu}$ symmetric. It can be shown that choosing $$\chi_{\lambda\mu\nu} = - \frac{i}{2}\left[ \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_r) } (I_{\nu\lambda})_{rs} \phi_s + \frac{\delta {\cal L}}{\delta (\partial^\lambda \phi_r) } (I_{\mu\nu})_{rs} \phi_s + \frac{\delta {\cal L} }{\delta (\partial^\nu \phi_r) } (I_{\mu\lambda})_{rs} \phi_s \right]$$ makes the new EM tensor symmetric. Here $(I_{\mu\nu})_{rs}$ is the representation of the Lorentz Algebra under which the fields $\phi_s$ transform. **Here's my question** \- Is it possible to obtain the symmetric EM tensor directly from variational principles by adding a total derivative term to the Lagrangian. In other words, by shifting ${\cal L} \to {\cal L} + \partial_\mu X^\mu$, and choosing $X^\mu$ appropriately, can be exactly get the shift in the EM tensor required, in order to make the EM tensor symmetric? **What I've done so far** \- It is possible to show that under a shift in the Lagrangian by a total derivative, one shifts the EM tensor by $T_{\mu\nu} \to T_{\mu\nu} + \partial^\lambda \chi_{\lambda\mu\nu}$ where $$X_{\lambda\mu\nu} = \frac{1}{2} \frac{\delta X_\lambda}{\delta (\partial^\mu \phi_r)} \partial_\nu \phi_r - \frac{1}{2} \frac{ \delta X_\mu }{\delta (\partial_\lambda \phi_r)} \partial_\nu \phi_r + X_\mu g_{\lambda\nu} - X_\lambda g_{\mu\nu} $$ **What I wish to do next** \- I now have a differential equation that I wish to solve. $$\frac{1}{2} \frac{\delta X_\lambda}{\delta (\partial^\mu \phi_r)} \partial_\nu \phi_r - \frac{1}{2} \frac{ \delta X_\mu }{\delta (\partial_\lambda \phi_r)} \partial_\nu \phi_r + X_\mu g_{\lambda\nu} - X_\lambda g_{\mu\nu} = - \frac{i}{2}\left[ \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_r) } (I_{\nu\lambda})_{rs} \phi_s + \frac{\delta {\cal L}}{\delta (\partial^\lambda \phi_r) } (I_{\mu\nu})_{rs} \phi_s + \frac{\delta {\cal L} }{\delta (\partial^\nu \phi_r) } (I_{\mu\lambda})_{rs} \phi_s \right] $$ Any ideas on how to solve this?


title: Could dark energy be the effect of gravity at great distances?

text: This may be a silly question, but is it possible that dark energy and gravity are related to each other? Space-time is deformed everywhere in space by objects with mass. The more massive the object, the more deformation in the local area, and, as a result, the more concentrated space-time is within that deformation. However, where is the "extra" space-time coming from to be able to form these super-concentrated regions of space-time? Is that what we observe as dark energy? Is it possible that at great enough distances, gravity could be pulling space- time apart due to the lack of mass in the great voids of space? Not only that, but if there was enough mass in a part of space to have a little more gravity than the surrounding area, it could prevent that area of space from being "stretched out." Thus, might dark matter just be regions of space where space- time is denser than the surrounding regions? I'm sure these aren't new ideas, but I'd like to know what premises and assumptions are incorrect.


title: What distinguishes a moon from orbiting space debris? Or in other words, when is a satellite "too small" to be a moon?

text: The Wikipedia article on Natural Satellites doesn't really give an adequate distinction as to what distinguishes a moon from other orbiting bodies. What I am looking for is a classification that defines a moon, i.e. when can something be classified as a moon, or definitely _not_ a moon? Saturn, for example, has lots of orbiting space debris that form its rings. Certainly, there might be some cutoff point.


title: How could they tell things weigh a sixth of their "Earth weight" on the moon?

text: I frequently keep hearing stuff about "gravity on the moon is only a sixth of that as Earth's" and "of course you'll weigh more on Jupiter". I do know the relative sizes of those bodies allow for gravitational acceleration that's different from the $9.8 \mathrm{\; m\cdot s}^{-2}$ we're accustomed to here, and I'm pretty sure nobody's ever bothered to bring a scale to Mars or something. How can one reckon how much you'll weigh on the moon if you don't know the "one-sixth" bit? How about on other planet(oid)s and satellites?


title: Implications of Unruh-inertia to theories of gravity

text: If it turns out to be true that the galaxy rotation curves can be explained away by Unruh modes that become greater than the Hubble scale at accelerations around $10^{-10} m/s^2$ as proposed in here, what modifications would have to be done to the effective General Relativity equations? Also, if anyones knows at this early point, what would be the implications for gravity theories that rely on the equivalence principle at a fundamental level, i.e: string theory?


title: Yang-Mills instanton

text: How can instanton solution to Yang-Mills theory with gauge group $SU(3)$ or $SU(N)$ be obtained? For $SU(2)$ it is explained in textbooks but what about more general color gauge groups? EDIT: How does $A^\mu$ look like for SU(3) or SU(N). Wikipedia only gives for SU(2). It is given by for SU(2) $$A^\mu_a = 2/g \frac{\eta^a_{\mu\nu}(x-z)}{(x-z)^2+\rho^2}$$


title: Question about pendulum

text: I came up with this problem by myself: How much force do I need to make a pendulum revolve? Now I imagined that the force $\vec{F}$ must be enough to make the pendulum swing until half of the circumference; I tried using the formula for the period if the pendulum $T=2\pi \sqrt{\frac{l}{g}}$ and formulas from circular motion but I still had lot of problems. Can someone help me? Also consider that the pendulum is has a weight.


title: Why does the coil in this apparatus reverse its direction of oscillation?

text: I've been given some notes and I have to 'unscramble' them and put them in order. They are supposed to describe what happens in the diagram below: ![enter image description here](http://i.stack.imgur.com/C34XW.jpg) The notes to unscramble and form a proper answer from are below:   * Field lines   * Once it is pushed until 90 degrees then passes it   * It turns clockwise    * Then reverses motion and oscillates   * Comes to a rest vertically Now, I understand that the order of things happening should be as follows, using the notes above, with little explanations to make a complete answer:   1. The magnet's poles cause magnetic field lines to go from north to south   2. Using the left-hand rule for each side of the coil, we can see that the forces do indeed go in the directions shown in the diagram. (Denoted in the diagram with "F" and arrows).   3. This causes the coil to rotate clockwise.   4. When it has rotated 90 degrees clockwise, it comes to a rest vertically.   5. It then reverses direction and is pushed past 90 degrees backwards, anticlockwise. And so it will continue to oscillate, reversing direction every time it gets to the vertical position. Am I correct? If so, why exactly does it reverse direction? Please if someone could clarify this explicitly. I've been to many videos and tutorials that explain similar things, but mostly in the context of proper DC motors (and this is not a DC motor), but they keep confusing me. On the other hand, if the coil doesn't reverse direction at all but continues in the same direction, please let me know!


title: Renormalization condition: why must be the residue of the propagator be 1

text: In on-shell scheme, one of the renormalization conditions is that the propagator, say, a scalar theory $$\frac{1}{p^2+m^2-\Sigma(p^2)-i\epsilon}$$ must have a unit residue at the pole of physical mass $p^2=-m^2$. Some textbooks say this is to make sure the propagator behaves like a free field propagator near the pole. But why?


title: $D$-brane and 5th dimensions

text: While I was looking up the 5th dimension of the Randall-Sandram model, I have wondered whether Kaluza Klein theory can be applied to the $D$-brane or $p$-brane. Can the $D$-brane and $p$-brane wrapped as compactification of the dimensions? If so, what is the main difference between $D$- and $p$-brane?


title: Transmission Lines + DC Current

text: I have a problem where I'm given a circuit that looks like: ![enter image description here](http://i.stack.imgur.com/YxYR1.png) It contains a transmission line with a characteristic impedance $Z_0$, a source resistance of $R_s$, and a load impedance of $R_L$. If the voltage source provides a constant DC voltage source of $V_0$, what are the voltages at points A and B? I was considering using the voltage divider equation, but I don't think that's the right approach.


title: Why does friction cause a car to turn?

text: I've had a lot of difficulty conceptually understanding the physics of how a car turns on an unbanked curve, so I'm hoping you could help me out. When a car is moving in uniform circular motion, we know that $|\vec{a}| = \frac{v^2}{r}$, and the direction of acceleration is towards the radius of the circle about which the car is moving. Drawing a free body diagram for the car shows that there are only three forces acting on it: gravity $(\vec{F_g})$, the normal force $(\vec{F_n})$, and friction $(\vec{F_f})$. Since gravity and the normal force negate each other, the car isn't accelerating in the $y$ direction. Because it is in uniform circular motion we know it is accelerating in the $x$ direction, and summing up the forces in this direction yields $$\vec{F_{net x}}=m\vec{a}=\vec{F_f}$$ which implies that the centripetal acceleration is due to the frictional force. What I am having difficulty understanding is why this intuitively makes sense. I've read some other people's answers on this question but I haven't found anything satisfactory. In particular, many people talk about how wheels "are pushing the pavement to the left or right", and this causes the pavement to exert a force on the car wheels by Newton's third law, but this hasn't made sense to me. Another way of putting this might be that I don't understand why friction should be directed inwards towards the center of the circle about which one is turning. I would expect that, since the wheels have been turned, that friction would be directed in the opposite direction of where the car is moving to prevent the car from continuing to move forward and skidding on the road. I hope this makes sense, thanks.


title: Super cooled steam and entropy change

text: I was thinking about a situation where I have some super cooled steam which suddenly freezes to water.What are the entropy changes(positive or negative) for the system and the universe? My thoughts:On transition from steam to liquid water the molecules gets more packed together which reduces their giggling around and hence, the entropy of the system would decrease. Since it is assumed to be a spontaneous process the entropy of the universe should increase.Is my thinking correct?


title: Electric Field in Circular waveguide in TE mode

text: I know that the magnetic field inside a circular waveguide is $B_z=B_0\dfrac{\rho}{R}\left(1-\dfrac{\rho}{2R}\right)\cos{\phi}\sin{\frac{\pi z}{d}}$ How can I find the two components of the electric field, $E_\rho, E_\phi$ that is?


title: gauge invariance of the Feynman amplitudes

text: When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ we find it very helpful that we can simply make a substitution: $$\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta\rightarrow-g^{\alpha\beta}$$ This is due to the equality: $$k^\alpha\mathcal M_\alpha(k)=0$$ Now Franz Mandl and Graham Shaw in their book Quantum Field theory attribute this property as the result of the gauge invariance of QED > Gauge invariance of the theory implies the gauge invariance of the matrix > elements, i.e. of the Feynman amplitudes. ...   >  For any process involving external photons, the Feynman amplitude $\mathcal > M$ is of the form$$\mathcal M=\epsilon_{r1}^\alpha(\mathbf > k_1)\epsilon_{r2}^\beta(\mathbf k_2)...\mathcal M_{\alpha\beta...}(\mathbf > k_1,\mathbf k_2,...),\;\;\;\;\;\;\;\;\;\;(8.30)$$ ...   >  The polarization vectors are of course gauge dependent. For example, for a > free photon, described in a Lorentz gauge by the plane > wave$$A^\mu(x)=const.\epsilon_r^\mu(\mathbf k)e^{\pm ikx}$$ THe gauge > transformation$$A^\mu(x)\rightarrow A^\mu(x)+\partial^\mu f(x), $$ with > $$f(x)=\tilde f(k)e^{\pm ikx}$$implies$$\epsilon_r^\mu(\mathbf k)e^{\pm > ikx}\rightarrow [\epsilon_r^\mu(\mathbf k)\pm ik^\mu\tilde f(k)]e^{\pm > ik^\mu }$$Invariance of the amplitude (8.30) under this transformation > requires$$k_1^\alpha\mathcal M_{\alpha\beta...}(\mathbf k_1,\mathbf > k_2,...)=k_2^\beta\mathcal M_{\alpha\beta...}(\mathbf k_1,\mathbf > k_2,...)=0,$$i.e. when any external photon polarization vector is replaced > by the corresponding four-momentum, the amplitude must vanish. My question is how to understand the statement " **Gauge invariance of the theory implies the gauge invariance of the matrix elements, i.e. of the Feynman amplitudes** ", and **does "the gauge invariance of the matrix elements" really mean that when we make substitution $A^\mu(x)\rightarrow A^\mu(x)+\partial^\mu f(x)$ in the amplitude $\mathcal M$, it will not change**? I saw in Peskins' book how he spent much argument to prove $k^\alpha\mathcal M_\alpha(k)=0$ using the diagrams, so I wonder whether this argument in Mandl's book is valid. Anyway, what is the significance of the gauge invariance of QED in this equality $k^\alpha\mathcal M_\alpha(k)=0$?


title: How do I find the electric field above the center of a square plate (rather than circular)?

text: I tried to integrate E due to a line of charge sweeping across the plate, but got bogged down. Any suggestions?


title: Can I excite an already unstable element for accelerated decay?

text: Say I had an unstable element ready to go through beta decay and I introduced it to high speed electrons: would this lessen the time needed for the product to go through beta decay?


title: Can a multipass x-ray absorption cell be constructed?

text: I've been trying to understand the various concepts behind x-ray optics compared to standard visible/IR optics like mirrors and such. However, the x-ray mirrors I've been finding typically have optimal angles of reflectance on the order of a few milliradians, particularly for hard x-rays. I think I mostly understand the reasons for this (having something to do with Bragg diffraction?), but, say, for absorption experiments with low sample density, it may be necessary to use something analogous to a multipass absorption cell. Since x-rays can't be reflected at anywhere near 90° with high efficiency, can a multipass absorption cell be constructed for x-rays (say, with fiber optics or something else)? Has anyone done so? Multiple Google searches for such a thing have turned up nothing, but maybe I'm just searching for the wrong thing.


title: Reflected and refracted wave sphased

text: When we derive refraction and reflection laws for a generical plane wave on a surface, we say that reflected and refracted must be in phase with the incident wave. Why a medium cannot do a sphased reaction beside incident wave? Sorry for my trivial question.


title: Why does current alternate in an AC generator?

text: I understand how generators work, but I can't for the life of me conceptualize why the current in an AC generator reverses every 180 degrees!!! I understand that, using the right hand rule, it can be seen that the current flows around the coil in a generator in one direction, but I can't see why the current reverses after half a rotation! I've been looking at the animations on this page to try and figure it out, but I just can't get there. In addition, I don't understand the concept of how split ring/slip rings work? I know split ring is for direct current, but not really why. For instance, if asked how could I 'explain the difference between a split ring or slip ring'?


title: Why is the central maximum the brightest?

text: This is a question directly from a homework sheet, however I can't find any decent answers online so hopefully someone can help! In single slit diffraction, why is the central maximum double the width of the other bands and the brightest? I understand vaguely that it is something to do with Fresnel zones, but I'm quite confused. Instead of making another question, I think this question also fits in with the above: Why does the intensity of light bands decrease away from the central maximum in single slit diffraction? Thanks!


title: When a star turns into a red giant what stops its core contracting

text: I recently asked this question When do stars become red giants? and am now wondering when the star's core is contracting after it has fused $H$ to $He$ what force stops the contraction just before it becomes a red giant?


title: Nomenclature of radial solutions to the Schrodinger Equation

text: For the free particle with quantum number $l=0$, the **_regular_** solution to the radial Schrodinger equation is $R_0 (\rho)=\frac{\sin{\rho}}{\rho}$ while the **_irregular_** solution is $R_0 (\rho)=\frac{\cos{\rho}}{\rho}$. Is there a reason for this nomenclature -- (ir)regular? Thanks.


title: Difference between coordinate and proper distance in Schwarzschild geometry

text: I'm trying to understand the difference between proper distance $d\sigma$ and coordinate distance $dr$ in Schwarzschild geometry. The bottom bit of the diagram represents flat space, the upper bit curved space. The inner circles represent Euclidean spheres of radius $r$, the outer circles radius $r+dr$. Is the proper radius of these circles the same as $r$? I think I mean if I measured the radius of these circles with a real ruler would I get the coordinate distance $r$ of the Schwarzschild metric. ![Schwarzschild radial distances](http://i.stack.imgur.com/NnhMW.jpg) The more I think about this the more confusing I find it. Thank you


title: Watercooling performance  and amount of water or liquid in the loop

text: Imagine a watercooling system. It consist of a reservoir, pump, tubes and a radiator. We all know how it works. My question is, only inreasing the reservoir's volum, say from 1 liter to 2, will actually increase the performance? I do remember some thermodynamic laws from school, Delta T of water to ambient after a given time will be same? Or becaue there is more water in the system it will perform better?


title: Free surface of inviscid fluid flow

text: The following problem seems like it should have a definite solution, but I've been thinking about it for months and haven't got anywhere. It might not be a well-posed problem, but if it isn't I'd like to understand why. An incompressible, inviscid fluid of density $\rho$ flows continuously (in a steady state) as shown in the following diagram: ![diagram](http://i.stack.imgur.com/Y1qJz.png) We know the height of the fluid (and hence its pressure) at points $x_1$ and $x_2$, but we don't know the velocity of the fluid or its height at any other value for $x$. The top of the fluid is a free surface, i.e. it's determined by the properties of the flow rather than being specified as part of the problem. I've drawn it as slightly concave but I've no idea if that's right. Let us assume that the velocity profile at $x_1$ is vertical (i.e. velocity does not vary with height above point $x_1$). Because the fluid is inviscid it seems to me that the constant vertical velocity profile should be maintained as the fluid travels to the right. So if we were to dye a vertical line of the fluid a particular colour, it would remain a vertical line as it travelled to the right, because the pressure differential across the line is constant with depth. If this is correct it means we can think of the velocity component in the $x$-direction, $v_x$, as a function of $x$ rather than $x$ and $y$. Because the flow is incompressible we know that $h(x)v_x(x)$ must constant over space, and this is the value I want to solve for (although it might not have a unique value - in that case I just want to know the function $h(x)$). If we need to we can also assume we know the initial and final velocities, $v_x(x_1)=v_1$ and $v_x(x_2)=v_2$. It seems like Bernoulli's equation should have some relevance here. That would certainly be the case if the fluid were confined to a pipe instead of having a free surface. (In this case the pressure difference would be independent of the difference in height, so we'd need to know that as well.) But every time I try to solve this problem using the Bernoulli equation I get into a terrible mess. I'm really not sure of the best way to approach this problem, so any insight anyone can offer would be much appreciated.


title: Origin of crossing relations in relativistic scattering amplitudes

text: What is the origin of crossing relations in relativistic scattering amplitudes? At first I thought it was CPT, but then it turned out that was not correct. That is, what is the formal reason that the same function $A(s,t)$ describing the process $A+B\rightarrow C+D$ can also be used to describe the crossed- reaction $A+\overline{C}\rightarrow \overline{B}+D$ provided the role of the invariants $s$ and $t$ are exchanged?


title: Potentials in Feynman path integral II

text: I am still working on the Feynman path integral, more specifically on the case of a free particle with an infinite potential wall, i.e. the quantum system defined by the Hamiltonian $$H_1 = \frac{\mathbf{P}^2}{2m} + V(\mathbf{Q})$$ where $V(\mathbf{Q})$ is the potential defined by $$ V(\mathbf{Q})=\left\\{ \begin{array}{cc} \infty, & \mathbf{Q} \leq b \\\ 0, & \mathbf{Q}>b. \\\ \end{array} \right. $$ It is clear that a general solution for the free particle case is given by $$\psi_E(q) = A_1 e^{i\frac{\sqrt{2mE}}{\hbar}q} + A_2 e^{-i\frac{\sqrt{2mE}}{\hbar}q}.$$ Using the fact that $\psi_E(0)=0$ I get that $A_2=-A_1$ so the general solution is $$A \sin\left(\frac{\sqrt{2mE}}{\hbar}q\right) = A \sin(kq)$$ where $k$ is defined as $$k=\frac{\sqrt{2mE}}{\hbar}.$$ The problem I have is the calculation of the constant $A$. In some references they say this constant should be $$A = \sqrt{\frac{2m}{\pi\hbar^2 k}}$$ and in other references I find $A=2$ or $A=-2i$,... Could you please help me to understand that point ? Thanks.


title: Nonlinear Opics - Connection to Condensed matter Theory

text: (This a rather widespread idea, you can help me to clarify) Lets assume we start with Top-Down approach, assuming a nonlinear effect coming from the susceptibility (such as a Second Order Harmonics Generation), following Boyd: $$ P(w_n + w_m) = \epsilon_0 \sum_{j,k}\chi_{ijk}(w_n+w_m;w_n, w_m)E_j(w_n)E_k(w_m)$$ The number of independent elements of $\chi_{ij}$ can be deduced from the symmetries of the material (such as the Kleinmansymmetries) and numerical values for the susceptibilites can now be estimated by measurements (for instance with the help of the Kramers-Kronig Relations by measuring the adsorption coefficient). If we want to predict the behavior of susceptibility, the first step can be do use some kind of semiclassical or quantummechanical description of the Energy to estimate the Response of the media (for instance with Two-Level Atom using the density matrix formalism). My main question is now: Did someone work on the connection between Quantum field theory (Statistical mechanics, the logical continuation of the Schrödinger Equation) and Semiclassical Nonlinear Optics? One could for instance use Thermal Greenfunctions to estimate the susceptibility with regards to lattice interactions, Speaking of:   1. What is the influence/ connection of Thermodynamic entities such as Entropy, Temperature, chemical Potential to the susceptibility, furthermore to effects such as the Kerr Effect?   2. Solitons and other Collective Behavior of lattices can be descriped with Quasiparticles in QFT, how to they relate to nonlinear makroskopic effects?   3. Assuming an hierarchical Ladder of competing nonlinear effects in a medium (Atomic Interaction, Interaction of photons with optical phonons,...) the dominant effect could be predicted by looking at the reponsetimes of these processes. When we include the possiblity of a interaction between these processes (assuming they lay in the same regime) this should not be possible to include on a semiclassical level. Is it in general possible to create such interactions? Lets assume nobody worked on this topic due to the inpracticability (in particular the different scope of QFT), might there be an elegent way to introduce a Effective Field theory such that certain effects and nonlinear phenomena can be reproduced and quantities estimated? (Surely this formalism could not describe practical issues like the Phasematching Condition, which still should be practically worked out with the nonlinear Maxwell Equations).


title: Why does dry spaghetti break into three pieces as opposed to only two?

text: You can try it with your own uncooked spaghetti if you want; it almost always breaks into three when you snap it. I am asking for a good physical theory on why this is along with evidence to back it up. Or, a reference to a good study previously done on this would also be satisfactory. The math behind everything would be a great bonus if it exists. My hypothesis is that a strand of dry spaghetti has two main pressure areas being put on it due to how brittle and how high the length to thickness ratio is, and that they snap at almost the same time due to the manufacturing process of the strand causing it to have a very consistent breaking point. Also that vibrations from a first break could influence the causing of another. I'm not sure how this could be tested, though.


title: Are proton, antiproton, electron, positron the only observed subatomic particles that can freely exist and don't decay, i.e. are stable?

text: Are proton, antiproton, electron, positron the only subatomic particles that can freely exist (i.e. I don't want particles that only exist in bound state as constituents such as quarks) and don't decay, i.e. are stable? What about muons? Are there other particles/hadrons that can exist freely (i.e. not in some bound states) and don't decay?


title: Effect of pressure increase on electron orbital wave functions

text: One of my nuclear physics exercises was to find out if increasing the pressure of a sample of $^{7}\textrm{Be}$ would increase the chance of electron capture to $^{7}\textrm{Li}$ occur. My reasoning was that the electron wave function is not pressure dependent and therefor it would not increase the likelihood of an electron capture. But I know that increasing the pressure does change the likelihood of electron capture. My question is how does increasing the pressure influence the wave function of the electron in orbit? My quantum mechanics class did not cover this and I could not find anything on the web about this.


title: What value of resistor is to be used in decreasing current & voltage respectively?

text: I m having a multimedia system which works at a.c 220 50hz . Now i want to use it on my car. Power supply of car is (12v) (35 A ) while power requirement is (12v) (1.2A) & (8.5v ) (0.2A). I want to know the value of resistors to be used for the same.


title: Why can't Schwarzschild wormholes exist?

text: So, I've recently been reading up on Schwarzschild wormholes and I've learned that they cannot exist becuase they violate the 2nd Law of Thermodynamics. What I'm asking is: Why do they violate the Law? I probably sound like an idiot, but I just can't understand why they violate Thermodynamics.


title: Do we need waves for fields?

text: I was pondering about EM Waves and fields and felt that there is an inconsistency in the physical picture of EM waves that I have in my mind. For example let us consider a charge at rest . Now lets say we want to test the electric field due to this charge Q at a point P. So to do this we need to place another charge at that point and find if we can feel any force due to that charge. Now I think for Q to exert a force on test charge or an electric field to be established at that point there must be EM waves propagating from the charge Q to the test charge. However there are no accelerating charges which are the prerequisites for EM waves to be generated . So this brings in an inconsistency in the physical picture of EM waves I have in my mind. I believe that there is some misconception I am having and I am positively looking forward to replies to clear it out.


title: Eigenvalues of an operator correspond to energy states in quantum mechanics, why?

text: When finding the discrete energy states of a operator I have been taught to use the time-independent Schrodinger equation which restates the definition of eigenvalues and eigenvectors. What I don’t understand is why the eigenvalues are the energy states, is there firstly a mathematical reason and secondly a physical reason? Does this arise from Hamiltonian or Lagrangian mechanics which I am not familiar with?


title: Cart on Ramp with Varying Acceleration

text: For a lab that I have to do, the teacher has given me a data table of the displacement of a cart on a ramp after successive intervals of time. I have used this data to derive the velocities and accelerations of the cart. This is all fine, the problem is that I am now being asked to find the angle of the ramp. I don't know how to figure this out because the acceleration is not constant. After every half a second the acceleration appears to switch between -1.68 m/s2 and -1.72 m/s2. There is no indication that any other forces are involved aside from gravity. How can this be possible if the acceleration of gravity is constant? My initial thought was that it might be a circular or spiral ramp of some sort, but the displacement never decreases as I would expect after the cart would reach a displacement equal to the diameter of the circle. What else could it be and how could I find the angle from it? Here is the data that I am given:               Time (s) | Displacement (m)     0.00     | -10.00     0.50     | -5.21     1.00     | -0.85     1.50     | 3.09     2.00     | 6.60     2.50     | 9.69     3.00     | 12.35     3.50     | 14.59     4.00     | 16.40      And here is the data that I have calculated:               Time (s) | Velocity (m/s)     0.50     | 9.6     1.00     | 8.73     1.50     | 7.88     2.00     | 7.02     2.50     | 6.18     3.00     | 5.32     3.50     | 4.48     4.00     | 3.62      * * *               Time (s) | Acceleration (m/s^2)     0.75     | -1.7     1.25     | -1.68     1.75     | -1.72     2.25     | -1.68     2.75     | -1.72     3.25     | -1.68     3.75     | -1.72


title: What is space made of?

text: General Relativity posits that matter curves spacetime, such that geodesics point towards the object in question, hence, gravity. Now, how does matter do this? What is spacetime "made of", anyway, such that it should interact with matter, being bent by it and forcing it to accelerate (via gravity)?


title: How was this dot identified as a mystery planet originally (Pluto in this case)?

text: I was watching a documentary on a mission to study Pluto. At 21:11, an image is presented with an arrow mark pointing a small dot which is now identified as Pluto. As there are hundreds of dots on the image (I'm not sure what kind of an image this is as I'm not an astrophysicist), how can stars, planets, asteroids and other objects be distinguished in this image? And what kind of an image is this? ![Enter image description here](http://i.stack.imgur.com/KXHRF.png)


title: Graphene Chern number for Dirac nodes

text: Why do we add winding number at two Dirac nodes to determine topological phase?


title: Are Normal Stress Differences in Newtonian Fluids Equal?

text: I was reading about normal stress differences in the context of Non-Newtonian fluids. There was a remark that the normal stress differences in Non-Newtonian fluids are not equal whereas the normal stress differences in Newtonian fluids are equal. I can't figure out why the normal stress differences in a Newtonian fluid should be equal. Can anyone highlight a proof?


title: Why are so many things squared in Physics?

text: I don't know much about Physics, and I wasn't sure whether to ask here or Mathematics, but I have always wanted to know why when it comes to the physical world/universe, there are so many descriptions and problems and solutions that are squared. I'm sure there are other constructs out there, but it seems everywhere I look when studying I see something squared, like meters per second squared, time with the t^2, the spring, bouncing ball, etc. Does the universe just happen to be that way? Why is there all this usage of squares?


title: What happen if we put permanent potential across conductor?

text: why if we put conductors under permanent potential like a battery ,it will not be equi-potential ?? and why if we just put it under electric field it is equi-potential although there is a surface charges positive and negative ?


title: Can inductance or resistance be negative or "infinite"?

text: ![enter image description here](http://i.stack.imgur.com/sooIy.jpg) Since the potential different or voltage drop is positive (am I allow to say **voltage drop** or **potential difference** in the presence of a changing current?), the current flows from right to left since $\Delta V$ is positive. That is, $V_b$ is at a higher **potential** than $V_a$. Case (1), Increasing current. So traversing from b to a (in the direction of the current) I get a $-IR - LI' = 9 \implies -2R - 0.5L = 9$ I get $-IR$ because the voltage drops from a higher to a lower potential as it crosses the resistor. I get $-LI'$ because since the current is increasing, the inductor opposes this increase by "becoming" a battery with - on the "a" side and + on the "b" side and I should get a voltage drop across that. Case (2), Decreasing current. So traversing from b to a (in the direction of the current) I get a $-IR + LI' = 5 \implies -2R - 0.5L = 5$ I get $-IR$ because the voltage drops from a higher to a lower potential as it crosses the resistor. I get $LI'$ because since the current is decreasing, the inductor opposes this decrease by "becoming" a battery with + on the "a" side and - on the "b" side and I should get +V by gaining potential. Solving http://www.wolframalpha.com/input/?i=RowReduce{{-0.5%2C-2%2C9}%2C{-0.5%2C-2%2C5}} I get some absurd answer. What is wrong with my argument?


title: Could the Higgs boson field be responsible for the dramatic mass increase when an object begins to travel close to the speed of light?

text: could the Higgs boson field be responsible for the dramatic mass increase incurred when an object nears the speed of light?


title: What allows new born suns to travel away from each other?

text: What allows massive new born suns to move away from each other, as they have been observed. I would think that their massive gravity would prevent this and cause them to slam into each other.


title: Why is there no upper-bound on power-efficiency of Hydro-turbines?

text: We have Betz's law, an upper bound on power efficiency, for wind-turbines. But there is no theoretical upper limit on hydro-turbines, Why this is so? Is it mainly due to the incompressibility of water?


title: Number of possible entangled states

text: Suppose we have four single particle states: $|u,\pm\rangle$ and $|v,\pm\rangle$. How many lineary independent entangled states can we have for a pair of particles? I know that if A and B are entangled, the state AB cannot be written as a product of state A and state B, i.e. $|AB\rangle \neq |A,i\rangle |B,j\rangle$. Does this mean that the state of AB has to have at least two terms? Is $|\psi\rangle = |u,+\rangle|v,-\rangle + |v,-\rangle|u,+\rangle$ such a state?


title: Can anyone analyze this perpetual machine that a Norwegian built?

text: Take a look at this video: http://www.youtube.com/watch?v=tlx2PgESXhs It shows a machine that a Norwegian artist built. It seemingly keeps going forever. They filmed it over 3 days and it kept going at the same time. Can someone analyze the energy losses in this machine? I'm seeing several losses at the moment:   1. The ball is losing energy due to friction while going around the track.   2. The pendulums are losing energy due to air friction. What other sources of energy losses can you notice?


title: Killing vectors for SO(3) (rotational) symmetry

text: I am reading a paper$^1$ by Manton and Gibbons on the dynamics of BPS monopoles. In this, they write the Atiyah-Hitchin metric for a two-monopole system. The first part is for the one monopole moduli manifold, and other terms for a 4-dimensional hyper kahler surface which is SO(3) symmetric parameterized by the euler angles. He obtains two sets of SO(3) killing vectors. What is the systematic way to obtain these two various sets? What are the equations involved? $$\xi^R_i=\cot{\theta}\cos{\psi}\frac{\partial}{\partial{\psi}}-\sin{\psi}\frac{\partial}{\partial{\theta}}+\frac{cos{\psi}}{\sin{\theta}}\frac{\partial}{\partial{\phi}}$$ $$\xi^R_2=-\cot{\theta}\sin{\psi}\frac{\partial}{\partial{\psi}}+\cos{\psi}\frac{\partial}{\partial{\theta}}+\frac{sin{\psi}}{\sin{\theta}}\frac{\partial}{\partial{\psi}}$$ $$\xi^R_3=\frac{\partial}{\partial{\psi}}$$ and the other set by $$\xi^L_1=\cot{\theta}\cos{\phi}\frac{\partial}{\partial{\phi}}+\sin{\phi}\frac{\partial}{\partial{\theta}}-\frac{\cos{\phi}}{\sin{\theta}}\frac{\partial}{\partial{\psi}}$$ $$\xi^L_2=-\cot{\theta}\sin{\phi}\frac{\partial}{\partial{\phi}}-\cos{\phi}\frac{\partial}{\partial{\theta}}-\frac{\sin{\psi}}{\sin{\theta}}\frac{\partial}{\partial{\psi}}$$ $$\xi^L_3=-\frac{\partial}{\partial{\phi}}$$ References: $^1$ G.W. Gibbons and N.S. Manton, _Classical and quantum dynamics of BPS monopoles,_ Nucl. Phys. B274 (1986) 183.


title: Accelerating expansion of the universe and cyclic model

text: So I've heard that recent observations indicated that the rate of expansion of the universe is accelerating. Does this indicate that the universe can NOT be cyclical, with an infinite series of big bangs and crunches extending forward and backward through time? Does it "prove" that the universe will not crunch?


title: Could tidal effects make matter hot enough for nuclear fusion?

text: There was a recent question about cosmological firewalls. Putting aside questions of entanglement and information and looking at the problem from a pure mechanical viewpoint, we know that although there is little perceptible radiation emitted from the blackhole, the tidal forces approaching the event horizon are enormous leading to spaghettificaton. Although the tensile forces will eventually tear a person apart, there are also compressive forces for material located in the same plane. A human body contains a considerable amount of hydrogen and other lighter elements. Would the compressive effects of spaghettification be sufficiently high to cause any of the hydrogen or other elements to fuse prior to reaching the event horizon?


title: How can we claim something violates some physical law, when so many physical laws have been postulated?

text: For example, Einstein postulated that the speed of light, `c`, is constant in all inertial frames of reference. Bohr postulated that electrons go around the atom in orbits and that there are pre-defined orbits, and that moving from a higher orbit to a lower orbit makes releases energy. I bet there are many other postulates that we take for granted. Therefore I've a question, how can we claim something violates some physical law, when so many physical laws have been postulated? All it takes is to disprove one of the postulates and suddenly a lot of things break down because of the claims that are based on the postulates.


title: What's the optimal shape for a continuous Galilean Cannon?

text: A Galilean Cannon is a toy similar to the famous basketball-and-tennis-ball demonstration. You take a tennis ball, balance it on top a basketball, and drop them both. The tennis ball will bounce up to a height several times as high as it was dropped from. The Galilean Cannon simply takes a series of several balls rather than two balls, allowing you to shoot the smallest ball many times the height it was dropped from. My question is about making a modified version from two pieces of steel. I'm assuming there's a base of mass $M$ and a cap of mass $m$, and $M>>m$, although the ratio is fixed. The base has some sort of cut-off conical/horn shape going from a radius $R$ at the bottom to $r$ at the top. The cap has radius $r$ at the bottom and is rounded off at the top, and sits on top the base. The physics of this device is now wave propagation. It's dropped onto a hard surface from a small height, causing a compression wave to travel up through the base. The wave will bounce off the sides of the base and hopefully concentrate to high energy density as it reaches the cap, ultimately shooting to cap off to a very high height. My question is, suppose the base is cylindrically-symmetric with a radius $radius(h)$ where $h$ is the height above the bottom of the base and $radius(0) = R$ and $radius(h) = r$. For a given $M,m,R, r, h$ bulk modulus ($K$) and density ($\rho$), what is the optimal $radius(h)$ to shoot the cap as high as possible? I would guess it is either exponential (constant ratio of adjacent "slices") or a straight cones (constant angle between boundary and net propagation direction), but I'm not sure. Please make any reasonable assumptions you need about boundary conditions for waves at the edge of the base, etc. Additionally, how sensitive is this shape to having the initial conditions be perfect? If it's dropped at a slight angle or surface it lands on isn't perfectly flat, how messed-up does wave propagation become?


title: Higgs Boson: The Big Picture

text: First, please pardon the ignorance behind this question. I know a fair amount of math but almost no physics. I'm hoping someone can give me a brief "big picture" explanation of how physicists were able to predict the existence of the Higgs boson. Here's a (perhaps completely wrong) example of the level of explanation I'm hoping for: "Consider the following group [insert precise specification of a particular group here]. This group is know to have precisely [insert number here] irreducible representations. All but one of these representations corresponds to a previously-observed particle via a correspondence in which the property [insert mathematical property of representation here] corresponds to the property [insert physical property of particle here]. The Higgs Boson is the particle that corresponds to the remaining representation." If I happen to have hit on the right story, I'd like someone to fill in the blanks. If, as is more likely, I've concocted a completely wrong story, I'd like someone to give me a more accurate story at about the same level of sophistication. Thanks!


title: Maximum precision of deterministic measurements

text: Okay, I tend to have some weird thoughts, so bear with my odd question here. Suppose you have a collection of particles that obey Newtonian mechanics. For simplification, all particles are identical and can be assumed to be hard spheres that collide elastically. Each particle has a position and a velocity. Now suppose we want to measure the position and velocity of a particular particle. By measurement, I mean a series of bits indicating its position, and a series of bits indicating its velocity. The only way we can obtain information about that particle is using other hard, spherical particles. With enough types of collisions between the various particles (the "experiment" in essence), we eventually get a digital readout of both values of interest. Now, intuitively it seems like there must be a theoretical limit to the amount of information we can get about the particle. Has someone done a calculation that determines what this is? In other words, what is the maximum amount of bits we can get that accurately describes the particle using other particles? If you need more clarification about what I'm asking, just let me know (because I am not that great at conveying what I mean to others). (Note this has nothing to do with HUP or quantum mechanics -- it's just an idealized classical situation.)


title: Hierarchy is no problem and susy is a mathematical tool for data fitting

text: I saw this paper in the arXiv: http://arxiv.org/abs/1206.4711. The author seems well-known and has many very well cited papers. But what he says sounds very strange. What I get from this paper are the claims that: There's no naturalness or fine-tuning problem in the Standard Model. And that Susy is mathematics that is presented as physics, so we should deal with it as a tool and not to expect to see real sparticles. My questions are, 1) What does it mean that: "perturbation theory is not designed to handle problems with widely separated time or energy scales?" And how accurate is this statement? 2) How valid is the conclusion that the naturalness and fine-tuning concerns over energy hierarchies do not exist? 3) How valid are the statements on Susy? 4) What I really what to know from our experts here, does this paper have any merit at all!


title: what does "medium-induced gluon radiation" mean

text: I've often run across phrases such as "medium-induced gluon radiation" from some papers,what is "medium-induced gluon radiation"?


title: What is the difference between induced current and eddy current?

text: I was reading today about electromagnetic induction and eddy currents. But while reading I was unable to differentiate between induced current and eddy current. What is the difference?


title: Can you help me with physics lab calculations?

text: My question is, how do you find the torque of a rotating spool with a connected string being pulled down by its hanging mass? So in this experiment we had a machine with two rotating discs, one on top of the other, and as we spin a disc, the machine counts how many of 200 lines on the edge of the disc pass through a sensor per second. In other words, it calculates the angular speed based on those lines. Then through calculation we can calculated the angular speed in radians through equation 2pi * counts per second/200. So in one part of this experiment we had to drop a ball down a ramp and have it be caught in a catcher attached to the top of the disc. This would set the disc rotating and thus we would determine the angular velocity and momentum caused by the initial speed/momentum of the ball. However, before setting it so we had to determine the moment of inertia, I, of the disc/ball catcher complex and this here is where I am confused. See, what we did was we attached a spool to the bottom of the disc which has a string attached to itself, and on the other side of the string was a hanging mass. We wound up the string and let the mass drop, and we noted the counts by the machine as they changed every two seconds. And from these we were supposed to determine the angular acceleration caused by the mass on the disc. And using the acceleration we were to determine the moment of inertia. This is where I am stuck. From what I discovered, I am supposed to find the torque of the spool using its radius and the mg of the mass (T=R*F), which I am then to equate to the equation T=A * I and find the I. Is this correct?? Than you for any help you can provide. I apologize for writing a whole book.


title: What's causing the effect of salt in voltage arcs?

text: I just came across this video demonstrating that salt increases length of voltage arcs. There is no explanation which leaves me quite confused. Does the salt decompose during the process?


title: Measuring voltage drop from induced current

text: I'm having trouble connecting voltage drops and induced current. Imagine you have a triangular loop make up off three resistors. You place this loop in a constantly changing magnetic field. This changing magnetic field will cause an EMF and a resulting induced current in the loop. Now imagine I place a voltmeter across one of the resistors. What does the voltmeter read? $I\times R$ or $I\times 2R$? If you look at the situation one way, you are measuring the voltage drop across one resistor, so V would equal $I\times R$. But if you look at in another way, you're also measuring the voltage drop across the other half of the circuit which contains TWO resistors (hence a voltage drop of $I\times 2R$). I have tried to model this situation in my schools physics lab and I do see that there is a voltage drop across the resistor so the answer is not "there is no voltage drop". My model wasn't perfect, but it seemed to imply that the voltmeter read $I\times 3R$? How could that be?


title: Do free electrons really not interact with photons?

text: If free electrons don't interact with photons, why are free electrons accelerated by electromagnetic fields?