title: Would the empirical behavior of a simple circuit match my model of it?

text: I have a practical problem in E&M which has baffled me and and my electrician. The copper water pipes in my house are carrying a current of small potential (~1V) AC current. Here is my hypothetical circuit diagram:                        R1     R2     ~~---o------+--------+              |           |        |     | R3      source   ground     |                    |     +--------------------+      Where `o` is my shower head and ground is actual ground from which the supply pipe enters the house. `R1` and `R2` represent the assumed (low) resistances of the copper piping. The way I detected the current was while changing a light fixture above the shower head and detecting a flow from my showerhead to the grounded junction box through my forearm. This current produced a mere tingle in my arm and has been confirmed with two different multimeters: my "toy" and the electrician's Fluke. `R3` represents my arm, an intermittent connection to ground. There is also a 2m copper ground spike embedded in the outside earth connected to nothing which can be used as a reference. The common/neutral line of the breaker box is currently tied at R2 near where the municipal supply line enters the house's basement. The source is unidentified but assumed since there is a measured, felt potential on the copper pipe. If the circuit is how I have drawn it, I believe the following would be true following Maxwell, Ohm, and/or Volta:   1. in the typical case with `R3` disconnected all current goes from source to ground via `R2`   2. while my arm is touching the pipe and the grounded junction box, most of the current goes from source to ground via `R2` while a small current goes through `R1` and `R3` where `R3` is presumed to be of much higher impedance than `R2`. Is this a correct interpretation of how the hypothetical circuit would behave? For the curious, the house is 80-ish years old with some olde-fashioned knob- and-tube (poorly insulated) wiring inside the walls that we guess could be in contact with the plumbing and thus be presumed current source.


title: Interference and energy question here

text: So Im reading this material on interference and I noted the following sentence : > During the interference of the light of two coherent light sources,the > intensity of the radiation changes periodically from one point to > another,alternating the maximums and the minimums of the interference. This made me question .What is going to happen to the energy transmitted by the sources before and after the interference?


title: How can I express the Riemann tensor of the 4-metric in terms of quantities derived from the 3-metric and the normal to it?

text: I want an expression for the Riemann tensor of the four metric in terms of extrinsic curvature, normal, lie derivative of the normal, etc. The first Einstein-Codacci eq. gives the Riemann tensor of the three metric in terms of the contracted Riemann four tensor and the extrinsic curvature. So this is not the one I want. Does anyone know a relation that I am looking for? And how to derive it?


title: Direction of compass needle nearby an electric wire

text: Let through a straight wire flow an electric current. Using a compass needle how the needles tip will be directed to the wire? What happens when we switch the current direction and approach the needle again to the wire? To get a source will be nice, but nicer it will be to get an answer from experiment which unfortunately I didn't in the past and not able to do at the moment.


title: Does the bolt really rise upward?

text: In this site,when the elevator rises up,the bolt falls downward under the force of gravity . But when distance is measured it is shown that it rises up,velocity becomes 0 & then it falls with respect to the shaft(earth) . One has asked the question in that site but the answer is not satisfactory. The bolt was falling downward so why in measuring distance, it rose up inspite of being under the gravity? What is the cause? Plz help.


title: Possible Error in deriving conformal generator

text: My professor gave me the following derivation for the full generator of the Lorentz transformations. The starting point is to consider a subgroup of the conformal group that leaves the origin fixed (as done so in Di Francesco, for example). Denote by $J_{\mu \nu}$ the full generator and so $J_{\mu \nu}\Phi(0) = S_{\mu \nu}\Phi(0)$, where $S_{\mu \nu}$ is the component of the full generator transforming only the field spin components. Infinitesimally, $\Phi'(0) = (1 + \epsilon S_{\mu \nu})\Phi(0)$ but also $\Phi'(0) = e^{-ix' \cdot P}\Phi'(x')$. This I understand. The next line is the first one I am not so sure of. He then writes $$\Phi'(0) = e^{-ix' \cdot P}(1+\epsilon J_{\mu \nu})\Phi(x)$$ How is this true? He seems to be using the transformation $\Phi'(x') = D \Phi(x)\,\,\,(1)$, but using $D$ as the **_full_** generator. If I had read that statement a few months back, I would have accepted it fine, but I posted a question here earlier that discussed the fact that in $(1)$, $D$ is the **_spin_** component of the generator because $x'$ and $x$ represent the same physical point in the space, they are just two different representations of the same point relative to two different coordinate systems. So the statement seems to be contradicting what I thought I understood. That was my first concern. My second concern is less fundamental (more of a computational problem) and I can edit it into my answer later. Many thanks! Edit: So assuming the last line to be correct, we proceed: $$\Phi'(0) = e^{-ix' \cdot P}(1 + \epsilon J_{\mu \nu})e^{i x \cdot P}\Phi(0) \approx (1 + \epsilon \underbrace{e^{-ix \cdot P}J_{\mu \nu}e^{i x \cdot P}})\Phi(0)$$ using the fact to zeroth order $x' \approx x$. The brace can be evaluated using the Hausdorff formula: \begin{align}e^{-ix \cdot P}J_{\mu \nu}e^{i x \cdot P} &\approx J_{\mu \nu} + [J_{\mu \nu}, ix^{\sigma}P_{\sigma}] \\\&= J_{\mu \nu} + i\left[x^{\sigma}[J_{\mu \nu},P_{\sigma}] + [J_{\mu \nu}, x^{\sigma}]P_{\sigma}\right] = J_{\mu \nu} + x_{\mu}P_{\nu} - x_{\nu}P_{\mu},\end{align} where the second commutator on the RHS there vanishes. Now compare with $\Phi'(0) = (1+\epsilon S_{\mu \nu})\Phi(0)$ as written at the top and we have the result $J = L + S$. My question is: why does this second commutation relation vanish? I should say I am going through 'Conformal field theory' Di Francesco section 4.2.1. The above argument was an alternate argument my professor posed when we sat down and agreed that equation (4.26) in Di Francesco is simply wrong.


title: Antipodes are mostly ocean - so what happens after digging that hole through earth?

text: Digging a hole through earth is a common **thought experiment** , often used to explain effects of gravity. But what would happen if someone finally **dug the hole**?   Sure, he took care to stabilize and isolate it inside with two and a half layer of unobtanium. But he forgot to check what exactly is on the other side of the earth, the antipode.   And, just like surprising 85% of earth [travel.SE: antipodes], it turns out to be ocean. The tunnel is under vacuum, and about the diameter of a two track railway tunnel. In the last step building it, obviously the ocean floor broke, and water is streaming in.   What happens then? I'm aware that a body would **oscillate** through the core - the water can not, if the ocean does not run dry assume - at least if the water coming in can mostly fill the diameter. First, I thought the water will just fill the hole, and directly end up in an **equilibrium regarding gravity and pressure**. But that assumes the water, filling the diameter at the ocean ground will do so in the whole tunnel; But doesn't the **stream** of water **get thinner** , as it accelerates up to the center of the earth, and thicker from there? So will it oscillate for a while?   Would it change if we assume the hole in the ocean floor is much smaller than the tunnel's diameter?


title: What is the difference between Quantum teleportation and Radio waves?

text: Quantum teleportation over 143 kilometres using active feed- forward What is the difference between Quantum teleportation and radio waves?


title: Is it possible to manufacture Helium?

text: Helium is a scarce resource, as it escapes the atmosphere over time. If we run out of Helium deposits, will it be possible to manufacture more helium through nuclear fusion or another nuclear process? If so, how much energy will be required?


title: Demagnetisation by throwing a magnet

text: I tried to answer this question in a book about electrodynamics: > How to demagnetise a permanent magnet, ie. described by $ D_T$ change into > described by (0,0) ![enter image description here](http://i.stack.imgur.com/ZiF8s.png) I figured out about heating it up and magnetizing back and forth, but in the answer section there was one more solution: > Drop the magnet on something hard How does this method work?


title: gauss vs mW/cm^2: same thing?

text: A friend of mine is concerned about electromagnetic field negatively affecting their health and got a "DMF meter" to measure the field strength in their house in units of milliGauss. They are trying to compare the reading to a background level measured in mW/cm^2. I am skeptical if such a measurement makes sense, but this is **NOT** meant to be a debate on whether cell phone towers, microwaves impact health: I just want to know if milliGauss and mW/cm^2 could possibly be referring to the same thing, and if so, what it might mean in terms of an electromagnetic field inside one's house. Thanks! P.S. The background rate they are using is 0.000000126mW/cm^2.


title: How does color of galaxies explain their distance?

text: Why do distant galaxies have different colors than closer ones?


title: Electromagnetic waves produced by a charged pith ball

text: Maxwell’s equations appear to have no limitation as to the length of an electromagnetic wave that can be produced by an accelerating electric charge. So in theory, if I use a charged rod to oscillate a charged pith ball at, say $1\, \mathrm{Hz}$, the wavelength of this wave is $3\times10^8\,\mathrm{m}$! Although the energy of this wave is very weak, it is an electromagnetic wave. I have two questions: How would someone go about to detect such a weak wave, if possible? Has anyone ever detected electromagnetic waves in nature (I am thinking outer space) with a comparable wavelength?


title: How to solve the Fukushima incident?

text: I am trying to find out if it is somehow possible to take all this nuclear material, put it in some type of gamma chamber or blast it with neutrons to change the uranium isotopes into something harmless. Somehow neutralize the entire reaction. It seems that if we can create enriched uranium, then we should be able to do something in the opposite direction. Even if a single chamber of this sort cost a hundred billion dollars, if it was able to neutralize all the spent nuclear waste across the world within a year, it would be well worthwhile for governments and organizations to invest. Perhaps teams of grant and proposal writers to put this into reality as soon as possible.


title: How to calculate flux density in a toroidal CT that has an electrical line pass through the center?

text: I have seen the Biot–Savart equation, but I don't know how to apply it. Does the conductor length need to be considered finite and equal to the core length, or will the calculation be for a conductor of infinite length?


title: What does electroweak vacuum lifetime refer to?

text: I just read an article about the correlation between the Higgs boson mass and the stability (or metastability) of vacuum, so I want to ask to someone this: When someone is talking about the electroweak vacuum lifetime, does it refer to a certain region of space, the time needed for quantum tunnelling to occur once in the whole vacuum, the lifetime of the entire vacuum or something else?


title: Some questions about virtual particles

text: When reading about quantum mechanics, I've stumbled upon a description of the force between two electrons as a result of virtual particles being "exchanged" by the two electrons. So far I've understood that the virtual particles are a "prediction" of the uncertainty principle, and that their lifespan is inversely proportional with their mass. Is an electron (or real particles in general) somehow stimulating the creation of virtual particles? If so, why? If these guys pop in and out of existence, then won't they interfere with real particles? If so, then I guess the average effect on a particle is zero, as the creation is completely random along with the momenta of the particles. Is this correct?


title: Feynman diagram for annihilation

text: What is the difference between these two Feynman diagrams? They should both describe the same physical process, annihilation between an electron and a positron.![enter image description here](http://i.stack.imgur.com/lsqRg.jpg) ![enter image description here](http://i.stack.imgur.com/o0KGU.gif)


title: Must string models that describe 4d effective field theories always have D-branes that extend in the 4 non-compact spacetime dimensions?

text: In string theory the D-branes give those directions that the strings are allowed to move along. The string excitations give the fields that we detect. Is it correct to think of a particle propagating in 4d spacetime as a string propagating in the same 4d spacetime (in other words if we could zoom in sufficiently far a photon for example would reveal itself to be a string). If so, this implies that a realistic model should always have D-branes that extend in these 4 spacetime directions. Otherwise how would the strings, and their associated excitations, propagate in the 'normal' spacetime we see at low energies?


title: What are the *necessary* conditions to deterministic chaos?

text: What are the _necessary_ conditions (not saying _sufficient conditions_ ) in mathematical terms that a deterministic dynamic system can transit to deterministic chaos? We collected yet:   1. A positive feedback loop   2. Non-linearity   3. Minimum of three instable eigenmodes   4. ...???


title: How is the double slit experiment modeled in contemporary physical theories?

text: Suppose I have the following double split experiment set up:   * a monochromatic electron source of low intensity, which we can model as emitting a single electron at a time with energy $T$.   * a diffraction screen at a distance $A$ with two macroscopic slits equidistant from the source with width $w$ and distance from the center of the screen $\frac{d}{2}$.   * a detector screen sitting parallel to the diffraction screen at a distance $B$ which consists essentially of a lattice of ammeters each connected with a square surface of side $r$.                                  ![Double slit experiment](http://i.stack.imgur.com/s6SyA.jpg) Classical quantum mechanics, and experiments, tell us that the following behaviour is experienced:   * Only one random ammeter is disturbed each time an electron is fired   * The probability distribution of the random ammeters being fired is as given by QM. The interaction of the electron with the detector is not modeled, the electron is essentially modeled as a wave with interference and which ammeter is fired, essentially an effect of particle behaviour, cannot be discussed within this picture. So, the measurement or decoherence of the electron wave function corresponds to this switch between wave-like and particle-like models of the electron - which is clearly unsatisfying, intellectually, because QM is vague about this - it merely associates mathematical operations with the procedure, without giving any particular physical or mathematical justification of it. The questions: > Do further refinements of QM (QED or QFT or ST) give any better explanation > of what justifies the measurement "recipe" of classical QM by correctly > modelling the electron/detector interaction? > > How, in layman terms, is the change of picture from wave to particle modeled > (if it is at all)?


title: Fermion boundary conditions at finite temperature

text: In a finite temperature QFT, fermions must obey anti-periodic boundary conditions. What is the reason for this?


title: What is nonlocal resistance?

text: We are first taught to calculate local resistance, where current and voltage are on the same part of the material. But many experiments measure nonlocal resistance, where current and voltage are measured on different parts of the material.   1. What is nonlocal resistance?   2. What is the advantage of measuring nonlocal resistance than its local counterpart?   3. How to calculate nonlocal resistance?   4. If local resistance increase, is it a must that nonlocal resistance must increase too?


title: fusing two air containers with fixed pressures $p_1,p_2$ and temperatures $T_1, T_2$, what end-result $T$ and $p$ will be?

text: Let's say that I have two boxes with both volumes equal $V$, filled with an air. Air in first box have pressure $p_1$ and temperature $T_1$, likewise air in second box have pressure $p_2$ and temperature $T_2$. Suppose this is ideal gas, then from Clapeyron equation we have: $$ p_1 V = n_1 R T_1 $$ $$ p_2 V = n_2 R T_2 $$ Thus, after simple transformation: $$ \frac{p_1 V} {R T_1} = n_1 $$ $$ \frac{p_2 V} {R T_2} = n_2 $$ Now, let's say that we want to fuse both boxes and remove bulkhead, so we will have instead 1 box with volume equal $2V$. What will be temperature $T$ and pressure $p$ of air in the new box? We can use the same law as above to get: $$ 2 p V = ( n_1 + n_2 ) R T = \left( \frac{p_1 V} {R T_1} + \frac{p_2 V} {R T_2} \right) R T $$, thus: $$ p = \frac { T } { 2 } \left( \frac { p_1 } { T_1 } + \frac { p_2 } { T_2 } \right) $$ **And there's my question:** If I had heated air after fusion of boxes to temperature $T'$, in other words I had known temperature, I could say what pressure is. Likewise, knowing pressure $p'$ I could say the temperature. But if I just fuse boxes of air and "let it be" (wait very long for air to mix), what the end result should be? Shouldn't (statistically) the pressure and temperature always fix to some certain, unambiguous state? If yes, how I can find them? I mean that I have one equation $ \quad $ $ p = \frac { T } { 2 } \left( \frac { p_1 } { T_1 } + \frac { p_2 } { T_2 } \right) $, $ \quad $ and two variables: $T, p$, so how can I find both of them? Did I missed something? Or I must to make some more assumptions?


title: What's the difference between $10\%$ of $10\text{ cm}$ and $1\text{ cm}$?

text: I overhead a physics professor at my university on the phone: > _I interviewed that student you sent me, but he didn't know the difference > between increasing the length of a $10\text{ cm}$ rod by $1\text{ cm}$ > versus by $10\%$, so I didn't accept him into the program._ Is this some sort of trick question? What difference could he possibly be talking about? A philosophical one?


title: Finding the creation/annihilation operators

text: Using Minkowski signature $(+,-,-,-)$, for the Lagrangian density $${\cal L}=\partial_{\mu}\phi\partial^{\mu}\phi^{\dagger}-m^2\phi \phi^{\dagger}$$ of the complex scalar field, we have the field $$\phi(x)=\int{\frac{d^3 \vec{p}}{2(2\pi)^3\omega_\vec{p}}}(a(\vec{p})e^{-ipx}+b^{\dagger}(\vec{p})e^{+ipx}).$$ I'm trying to now find an equation for the $a(\vec{p})$ and $b(\vec{p})$ (with the final goal of finding an expression for $[a(\vec{p}),b^{\dagger}(\vec{q})]$ using $[\phi(x),\Pi(y)]$). What I should note is that we are considering all of this in the Schrodinger picture (t=0) so I suppose the very first thing to do is change all the $x$'s to $\vec{x}$ right? The strategy I'm struggling to implement and failing at many points along the way:   1. Find the momentum $\Pi^{\phi}(x)=\frac{\partial L}{\partial \dot{\phi}}=\dot{\phi^{\dagger}}$.   2. Add some combination of $\phi(x)$ and $\Pi(x)$ to get rid of one of the creation/annihilation operators.    3. Do an inverse Fourier transform to find $a(\vec{p})$ in terms of $\phi(x)$, for example.  None of the major text books seem to actually carry this through, and instead write something like "and it's easy to show…". However I don't find it too easy, especially part 3. as I'm not a Fourier transform expert. Could anyone either direct me somewhere where the above is computed explicitly (in more than 2/3 lines), or help me understand each of the 3 steps above? (I realise it is easy to find a reference where this is done for the real scalar field, in which case we have $a(\vec{p})$ and $a^{\dagger}(\vec{p})$. Even still, I find it hard to follow parts.)


title: How do aspherical gravitational monopoles look like?

text: I was recently pointed by laboussoleestmonpays to a beautiful paper from some time ago, > _Aspherical gravitational monopoles._ Alain Connes, Thibault Damour and > Pierre Fayet. _Nucl. Phys. B_ **490** no. 1-2 (1997), pp. 391-431. arXiv:gr- > qc/9611051. They show that the class of homogeneous mass distributions that is completely monopolar outside of some finite domain (i.e. a lump of homogeneous matter that's confined within some volume $\Omega\subset\mathbb R^3$, but is indistinguishable gravitationally from a point mass located somewhere in that volume) is much broader than simply the spherically symmetric distributions. Instead, starting with (i) a given centre of mass $\mathbf{x}_O$ and (ii) the outer surface $\Sigma=\partial\Omega$ of the lump of matter, they construct a continuum of homogeneous (but hollow) bodies that are gravitationally indistinguishable from a point mass at $\mathbf{x}_O$, and which is parametrized by the thickness of the shell of material within $\Sigma$. The principle is actually surprisingly simple. If you have a unit electrostatic charge at $\mathbf{x}_O$ within a connected surface $\Sigma$ acting as a grounded conductor, there is a unique electrostatic potential $\phi_{\mathbf{x}_O}(\mathbf{x})$ that's zero at $\Sigma$ and $\sim 1/|\mathbf{x}-\mathbf{x}_O|$ near the charge. Seen globally, this can be seen as the effect of the negative charge density $\sigma_{\mathbf{x}_O}(\mathbf{x})\propto\hat{\mathbf{n}} \cdot\nabla \phi_{\mathbf{x}_O}(\mathbf{x})$ at the boundary. Similarly, the _negative_ of this surface charge distribution is, from the outside, electrostatically indistinguishable from the unit charge. That's, by itself, a (very thin) aspherical electrostatic monopole. Connes et al. then go on to describe, in quite some mathematical detail, a process of "deposition" of mass on the inside of the shell that makes up progressively thicker shells that are, still, indistinguishable from the outside from a point mass. * * * However, their paper contains few specific solutions, and I'm quite curious to know what these aspherical monopoles could look like in their "thick" versions. (Connes et al. only treat thin planes, spheres and cylinders.) Looking at the citing articles on Google Scholar yields very little that looks promising. Has this been explored in the literature? In general, how do these bodies look like? I'm looking to gain some intuition into their general behaviour and properties. How do thick shells look like, say, for taking $\Sigma$ to be a sphere, or a box, or an ellipsoid?


title: Wavefunctions of different observable values are orthogonal because for any state one of them equals zero. Right?

text: I'm trying to understand correspondence between observables and quantum operators. Let's assume that $\phi_1$ and $\phi_2$ are wavefunctions that can be obtained after the measurement of some observable (in other words - quantum states of the system immediately after measurement). $\phi_1$ is a quantum state if the measurement result equals $\lambda_1$, and $\phi_2$ is a quantum state if the measurement result equals $\lambda_2$ ($\lambda_1 \neq \lambda_2$). Let's assume that $x$ is a classical state of the system, i.e. point in position and momentum space of the system ($x = \\{p_i,q_i\\}$). And $f(x)$ is a value of the aforementioned observable in state $x$. If $\phi_1^*(x) \phi_1(x) \ne 0$ than $f(x) = \lambda_1$ (i.e. there is non- zero probability for the system in quantum state $\phi_1$ to be in point $x$). If $\phi_2^*(x) \phi_2(x) \ne 0$ than $f(x) = \lambda_2$ (i.e. there is non- zero probability for the system in quantum state $\phi_2$ to be in point $x$). It means that, for any $x$ either $\phi_1^*(x) \phi_1(x) = 0$ or $\phi_2^*(x) \phi_2(x) = 0$ (or both). So we can suppose (can we?) that for any $x$ either $\phi_1(x) = 0$ or $\phi_2(x) = 0$ (or both). Therefore for any $x$ $\phi_1^*(x) \phi_2(x) = 0$ , and therefore $\langle\phi_1 | \phi_2 \rangle = 0$. The last equality means orthogonality of $\phi_1$ and $\phi_2$. Having full set of possible observable values and corresponding orthogonal wavefunctions by spectral theorem we can build an operator $A$ for this observable as following: $$ A = U\Lambda U^*$$ where $\Lambda$ - diagonal matrix with $\Lambda_{ii} = \lambda_i$ and $U_{ij} = \phi_i(x_j)$. Is this derivation correct?


title: Can you both supercool and superheat a substance simultaneously?

text: There are certain temperatures and pressures for substances at which they exist as a liquid. Also there are temperatures and pressures for which they usually are at equilibrium between solid and gas. Superheating is where you take a liquid and put at a temperature and pressure where it would usually be a gas, but does not become a gas until disturbed. Supercooling is the equivalent for solids. My question is, **is it possible to both superheat and supercool a substance,** meaning take a liquid substance, bring it to a temperature and pressure on its sublimation curve, yet maintain its liquid state. If it is possible, what would happen if it were disturbed (like say by a loud blast of sound?)


title: What are particle multiplets in the Standard Model?

text: The particles of the standard model are often displayed in groupings known as multiplets. I know that this somehow relates to the underlying symmetries of the standard model, which can be viewed as tranforming these particles into each other. I have still struggled to pin down exactly what is meant by these multiplet groupings however, and to get a good 'feel' of the concept. Could somebody elaborate please?


title: Soda bubbles in free fall in air

text: The question of soda bubbles in free fall has come up and again, and the consensus (backed by many fun space borne experiments) is that soda bubbles do not "rise" in a free fall environment because the pressure is distributed evenly across the liquid surface. The question I'm being challenged on is whether if the liquid in question is in free fall when the surrounding air is not in free fall (for example by throwing a beer mug from a tall tower), will the difference in pressure between the top and bottom of the falling glob of liquid (assuming for a minute that it is not immediately dispersed) be enough to cause the bubble to rise relative to the liquid?


title: Using piezoelectiricty to produce electricity

text: What if piezoelectric materials could be placed under a runway to then produce electricity to power (street) lights - I don't know what voltage certain piezoelectric compounds can produce, but would this be possible?


title: What is the quantity in physics that is advanced from speed?

text: What is the quantity in physics that is advance from speed? i know one is velocity, one is speed, one is acceleration.


title: Casimir Invariants of the Galilean group

text: I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I should be able to obtain Mass ($M$) as a Casimir Invariant. $$ [B_i,P_j] = iM\delta_{ij} $$ One attempt at a (scalar) representation of boosts are : $$ B_i = v_i\delta t\frac{\partial}{\partial x^i}$$ But with this, how am I supposed to arrive at the commutators like the one above and also, $$ [B_i,L_j] = i\epsilon_{ij}^{\:\:k}B_k $$ I am also interested in understanding how to find the Casimir Invariants of a given Lie algebra in general.


title: Order of magnitude estimation for some intriguing questions

text: The physics TA showed us a few examples in which one can estimate many things from first principles and sound logic based and scaling arguments. This led usually to understanding of why some numbers have the values they do. I asked myself a few questions and after struggling with them, I could not get a clear answer: why our body temperature is about 30 C, is there a way to understand where that number come from? why pregnancy period in humans is about a year, not 10 years, not a month? why our life time is about 100 years, not 1000, not a year? Any help will be really appreciated


title: Drift velocity of electrons in a superconducting loop

text: Do electrons travel at the Fermi velocity in a superconducting loop? For metals the Fermi velocity seems to be around $10^6$ m/s. So would electrons (in a Cooper pair) travel around the loop at this velocity if no voltage is applied?


title: Force of a magnet in a magnetic field?

text: Let's assume you have a simple bar magnet in a magnetic field. I know that the tendency is for the magnet to line up with the magnetic field. I'm trying to figure out how much force that actually corresponds to. I know the mass of the object, the magnetic strength, and the force and direction of the magnetic field. The field could have any orientation with respect to the magnet.


title: Why does a candle blow out when we blow on it? Our breath is 16% oxygen and only 4% CO2

text: Don't say that a layer of carbon dioxide covers the flame, because our breath has more oxygen than carbon dioxide. Also, our breath does not cool the flame as it is itself warm. So what is happening here?


title: Is it possible for dark matter to somehow turn into regular matter?

text: Is it possible for dark matter to create the regular matter that we, the stars, and the galaxies are made of? The reason I'm asking this is because I have a hard time imagining how something can basically just come out of nothing (The Big Bang). So I was thinking, what if there was dark matter "before" big bang. Is it possible for dark matter to have existed before The Big Bang? Did dark matter actually come into place because of The Big Bang?


title: Symbol for dashpot/damper (in a harmonic oscillator)

text: In diagrams that contain the dashpot symbol, sometimes the mass is attached to the "interior" end of the dashpot, other times the mass is attached to the "base" end. For example, consider the following diagram (please ignore the equations): ![enter image description here](http://i.stack.imgur.com/85DmC.jpg) Does it make any difference if the dashpot symbol in the above figure is reflected in the vertical line? If not, which is the conventional orientation to draw the dashpot in? Thanks.


title: An electromagnetic space elevator?

text: If you surround the equator with a continuous Niobium Tin superconductor ring, and ran somewhere near but less than the maximum current density through, the magnetic field of the Earth would support the ring at low Earth orbit. Could such a ring substitute for a space elevator and space station? Obviously there are no launch costs associated to such a thing, you can just turn on the current and let it lift itself into orbit. The Earth's rotation would supply the required lift.


title: Are locality and separability two distinct notions?

text: Is there any difference between locality and separability in quantum mechanics, or do they mean the same thing? It seems authors do not always agree.


title: Newtonian approximation in cosmology

text: In Peeble's "Large scale structure of the Universe" the Newtonian approximation in cosmology is examined by looking at a transformation that makes the metric locally Minkowski. On pg 38 it is stated that > To make $g_{ij,kl}=0$, we would add 10$\times$10 equations for a total of > 150 to be satisfied by the choice of 56+80=136 transformations. The 56 is explained a couple of lines earlier but I am having trouble seeing where the 80 comes from. I would very much appreciate any help with how to derive that an additional 80 transformations are needed in the above quote.


title: A question related to "old covariant quantization" of string theory

text: I have a question about "old covariant quantization" in Polchinski's string theory p. 123. It is said > The only nontrivial condition at this level is $(L_0^{\rm m} + A) | \psi > \rangle =0 $, giving $m^2=A/\alpha'$. I have no idea where does $m^2=A/\alpha'$ come from... How to get this result?


title: Is the fraction of radioactive isotopes on the near side of the moon higher than on the far side?

text: As time passes more slowly in a region of space close to the source of a gravitational field, shouldn't the moon, which always has one side facing towards the earth, have a higher fraction of radioactive isotopes on that side than on the far side? Could the fraction be used to determine the time tidal locking occured? Also, shouldn't the fraction of radioactive isotopes be different in the earth depending on how deep you dig? Gravitation drops off with $r^2$, whereas the gravitationally relevant mass increases with $r^3$ (only the mass of the earth's sphere lying below the radioactive atom results in gravitation due to Gauss' law) , so outer layers should have more time dilation and therefore a higher fraction of radioactive isotopes. Can this be observed?


title: Magnetic Levitation For Space Travel

text: At 1 G, we feel at home.   At 5 G's, normal people can stay awake.   At 9 G's, trained pilots with G-suits can stay awake.   At 25 G's, R.I.P. Unfortunately, these numbers are limiting for space travel, especially for the astronaut. For example, if you and I wanted to visit Alpha-Centauri (4.2 light-years away) and come back and tell everyone about our trip, at a comfortable 1 G acceleration and deceleration, our round-trip travel time would be 11.64 earth years and 7.06 rocket years. That's 7 years we'll never get back! We can't save much on the round-trip travel time by earth's standards (traveling at light speed would only save 3.24 earth years from our previous example's earth time). However, we can really cut down on our perceived time by accelerating at a faster rate. For example, if we accelerated/decelerated at an uncomfortable 9 G's for the whole trip, while earth's perceived time only drops a little (8.82 years, or 76% of the original time), our perceived time drops to 1.6 very uncomfortable years: just 23% of the original time...nice! At 150 G acceleration, our perceived travel time is only 1 month there and 1 month back! Obviously, a big problem with our 150 G trip is that under normal circumstances we died 125 G's ago. Thus, my questions are:   1. Can we make 150 G's (or other large G amounts) survivable to humans using levitation techniques (for example, I'm worried that your blood might be "locked" into place and thus be unable to pump)? Note that solutions could involve regulating your internal body composition so that each part "pulls its own weight" in the suspension (as opposed to only your stomach being lifted).   2. Can we make 150 G's feel like 1 G so that we are not just levitating frogs for our whole trip?


title: Problem in the Ladder paradox in relativity?

text: The ladder paradox consists of a ladder rushing towards a garage with two open doors. In the actual paradox, proper length of the ladder is greater than that of the garage, but in this case lets consider them to be of the _same proper length_. In the frame of the garage, the ladder is Lorentz contracted, and hence it is possible to "trap" the ladder inside the garage. By "trap" I mean that both doors of the garage must be closed while the ladder is completely inside the garage. But in the frame of the ladder, the garage is Lorentz contracted, and hence it is never possible to "trap" the ladder inside the garage. If I am able to trap the ladder in one frame, I should be able to do it in the other frame too right? Why then is there this paradox?


title: Why aren't airplanes like golf balls?

text: Ok this is a silly question but here it goes Although it is good to have a laminar flow of the air around the object for low drag but the laminar flow is prone the phenomena called separation (sounds like breakup) which dramatically increases the drag on the object. On the other hand turbulent flow has a greater drag around the object in the beginning but is less prone to separation as compared to laminar flow , and this is the reason why golf balls have been introduces to dimples to create a controlled turbulent flow to get rid of separation. So my question why don't surface of airplanes have dimples on them, as it would reduce the drag on the airplane and thus fuel consumtion, or does the effect which reduces the drag in the case of golf ball fails at higher speed and bigger size or is it something else


title: Are the Hamiltonian and Lagrangian always convex functions?

text: The Hamiltonian and Lagrangian are related by a Legendre transform: $$ H(\mathbf{q}, \mathbf{p}, t) = \sum_i \dot q_i p_i - \mathcal{L}(\mathbf{q}, \mathbf{\dot q}, t). $$ For this to be a Legendre transform, $H$ must be convex in each $p_i$ and $\mathcal{L}$ must be convex in each $\dot q_i$. Of course this is the case for simple examples such as a particle in a potential well, or a relativistic particle moving inertially. However, it isn't obvious to me that it will always be the case for an arbitrary multi- component system using some complicated set of generalised coordinates. Is this always the case? If so, is there some physical argument from which it can be shown? Or alternatively, are there cases where these convexity constraints _don't_ hold, and if so what happens then?


title: Rotating frames

text: A bird of mass $m$ is on a merry-go-round of radius $a$ which rotates at constant angular velocity $-\omega_b$ in the $y$ direction. A woman of mass $M$ is on a second merry-go-around of radius $b$ which rotates at constant angular velocity $\omega_s$ in the $z$ direction around the same origin. At $t=0$ the bird is at $(a,0,0)$ and the woman at $(b,0,0)$. What is the force of friction acting on the bird as seen by the woman?


title: Lagrange multiplier and constraint force

text: The Lagrangian with Lagrange multiplier in the form $$L= T- V + \lambda f(q, \dot{q},t).$$ But there are different ways of writing the constraint $f = 0$. Will that lead to different EOMs? Let me give an example: A pendulum with mass $m$ and length $l$. We can use let $$I=\int_{t_0}^{t_1}\left[\frac{1}{2}m(\dot{x}^2+\dot{y}^2)-mgy-\lambda\left(\sqrt{x^2+y^2}-l\right)\right]dt$$ or $$I=\int_{t_0}^{t_1}\left[\frac{1}{2}m(\dot{x}^2+\dot{y}^2)-mgy-\lambda\left((x^2+y^2-l^2)^2\right)\right]dt$$ In the first case, we have $$m\ddot{x}=-\lambda\frac{x}{l}, m\ddot{y}=-mg-\lambda\frac{y}{l}$$ which are the correct EOM. But for the second case, we have $$m\ddot{x}=0, m\ddot{y}=-mg$$


title: Solar system, visible stars and deep sky objects

text: Since I've seen that galaxies are often called "deep sky objects", as opposed to individual stars, does this mean that all visible stars in the night sky actually only belong to The Milky Way Galaxy? Or are there stars which belong at least to the galaxies in the Local Group? I always thought that Milky Way was that lighter band (since it is said that the Galaxy is a "disc"), and that other stars might be part of other galaxies.


title: Does or should the metric expansion of space imply a locally observable increase in kinetic energy?

text: The title is the question. Here's why it seems like local kinetic energy should increase: Numerous questions and answers here and elsewhere suggest that the reason the metric expansion of space is not observable locally (even on a galactic scale) is that local forces maintain the metric distance between near objects, with "near" meaning anything from two subatomic particles to two celestial bodies. My mental picture is of ants on an expanding balloon. The ants get farther apart, but the expansion of the balloon beneath their feet is not going to tear the individual ants apart. They do however have to do a little dance to keep from doing the splits. It seems to me that this should imply a continuously increasing kinetic energy, presumably generalized as random motion -- i.e. things get hotter. Here is a simple illustration. A and B could be particles attracted by the electromagnetic force, or whole planets attracted by gravity:   1. A begin state with an arbitrary distance and energy level: ![T 0](http://i.stack.imgur.com/pCBW5.png)   2. A little bit later, the two objects are farther apart, implying an increase in **potential energy** : ![T 1](http://i.stack.imgur.com/Cj5bz.png)   3. But the force at work brings the objects back to their original ~~positions~~ distance, implying the potential energy was converted to (kinetic?) energy through work W: ![T 2](http://i.stack.imgur.com/THhVQ.png) Obviously A and B don't actually wiggle apart and then back together, rather the force between them acts constantly as the metric expands constantly, implying a smooth increase in kinetic (or some other type) energy while the measurable distance between the objects stays the same. **Scenarios**   1. Gravity at planetary distances: Jerry Schirmer's answer suggests the effect would be too small to measure   2. What about at subatomic scales? The color force between quarks in a nucleon is a distance-dependent force whose potential energy is orders of magnitude greater than gravity. Should metric expansion not cause an increase in energy of a individual nucleon, detectable as a few extra photons emitted over the course of some time?


title: Smallest view-able object by radio wave or UV magnification with metamaterial?

text: **What is the theoretical and in practice microscopic maximum/best resolution of a meta material radio wave XOR UV lens (assuming diffraction or beyond diffraction techniques)?** I'd also like to use diffraction or beyond diffraction as described in this paper: A three-dimensional self-supporting low loss microwave lens with a negative refractive index. Given the Theory of Optical instruments defines the maximum resolving power of a light based microscope as: ![enter image description here](http://i.stack.imgur.com/vRmVh.png) ![enter image description here](http://i.stack.imgur.com/2cLag.png) Diffraction based analysis allows for an increased resolution but I have not found those formulas. If a meta material lens and diffraction alone do not result in a sub cellular wave what additional tools could be used to generate the tiny subwave? Would UV metameterials and defection techniques result in a small enough wave? I also have not found a radio wave scanning device consistent with an A4 scanner. These are the numbers I know: 11Ghz or wavelen 27.27mm, the focal length between 6 and 10cm, a refraction index of -1, a lens of 255mm by 255mm which is 40mm thick.


title: Why do rockets need a cosmic ray detector?

text: I was watching the video _Video camera installed on rocket that reaches 121,000 ft._ , and this rocket has a cosmic ray detector. Why is this needed in a rocket?


title: Will Neptune change Pluto's orbit some day?

text: My seven-year-old son loves astronomy-- so much so that we read space books before bed time. One of our books talks about Pluto's orbit crossing over Neptune's orbit and will be (or is) closer to the Sun than Neptune for a period of years. I'm assuming the orbits actually never have a collision path, but what will happen when Neptune and Pluto get as close to each other as possible-- will Neptune's gravity do something to Pluto's orbit?


title: Textbook Problem: Free energy expression

text: > In Klotz, Introduction to Chemical Thermodynamics, Ex. 8.2 requires me to > derive $$ dG = V \left( \frac{\partial p}{\partial V} \right)_V dV + \left[ > V \left( \frac{\partial p}{\partial T} \right)_V - S \right]dT, $$ where $G$ > is the Gibbs free energy, $S$ is the entropy and all the other variables > have their ordinary common-sense meaning. I'd appreciate feedback on my solution, which I find just very simple, maybe too simple to be right. First of all, when recognizing that $G$ is a function of $V$ and $T$, we can write the total differential as $$ dG = \left( \frac{\partial G}{\partial V} \right)_T dV + \left( \frac{\partial G}{\partial T} \right)_V dT $$ In Eq. 8.19, we learn that $$ dG = V dp - S dT $$ and so, when multiplying both sides by $1/\partial V$ at constant temperature, we find $$ \left( \frac{\partial G}{\partial V} \right)_T = V \left( \frac{\partial p}{\partial V} \right)_T - S \left( \frac{\partial T}{\partial V} \right)_T $$ where $(\partial T /\partial V)_T$ is zero, because we're at constant $T$. A similar procedure yields the bracket expression, this time instead we just multiply both sides with $1/\partial T$ and using constant $V$, we arrive at $$ \left( \frac{\partial G}{\partial T} \right)_V = V \left( \frac{\partial p}{\partial T} \right)_V - S \left( \frac{\partial T}{\partial T} \right)_V = V \left( \frac{\partial p}{\partial T} \right)_V - S $$ and from comparison with the total differential expression, one immediately recognizes the above very first expression. Is this a valid solution/Ansatz?


title: Hill's and Mathieu's equation

text: I am supposed to apply Hill's and Mathieu's equation to parametric pendulum.   1. Can you tell me what is the difference between them?    2. Why are they used?    3. What do they describe?


title: Missing radio source coordinates in G/T measurement technique ITU-R S.733.2

text: Section 3 ‘Suitable radio stars’ of this recommendation lists the different stars/nebula and their corresponding flux-densities that can be used in the G/T measurement. There is no reference to the coordinates these flux densities were measured at. Some of the Nebula have large angular extension and I’m not sure where to point my antenna. > Is there a list of celestial coordinates of the radio stars used in this > recommendation? http://www.itu.int/dms_pubrec/itu-r/rec/s/R-REC-S.733-2-200001-I!!PDF-E.pdf


title: Calculations with operators - Proof: Equation of Operators

text: I have a problem in Quantum mechanics 1 with Operators. I have to prove the following equation. I tried it for about 4 hours without any result: Condition: $[[\hat A,\hat B],\hat A]=[[\hat A,\hat B],\hat B]=0$ $$ e^{\hat A} \hat B = (\hat B + [\hat A,\hat B]) e^{\hat A} $$ Info: $e^{\hat A}=\sum\limits_{n=0}^\infty \frac{(\hat A) ^n}{n!}$ Maybe you could help me? I've done these steps: $$ [e^{\hat A}, \hat B] = [\hat A,\hat B] e^{\hat A} = e^{\hat A} [\hat A,\hat B] $$ $$ \sum\limits_{n=0}^\infty \left( \frac{(\hat A)^n}{n!} \hat B - \hat B \frac{(\hat A)^n}{n!}\right) = \sum\limits_{n=0}^\infty \left( \frac{(\hat A)^n}{n!} \hat A \hat B - \frac{(\hat A)^n}{n!} \hat B \hat A\right) $$ But now I don't know how to go on...


title: Are there two theories that are mathematically identical but ontologically different?

text: I have no background in physics but there is a question that has been bothering me, so I'm asking you. Are there at least 2 physical theories that are :   * Mathematically identical, which means that they would yield identical predictions for EVERY situation that these theories can cover, and therefore can not be compared through experimentation : the validity of one of them is equivalent to the validity of the other.   * Physically different, that is to say, based on a different spatio-temporal-whatever realities, whose differences are not only semantic. If there are at least two theories that satisfy those requirements, it would mean that the "absolute", "metaphysical" reality can never be known. However, if we are capable of mathematically demonstrating that such theories can not mathematically exist, it would mean that absolute reality can be known. When I say "mathematically identical", I am not speaking of theories that can not be experimented on, due to technological constraints (like atomism at the time when this was still debated) but really of theories that can theoretically not be compared, even by a Laplace demon. Do you agree with my assumptions? If so is there such theories and/or a demonstration that they can not exist?


title: Maximum efficiency for a counter-current heat exchanger (double flux controlled motorized ventilation)

text: I am not sure if I can explain the question correctly because I don't know the name of this mechanism in English. This is my explanation attempt: In a house, a tube is expelling the air from the inside to the outside, and a tube is aspiring the air from the outside to the inside. The 2 tubes are interlaced in order to transmit the heat between their contents. The goal is to have a good thermal isolation between inside the house and outside:   * When the house is more hot than the outside, the outgoing air is warming the incoming air.   * When the house is more cold than the outside, the outgoing air is cooling the incoming air. Question: **In theory** , what is the maximum efficiency of such thermal exchange? Could it be possible to reach something close to 1 or the upper bound of the efficiency is well under?


title: Questions about the second law of thermodynamics

text: I can not understand the second law of thermodynamics and have trouble explaining the following questions: 1) In the tropics the water near the ocean surface is warmer than the deep water. Does the second law of thermodynamics would be violated if a machine operate between these two levels of water? 2) A car battery is connected to an electric motor is used to raise a weight. The battery remains at a constant temperature hot air getting around it. Is this a violation of the second law? In my opinion I think that both violate the second law because Kelvin postulate. However, I can not raise my good idea, if you could explain me, they are grateful.


title: Determining if a particle is bounded or unbounded with motion in polar coordinates

text: ![a](http://gyazo.com/5be8000bab6937ba21923ffa75cf0997.png) Firstly, I determined the equation for the particles path for $k <-mV^2a^2$ as $u = {Ae^{\sqrt{\alpha}\theta}+Be^{-\sqrt{\alpha}\theta}}$ where $ \alpha = 1 + \dfrac{k}{mV^2a^2},$ $u = 1/r$ I have two questions; (1) Could I solve for the constants $A,B$ with the information given? (It is not given that at r = a, $\theta = 0$, so I figured no) (2) I'm not sure how to determine if the motion is bounded or unbounded in polar coordinates - For instance, if we were dealing with $r(t)$ then I'd take $t \to \infty$ and see what happens, but we have theta here, how can we deal with theta? In this case with $k <-mV^2a^2$ it is bounded (if we take $\theta \to \infty$)


title: Calculating Expected Systematic Error in a Pendulum Experiment

text: I am a little confused by part c of problem 4.28 of Taylor's Introduction to Error Analysis book. A student measures the acceleration due to gravity by using a steel ball suspended by a light string. He records five different lengths (51.2, 59.7, 68.2, 79.7, 88.3)(all in cm) and five different periods (1.448, 1.566, 1.669, 1.804, 1.896)(all in seconds). He uses the formula $$g=\frac{4\pi^2 l}{T^2}$$ To calculate the mean and SDOM of the acceleration due to gravity, which I calculated to be $965.6\pm 1.5\,cm/s^2$. I have double checked this value, and am pretty sure of the result. The student is concerned that the accepted value $g=979.6\,cm/s^2$ is not contained within the calculated uncertainty, and looks for systematic error. The question: how large would a systematic error in length l have to be so that the margins of the total error just include the accepted value of g? What I did was set $$Avg(\frac{4\pi^2(l+\Delta l)}{T^2})+SDOM(g)=979.6$$ $$\rightarrow Avg(\frac{4\pi^2l}{T^2})+Avg(\frac{4\pi^2\Delta l}{T^2})+SDOM(g)=979.6$$ $$Avg(\frac{4\pi^2\Delta l}{T^2})=12.5$$ $$\rightarrow \Delta l=0.894$$ This is about 1.3% of the average length. However, in the book, it says that my answer should be approximately 1.5%. Am I doing something wrong? Is my procedure or calculation wrong, or I am over-analyzing the discrepancy between my value and the book's?


title: What is the next step beyond quantum computation?

text: Assuming we develop quantum computers one day, what would be theoretically the next step? Would it be string-theory based computers? How would these computers differ performance-wise (ie what can they possibly do that Quantum Machines cannot)


title: Quantum states as rays as opposed to vectors

text: I recently read that a quantum state is actually defined by a ray and not a vector. That is it is possible to multiply a state $\psi$ by any complex number $c\in \mathbb{C}$ and you won't be changing the physics in any way. I understand this mathematically, but I don't understand what the physical meaning of such an "equivalent state" would be since the new state need not be normalised if $c$ is not of the form $e^{i\phi}$.


title: When pressure is exerted on parallel hydraulic pistons, do they start extending at the same time?

text: If there are two hydraulic cylinders connected in parallel, each with a different load (shown in the picture below), will they start extending at the same time? I'm having a disagreement with my tutor, he has told me that the cylinder with least resistance will fully extend, and only once it has fully extended will the other cylinder start to extend. I would have thought that both cylinders will start extending at the same time, and the cylinder with lower resistance will just extend faster. Much like parallel resistors in an electrical circuit. The reason I think this is because there is still a net force on both cylinders. In the picture below, if the pressure of the system is 50000 Pa and the area of each cylinder is 0.03m^2, then there is a force of force of 1500N on the cylinders. Cylinder 1 has a load of 491N, and cylinder 2 has 981N, so cylinder 1 has a net force of 1009N, and cylinder 2 has 519N. So surely both cylinders will accelerate as there is a force on them? Another reason I believe the tutor is wrong is that if the masses have very similar weights, say 50kg for cylinder 1 and 50.0000000000001Kg for cylinder 2, would they still only extend one at a time? If that is true then surely it is impossible for them ever to extend at the same time as no two weights will be _exactly_ the same. The only explanation I can think of to them extending one at a time is that the pressure relief valve (shown in the picture below, just to the left of the switch) plays some part. The pressure relief valve works exactly as the picture makes it look like it would. if the pressure of the fluid coming down the dotted pipe is enough to push the arrow so that it connect the above pipe and the reservoir, then water coming from the pump will flow straight to that reservoir. There is a spring that pushes the arrow to the right, so if that spring takes e.g 2000N to be compressed so that the arrow can connect to the reservoir, then this will prevent the system from ever having a higher pressure than 2000N. Everything else in the circuit is pretty self explanatory so I wont bother explaining what they do. So please can somebody explain to me, in the diagram below If switch A is pressed down, will both cylinders start extending at the same time? ![enter image description here](http://i.stack.imgur.com/03R0W.jpg)


title: Do ice crystals grow only as heat is being removed or also when an item is at a set temperature?

text: Chicken develops ice crystals between -2C to -4C. Now as chicken's temperature moves slowly from -2C to -4C ice crystals will grow. However, let's say that in a freezer, we set the final temp to -3C. Ice crystals will grow from -2C to -3C however when the item is at -3C and the temperature isn't increased further, assuming we leave it the chicken for a bit, will ice crystals stop growing or continue to grow? What I mean is will ice crystals grow only whilst heat is being removed or will they grown even when it has reached the set temperature which is considered a freezing temperature? Another way of looking at it might be, If you brought an item to -3C gradually and another in an instant, would ice crystals in the later continue to grow even though no more heat is being removed? Also which one would have the larger crystals, the gradual freeze or the instant at a freeze point temperature? The temperatures I have mentioned may not be exact but the exact temperature isn't my question. It is ice crystal growth in gradual vs instant freeze and also which would grow bigger crystals.


title: Goldstone boson couple to conserved current

text: The Goldstone boson in spontaneous symmetry breaking problem couples naturally to the associated conserved current of the broken symmetry. How can I see a rigorous (mathematical) derivation for that?


title: Gravitational Behavior of Rotating Body

text: Consider a stick with a (ball-shaped) weight at the end of it. Let's say this stick is in a state of rotation (it's floating in vacuum) and is also in a state of translational motion. Consider a stationary observer who witnesses the stick fly past him, while it was rotating. From the perspective of the observer the magnitude of the velocity of the ball is the magnitude of the vector sum of the tangential velocity of the ball and of the translational velocity of the stick. From the perspective of an arbitrary observer in the same rotating/translating frame as the stick nothing seems to be going on. With this model in mind I pose the following questions:   1. Doesn't the observer in the stick's frame observe an overall different total energy of the stick system that he is on and therefore observe force of gravity (which after accounting for the fact that he is closer to the stick than the stationary observer) may still be lower than the gravitational pull that the stationary observer. I say yes because if the total energy of the system is related to the magnitude of the velocity of the system and therefore even if two observers are in the exact same location the choice of whether the observer is stationary or part of the stick's frame makes a massive difference on the percieved gravitational effect. As a corrolary does this mean that for a temporary period of time, a comet passing by earth would feel a much stronger pull than say a person on a tower of equal distance from earth's center as the comet?   1. From the view of the stationary observer does the gravitational pull of system increase and decrease based on when the ball is in the same direction of motion as the translational direction of the system and when the ball is in the opposite direction?


title: What are the good introductory resources for M-theory towards AdS/CFT?

text: I see a list here with a section titled M-theory - http://www.superstringtheory.com/links/reviews.html In there these two look promising, http://arxiv.org/abs/hep-th/9607201 and http://arxiv.org/abs/hep-th/9802051 I would like to know if people have opinions of good starting points towards understanding M-branes and how they are used for constructing exact examples of AdS/CFT. [...I guess all exact AdS/CFT scenarios are M-theory constructions..]


title: How does a gas of particles with uniform speed reach the Maxwell-Boltzmann distribution?

text: Take an empty container and fill it with $N$ gas particles (ideally a monoatomic gas), each having the same kinetic energy $E$, then isolate the container. Since initially the speeds don't follow the Maxwell-Boltzmann distribution, such a system cannot be in thermodynamic equilibrium. On the other hand, assuming perfectly elastic collisions (and there is no reason to assume otherwise, since the only form of energy the particles can possibly have is kinetic), I see no way such a system could spontaneously evolve to equilibrium: elastic collisions among equal masses keep speeds unchanged! What gives? I have no background in non-quasistatic processes, but I tried nonetheless to work out a solution taking into account the container, which necessarily has a certain heat capacity, a certain initial temperature, and whose walls are not necessarily perfectly elastic, etc. Knowing the number of particles and their individual speed, it's possible to compute the system's total heat content (but is this exactly $NE$, or less?) and thus derive it's equilibrium temperature. Since the system is isolated, I take it the quantity that has to change must be entropy (namely increase, as the uniform speed state seems less likely; the change can probably be arrived at from a strictly combinatorial point of view). At any rate, the process I imagined goes like this: initially, the particles bombarding the wall transfer some amount of heat to it while slowing down; in turn the wall, now heated up, will transfer back some heat to the gas; eventually, the system will reach the expected equilibrium. Is my assumption of perfectly elastic collisions wrong, and if so, where does the dissipated energy go? Is there an increase in temperature that accompanies the increase in entropy? Can someone point me to the rigorous mathematical framework for analyzing the problem? Is there direct experimental evidence that the speed of gas particles attains the Maxwell-Boltzmann distribution, or is it just a theoretical result that everyone is just happy to work with? Thanks for any suggestion.


title: What's the relationship between weakly hypercharged bosons and Higgs bosons?

text: In this video, Leonard Susskind does a good job trying to explain succinctly the Higgs field and exactly how it gives elementary fermions mass, except for one point he seems to skip a few things. The weak hypercharge is endearingly called 'zilch' ( _0:46:00_ ). He goes on to explain how (e.g.) an accelerating electron (or other zilch-charged particle) can emit a $Z$ boson. He then postulates ( _0:48:16_ ) the existence of a field (none other than a 'ziggs boson condensate'), which (in a similar manner to a uniform electric field giving electric dipoles a potential energy - and therefore an extra mass - that depends on their orientation) gives fermions mass by the Dirac mechanism (explained earlier in the video). He adds how the ('zilch'-less) $Z$ boson also interacts with the 'ziggs' field to intermittently acquire 'zilch' (and becoming itself a 'ziggs'), and lose 'zilch', thereby acquiring mass as well. At that point, he jumps to the Higgs boson without apparently any connection to the mechanism just explained (he employs different names for the fields). He explains that the Higgs boson is a particular excitation mode of the Higgs field, but what is then the (general) 'ziggs' boson? Are Higgs and ziggs actually the same? The $Z$ boson has been known experimentally for decades, what about its weakly hypercharged product? Does the Higgs boson actually have nothing to do with the Higgs phenomenon, being merely a consequence of the theory that was begging to be discovered experimentally?


title: Principle of locality and forces

text: I have a silly confusion about the statement written in the link Einstein and Locality _''external influence on A has no direct influence on B; this is known as the Principle of Local Action.''_ Since GTR and Electromagnetism obey principle of locality. And in both cases change in A position affect the B and vice versa. Then why this contradiction come. Please correct me.


title: What does it mean for electrons to be "diffusive"?

text: I'm reading this paper and it has the line (end of 3rd paragraph, page 2): > It turns out that the simple fact that electrons are diffusive instead of > freely propagating leads to a profound modification of the traditional view > based on the Fermi-liquid theory of metals. So it kind of suggests it means something that's _not_ freely propagating, like bound I guess?


title: Why does a larger sprocket need more power to accelerate at the same rate?

text: Why does a large drive sprocket require more power to accelerate at the same rate as a smaller drive sprocket if the overall gear ratio is the same (with all other components such as the chain the same between systems)? As an example, we could compare 11/33 to 13/39 (same 1/3 ratio). Why does the 13 tooth sprocket need more power to accelerate at the same rate as the 11 tooth setup? ![enter image description here](http://i.stack.imgur.com/QmYrH.jpg) Can we agree that the top sprocket will need more torque to accelerate an atv at the same rate as the same atv with the bottom sprocket? And assuming the overall gear ratio is the same. The moment of inertia differences of the sprockets are insignificant. Assume the moments of inertia are equal.


title: Huygens wave theory not applicable to lasers or parallel beams of light?

text: According to Huygens wave theory, every point on a wavefront acts as a secondary source of waves. > Using this principle we can never have pretty narrow parallel beams of light > right? Like lasers? There will always be _"leakage"_ (wrong terminology?) of > waves from the edge of the beam right?


title: Can a magnet magnetise an object with greater strength than it possesses?

text: Trivial thought ... Materials may be broadly superconductive, diamagnetic, paramagnetic, ferromagnetic. An object is magnetized by repetitive motion of a magnetic field across it's surface Say a field of strength 1T were to be moved across a steel cylinder. Could the field created in the cylinder be greater than 1T? What if the same field were to be applied to a more strongly ferromagnetic material?


title: How do I calculate integral analytically for small $k$?

text: In a Heisenberg antiferromagnet, the dispersion relation is \begin{equation} \omega_{\mathbf{k}} =JSz\sqrt{ 1-\gamma_{\mathbf{k}}^2} \end{equation} where $\gamma_{\mathbf{k}}=\frac{1}{d}\sum_{i=1}^d \cos k_ia$, where $d$ is the dimensionality of the cubic lattice. In staggered magnetisation calculation, we get an integral which is given by \begin{equation} \delta m =\int_{BZ} \frac{d^dk}{(2\pi)^d}\frac{1}{\sqrt{ 1-\gamma_{\mathbf{k}}^2}}. \end{equation} This integral is dominated by small $k$, since we have Goldstone modes at $k=0,(\pi,\pi,\dots)$. Using this property, we can extend the limits of this integral from Brillouin zone to infinite $k$-space and we replace $\gamma_{\mathbf{k}}$ by its small $k$ limit: \begin{eqnarray} \delta m=\frac{\sqrt{d}}{a}\int_0^\infty \frac{d^dk}{(2\pi)^d}\frac{1}{k} \end{eqnarray} In 1D, its gives the logarithmic divergence which is expected. But, in 2D and 3D we get \begin{eqnarray} \delta m &\sim& [k]_0^\infty, \quad \text{in}\, 2D\\\ &\sim&[k^2]_0^\infty, \quad \text{in}\, 3D \end{eqnarray} which still show divergence. This is not correct as if we solve the Brillouin zone integral we get some finite value. I do not understand what is wrong with the infinite k space integral? Could anybody please tell me how to solve such integral analytically for small $k$?


title: How to find momentum of different pieces of the same object after it explodes?

text: If a stationery object explodes into a specific number of pieces due to internal force, how can I find the momentum of these pieces?


title: Finding coefficient of friction between block and plane

text: An inclined plane makes angle $\theta$ with horizontal. Upper half plane is perfectly smooth where as lower half is rough. The block of mass _m_ starts sliding from top. If the block again comes to rest at bottom. The coefficient of friction between block and plane. This means it will first accelerate and the there will be retardation. I am confused as both the thing have come together.


title: Photon striking a molecule and getting reflected

text: I am writing a simple simulator which simulate absorption of UV light in solution. The idea is to see if I can see Beer-Lambert laws in my model. It is not intended to be a precise simulator but rather a small educational demo on modeling. I have the following problem: I have approximated solvent and solute molecules as sphere. I also assume that UV does not get reflected by solvent molecules therefore solvent molecules are not taking part in any computation in my model. Now I want to insert a model into my simulator. A photon $P$ strikes a molecule at angle $\theta$ and gets reflected by an angle $\phi$. Is $\phi$ completely dependent on $\theta$ only or there is more complex relation between them? I want to keep it quite simple so I am ignoring quantum effects et. al. from my model.


title: Is there a meaning to the E,B analogues of other gauge fields?

text: From the gauge field $A_\mu$ and the QED lagrangian we can derive maxwell's equations in terms of electric and magnetic fields. Are there any situations where similar derivations using the other gauge fields like $W^{\pm}_{\mu}$, $Z_\mu$ or the gluon fields, e.g. $curl W$ could become useful? edit: reformulated for clarity.


title: Chaos and continuous flow

text: What needs to be the case for a dynamical system with a continuous flow to exhibit chaos? It looks like 1D systems with a continuous flow can't exhibit chaos. Are two dimensions enough or do you need more? I was just thinking about what sort of phase portraits you could have in two dimensions, and it's not immediately obvious if they will always have stable attractors...


title: Equation for the trajectory of a frisbee?

text: I'm the lead programmer on a FIRST robotics team, and this year's competition is about throwing Frisbees. I was wondering if there was some sort of "grand unified equation" for Frisbee trajectory that takes into account the air resistance, initial velocity, initial height, (lift... It has to fly at max 50') etc. and solves for the required angle to reach a specific distance (angle will be the only manipulated variable). Basically, I would like to acquire data from an ultrasonic rangefinder, the encoders that determine the speed of our motors, the angle of our launcher, the rotational force (should be pretty constant. We'll determine this on our own) and the gravitational constant, and plug it into an equation in real time as we're lining up shots to verify/guesstimate whether or not we'll be close. Probably other variables, as I was informed on StackOverflow. There is no wind. If anyone has ever heard of such a thing, or knows where to find it, I would really appreciate it! (FYI, I have already done some research, and all I can find are a bunch of small equations for each aspect, such as rotation and whatnot. It'll ultimately be programmed in C++.)


title: How is graphene a major breakthrough?

text: What is graphene from a physics standpoint? Why do I keep hearing that graphene is considered to be such a major breakthrough? How is graphene going to transform the world?


What is the role of Mandelstam variables in strings theory? What is relationship between Mandelstam variables and Veneziano amplitude?


title: Internal resistance V=IR circuit question

text: I don't know how to resolve this problem. > A complete circuit consists of a 18,0 V battery (internal resistance r) and > a resistor R. The terminal voltage of the circuit is 15,8 V and the current > is 4,00 A. What is: > > a) the internal resistor r of the battery. > > b) the resistance R of the circuit resistor. I am not sure how to resolve it. I know the Ohm's Law, but not sure how to apply it here. Sorry for the basic question (just starting with Physics again after very long time).


title: What is the significance of supernova imaging in the DES' hunt for dark energy?

text: Why may supernovae reveal the dark energy responsible for the accelerating expansion of the universe? More specifically why supernovae opposed to other cosmological species?


title: Force between two bar magnets

text: I need to know how to calculate force between two bar magnets. I searched and found an answer on Wikipedia, but I don't really trust Wikipedia, a lot of crazy stuff is posted there. So I searched again and didn't find an answer that matches Wikipedia's. So my question: Is Wikipedia's answer right?


title: Quantum Regime of Particles in Solids

text: On my midterm today, I read that when the deBroglie wavelength of a particle exceeds the spacing between the particles in a solid or liquid, the particles begin to behave quantum dynamically. Why is this? I thought a larger deBroglie wavelength implied a less quantum mechanical behavior.


title: Equivalence between different formulations of QED

text: I have looked at Greiner's book on QED, where he uses the Feynman propagator approach for QED. He solves a lot of things and calculates several processes without "second quantisation" (and without ever introducing path integrals), it is all basically a classical field theory. In older books in QED however, the second quantisation procedure is used and they take the classical theory and quantise it promoting fields to operators and so on. My question is: Why are both approaches equivalent (are they?), it is not obvious to me that they should produce the same results, they look quite different to me: One is the noncommutative version of the other in some sense. Is there a proof, or an argumentation on why they should be equivalent, or some intuition behind this idea?


title: Truck Mass & "4th power law"

text: Is it true that the damage caused to a road surface is proportional to the 4th power of vehicle axle weight, and if it is, what factors cause it to be related by a power of 4, or is it just the results of some measurements? I'm chiefly looking for the answer to "why?", although it'd be handy to know if it is indeed the 4th power, and if not the 4th power, then what?


title: 1-Dimensional Sigma Models

text: I'm currently interested in 1-dimensional (linear) Sigma Models. In the theory of 2-Dimensional GLSM, the fields can be viewed as an embedding of the worldsheet in some target Manifold of higher dimension. **Is there a similar, geometrical, interpretation of the 1-dimensional case?** So far i could only find references to superconformal quantum mechanics, where the $N$-dimensional target space is taken to be $N$ particles. I'm however interested in geometrical insight **See for example Witten's famous "Phases of N=2 Theories in 2 Dimensions", is there an equivalent in 1-Dimension?**


title: What can $E=mc^2$ do?

text: In the famous equation $E=mc^2$, the variables stand for: > $E$ is energy, $m$ is mass, and $c$ is the speed of light (in vacuum). And I understand the equation fairly but limited in knowing in its effects/outputs in reality, honestly.   * Some example? Could anybody please give me some sort of examples in real world which are done by this equation?


title: Quantum states and state vectors

text: Does a state vector correspond to only one quantum states and the components in the state vector correspond to different states of this quantum state or is it that the components of the state vector correspond to different quantum states? Also is it correct to say that (presuming that only one quantum state is discribed by a state vector) a particle can move between the states described by the components of the state vector easily but not between quantum states?


title: What is the electric field outside a cylindrical solenoid?

text: What is the electric field outside a cylindrical solenoid when inside is turned on a magnetic field? The question is related to the question aharonov- bohm-effect-electricity-generation


title: How can time be a dimension?

text: In physical terms, dimension refers to the constituent structure of all space and its position in time. Time is same throughout the universe. So, how can time be a dimension?


title: What would happen to the plateau in QHE under gradual heating ?

text: In quantum Hall effect (QHE), the plateau observed in $R_H$ (Hall resistance) appearing precisely at multiples of $e^2/h$ is a characteristic feature. It can be observed only at low temperatures. My question is, what would happen to these plateau if the systems is heated gradually ? I imagine the plateau will disappear finally and the classical $R_H \sim B/ne$ may be recovered. Is there any experiments on this ? Is the recovery sharp or just a crossover ? Is there any scaling phenomena, say, quantities dependent on $k_BT/\hbar\omega_c$, with $T=$temperature, $\omega_c=$cyclotron frequency ?


title: Einstein Equation at the Singularity. Understanding the Dr. Michio Kaku's explanation

text: I'm trying to understand what Dr. Michio Kaku is exaplaining in this video: http://www.youtube.com/watch?v=hydDhUNvva8 I'm just able to rewrite this two equations. I think I've probably made some mistake in the process of copying. Otherwise, I don't understand the meaning of the two $\mathrm O$ and the $I^{'}$ in the second equation. In the video the Dr. Michio Kaku is solving the first equation right? But I saw that is slightly different from the classical field equation, why? What's the difference? $As^2$ is the solution of the first equation? Is possible understand something from the video or is it too cutted? \begin{equation} R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R=T_{\mu\nu} \end{equation} \begin{equation} As^2=\left(_{\mathrm O}\left(1-\frac{2MG}{r}\right)^{I^{'}\mathrm O}\right) \end{equation}


title: What are the details of the renormalization of Chern-Simons theory?

text: What is a good, simple argument as to why Chern-Simons theory' is renormalisable? Any good books/references dealing with this effectively? Why does the $\beta$-function vanish? Thanks!


title: On Electromagnetic Self Energy

text: In the process of pair annihilation an electron and a positron annihilate each other to produce a pair of photons, conserving momentum and energy. As the oppositely charged particles approach each other, the field around them decreases. We may consider them as a dipole with a decreasing dipole moment and radiating energy. As the field decreases the value of **E** changes. Consequently, **B** should change: $$ \nabla \times \mathbf{B}=\epsilon_0\mu_0\frac{\partial \mathbf{E}}{\partial t}$$ and $$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}.$$ So we have a Poynting vector that drives energy in the outward direction (If it was in the inward direction the field would grow stronger with the approach of the particles which is not the case). By the time the electron and the positron are close enough to clash the classical self energy (electromagnetic self energy) has moved out to an infinite distance. Quantum Mechanical Picture:Virtual photons emitted by the electron (or the positron) hit back the particle increasing its KE.This extra energy gets included into the mass of the particle leading to the dressed mass of the particle. In pair annihilation this energy is included in $E=mc^2$.And we get it after the collision of the particles. But the classical electromagnetic self energy, as we have seen in the previous paragraph, flows out to infinity before the collision of the particles. So the classical self energy of the electron and its QM self energy must be physically different. Is this true?


title: Is the minimum radius of a positronium system of the order of compton wavelength or less than that?

text: Since from electron-positron annihilation energy and uncertainty principle,the minimum radius of positronium comes out as half of the compton radius.


title: Units in cgs system

text: How do I find the dimensions of this quantity (in $cgs$)... $$\frac{4\pi me^2}{h^2n_o^{1/3}}$$ where $m$ is the mass of electron $e$ is the magnitude of electronic charge $h$ is the Planck's constant & $n_o$ is equilibrium number density of electrons


title: Determining distance from object in concave lens

text: so I was studying for my Yr11 Physics test tomorrow and I came across a question that I got the wrong answer on, all of my friends are getting the same answer. Question: You wish to project the image of a lamp, magnified three times, onto a screen 5.0m from the lamp. How far from the lamp should the mirror be placed? I though that we would just use $M=\frac{-d_i}{d_o}$ where $M=3$ and $d_i=5$, which will work out that $d_o\approx -1.7$ which has a magnitude of 1.7m from the lamp However, our answers book says that the answer is 2.5m What have I done wrong? Also, please keep in mind that I am in year 11 and may not understand anything beyond that level


title: Topological band structure, difference between a sphere and a donut

text: Kohmoto from TKNN(Thouless-Kohmoto-Nightingale-deNijs) who described the topology of the integer quantum hall effect always stressed the importance of the 2D Brillouin zone being a donut due to periodic boundary conditions. \--> http://www.sciencedirect.com/science/article/pii/0003491685901484 Now I don't really see why this is relevant. Shouldn't the zeros of the wavefunction always lead to a Berry phase?. What would happen if we have a sphere instead of a donut? I think I am missing a major point here, because I can't see how the Gauss-Bonnet theorem that connects topology to geometry plays a role. For a sphere with no holes the Gaussian curvature gives us 4$\pi$, for a donut if gives us 0. In both cases Stokes' theorem should still give us a nonzero value? Charles Kane then uses this argument to compare a donut with the quantum hall state and a sphere with an insulator. He then writes down the Gauss-Bonnet theorem and immediately talks about topological insulators, and again I don't see the connection or is it just an analogy and I shouldn't waste any time on this? If there is a connection, I would like to know if there is a simple explanation for using the Gauss-Bonnet theorem in the context of topological insulators. I'm even more confused because Xiao-Gang-Wen said in a recent post here, that a topological insulator is NOT due to topology but due to symmetries...


title: Can a magnet be tuned to attract only to one other magnet?

text: So think magnet X is only attracted to magnet Y , but magnet A is not attracted to either magnet Y or X. Only X and Y can attract each other???


title: When blowing air through a tube, why does it act differently if I press the tube against my mouth, or hold it an inch away?

text: So I have a tube of wrapping paper. It's at least a couple of feet long and maybe two inches wide. If I press one end of the tube firmly against my mouth and blow, I barely feel warm air come out the other end. If instead I hold the tube about half an inch to an inch away from my mouth and blow into it, I feel a good flow of air come out of the other end. My question is why is there a difference? In both cases I would expect that since air is going in one end, it would come out the other. When I press the tube against my mouth and blow, but very little air comes out the other end, where does the rest of it go? _PS: I don't know what tags to give this question and I can't think of a good question title. I'm new to the physics sub._


title: Relativistic drift velocity of electrons in a superconductor?

text: Is there a formula for the effective speed of electron currents inside superconductors? The formula for normal conductors is: $$ V = \frac{I}{nAq}$$ I wonder if there are any changes to this formula for superconductors. Is there any regime for existing superconductors where the electrons will be flowing at speeds near light speed? Or more precisely, is it possible to have carrier currents that produce drift velocities that are relativistic, while maintaining the superconducting phase?


title: Why does letting air into a box of wine help the flow?

text: I've notied that when I get down to the last part of a box of wine, the flow slows to a trickle. If I open the nozzle, tilt the box back (letting air gurgle into the bladder) and then tilt it back forward the flow is greatly increased. Why does letting air into the bladder help increase the flow?


title: Self energy, 1PI, and tadpoles

text: I'm having a hard time reconciling the following discrepancy: Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be the generating functional of 1-particle irreducible Green's functions $\Gamma^{[n]}$. In particular, the 2-point function is the reciprocal of the connected Green's function, $$\tilde \Gamma^{[2]}(p)=i\big(\tilde G^{[2]}(p)\big)^{-1}=p^2-m^2-\Sigma(p)$$ which is the dressed propagator. But, the problem is this: in the spontaneously broken $\phi^4$ theory, the scalar meson (quantum fluctuations around the vacuum expectation value) receives self energy corrections from three diagrams: $-i\Sigma(p^2)=$ ![](http://i.stack.imgur.com/CvrwN.png) \+ ![](http://i.stack.imgur.com/9itm1.png) \+ ![](http://i.stack.imgur.com/whH1G.png) Note that the last diagram (the tadpole) is _not_ 1PI, but must be included (see e.g. Peskin & Schroeder p. 361). In the MS-bar renormalization scheme, the tadpole doesn't vanish. If the tadpole graph is included in $\Sigma$, and hence in $\tilde{G}$ and $\tilde\Gamma$, then $\tilde\Gamma$ cannot be 1PI. If the tadpole is not included, then $\tilde G$ is not the inverse of the dressed propagator (that's strange, too). What's going on?


title: Falling into a black hole emitter vs observer

text: Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole. Suppose we define the quantity $$u=t- v$$ where $$dv/dr= 1/(1-r_{s}/r)$$ where $r_s$ is the Schwarzschild radius. What is the $u$ as observed by the emitter? I just need a _definition of $u_e$_. I have problems identifying the quantities as measured by an observer at large $r$ and that of the emitter. Would I be right at least to say that $$t_{e}=\tau$$ the proper time? Many thanks. * * * In fact, I've been told that $$du_o/d\tau=du_e/d\tau$$ Why is it? * * * My apologies for leaving out a subscript $e$ in the question. It has been added.


title: why aren't there nuclear powered aircraft?

text: I know this might sound like more of an engineering question that about physics, and it probably is, but bear with me: i'm still not sure if the answer to my question lies in the physics or in the engineering, or even in the politics. Most if not all of modern submarines are powered by a nuclear reactor. At sea, only the most heavyweight (like air-carriers) use a nuclear reactor. But i've never heard of nuclear-powered aircraft Is there a weight-to-power density relation making it difficult or impossible to have nuclear aircraft? or is something related to perceived safety/politics?


title: Showing that electron and positrons have the same absolute charge

text: In Zee's quantum field theory in a nutshell, 2nd edition, pg 551 he has the charge of a Dirac field written as > $Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s > \\{b^\dagger(p,s)b(p,s)-d^\dagger(p,s)d(p,s)\\}$ He then goes onto write > We find $[Q,\psi(0)]=-\psi(0)$, thus showing that $b$ and $d^\dagger$ must > carry the same charge. I would very much appreciate if someone could explain to me how one deduces this. He writes the Dirac field as $\psi(x)=\int\frac{d^3p}{(2\pi)^{3/2} (E_p/m)^{1/2}}\sum_s [b(p,s)u(p,s)e^{-ipx}+d^\dagger(p,s)v(p,s)e^{ipx}]$. So doesn't this imply that $[Q,\psi(0)]\left|0\right>=Q\psi(0)\left|0\right>=-\psi(0)\left|0\right>$ and if so this seems to be independent of $b(p,s)$ so I don't understand why he writes > We find $[Q,\psi(0)]=-\psi(0)$, thus showing that $b$ and $d^\dagger$ must > carry the same charge.


title: What is the physical meaning of weak expectation values?

text: In the two-state formalism of Yakir Aharanov, the weak expectation value of an operator $A$ is $\frac{\langle \chi | A | \psi \rangle}{\langle \chi | \psi \rangle}$. This can have bizarre properties. If $A$ is Hermitian, the weak expectation value can be complex. If $A$ is a bounded operator with the absolute value of its eigenvalues all bounded by $\lambda$, the weak expectation can exceed $\lambda$. If $A = \sum_i \lambda_i P_i$ where $\\{P_i\\}_i$ is a complete orthonormal set of projectors, the strong expectation value is $\frac{\sum_j \lambda_j |\langle \chi |P_j | \psi \rangle|^2}{\sum_i | \langle \chi | P_i | \psi \rangle |^2}$ which is also confusing as the act of measurement affects what is being postselected for. More specifically, $|\langle \chi |\psi\rangle|^2 = \sum_{i,j} \langle \psi | P_i| \chi \rangle \langle \chi | P_j | \psi \rangle \neq \sum_i |\langle \chi |P_i|\psi \rangle |^2$ in general.


title: Bohr model with all Quantum numbers for hydrogen atom

text: bohr model: $$E_n=-\frac {\mathcal R}{n^2(1+\frac {m_e}{m_p})}$$   * can we developed bohr model with all Quantum Numbers of the Hydrogen Atom? $R(r)$ Principal quantum number $$n=1,2,3,4,5,...,n$$ P(θ) Orbital quantum number $$\ell=n-1$$ F(φ) Magnetic quantum number $$m_{\ell}=-\ell,\ell+1,0,\ell,\ell-1...$$ Spin quantum number $$m_s=+\frac {1}{2},-\frac {1}{2}$$ Q numbers


title: Apart from Alfvenic turbulence, what is the most important unsolved problems in plasma physics?

text: **Apart fromAlfvénic turbulence**, what is the most important unsolved problems in plasma physics? Is there a review article describing some important unsolved problems in plasma physics, I repeat, apart from turbulence, which is an unsolved matter in all areas of physics.


title: How does the boiling time depend on the amount of water?

text: For example we have 1 electric kettle with 1 litter of water and we have another (the same type) electric kettle with 2 litters of water. How much time each kettle will need to boil and why? **How does the boiling time in electric kettle depend on the amount of water?**


title: Poincare recurrence and the multiverse

text: In this paper Susskind claims that a stable de Sitter universe is problematic (among other things) due to the existence of Poincare recurrence, which happen because of finite entropy. I disagree that this is a problem for reasons similar to those given here. In any case, he also proposes a variant of eternal inflation driven by false vacuum decays. These decays, as far as I know, are driven by Coleman - de Luccia instantons and are probabilistic in nature, that is to say there is always some probability of instanton creation via quantum fluctuation. My questions are:   1. Since false vacuum decay is probabilistic is it possible that in this bubble cosmology setup there are casual patches which live beyond their Poincare recurrence time?    2. Is there any possibility in string theory that our Universe, assuming it has finite entropy, will eventually be stabilized for an infinite amount of time or is this question settled beyond all reasonable doubt?  Thanks!


title: Why are the quarks so named?

text: Quarks have a variety of names (or flavours):   * Up   * Down   * Strange   * Charm   * Bottom or Beauty   * Top or Truth Why do they have such odd names?


title: Why do space crafts take off with rockets instead of just ascending like an aircraft until they reach space?

text: I guess it's not a very educated question, but I never quite understood why spacecrafts have to shoot up and can't just reach space by simply continuing an upwards ascent like an airplane.


title: Velocity and acceleration with displacement

text: Find the velocity and the acceleration for a moving object with displacement $= te^{-t}$. The $e$ is the exponential function.


title: Is the mathematical truth 1+1=2 analogous to the conservation of energy?

text: They seem to express the same concept in different fields.


title: Gravitational sphere

text: I was reading this article that mentions a blackhole as having `a gravitational sphere of 4,000 light-years`. I'd not heard of the term (gravitational sphere) before so looked it up, and it looks like a simple definition is the same as sphere of influence and according to Wikipedia is > A sphere of influence (SOI) in astrodynamics and astronomy is the spherical > region (actually is an oblate sphere) around a celestial body where the > primary gravitational influence on an orbiting object is that body. From the above, I take it to mean that an object could be tiny, but providing there are no objects anywhere near with another object with a bigger gravitational pull near them, then its sphere could be larger than a more massive object. i.e. I can't directly look at a gravitational sphere of 4000 light-years and think "that must be a huge object". Is my understanding correct?


In Holstein-Primakoff and Dyson-Maleev representation, spin operators are represented by bosonic operators. Roughly speaking, a state with $S^z=S-m$ corresponds to a state containing $m$ bosons. In the Dyson-Maleev representation, $(S^+)^\dagger\neq S^-$, so we have a non-unitary transformation. Are eigenvalues and matrix elements invariant under such a transformation? In matrix form, what exactly are the two transformations that will give rise to the two representations, say for spin $S=3/2$?


title: Temperature change as function of solar elevation, current temperature, and cloud cover?

text: If it's 80F with clear skies, and the sun is at a 54 degree angle, what is the rate of temperature increase or decrease? More generally, where can I find a formula or approximation that takes these three inputs:   * Current temperature (degrees F)    * Current solar elevation (degrees of arc)    * Current cloud cover (as fraction)  and returns the rate at which the temperature is increasing or decreasing?


title: how do we know that the base of entire universe is the proton (hydrogen) and not the antiproton?

text: It may be that the base of a part of the world is anti-proton, We've always been on the planet Earth and the Milky Way. **how do we know that the base of entire universe is proton (hydrogen atom)?**


title: Problem with Big Rip Theory

text: I have heard of the "Big Rip" as one theory for the eventual end of the universe. If the speed at which the universe is expanding, and all the matter inside it is moving away from all other matter at an increasing rate, would the matter eventually have to move at the speed of light? Or would it have to slow down?


title: Second law of thermodynamics and a bunch of magnets

text: Say I put a bunch of powerful square magnets on a nearly frictionless table in a disordered fashion. The second law of thermodynamics states that the system shall spontaneously get more disordered, yet the magnets will attract each other and form a chain (typically), thereby increasing the order of the system-and, seemingly, decreasing its entropy. It would seem to me that the system is closed and the lattice is indeed the equilibrium state. Therefore, I suspect that by attracting each other, the magnets increase their own entropy by a larger amount than the decrease in entropy caused by the lattice formation. Is it true? If yes, what are the thermodynamics of magnets responsible for this? Is there a microscopic explanation? Thanks!


title: electric dipole momentum calculation

text: I'm studying the linear electric susceptibility, using Schroedinger equation and perturbation theory of the interaction potential $$V=-\mu \cdot E$$ and the book arrive to an expression where $$\mu_{mn}=\langle \psi_m\mid\hat\mu\mid\psi_n\rangle$$ is a "parameter" of the problem. My question is: which theory describes and calculates $\hat\mu$?


title: Particle in a box: simultaneously bounded momentum and position

text: While writing an answer to this question, I started doubting about the interpretation of the uncertainty principle for the particle in a box. In the 1-dimensional particle in a box problem, explicit solutions for the energy eigenstates exist, and are essentially of the form $\sin nx$ outside the support of the potential, and 0 where the potential is infinite. These somehow feel as if they should have definite momentum (up to direction), since they are free where the potential is 0, so that their energy is kinetic energy, and they cannot be in the region where they are not free. On the other hand, position is strictly restricted to some interval. Consequently, any state must have bounded support in positional representation, and one would say there can be no states with bounded support in momentum space (by Paley-Wiener if you want). Indeed, the energy eigenstates involve an infinite number of momentum eigenstates (as they are zero outside an interval). What is the way out? I think it must be that part of the energy in the energy eigenstates is potential energy. To see that, we can think of the idealized infinite potential as a limit of some sequence of finite potentials, which also is necessary in order to be able to give a meaning to the second derivative appearing in the Hamiltonian. This second derivative in the boundaries of the well tends to a multiple of a Dirac mass which has to be compensated in a very essential way by the term $V(x)\psi(x)$ in the Schrӧdinger equation $\psi''(x) + V(x)\psi(x) = \psi(x)$ (up to constants), so that in any approximation to the infinite potential will have a non-negligible contribution from the potential energy. Is this a correct interpretation?


title: Space expansion effect on wavelengths across two points in space

text: Is the expansion of space taken into consideration when calculating light or any (Radio to Gamma) wave length distance and speed? I know C is a constant, but my concern is if "space expansion" is somehow altering the speed of light or any other wave length relative between two points.


title: Lag model (using Tustin's first order algorithm)

text: I have an environment control system where I need to control and lag a temperature to 200C value.I am trying to perform dampening of the temperature in such a way that the fluctuation doesn't occur beyond +/- 10C range. The formula I have got is: T_LAGGED = T_LAGGED_old + 1st_ORDER_CONSTANT*(T_IN - T_LAGGED_old) where: T_LAGGED_old is the state value of the output T_IN is the new value 1st_ORDER_CONSTANT is a coefficient between 0 - 1 (to tune the dampening). I tried to run some simulation on MATLAB, but didn't get anything that I can say good. Does anyone have any suggestion? btw....my question title said Tustin's first order algorithm, but my formula clearly is not using it. I was researching into it, but got lost into z-transforms and other mathematical diabolics!!!


title: Time derivative of angular velocity in rotating reference frame

text: I am going through a section in a textbook regarding the Newton Euler equations for a system of rigid bodies (robotics text). There is a particular line in the derivation I don't understand, I've attached the image to make it clear: ![enter image description here](http://i.stack.imgur.com/scZIL.png) I think the derivative of the second term on the right-hand side of 3.28 is using the product rule to get to 3.32, but I don't understand where the cross- product comes from. Could someone explain this particular part of the derivation? Thanks.