title: Does the extended probability ensemble interpretation of quantum mechanics make any sense?

text: Gell-Mann and Hartle came up with the extended probability ensemble interpretation over here. Basically, they extended probability theory to include real numbers which may be negative or greater than 1. This necessitates an unconventional interpretation of probabilities, and for that, they used the "no Dutch book" interpretation of probability theory. For the "no Dutch book" interpretation to even make any sense, they have to introduce cybernetic agents, which they call Information Gathering and Utilizing Systems (IGUS). These agents can make bets, and a Dutch book against them is a collection of bets made with the agent such that individually, the agent would prefer to make the bet, but collectively, the agent will lose a fixed amount _no matter what the outcome of the bet is_. The condition that no Dutch book can be made against an agent is equivalent to the agent's belief system satisfying the axioms of classical probability theory. An agent with negative probabilities or a probability greater than one is susceptible to Dutch books. Only bets on outcomes which can be recorded can be settled, but such outcomes aren't susceptible to Dutch books, or so they claim. Otherwise, don't bet. This already brings up a whole host of issues. Do the bets really have to happen, or is it enough to merely imagine them? Or is it enough that the agent is prepared to bet should the need arise? Or does the bet happen at the meta level? Is the agent free to choose whether or not to bet? Besides, an agent which always loses isn't necessarily an inconsistent agent, merely one which fails to satisfies its goals. An agent can have a belief system not susceptible to Dutch books but is still lousy anyway. Another more knowledgeable agent can exploit their better knowledge to offer a series of bets, which while not guaranteeing a profit all the time, is likely to bring a profit most of the time, and only a loss rarely (whatever "most of the time" and "rarely" really mean). The authors state that the preferred basis is the basis of the Feynman path integral, but what about S-dualities? Even without S-dualities, a quantum field theory can be described equivalently either as a path integral over field configurations, or a path integral over Feynman diagrams with edges and vertices. Which basis is preferred? The fine-grained probability distribution can have negative probabilities, but there are coarse-grainings with only non-negative probabilities, and at least one such coarse-graining always exists; the coarse-graining with no resolution. A maximal coarse-graining is one associated with non-negative marginal probabilities for which any extension of it will contain negative probabilities. Such coarse-grainings are referred to as realms. Unfortunately, mutually incompatible realms are the norm, and not the exception. No problem, they write. There "really" is a "real" fine-grained history, and whichever realm we choose, the "real" history is the one containing the "real" fine-grained history, which is _unobservable_. We may choose incompatible realms if we so wish, and whichever one we choose, there is a corresponding "real" history. But what is the probability distribution for the "real" fine- grained history? It can be **negative** or greater than 1! How can something with _negative_ probability happen? So just how real is it anyway? As they so clearly pointed out, the past history is unobservable. Only present records are observable. But there's always the possibility that the present record is misleadingly deceptive about the past history, assuming an actual past history even exists. When should we choose to measure the records? Now? When is "now"? Why isn't now one second ago or a year from now? The records are only approximately recorded and approximately decoherent anyway. So, we can in principle make a Dutch book with exponentially small payoff against such agents. Realms which are "typical" are preferred over realms which are not. Typicality means the log of the coarse-grained probability for the "real" coarse-grained history is much less than the Shannon entropy. But why is typicality preferred?


title: Should a Faraday cage block a radio's signal?

text: Today, I tried creating a very basic Faraday cage by surrounding a radio with two baking trays made out of iron. It didn't seem to affect the radio's signal (AM was being used, not FM). In theory, should what I used block the radio's signal? I can't remember how thick the baking trays were. There was some gaps totalling a few square centimetres, because the two baking trays were not identical. I didn't attempt to "Ground" the baking trays.


title: Why is supercritical fluid not considered a separate state of matter?

text: As given on this link, supercritical fluids are viewed more as a continuum which has both liquid and gas properties. This continuum is obtained when a gas is brought to a pressure and a temperature higher than its critical values. The intermolecular distances of a pure supercritical fluid are in between that of a liquid and gas. With so many qualitative differences between a supercritical fluid and a gas and a liquid. Why is it not considered a separate state of matter?


title: Is there some special cutoff density after which spacetime "collapses" and forms a black hole?

text: With crude calculations following densities can be approximated: Given that radius of proton is $1.75×10^{−15} m$ and it's mass is $1.67 × 10^{-27}kg$, this gives density of proton to be $\dfrac {1.67 × 10^{-27}kg} {\frac{4}{3}(1.75×10^{−15} m)^3}=\dfrac {3}{4} \dfrac{1.67 × 10^{-27}}{5.36×10^{−45}} \dfrac{kg}{m^3}=2.34 \times 10^{15} \dfrac{kg}{m^3}$ Density of the heaviest naturally occurring solid $\mathrm U^{238}$: 1 cubic meter of Uranium is about $2 \times 10^4 kg$, and since there are 238 protons+neutrons in Uranium, this gives the density $8 \times 10^{-3} \times 10^4 \dfrac{kg}{m^3}=8\times10 \dfrac{kg}{m^3}$ This means the protons are dispersed by a factor of $2.92\times10^{13}$, in other words there are $2.92\times10^{13}$ empty space units to each unit of space filled with proton. Density of water $=\frac{1}{20}\times10 \dfrac{kg}{m^3}=5\times10^{-1}\dfrac{kg}{m^3}$ The density in the core of neutron star is $8×10^{17} kg/m^3$, and the density of a black hole is supposedly infinite according to Wikipedia, but then again before transitioning to a black hole there must have been some finite mass distributed over a non zero volume of space therefore having a finite density. So far on logarithmic scale (base 10) followings look obvious for $\operatorname {log}_{10}(density \dfrac {kg}{m^3}) = \operatorname {log}_{10} \dfrac{kg}{m^3} + \operatorname {log}_{10}density$ Let $ d =\operatorname {log}_{10}density,\quad \operatorname {log}_{10} \dfrac{kg}{m^3}= \text{what is one to make of this}?$ Then following crude observations can be made: $-1\leq\mathcal O(d)\leq1$: Order of density of life as we know it. $\mathcal O(d)\approx 15$: Order of density of matter packed space $\mathcal O(d)\approx 17$:Order of density at the core of a Neutron star $\mathcal O(d)\geq x$:Order of density of black holes, (collapse of space to contain matter?) what is $x$? My question is: does these calculations make sense and is there anything more to the order of densities than these naïve observations?


title: Bending of light - photon's inertia instead of mass

text: Using classical mechanics, the formula for gravitational attraction is $$F = G\frac{m_1m_2}{r^2}.$$ This formula does not work for photons, and we need to use Einstein's theory of gravity to account for that, as the photon is massless. What if, instead of using the mass of the photon, we rather used the inertia of it? The momentum of a photon is $$p=\frac{h}{\lambda}.$$ Thus, using that, we can calculate its supposed 'mass' (inertia) as momentum is also equal to mass times velocity. So 'mass' of a photon is $$m=\frac{p}{v}=\frac{h}{\lambda c}.$$ If we use this mass as the mass of a photon, can we use Newton's equation for gravitational attraction?


title: Simple Parallel Electric Circuit

text: Ammeter (A1) and voltmeter (V) in series have parallel connection to another ammeter (A2). Currents in A1 and A2 are respectively 0.2 and 1.7 amp. Voltmeter's voltage is 6 volts. ![enter image description here](http://i.stack.imgur.com/w9oZl.png) How should I find resistances of all elements?


Could a ship equipped with Alcubierre drive theoretically escape from a black hole? Also, could it reach parts of the universe that are receding faster than the speed of light from us?


title: Does the Opera result hint to a discrete spacetime?

text: Could the Opera result be interpreted as some kind of hint to a discrete spacetime that is only seen for high enough energy neutrinos? I think I've read (some time ago) something like this in a popular article where among other things tests of quantum gravity theories, that assume a discrete spacetime, are explained. Looking around in blogs and other places in the web, I notice that this is disussed seldom or not at all... ``


title: Do asymptotically similar potentials yield similar energy levels asymptotically?

text: Let there be given two Hamiltonians $$H_1~=~ p^{2}+f(x) \qquad \mathrm{and} \qquad H_2~=~ p^{2}+g(x). $$ Let's suppose that for big big $x$, the potentials are asymptotically similar in the sense that the quotient $$ \frac{f(x)}{g(x)}~\to~1 \qquad \mathrm{for}\qquad x \to \infty.$$ Then if we quantize these Hamiltonians, $$ \hat{H}_1y(x)~=~E_{n}y(x) \qquad \mathrm{and} \qquad \hat{H}_2y(x)~=~B_{n}y(x), $$ since the potentials $ f(x)$ and $g(x)$ are asymptotically close to each other, does it mean that for big quantum number $n$ $$ \frac{E_{n}}{B_{n}}~\to~1 \qquad \mathrm{for}\qquad n \to \infty,$$ at least in one dimension?


title: Does the lack of modular nuclearity in string theory mean anything?

text: Nuclearity is a postulate in algebraic quantum field theory (AQFT). Basically, it says thermal states at any temperature always have a thermodynamic limit with extensive quantities. This is violated by string theory at the Hagedorn temperature. Does this mean anything?


title: Are human eyes the best possible camera?

text: I am not a physiologist, but whatever little I know about human eyes always makes me wonder by its details of optical subtleties. A question always comes to mind. Are human eyes the best possible optical instrument evolved by natural selection? Is there any possible room for further major improvement as per the laws of physics in principle? Can there be any camera prepared by human beings which can be superior to human eyes?


title: Can a disk like object (like UFO's) really fly?

text: UFOs as shown in movies are shown as disk like objects with raised centers that emit some sort of light from bottom. Can such a thing fly? My very limited knowledge in physics tell me that a disk like object may not be able to maneuver unless it has thrusters on sides and simple light can not be enough to make any object go up in the air. Is it possible?


title: Why does ice melting not change the water level in a container?

text: I have read the explanation for this in several textbooks, but I am struggling to understand it via Archimedes' principle. If someone can clarify with a diagram or something so I can understand or a clear equation explanation that would be great.


title: Trajectory of falling object, with and without initial velocity

text: If an object is dropped from a roof with no initial velocity and wind is blowing along the side of the building exerting a constant force on the object, then its trajectory will be a straight line. But if the object has an initial velocity downwards, then its trajectory will be a parabola instead (according to my book). I don't understand why! Why does it not just become a steeper straight line? It will still have the same vertical and horizontal accelerations right?


title: Magnetic Dipole: How to plug into Maxwell's equations?

text: I read Magnetic Dipole point source in computational electro-magnetic literatures where it is used as exciting source. But I do not know how to plug this source into Maxwell's equations. Does it go into the free electric current density $J_f$? Does the point dipole gives a Dirac function somewhere in Maxwell's equation?


title: Head losses on parallel pipes

text: I've been studying Fluid Mechanics recently and on the book _Fundamentals of Fluid Mechanics 7e, Munson et al._ on page 456, the book states > Another common multiple pipe system contains pipes in parallel ... However, > by writing the energy equation between points A and B it is found that head > losses experienced by any fluid particle traveling between these two > locations is the same, independent of the path taken. Can someone please clarify this for me. How is it possible that two pipes different in diameter have the same losses? I thought, $$h_L = f\frac{l}{d_i}\frac{v^2}{2g}$$ Edit 1: I'm sorry that I wasn't clear enough. Here's a diagram I sketched on the problem at hand. As you can see the pipes are parallel, and the flow is unidirectional, that is from A to B. ![enter image description here](http://i.stack.imgur.com/DEAgd.png) However they all have different diameters, but are equal in length. Note: Regarding the name and nomenclature. These aren't heat losses, they're actually called head losses. The equation is called the major head loss during a viscous flow in a pipe. According to this equation, the losses experienced by the fluid are proportional to the velocity squared and to a roughness factor f. The rest is also self-explanatory I believe. What I can't seem to grasp is how this is equal to the three pipes in this configuration.


title: Chain of balls on an inclined plane

text: Suppose we have some inclined plane, and there is some chain of balls of length $l$ and mass $m$ lying on it. No friction at all in the system. 1) What is $x_0$ (the vertical hanging part of the chain) needed for the chain to be in equilibrium? _Answer_ : $l/3$ 2) If we push the chain a little bit to the right, what is the acceleration of the chain, at instant when the vertical part of the chain is $x$ long ($x > x_0$)? _Answer_ : $a(x)=\frac{g}{l}(\frac{3}{2}x-\frac{l}{2})$ 3) What is the velocity of the chain at instant when all of it is vertical (e.g. all the left part on the inclined plane "became vertical")? ( _no answer_ ) ![enter image description here](http://i.stack.imgur.com/jydqH.png) 1) I do not understand, why the component of the weight of the left part should be equal to the weight of the right hanging part. Their vectors are not along the same line, so why should this condition be necessary for equilibrium? Also, the left part is being pulled by the right, so there should be another force along the incline. 2) Based on the first question, this one should be: $(1-\frac{x_0}{l})mg \sin 30^{\circ}-\frac{x_0}{l}mg=ma$ However, this leads to a wrong $a$, according to the answer. 3) Based on the book's answer of 2), is this right? From Torricelli's equation: $v^2=v_0^2+2a \Delta x$ $v(x)=\sqrt{v_0^2+2 \int_{l/3}^{x} a(x) dx}$ Therefore: $v(l)=\sqrt{\frac{20}{3}l}$


title: Why does a superfluid climb up the wall of container?

text: This has been asked  but I couldn't find a good answer why does super-fluid climb up the walls of container? What if the walls were too high? What forces are involved? ![enter image description here](http://i.stack.imgur.com/rgYNn.jpg)


title: Method of determining peculiar speed of the galaxy which moves on celestial sphere and emits the light

text: This question is the continuation of this one. I came up with solution, but I'm not sure that it is correct. Can someone check it? Let's introduce transverse (to the observer) proper speed $v_{\perp}$ of the galaxy. The galaxy travels distance $\Delta D$ in a time $\Delta t_{0}$: $$ \Delta D = v_{\perp}\Delta t = v_{\perp}\Delta t_{0}\frac{a(t)}{a_{0}}, $$ where $dt_{0}$ refers to the time interval of observation of the galaxy, $dt$ refers to the time interval of light emission. So $$ d\theta = \frac{dD}{a(t) r(t)} = \frac{v_{\perp}dt_{0}}{a_{0}r(t)}, $$ where $r(t)$ is the galaxy position, and finally $$ \frac{d \theta }{dt_{0}} = \frac{v_{\perp}}{a_{0}r(t)}. $$ Is this method correct? Also, can I identify the left side of this equation with the observing angular velocity? And how to find $r(t)$? To consider the FLRW interval for the light? $$ ds^2 = dt^2 - a(t)^2\frac{dr^2}{1 - kr^2} = 0 \Rightarrow f(r) = \int \limits_{0}^{z} \frac{dz}{H(z)} \Rightarrow r = f^{-1}\left[ \int \limits_{0}^{z} \frac{dz}{H(z)}\right]? $$


title: Maximum angular velocity to stop in one rotation with a known torque

text: I have an object I can rotate with a given torque. I would like to stop applying torque once I've reached a defined maximum rotational speed. The maximum rotational speed should be defined so that applying maximum torque will stop the rotation of the object within one rotation. If I know my torque and moment of inertia, how can I find the maximum rotational velocity to allow me to stop the object in one rotation? Time is whatever is needed. I've tried finding the angular acceleration required to stop the object, but that leaves me with the time variable. Of the equations I've tried, I'm left with a time variable as well as the maximum angular velocity.


title: Derivation of a gamma matrices identity

text: While studying Srednicki's book on quantum field theory, I encountered a particular identity that is of interest to me (equation 36.40): $$\mathcal{C}^{-1}\gamma^\mu\mathcal{C}=-(\gamma^\mu)^T$$ where $\mathcal{C}$ is the charge conjugation operator, and $\gamma^\mu$ the well-known gamma matrices. This identity is shown to be true using the chiral/Weyl representation. However, I would like to be able to show it to be true without choosing a representation. Is something like this possible? If yes, could someone outline the procedure for me? Any help would be much appreciated.


title: What is anti-time?

text: I've been trying to wrap my mind around the concept of anti-time and wondered what it is. If there is anti-matter and anti-gravity, does time have its negative? Your help is appreciated.


title: Where is the potential energy due to internal interactions in total energy?

text: In thermodynamics the total energy of a system consists of kinetic energy of motion of the system as a whole, potential energy of the system as a whole due to _external_ force fields, and energy contained within the system known as internal energy, $$ E = E_{\mathrm{k}} + E_{\mathrm{p}} + U \, . \tag{1} $$ That is the way it is said in many books, lecture notes and online source. For instance, the first paragraph of Wikipedia article on internal energy says: > In thermodynamics, the _internal energy_ is one of the two cardinal state > functions of the state variables of a thermodynamic system. It _refers to > energy contained within the system, and excludes kinetic energy of motion of > the system as a whole, and the potential energy of the system as a whole due > to external force fields_. It keeps account of the gains and losses of > energy of the system. Well, if a system is just one macroscopic body, I have no problems with these definition. But what if we have more than one body in our system? Consider, for instance, an isolated system composed of two bodies of mass $m_{1}$ and $m_{2}$. According to classical mechanics, between two masses there always always exists a gravitational force $$ F = \frac{G m_{1} m_{2}}{r_{12}^2} \, , $$ and there exist a gravitational potential energy $$ V = - \frac{G m_{1} m_{2}}{r_{12}} \, , $$ due to this interaction. Now, this potential energy $V$ is not a part of $E_{\mathrm{p}}$ in (1), since it is not due to external, but rather internal force field. Clearly, it is also not a part of $E_{\mathrm{k}}$. Where is it then? **Is it included into internal energy $U$ or it is just an additional term for the total energy that has nothing to do with internal energy $U$?** In other words, **the increase in which quantity (according to the 1st law of thermodynamics) is equal to the heat supplied to the system plus the work done on it: internal energy counted with or without this potential energy $V$ due to gravitational interaction?**


title: Why does the current increase in an LC circuit while the capacitor is being discharged?

text: From the maths governing an LC circuit (eg. $E_B=\frac{LI^2}{2}$) we can deduce, that the current through the inductor will have a maximum value, when there's no energy stored in the capacitor, or else $E_B = max \iff I=max$. But how to explain it intuitively? Suppose we have a fully charged capacitor and we connect it to a inductor. As the voltage between the capacitor's plates decreases, so should the current flowing through the circuit. Yet, we observe the opposite, as the current increases. I suppose it's due to the EMF induced in the inductor, but shouldn't it merely decrease the rate with which the current is decreasing?


title: Non-unqiue basis sets of reduced density matrix in quantum mechanics/decoherence

text: In _Why decoherence solves the measurement problem_ by Art Hobson: $|\psi \rangle _{SA} = c_1|s_1 \rangle |a_1 \rangle + c_2 |s_2\rangle |a_2 \rangle$ which is a wavefunction that describes non-local entangled state of system $S$ with measuring apparatus $A$ and reduced density matrix that describes subsystem is $\rho_S = (|s_1 \rangle |c_1|^2 \langle s_1|\,\,+\,\,|s_2 \rangle |c_2|^2 \langle s_2| )/2$ and $\rho_A = (|a_1 \rangle |c_1|^2 \langle a_1|\,\,+\,\,|a_2 \rangle |c_2|^2 \langle a_2| )/2$. Now then paper says that when $c_1 = c_2$, reduced density matrices have non- unique basis, but have unique basis when $c_1 \neq c_2$. Can anyone present the reason why this is the case when $c_1 \neq c_2$? (So I do get that $c_1 = c_2$ case.) Add: $\langle s_1 | s_2 \rangle = 0$ and $\langle a_1 | a_2 \rangle = 0$ is assumed.


title: What force counteracts friction when a block is pulled?

text: Firstly, I understand and apologize that this is more of a physics question than a math question. I noticed that when I pulled a book out from under a pack of gum, the gum stayed largely in place (it did not move with the book). This confused me, so I decided to draw a diagram of the situation, assuming that my answer would be apparent once I could represent all of the forces in play. Of course (as the book was orthogonal to the ground) gravitational force and normal force could be ignored. The only other force that I see that can be in play is the friction between the book and the gum, which should make the gum move along with the book. There must, then, be some sort of force acting opposite and with a greater magnitude than friction. Is this correct, and if so, what is that force and how can it be calculated?


title: Is "scalar electromagnetics" real science?

text: This page claims that original Maxwell's equations, when formulated by Maxwell himself in quaternion form, had some special scalar part of electromagnetic field, which somehow appeared to describe gravitation. The author says that further development of this is called "scalar electromagnetics" or, as Soviets are claimed to have called it, "energetics". While I read that page, my gut feeling tells me this is all nonsense. But am I right? I've tried googling for this term, and found some antiscientific sites, and nothing like that in any respectable sources like science journals or wikipedia. So, is this really some real science, or is it antiscientific trash? If it's for real, are there any credible sources to read more about this?


title: How do whitening toothbrushes work?

text: Certain "whitening" toothbrushes are sold and I was wondering about the mechanisms behind the tooth whitening process. I suspect this is related to the shape and arrangement of the fibres, probably somewhat similar to how a microfiber cleaning cloth works, but couldn't find any authoritative confirmation. So how does a whitening toothbrush work? I'm only interested in the physical effects - whitening toothpastes rely on their chemical properties so they're a completely different story.


title: Does a square wave "smooth out" in the air?

text: I understand that playing a square wave from speakers cannot produce a PERFECTLY sharp division between compression and rarefaction. But it's sharp enough to sound distinctly different from a sine wave. As it travels, does the wave "smoosh out" even further as it travels, changing from a square wave into something closer to a sine wave?


title: Bandwidth of telephone wire

text: Internet providers try to sell us the more and faster "fast internet" - 15Mb, 40Mb, 100Mb, and so on. But it's well known that the bandwidth the channel (in the most cases it's the telephone wire) restricted by the nature law. And this law is so fundamental as the light speed. (see, e.g., V.A.Kotetlnikov theorem). The bandwidth of a telephone wire is significantly less than providers propose us. Can someone explain what is the matter here?


title: Is there a fundamental particle that gives rise to energy?

text: I was wondering if there exist a particle analogous to the Higgs boson that gives rise to energy, I´m sorry it´s not the big question but I feel confused about how the universe works, also I have been searching and I couldn't find anything


title: Seeking a quality plain-language description of the Wigner-Eckart theorem

text: I'm a third year physics undergrad with a very cursory knowledge of quantum mechanics and the formalism involved. For instance, I understand roughly how tensors work and what it means for a tensor to be irreducible, though it would take me a lot of work to apply this knowledge to a problem/extend it past what I've already seen. As part of a project, I'm studying atomic nuclei in electric and magnetic fields. I'm trying to understand the energy of a nuclear quadrupole's interaction with an electric field gradient. The equation for this is $E_Q = \sum_{\alpha,\beta} V_{\alpha\beta} Q_{\alpha\beta}$ where $\alpha$ and $\beta$ each iterate over $x, y, z$. $Q$, the electric quadrupole moment, is given by $Q_{\alpha\beta} = [\frac{3}{2}(I_{\alpha} I_{\beta} + I_{\beta} I_{\alpha}) - \delta_{\alpha\beta}I^2] * constant$ (taken from this powerpoint.) An electric quadrupole moment should have nothing to do with nuclear spin... or so I thought, until I ran across the idea of "spin coordinates" and the Wigner-Eckart theorem. This is roughly all I know about the theorem -- that it exists and that it can somehow convert between Cartesian and spin coordinates in quantum systems -- and I'd like to understand it better. THE SHORT VERSION: I do not need a detailed mathematical understanding of the Wigner-Eckart theorem, but I'm very curious as to the general idea of it. Can anyone think of a plain-English (or rather, minimal-math) explanation of the theorem that would make sense to a beginning quantum physics student?


title: How Long does it take for a roller coaster cart to reach point $x_1$?

text: Assume that we have a particle with weight m and initial speed v0, that follows a roller coaster path y(x). ![Roller Coaster Path](http://i.stack.imgur.com/kyUeA.png) Assuming no energy loss to friction or air resistance, the total energy in the system is $$E0 = m g y(x0) + 0.5 m vo^2$$ then the speed at each point $x_f$ is ![enter image description here](http://i.stack.imgur.com/jMCyQ.png) So, using the energy conservation principle, we can derive the speed at each point of the curve. It gets tricky though, to try to figure out at what time the particle reaches a specific point of the curve. Turning our attention to dynamics, should help us achieve the goal. $$dS/dt = v(x)$$ Is the approach followed correct? ![enter image description here](http://i.stack.imgur.com/hz3U7.png)


title: Finding Tension in an Elastic String?

text: I know that this is a homework type question and I'm not asking a particular physics question, but I'm really desperate for help. Here's the question: ![enter image description here](http://i.stack.imgur.com/Ob5xP.png) I tried to divide the string to 2 parts with $O$ as the mid-point of $AB$. Let $AO$=$T_{1}$ and $OB$=$T_{2}$, then $T_{2}-T_{1}=m\ddot x $. I don't know what to do next. Here's the marking scheme: ![enter image description here](http://i.stack.imgur.com/qtU0o.png)


title: Stoke's Drag Constant

text: I'm trying to calculate Stoke's drag constant using the equation found here. The system I wish to calculate it for is a mass oscillating vertically on a spring through air. The temperature is 25 degrees celsius. The area of the base of the mass is 4.9x10^-4 square metres. I'm not sure how to find the 'fluid viscosity' in the linked equation, or what 'Stoke's radius' is.


title: Ground State Energy in Euclidean Spacetime

text: Calculating the transition amplitude in Euclidean spacetime is useful because from it we can extract the ground state energy and ground state wave-functions values. For example, let's assume we are calculating: $\left<x=b\left.\right|e^{-\hat{H}T}\left.\right|x=a\right>$. Assume we can calculate this quantity via the path-integral formalism and we have found it to be equal to $f(T)$.   * We insert a complete set of energy eigenstates into the transition amplitude: $$ \left<x=b\left.\right|e^{-\hat{H}T}\left.\right|x=a\right> = \left<x=b\left.\right|e^{-\hat{H}T}\sum_n\left|n\right>\left<n\right|\left.\right|x=a\right> = \sum_n e^{-E_nT}\left<x=b\right|\left.n\right>\left<n\right|\left.x=a\right> = f\left(T\right) $$ The usual trick now is to take the limit $T\to\infty$ of the above equation and say that the most important term is the lowest energy eigenvalue, and so: $$ \lim_{T\to\infty} \sum_n e^{-E_nT}\left<x=b\right|\left.n\right>\left<n\right|\left.x=a\right> \stackrel{?}{=} \lim_{T\to\infty} e^{-E_0T}\left<x=b\right|\left.0\right>\left<0\right|\left.x=a\right> = \lim_{T\to\infty} f\left(T\right)$$ $f\left(T\right)$ usually is of the form $A\times e^{- \varepsilon T} $ and so we say $E_0 = \varepsilon$. I feel funny about this procedure because taking this limit, if $E_0$ is positive then this term should go to zero _as well_. In this sense, is the equality with the question mark merely an estimate, and not a true equality? If so $E_0$, which we obtain in this way, is just an approximation? Why is it then that for the SHO we get the exact result in this way $\frac{\omega}{2}$? Even worse, when $f\left(T\right)$ is of the form $f\left(T\right)=A\times e^{- \varepsilon_0 T}+B\times e^{- \varepsilon_1 T}$, then I have seen (if I understand correctly) that the conclusion is then that $E_0=\varepsilon_0$ and $E_1=\varepsilon_1$ (i.e. the 2nd lowest energy eigenvalue is extracted _as well_ ) (for example, see Coleman "Aspects of Symmetry" page 274 equation 2.31). Can anyone shed some light at the mathematical background of this "trick"? Is it not the same limit as the epsilon delta limit? Can I extract the whole spectrum in this way, just from knowledge of $f\left(T\right)$? If I can calculate the path-integral for various different values (not just $x=a$ and $x=b$) then could I, in principle, extract in this way also the whole set of energy eigenstates at all points? Is the information obtained in this way always an approximation? How can I find out the margin of error on this approximation then?


title: Does wind speed things up or accelerate things?

text: This question may seem odd, but I can't think of anything better. So I'll go straight to the point. Let's say there's a projectile in air going east, shot at a certain angle, with a certain speed. Then there's the wind blowing, for let's say 5 meters per second in the same direction as the projectile. So how will the wind affect the projectile? Will it accelerate for 5 meters per second every second it lasts in the air, or will the speed just increase by 5 meters per second all through out? And what if the wind goes exactly the opposite direction? Will it have a negative effect? Should I also take into consideration the drag the object makes, the mass, the terminal velocity, or if there are other things I've missed? I don't mind if you give formulas. It would also help. But I just wanted to know, in simple terms because I'm not really that inclined with terms used in physics, the effects of a blowing wind to a projectile motion. Thanks in advance and sorry if I made some errors or misunderstanding with this post or if I used the wrong tags. Feel free to edit it. Thanks again,   Vincent :)


title: Which cosmologies support Eternal Life?

text: Which cosmologies consistent with physics as we currently know it is consistent with Eternal Life lasting forever starting from here on Earth while preserving the memories of human life? With computers and robots colonizing the universe and growing without bound? Tipler had suggested an Omega Point associated with a big crunch in a closed universe, but unfortunately, scales below the Planck length do not exist. Dyson had performed an analysis in the article "TIME WITHOUT END: PHYSICS AND BIOLOGY IN AN OPEN UNIVERSE".


title: Why Zeta regularization is not valid for multiple-loops?

text: Why zeta regularization only valid at one-loop? I mean there are zeta regularizations for multiple zeta sums. Also we could use the zeta regularization iteratively on each variable to obtain finite corrections to multiple loop diagrams.


title: Do radio waves interact with electrical wiring?

text: AFAIK radio waves can be influenced by magnetic fields (when not traveling through a vacuum). Electrical wires create a magnetic field perpendicular to the length of the wire, as a function of the current running through it. In air, water, or other medium, would radio waves be influenced by this magnetic field (or conversely by the electric field)? Say for this purpose I have a radar which scan through walls, and I am interested in knowing wether the wires in the wall are currently "on" or "off". Would this be possible? How weak, or strong magnetic field (conversley electric field) is needed to influence radio waves (when not in a vacuum)? Or have I completely misunderstood something here :) ? Thanks alot!


title: "Dictionnary" between QFTs in D and D-1 dimensions?

text: Considering Einstein equations, suppose, for instance, that the RHS, the stress-energy tensor, is uniquely due to the electromagnetic field. Now, if we imagine a quantized version of these Einstein equations, we have a quantum field theory in $D$ dimensions (here the quantum electromagnetic field) as "source" of a "quantum gravity" theory in $D$ dimensions, so we may consider these equations as a kind of "dictionnary" between these two theories. On an other way, there are some holographic dualities, which relates some quantum theory of gravity in a $D$ dimensional space with boundary, with some quantum field theory on the boundary ($D-1$ dimensions) So, the question is, if, "skipping gravity", it is possible or not, and how, to directly relate the QFT in $D$ dimensions (source of gravity), and the other QFT (on the boundary) in $D-1$ dimensions.


Any FLOSS Monte-Carlo package for reactor physics? Are there any Free and Open Source software packages for nuclear reactor processes simulation? Maybe, something similar to MCNP?


title: No hair theorem and black hole entropy

text: The _no hair_ theorem says that black holes rapidly converge to a state that is completely described just by their mass, spin and charge. Black hole thermodynamics says that the black hole entropy is proportional to the surface area of the event horizon. As I understand it in information theoretic terms the black hole entropy is 1 bit per planck unit of area, which should then be the amount of information required to fully describe a black hole. These two statements seem to be incompatible. It seems that the thermodynamics says that if we fix the macroscopic no hair parameters there still remain all the surface bits to be fixed. Is there any real conflict here or is somehow illusory? Is it a quantum vs classical issue? Does the entropic information not count in some sense? If not why, can 2 equal mass Schwartzchild black holes be distinguished by their "surface information"? Is it that the surface information is just not observable because the surface is considered _in_ the black hole? Or is this apparent discrepancy part of the black hole information paradox? There is a very similar question with a detailed answer here, but I believe I am actually asking something different. The question and excellent answer there focus on the objects as they fall into a black hole. I am more interested in how to think about the total information in a steady state black hole and the current status of the no hair theorem wrt black hole entropy and the information paradox.


title: How do you represent an equation with four variables?

text: As the title asks, how do you represent an equation with four variables? Is there a practical way of representing them? (I've thought of one, but I don't think I can explain it clearly. This question has got me really curious.) Additionally, is there any practical way of solving these equations?


title: Spin decomposition in general

text: I can turn-the-crank and show that $\frac{1}{2}\otimes \frac{1}{2} = 1\oplus 0$ etc, but what would be a strategy to proving the general statement for spin representations that $j\otimes s =\bigoplus_{l=|s-j|}^{|s+j|} l$.


title: What is the fundamental probabilistic interpretation of Quantum Fields?

text: In quantum mechanics, particles are described by wave functions, which describe probability amplitudes. In quantum field theory, particles are described by excitations of quantum fields. What is the analog of the quantum mechanical wave function? Is it a spectrum of field configurations (in analogy with QM wave functions' spectrum of particle observables), where each field configuration can be associated with a probability amplitude? Or is the field just essentially a superposition of infinitely many wave functions for each point along the field (as if you quantized a continuous mattress of infinitesimal coupled particles)?


title: How do we resolve a flat spacetime and the cosmological principle?

text: As I've said elsewhere, I've not had the opportunity to take a class in general relativity. Nonetheless, I understand that two major aspects of the standard cosmological model are the cosmological principle and the observation of a flat space. To get where I'm coming from, I'll try to give a brief description of my understanding of these concepts:   * cosmological principle - This principle states that there is no privileged position within the universe. In other words, wherever any observer is located, s/he will observe approximately the same thing. Obviously the specific celestial bodies observed will change, but the expansion of the universe will be judged the same and the universe will essentially appear isotropic.   * flat space - This observation, tested and largely verified by the WMAP satellite, shows that the large scale universe is not curved. My natural inclination is that these two things cannot be simultaneously true. The reason it seems this way to me is that if any observer can see roughly the same amount of the universe in any direction, and the universe is of finite size, the observable portions must overlap somewhere. If the observable portions overlap, it must be possible to continue traveling in one direction and eventually end up where you started. To me, this seems to be what curvature is. How do we reconcile these two concepts? $\dagger$ I have read some of the articles on the subject such as those on Minkowski space and multidimensional toruses. I believe I can reconcile the two concepts and imagine a higher dimensional flat torus, but the concept is still a difficult one for me and I would love some clarification.


title: Depalma Free Energy fields

text: Few years ago I read some papers about Free Energy, written by Bruce de Palma, a physicist who is said to be the inventor of the N-Machine, which is an device that works with free energy latent in the space around us. There are several informal references to him and his work. However, I tried to find papers of him several times in Scielo, Science Direct, IEEE, Physical Letters, Nature and several other scientific databases and found no references to Dr. Bruce de Palma. Personally I find quite strange that a research of such importance do not have a formal paper in an journal of big impact. Does his work make sense?


title: Is there a "difference" between photons that act as virtual particles and photons that act as the quanta of EM radiation?

text: I) I know that virtual-photons are known to be the force-carriers for the Electromagnetic force, and that they are called "virtual" because the Energy- Time-inequality version of the Heisenberg Uncertainty Principle allows for particles that are high enough energy that they are very difficult to observe (because higher energy means a smaller possible time-scale for observation). But I also know that photons are the quanta of EM radiation; i.e. they emitted from atoms at some point in space, and absorbed at other points in space as a means of transmitting radiation energy. My question is this: are the photons that act as the force carrier of the Electromagnetic force the "same" photons (i.e. the exact same particle) as the photons that act as the quanta of EM radiation? Is it just that the photons emitted as virtual particles have high enough energy that they act as a force carrier? If so, what causes charged particles to emit photons of such high energy? II) As an add-on question: I'm being introduced loosely to Electro-weak Unification and the idea that at high enough energy, the EM- and Weak forces become indistinguishable from one another (and, I believe, that the difference between the EM-force and the Weak force, at low energy, is that the W and Z bosons that mediate the Weak force are massive, and therefor act at low range, whereas photons are massless and therefor act at long ranges). And subsequently, that the Higgs Boson helps to explain what gives W and Z bosons mass. But what is the difference between the W and Z bosons and the photon that makes them interact with the Higgs mechanism, and the photon remain unaffected? I hope these questions make sense.


title: understanding why inversion cannot be accomplished by a rigid change

text: Goldstein pg 151 says "it is clear that an inversion of a right-handed system into a left-handed one cannot be accomplished by any rigid change in the coordinate axis..." I am trying to understand what he means by a rigid change... is he saying that an inversion is a discontinuous jump that is impossible for an object to achieve? why can't it? I can see clearly that the inversion (improper rotation) will be associated with a sort of jump(discontinuity) upon the mirror reflection... but I'm a little confused on the definition of a "rigid change". maybe the problem isn't the discontinuity of a mirror reflection but has to do with the change of handedness upon reflection?? goldstein also writes: " An inversion never corresponds to a physical displacement of a rigid body." i'm a little confused as to what is the problem with inverting the z-axis??? how does that change the physics? also, please do not talk about the quantum tunnelling aspect, I am having a problem understanding this classically and I don't want to get into all that ... ( let's say you take the vector r = (1,0,1) in a right handed cartesian coordinate system, then you rotate it 180 degrees you get the vector r' = (-1,0,1) in the new coordinate system, now if you "invert" the z-axis what is the problem with that in terms of "rigid change". why is that not a rigid change????) as a further note in the example I am working with I think it's important to keep the transformations passive ( rotate the coordinate system 180 degrees counterclockwise and then do the inversion).


title: Synthesizing elements (Nuclear Physics/Alchemy?)

text: Based on my limited knowledge of nuclear physics, it seems that one day it may/will be possible to synthesize whatever elements we may need, given enough energy. Is this accurate? Is there a table that lists the most efficient ways to create certain elements from more abundant ones via fusion or fission? I daresay this has rather large implications for precious metals such as gold/silver which are used as stores of wealth, provided the energy requirements are not exorbitant.


title: Why same formula describing Doppler effect in the case of light in different situations?

text: I made comparison between Doppler effect in light and sound and one interesting thing that I saw was that in the case of sound there are different formulas to find the apparent frequency in different situation (like observer moving,source moving,both moving etc) due to Doppler effect but in the case of light there is only one formula necessary to describe these situations.Why is it so? My thoughts:I thinks it's a consequence of constancy of light speed in any reference frame.


title: Heat diffusion: evanescent waves?

text: It has been recently pointed out to me that the solution of the heat equation in a semi-infinite material with an oscillating boundary condition at the surface is **not an evanescent wave**. The argument was that in the solution to the equation (which is a temperature field that oscillates in an exponentially decaying envelope), the oscillating part is a **propagating wave**. Do you agree with this argument? Is the solution an evanescent wave or not? To make things clear, I am talking about waves of this form: $T(z,t) = T_0 + A \exp(-z/\delta) \cos (\omega t - z/\delta)$ I am myself a bit concerned about the argument since Wikipedia simply states: > An evanescent wave is a near-field wave with an intensity that exhibits > exponential decay without absorption as a function of the distance from the > boundary at which the wave was formed. Also, another definition I found is that of a plane wave which amplitude decays exponentially with the distance to the source. From both definitions, it seems to me that the solution to the heat problem described above is an evanescent wave. While investigating the question, I found that it is widely accepted that the two following examples are evanescent waves:   * The field behind an interface in the case of a plane light wave hitting the interface in the normal direction in conditions of total reflection. In that case, the field is a **standing wave** in an exponentially decaying envelope.   * Same as above, but with the light wave hitting the interface with an incidence other than normal. Here, the evanescent field has a **propagating part parallel to the interface**. However, I did not find an example that has a **propagating part in the direction normal to the interface** and that is clearly called an evanescent wave.


title: How long do reflections take?

text: How long does it take for a photon to be reflected? Starting with the photon being absorbed by some atom to the point it's reemitted? And what's the same point with pressure waves, like sound?


title: How to bend 3d space embededd in a 4d enviornment?

text: > **Possible Duplicate:**   >  Calculating position in space assuming general relativity I recently started to program a 4 dimensional visualization program. I have the 4 dimension space perspectively projected in the 3d space. Now I describe 3d sphere inside this space. I want to describe the movement of those 3d spheres. What I thought it will be cool is to apply the general relativity theory to it. As far as I know from the general relativity theory, is that masses bends the space around it. What I think it means: let's imagine a 2d plane. if I put a mass on this 2d plane, the plane would be actually pinched in the 3d space. Parctically what I have to do is to find a function that describe this pinch, in function of the mass. like a Gauss distribution under the mass. Now this transformation will be applied to the moving objects, which I think would bend the trajectory of the objet to a curve. What I want to do is to apply this to the 3d space: if you put a mass in the 3d space it will cause a pinch in the 4th dimension. So what I want is to find the transformation function which describe this pinch. I think that what Zaslavsky is the actual answer, I din't got it at the beginning because I didn't tought it was actually what I was looking for but anyway: $$\frac{\mathrm{d}^2x^\lambda}{\mathrm{d}t^2} + \Gamma^{\lambda}_{\mu\nu}\frac{\mathrm{d}x^\mu}{\mathrm{d}t}\frac{\mathrm{d}x^\nu}{\mathrm{d}t} = 0$$ The solution to this differential equation should give the pinch I mean, am I right? PS: found by surfing random on the internet: Lorentz transformations are just hyperbolic rotations. edit: I've edited the question, I hope, in a way is comprehensible.


title: Is quantum gravity, ignoring geometry, the theory of a fictitious force?

text: This question is motivated by this question and this one, but I will try to write it in such a way that it is not duplicate. In short, I don't understand the motivation for a "quantum theory of gravity" that predicts a particle such as the graviton, because it stands in opposition to the entire framework of general relativity. Let me explain. First, a personal comment: I am a mathematician with a general understanding of what GR is (I took an undergraduate course from Sean Carroll, which used Hartle's book because his own was not yet published). I know slightly less than the corresponding amount of QM, which I do understand at the level of "an observable is a Hermitian operator acting on a Hilbert space of which the wave function is an element"; I know nothing technical about QFT, though I believe that "a particle is a representation of the gauge group" is true. However, I do have a popular-science understanding of elementary particles (at the precise level of Asimov's _Atom_, which I read a lot in high school). Now for the framing of the question. GR in a nutshell is that that spacetime is fundamentally a 4-manifold with a metric locally isomorphic to Minkowski space and that particles are timelike geodesics in this manifold. The force of gravity only appears as such when these geodesics (i.e. curves) are parametrized in a coordinate patch, where "geodesic" and "coordinatewise unaccelerated" are different concepts; the apparent acceleration seems to reflect a force (via Newton's second law) that we experience as gravity. This phenomenon is identical to the appearance of a centrifugal force in a rotating coordinate system where none exists in a stationary one (it is identical in that this is a particular instance of it). I understand that the standard model is formulated in a _flat_ spacetime, and its use for the hypothetical graviton is to mediate the force of gravity. I also understand that quantum gravity is a (shall we say) paradigm in which the standard model is made consistent with GR, and that the hallmark of a theory of quantum gravity is that it predicts a graviton. But this seems to be barking up the wrong tree: you cannot remove the geometry from GR without changing it entirely, but you cannot consider gravity a force (and thus, have a corresponding quantum particle) without removing the geometry. It does seem from this question that I have oversimplified somewhat, however, in that some theories, which I had thought were not very mainstream, do treat gravity in an "emergent" manner rather than as an interaction. **My question:** What I want to know is: rather than pursuing a "quantum theory of gravity", why not pursue a "gravitational quantum theory"? That is: since the formulation of standard quantum physics is not background independent in that it requires a flat spacetime, it cannot be compatible with GR in _any_ complete way. At best it can be expanded to a _local_ theory of quantum gravity. Why is it that (apparently) mainstream opinion treats GR as the outlier that must be correctly _localized_ to fit the standard model, rather than as the necessary framework that supports a _globalization_ of the standard model? One in which the graviton is _not_ a particle in the global picture, but a fictitious object that appears from formulating this global theory in local coordinates? PS. I have seen this question and this one, which are obviously in the same direction I describe. They discuss the related question of whether GR can be derived from other principles, which is definitely a more consistent take on the unification problem. I suppose this means that part of my question is: why must Einstein's spacetime be replaced? Why can't the pseudo-Riemannian geometry picture be the fundamental one? PPS. I'd appreciate answers at the same level as that of the question. I don't know jargon and I'm not familiar with _any_ theoretical physics past third- year undergrad. If you want to use these things in your answer you'll have to unravel them a bit so that, at least, I know what explicit theoretical dependencies I need to follow you.


title: How does spring constant change with resistivity changes

text: I want to create a set of silicon based materials that have been doped with different materials and/or different amounts of dopants. The purpose of this is to see how the spring constant of silicon changes with the different electrical properties, specifically, with the change in resistivity (because we are all set up to measure resistivity to a highly accurate degree). Now, I know that the physical deposition of the interstitial dopants will, by themselves, change the spring constant. What I am looking for is effects beyond that, effects that are due to changes in the electron mobility as quantified via resistivity. As such, the particular material (silicon) and the various dopants are actually irrelevant to this question. They were included for context only. My true question is as follows: Are there any formulas or concepts that will explain or predict how does the spring constant of a given material change as its resistivity changes? Any papers cited and/or books (Kittel, Mermin, Dieter, etc) would be appreciated. If the only way to understand this is through the densities of the dopants vs substrate, or any other of the usual suspects, that's fine. But what I would really like is a more "magical" argument I guess: I have a material with a certain resistivity. I wave a magic wand and change its resistivity. What is the new spring constant? Hmm, I hope that's clear. Let me try one more: I am looking for an Ohm's "law" like equation that relates spring constant to resistivity with a few physical constants thrown into a constant somewhere in the equation. Does such a thing exist? Okay, well, any help is appreciated!


title: Could gravity hold electron charge together?

text: Could the gravitational force be what holds the charge of the electron together? It seems to be the only obvious possibility; what other ideas have been proposed besides side-stepping the issue and assuming a "point charge"? How would this affect the electron "self-energy" problem? The question is related to the idea of geons.


title: Ginzburg-Landau model for superconductivity

text: Could someone kindly elaborate more on the Simple Interpretation section from this Wikipedia Article? I refer to the part on the natures of $\alpha , \beta$. Why can one assume that $\alpha(T)=\alpha_0(T-T_c)$, for example?


What shape is formed by the set of all raindrops which create a rainbow to specific observer? Maybe it's easier to narrow this down and consider it this in parts: what's the set of positions from which a raindrop can refract and reflect a beam of red light in the primary rainbow? What shape does that set form? How about the inner brighter part of the rainbow? Someone asked me this when I describe why the inner part was brighter, but I'm not sure how to work this out! ![Renee Descartes' sketch of how a rainbow is formed](http://i.stack.imgur.com/dqE6J.png) One commenter suggested this sketch as an explanation, which suggests the shape is a flat plane.


title: Pull Force of an electromagnet

text: How do I calculate the pull force of a cylindrical electromagnet to Iron as a function of distance? Is there any difference betweeen magnets and electromagnets?


So I have a solid state and thermodynamic exam next week and I've been going through some of the previous exams from years gone by to prepare. I came across this question "Distinguish electron-like and hole-like orbits in reciprocal space, with reference to the Brillouin Zones of squarium by sketching an example of each type." Apologies if this seems simple, solid state physics is not a strong point. Any help at all would be great! Also, what is squarium? I can't find anything in my notes on it and I'm wondering if it is simply referring to some sort of 2D square layout on which to sketch on. Thanks :)


title: A simple electromotor?

text: I have to build a simple electromotor in the following way: I attach a permanent magnet to a battery, connect some metal supports to the terminals of the battery, and place a coil of wire on the supports, suspended above the magnet. My question is, will it still work just as well (or at all) if the wire is insulated? Thanks!


title: Kinetic energy absorbing in order to avoid damages?

text: is this possible? To absorb kinetic energy and disable inertia force? http://www.youtube.com/watch?v=KnKPbAbJI0w http://www.youtube.com/watch?v=4_5oseSVUc4


title: How complete is our understanding of general-relativistic solutions for extremal black holes?

text: Putting aside quantum mechanics (or at least putting aside the question of fermions), is our knowledge of extremal General-Relativity solutions good enough that we would be able to rule out a classical theory of spinning charged relativistic particles based on extremal black holes? I ask this in the context of my curiosity about geons and in the spirit of recognizing the difficulty of quantizing a system whose classical theory is not well understood.


title: Net work done on the body when we lift it and put it on the table is zero?

text: I'm little confused here. Work done on the body when we lift it and put it on the table is zero, because according to work energy theorem, change in kinetic energy of the body is zero. So, the net work done is zero. Fine, but now the object has $mgh$ (where $m=$mass of body; $h=$height of body) amount of potential energy stored in it. If the net work done is zero then who has increased its energy? I'm confused and unable to think it through kindly help.


title: Expected and maximum likelihood estimate positions of particle in a box

text: From Causal Entropic Forces, A. D. Wissner-Grossand C. E. Freer, Physical Review Letters Regarding a particle exhibiting brownian motion within a box... > ...In contrast, if the particle had merely diffused from its given initial > state, while its expectation position would relax towards the center of the > box, its maximum likelihood position would remain stationary. My intuition here is that for as time progresses the expected and maximum likelihood positions both tend towards the centre of the box. And for small t they are both nearer the starting point. That is, after a long period of time the particle will have been restricted from moving beyond the boxes bounds many times such that the bias it has towards the starting position is decayed - towards the centre of the box. So how is it that the maximum likelihood estimate remains stationary?


title: Quantum computing and Pauli exclusion principle?

text: Ok so I saw this video by Brian Cox where he explains how no 2 particles can have same energy level. Later I watched video "Was Brian Cox wrong?". Where they explained that he (probably on purpose) oversimplified it. And in fact it means that in fact no 2 particles can be in same quantum state. And that quantum state is defined by multiple properties. So it sort of made me think. Quantum computer relies on certain quantum properties to operate, yeah? So if in order to perform some operation, some property need to be set to different state? And if that change would force it to enter to same quantum state as some other particle in universe? What would happen then? Or another scenario if in order to maintain some state of machine, some particular particle has to stay in some particular quantum state. But at same time somewhere, some other particle tries to enter that state? Would that alter the particle in the machine, ruining it? Or am I over simplifying things too much? Sorry if this is a stupid question, I am not a physicist at all as yous may tell. It's just that video made me curious :)


title: Is glass a liquid?

text: I was told by a condensed matter physicist that glass is a liquid with a very high viscosity (it would be more precise to say that it is a supercooled liquid). The example given was that in cathedral windows the glass flows very, very slowly, so they are thicker at the bottom. I recently read this article in Scientific American, which contradicts the previous statement. Are there any serious studies about this aspect of glass? Is it only a problem of definition?


title: Protons' repulsion within a nucleus

text: Do the protons inside the nucleus repel each other by the electrostatic force? If they do, why doesn't the repulsion drive the protons apart so that the nuclei get disintegrated?


> **Possible Duplicate:**   >  Protons' repulsion within a nucleus How positively charged protons remain glued to each other while they should repel each other out of nucleus?


title: Motivation for the Deformed Nekrasov Partition Function

text: I have recently been doing research on the AGT Correspondence between the Nekrasov Instanton Partition Function and Louiville Conformal Blocks (http://arxiv.org/abs/0906.3219). When looking at the Nekrasov Partition Function one defines a deformed metric in terms of the "deformation parameters" $\epsilon_1, \epsilon_2$ which seem to define a $SO(4)$ action on a standard Euclidean Metric, breaking translational symmetry. Much of the literature on these functions seems to be in the math department, defining the functions categorically in terms of sheaves and what-not (http://arxiv.org/abs/math/0311058) and even the original paper (http://arxiv.org/abs/hep-th/0206161) approaches the subject from a cohomological perspective. Is there any obvious physical motivation for looking at partition functions in this strange deformed spacetime? Or should I view it as simply a mathematical manipulation?


title: Current between supeconducting rings

text: How to calculate the current between two superconducting rings with radius r separated by a distance d? Please note that being unfamiliar to the concept of superconducting rings, I can't approach this problem. It would also be useful if anyone tells me which special property of superconductors can be used here.


title: Conservation of energy issue with pair creation/annihilation

text: Question: what is the energy balance in this situation? (Fig A)   Two gamma rays collided and produced an electron/positron pair $(e-/e+)$. (Fig B)   1\. because all particles are accelerating electromagnetic energy (photons) were radiated and spread away.   2\. they evolved and nearby neutral/charged particles were set in motion due to the gravitational/electrostatic field of the particles.   3\. an electron $e-$ and a positron $e+$ pair got annihilated and gamma rays produced. (Fig C)   4\. Further away more neutral/charged particles were set in motion due to the propagating gravitational/electric (previously originated by the e+, e- pair). 5\. Further away more neutral/charged particles were set in motion due to … 6\. …   Further away more neutral/charged particles were set in motion .. ## Conlusion: all universe is set in motion at the expense of a bit of energy ? Questions:   Q1 - how can the e+/e- pair have the same energy content in the beginning and at end of situation B) when, admittedly, the kinetic energy of the pair can be as little as we wish?   Q2 – how to evade from situation C ? (I admit that the electromagnetic/gravitational field do propagate and cannot be set to null instantly) ![pair/production/annihilation](http://i.stack.imgur.com/Xka89.png)


title: Order of phase transitions

text: I got to read things like > _In case of a first order phase transition, the volume and temperature > change in a discontinuous manner. However for phase transitions of higher > order the change in volume and temperature can be continuous._ I could not exactly understand the statement and thats why I thought what exactly it means by the order of a phase transition. May I know what exactly it means by the order of phase transition?


title: How do I correctly express the work required to put an object with positive buoyancy down into a certain depth (of water)?

text: It seems to me that I can express the work required to put an object under water in the same way that I express lifting an object up against gravity. I. e., in both cases I increase the potential energy of the object by moving it vertically against the direction of the force. Conversely, when the object is allowed to surface, it would be comparable to an object falling down (just with significantly more drag in the water, I guess). Is that comparison viable?


title: What are the differences between indistinguishable and identical?

text: What is the difference between indistinguishable particles and identical particles?


title: Do scientists literally believe the Schröedinger's cat though experiment?

text: I've heard the Schrödinger's cat "paradox" (although there's nothing particularly paradoxical about it, just counterintuitive), but I've never been clear on whether or not it's meant to be taken with a grain of salt. I've always assumed it was just a metaphor for the behavior of particles at the quantum scale, not a description of what would actually happen if you put a cat in a box. The idea that a conscious, human observation of the contents of the box - rather than a more mechanical interaction such as the dead cat hitting the bottom of the box or the live cat breathing the air in the box - would have any bearing on the state of the system quite honestly seems _insane_ to me. I see no reason that the gravitational effects of the massive particles in the cat, the interaction of the cat with the box, the air, or other parts of the cat itself wouldn't be sufficient to collapse the wave- function. Why does someone need to _see_ it? Is nature really supposed to treat conscious observers differently from any other object? So, my question is this: Do quantum physicists literally believe the implications of this thought experiment, taken at face value, or is it an impossible but conceptually illustrative explanation of what happens when observing single particles? This paradox has been explained to me many times by different sources, and not once have a heard a disclaimer at the end along the lines of: "but, of course, this is completely ridiculous and only really happens with very small objects, not complex systems like cats and boxes." Is this disclaimer implied, or do people really believe this? (in which case my philosophical understanding of quantum physics needs serious revision to understand how this cat predicament could actually be the case.) Thanks in advance!


title: What's the weight of the earth?

text: What's the weight of the earth? That is, what's the weight of the earth in the gravitational field of the sun? I imagine it's either   * $0$, because there's no net fall toward the sun, so the downward component of acceleration is $0$ and $F=ma=0$, or   * $Gm_1m_2/r^2\approx7\cdot10^{-11}\cdot6\cdot10^{24}\cdot2\cdot10^{30}/(1.5\cdot10^{11})^2\approx4\cdot10^{22}$ Newtons, but which, and why?


title: Chemical Potential of Ideal Fermi Gas

text: In Wikipedia's article on Fermi Gases, they have the following equation for the chemical potential: > $$\mu = E_0 + E_F \left[ 1- \frac{\pi ^2}{12} \left(\frac{kT}{E_F}\right) ^2 > - \frac{\pi^4}{80} \left(\frac{kT}{E_F}\right)^4 + \cdots \right]$$ where > $E_0$ is the potential energy per particle, $k$ is the Boltzmann constant > and $T$ is the temperature. I don't understand how they get the third term, particularly the 1/80 factor. I've often seen this equation expressed just to the tau^2 term, and I understand how to get the 1/12 factor from a binomial expansion of $$\left( 1 + \frac{\pi^{2}}{8} \left(\frac{\tau}{E}\right)^{2}\right)^{-2/3} $$ However, I've tried continuing the binomial expansion and cannot figure out why the factor is 1/80.


title: Is randomness deterministic?

text: Is randomness based on lack of knowledge or behavior of universe is true random? Or in other words, are the allegation by EPR about hidden variable in the QM theory justifiable? What evidence can disprove/prove EPR?


title: Solving a time independent Schrödinger equation with a given potential

text: I'm trying to rework this old homework problem, and I am having problems arriving at the same solution on the answer sheet: > _Let $$V(x)=\begin{cases}\infty &\text{ if } x < 0\\\ \alpha\delta(x-a) > &\text{ if } x \geq 0 \end{cases}$$ where $a$ and $\alpha$ are of the > appropriate units._ > > _A particle starts out in the well $0 < x < a$, but because of tunneling its > wave function gradually leaks out through the delta-function barrier._ > > _(a) Solve the time independentSchrödinger equation for this potential; > impose appropriate boundary conditions, and determine the energy $E$. An > implicit equation will do._ Here is what I know: $$\psi(x)=\begin{cases}Ae^{ikx}+Be^{-ikx} &\text{ if } 0 \leq x \leq a\\\ Fe^{ikx} &\text{ if } x > a \end{cases}.$$ $\psi(0)=A+B$ and this implies $-A=B$. I also understand that $\psi$ is continuous at $a$. What I am stuck on is why $\psi'(a)$ is discontinuous. Specifically, why is it that: $$ikFe^{ika}-ikA(e^{ika}+e^{-ika})=\frac{2m\alpha}{\hbar^2}\psi(a).$$


title: How long it will take for a upright rigid body to fall on a ground

text: Let's suppose there is a straight rigid bar with height $h$ and center of mass at the middle of height $h/2$. Now if the bar is vertically upright from ground, how long will it take to fall on the ground and what is the equation of motion of the center of mass (Lagrangian)?


title: How do home-made capacitator bottles affect a tesla coil?

text: In the tutorial I'm following, the guy uses 6 snapple bottles to make capaciter (by covering them with foil and filling them with salt water) for a 9kV 30mA input. I have a stronger transformer (15kV 60mA), and no snapple bottles. I do have an assortment of other cans and jars (jam and suchlike) which togeather have a much greater capacity than six snapple bottles. Can I mix bottle types? Is a greater bottle a subsitiute for less bottles? How should I adjust for increasted voltage and current? How can I imporve my chances of having a simmilar capacitance as the tutorial? EDIT: it was actually 15kV


title: Cerenkov light - a practical calculation

text: I need to calculate the approximate total amount of energy radiated, via Cerenkov, by a muon as it traverses $10\:\rm{cm}$ of quartz glass. Unfortunately I've spent so much time fiddling with electronics in the lab recently that I've completely forgotten how to do maths. The formula to use is the Frank–Tamm Equation: $$\frac{dE}{dx} = \frac{q^2}{4\pi} \int_{v>c/n(\omega)} \mu(\omega)\omega\biggl(1-\frac{c^2}{v^2n^2(\omega)}\biggr)d\omega$$ Where $\mu(\omega)$ and $n(\omega)$ are the permeability and refractive index of the medium being traversed by the charged particle. For a $5\:\rm{keV}$ muon travelling through quartz glass I have looked up the following numbers (but I'm really not sure over what frequency range to consider the last two): $$x=0.1\:\rm{m},$$ $$q=1.6\times10^{-19}\:\rm{C},$$ $$v\approx c,$$ $$n(\omega)=1.54-1.46 (\lambda=200-700\:\rm{nm})\approx1.5,$$ $$\mu(\omega)\approx1NA^2.$$


title: Efficiently calculating the gravitational force from spherical shell

text: I am reading Kolenkow and Kleppner's _Classical Mechanics_ and they have tried to calculate the gravitational force between a uniform thin spherical shell of mass $M$ and a particle of mass $m$ located at a distance $r$ from the center. The shell has been divided into narrow rings.$R$ has been assumed to be the radius of the shell with thickness $t$ ($t<<R$). The ring at angle $\theta$ which subtends angle $d\theta$ has circumference $2\pi R\sin\theta$. The volume is $dV=2\pi R^2t\sin \theta d\theta$ and its mass is $pdV=2\pi R^2t\rho\sin\theta d\theta$. If $\alpha$ be the angle between the force vector and the line of centers, $$dF=\frac{Gm\rho dV}{r'^2}\cos\alpha$$ where $r'$ is the distance of each part of the ring from $m$. Next, an integration has been carried out using $\cos\alpha=\frac{r-R\cos\theta}{r'}$ and $r'=\sqrt{r'^2+R^2-2\pi R\cos\theta}$. Question: I would like to avoid these calculations and I was wondering if there exists a better solution.


title: Photons arriving from the Sun

text: Given that the Sun is a bit less than 10 light minutes away from Earth, is it correct to assume in principle (I understand actual processes in the core of the Sun make the situation at a photon's emission far more complicated) that the photons that hit a human eyes on a clear day actually departed from the star less than ten minutes ago? If you don't mind me saying so in a scientific forum, I find this notion (if confirmed) similarly endearing as the other notions that most elementary building blocks (chemical elements) in our bodies stem from bygone distant stars, and that we never see distant parts of the universe (or the Sun, for that matter) as the are "now", just as they were at a certain past distance in time.


title: Mechanism by which electric and magnetic fields interrelate

text: I read that force due to electric field on some particle in one reference frame can exhibit itself as force due to magnetic field in some other reference frame and that electric and magnetic fields are two aspects of same underlying electromagnetic field. My question is what is the mechanism which can explain how an electric field becomes/creates magnetic field in some other reference frame. Is there any such explanation available in relativity theory? I am not looking for mathematics but a physical explanation. Wikipedia article http://en.wikipedia.org/wiki/Relativistic_electromagnetism explains something about origin of magnetic forces in a wire as a consequence of lorentz contraction and motion of electrons in the wire _**Calculation of the magnitude of the force exerted by a current-carrying wire on a moving charge is equivalent to calculating the magnetic field produced by the wire. Consider again the situation shown in figures. The latter figure, showing the situation in the reference frame of the test charge, is reproduced in the figure. The positive charges in the wire, each with charge q, are at rest in this frame, while the negative charges, each with charge −q, are moving to the left with speed v. The average distance between the negative charges in this frame is length-contracted to: where is the distance between them in the lab frame. Similarly, the distance between the positive charges is not length-contracted: Both of these effects give the wire a net negative charge in the test charge frame, so that it exerts an attractive force on the test charge._** But this still does not explain origin of magnetic field in case when there are no positive charges.


title: Why are physicists interested in graph theory?

text: Can you tell me how graph theory comes into physics, and the concept of small world graphs? (inspired to ask from comment from sean tilson in): which areas in physics overlap with those of social network theory for the analysis of the graphs? Best,


title: Self Balancing Unicycle

text: Here is a link to a video of a self-balencing unicycle. I'm curious as to how this works. In particular:   * What provides the torque to keep the rider from falling over? I know it's somehow provided by the motor, but this isn't an external torque (if we define the unicycle as our system), and I assume we need an external torque to change the angular momentum of the unicycle.    * If you were to try to ride this thing on ice, I assume that it could not prevent the rider from falling over. Is this correct?    * What would the free body diagrams look like for this unicycle when it is in the act of falling over? When it is righting itself?


title: The Concepts of Path Integral in Quantitative Finance

text: I realize that path integral techniques can be applied to quantitative finance such as option value calculation. But I don't quite understand how this is done. Is it possible to explain this to me in qualitative and quantitative terms?


title: Bragg's law in photonic crystals

text: So in photonic crystals when looking at diffraction the refraction of light has to be taken into account. I am told this would lead to the "photonic bragg's law" which is $$n \lambda = 2d\sqrt{n-sin^2\theta_i} $$ ![The situation in question](http://i.stack.imgur.com/1W33r.png) Where $\theta_i$ is the incoming angle, d the distance between the planes and n is $n_{eff}$ or the coefficient of the medium (also $n_0$=1). However using basic trigonometry and Snell's law I can't get past $$n\lambda = 2d(\frac{n}{cos\theta_i}-\sin\theta_i\tan\theta_t)$$ Where $\theta_t$ is the refraction angle. Using $\theta_t = \arcsin\frac{\sin\theta_i}{n}$ from Snell's law doesn't seem to help. Pointers on how to approach this problem would be greatly appreciated.


title: Can a megatsunami have a height of 30,000 feet or more?

text: Is it possible on Earth? Roughly what size would an impactor have to be to cause a tsunami of this height? And it's speed, energy equivalent in tons, megatons, etc.?


title: Why molecular forces do not obey inverse square law?

text: Most of the forces in physics obey inverse square law, but why molecular forces don't obey it.. Since molecular forces is also a form of electromagnetic force..


title: Reason behind cohesive and adhesive force

text: What is the real cause behind the cohesive and adhesive forces?


title: Is acceleration $a = s/t^2$, or $a = 2s/t^2$, or something third?

text: I'm having trouble understanding some of the stuff regarding movement in my introductory physics class (I never thought I'd say that...) Acceleration is defined as $ a = \frac{s}{t^2}.$ Distance can be calculated as the area under velocity-time line; given a constant accelation, and an initial velocity of 0, this forms a triangle: $ s = \frac{at^2}{2} $. The latter, though, gives me the definition $ a = \frac{2s}{t^2}$. Is the former, then, wrong? Perhaps I'm just better of using integrals? EDIT (from comment below): What confuses me is that $a = \frac{\Delta v}{\Delta t}$, and $\Delta v$ when $a$ is constant and $V_0$ is 0 is $v = \frac{\Delta s}{\Delta t}$. Substituting $v$ in the former equation: $a = \frac{\frac{\Delta s}{\Delta t}}{\Delta t}$, or $a = \frac{\Delta s}{\Delta t^2}$. Along with, of course, the SI unit $\frac{s}{m^2}$.


title: Derivation of Lagrangian density for an infinite classical dielectric in interaction with the EM field

text: I am tasked with reading and reproducing all the steps in J.J. Hopfield's 1958 paper "Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals". Embarrassingly I am stuck on equation (3). Hopfield takes the Lagrangian _density_ for an infinite classical dielectric in interaction with the electromagnetic field to be ![enter image description here](http://i.stack.imgur.com/0byQD.png) Instead of taking this equation at face value, I would like to fully derive this Lagrangian density, but am unsure how to approach the problem. I have found many articles and sites tackling a similar problem, but never ending up with an expression as here. Any pointers on how to approach the problem or links to material that could be useful would be very much appreciated.


title: Is quark electric charge also confined?

text: Since we will (maybe) never observe free quarks which has fraction charge, is it logically correct to say that the fraction (1/2,2/3 etc) electric charge is also confined. I.e. the charges that we do se (+1,-1 etc) are "white" in the sense of color?


title: Where is a particle bound in a delta potential?

text: I can picture a bound state in a harmonic oscillator, or in an infinite square well, but where is a particle bound in a delta potential?


title: Why can't a spin-1 particle decay into two identical spin-0 particles?

text: **I've got this far:** Suppose a spin-1 particle with $j$,$l$,$s$ decays into a system of two identical spin-0 particles with $J$,$L$,$S$. The RHS must have total spin $S=0$, so $J=L$ which must be even since the particles are Bosons and their states must be symmetric in their exchange. Then by conservation and addition of angular momenta, the LHS must have $L=J=j=\left\\{\begin{array} \\.l-1,l,l+1 &\text{ if }l\neq0 \\\ 1 &\text{ if }l=0 \end{array}\right.$. Mistakes are likely. **Two possible ways to proceed (but I can't motivate either):**   1. Can I choose to take $l=0$ for some reason?   2. I know (I think) that a system of two identical Bosons has to have $l$ even, because of symmetry of their wavefunctions under exchange of the two particles. Does the value of $l$ for a single Boson also have to be even? If so, can I then somehow rule out the $j=l\neq 0$ case and get a contradiction?


title: Does the radius of the Universe correspond to its total entropy?

text: I heard a claim that due to holographic principle, the surface area of the cosmic horizon corresponds to the universe's total entropy. As such the initial state had zero surface area and later expanded. Given this, I wonder whether any increase in entropy (such as producing heat by means of electric power) causes the universe to expand?


title: A "Hermitian" operator with imaginary eigenvalues

text: Let $${\bf H}=\hat{x}^3\hat{p}+\hat{p}\hat{x}^3$$ where $\hat{p}=-id/dx$. Clearly ${\bf H}^{\dagger}={\bf H}$, because ${\bf H}={\bf T} + {\bf T}^{\dagger}$, where ${\bf T}=\hat{x}^3\hat{p}$. In this sense ${\bf H}$ is "formally" self-adjoint. It turns out that $$ \psi_{\lambda}(x)=\frac{1}{|x|^{3/2}}e^{-\lambda/4x^2} \in L^2[-\infty,\infty]$$ is an eigenfunction of ${\bf H}$. In fact $${\bf H}\psi_{\lambda}(x)=-i\lambda\psi_{\lambda}(x).$$ If we go through the usual proof that Hermitian operators have real eigenvalues, we see that something has to go wrong in the following steps: $$ \langle\psi_{\lambda}(x)|{\bf H}\psi_{\lambda}(x)\rangle= \langle{\bf H}^{\dagger}\psi_{\lambda}(x)|\psi_{\lambda}(x)\rangle=\langle{\bf H}\psi_{\lambda}(x)|\psi_{\lambda}(x)\rangle=\langle\psi_{\lambda}(x)|{\bf H}\psi_{\lambda}(x)\rangle^{*}.$$ Clearly ${\bf H}\psi_{\lambda}(x) = -i\lambda\psi_{\lambda}(x)\in L^{2}.$ So all these operations _seem_ to be well-defined. Our book suggests that we look at ${\bf T}\psi_{\lambda}(x)$. It turns out that ${\bf T}\psi_{\lambda}(x),{\bf T}^{\dagger}\psi_{\lambda}(x) \notin L^{2}$. So when we are writing $$\langle\psi_{\lambda}(x)|{\bf H}\psi_{\lambda}(x)\rangle$$ we are _really_ writing $$\langle\psi_{\lambda}(x)|({\bf T} + {\bf T}^{\dagger})\psi_{\lambda}(x)\rangle=\langle\psi_{\lambda}(x)|{\bf T}\psi_{\lambda}(x)\rangle+\langle\psi_{\lambda}(x)|{\bf T}^{\dagger}\psi_{\lambda}(x)\rangle$$ where these inner products are no longer defined. Does the fact that these two inner products are undefined lead to this _seemingly_ (and "formally") self- adjoint operator having imaginary eigenvalues? And how?


title: Ionization Energy and Bohr

text: I was having problems with ionization energy - but all it is is the energy required to remove first electron that pops off right? In the case of Bohr's atom, there's only one electron, so it's that electron in it's ground state. In the case of a multielectron atom, it's the energy required to remove the outer electron, in _it's_ $n = 1$ state, right?


title: Maximum liquid velocity in a siphon

text: According to wikipedia: Siphon, the velocity of liquid in a siphon is equal to $\sqrt{2gh}$, where h is the difference in level between the water surface and the opening of the siphon. But it also mentions that there exists a maximum velocity which can be attained; hence the velocity of the liquid coming out of the opening of the siphon cannot be increased beyond a particular limit by merely increasing $h$. But wouldn't this violate Bernoulli's equation if applied for the water surface and the opening if $h$ is taken beyond the value at which maximum velocity is obtained?


title: Moment of inertia of rotating particles in center of mass frame?

text: I am trying to simulate a collision between two molecules. I know the energy for every position/orientation, from which I can calculate the forces. The treatment is classical and the molecules are assumed to be rigid. I converted this situation to the center of mass frame so I only need the relative position, and I use the mass $m_{1} \cdot m_{2} / (m_{1} + m_{2})$. But I get stuck at the rotations. Can I use rotating particles in center of mass frame, because all I can find is examples of point particles? If I can, what do I use for the moment of inertia? If not, what's the best alternative? **EDIT** : Hopefully this clarifies things: the reduced representation seems to be for point particles. I would like to know if I can use it for rotating (non-point) particles in some way. It seems to me that if I can use it at all, I would need to use a special moment of inertia for individual particles. I think that because the mass is changed, so if I use normal moment of inertia but scaled linear inertia, then rotations will be disproportionately slow or fast. Then again, maybe I can't use the reduced representation at all.


title: What is Scale invariance?

text: Could anybody tell me what does scale invariance means? Is there any book or article that describes [ and gives examples ] about it.


title: Time, what is it?

text: If you ask any person about time, she/he will give you some answer. I suspect that it is extremely difficult, (if not impossible) to define time. Is there a definition of what it is in physics? Is it an "axiom" that has to be taken as it is, without explanations? I also noticed that the tag "time" has no pop-ups with comments/definition/explanations.


title: Does Planet revolution time is always greater the more it's getting away from the center?

text: The entire question is in the title . It's the case for the solar system but is it always the case ? Can a planet do a revolution faster than another that is closer to the center ? As far as I searched , it's not but I prefer ask here to be sure. Of course I'm talking about similar orbits (all with the same eccentricity). (When I'm talking of the center, I mean the body in the center (in general a sun), even if it's not always the center)


title: Derivation of master equation

text: In this article* I want to get the Equation(9) with comparing the equation (2). Please elaborate the left side of equation (9). * _Small amplitude quasi-breathers and oscillons_ by G. Fodor, et al. arXiv:0802.3525.


title: Constant pressure and temperature mixing of 2 different ideal gases - possible work and heat?

text: A simple question I hope... **Initially** , have two separate containers of 2 different ideal gases, 1.) N1, P, T, V1 and 2.) N2, P, T, V2. **After mixing** , the pressure and temperature are still P and T, but the volume is additive. Assuming isolated system. So I calculated the change in entropy with $\Delta\,S_i = n\,R\,\ln((V1+V2)/Vi)$. I found the change to be positive, which is to be expected. Then when I look at the first law, $d\,U = \delta\,Q - \delta\,W$, I think that as the temperatures did not change then the internal energy of the gases did not change and $d\,U = 0$. Also, I think that there was no work done and so there is no heat transfer, $\delta\,Q$. ***Is this right? *** * **Is the total energy change zero too? ***


title: A ball inside a cavity

text: Seems not a trivial problem: There is a semi-cylindrical cavity, with radius $R$ as shown in the Figure. A small ball (point mass for simplicity) with an initial horizontal velocity $v$ flies into the cavity. Friction is absent, blows against the cavity's wall are absolutely elastic. What should be the value of $v$ so that the ball is spending minimum time inside the cavity before flying off ? ![enter image description here](http://i.stack.imgur.com/cSpsP.jpg)


title: How do I measure the total weight of a container with scales on four corners?

text: I have a very large movable trash container, and I have mounted four scales, one on each corner. How do I get the **total weight** of the entire container? Is it simply a sum of the four weights, or is it more complex than that? The contents of the container are not evenly distributed, one corner will be heavier than the others. Also, there is a possibility that one corner will not be completely resting on the ground, and thus the scale on that corner will read zero, but the other three corners will bear it's weight.


title: Sunrise/Sunset on a planet with an A-Class or B-Class Star

text: I'm a sci-fi writer, and I have a question regarding a hypothetical planet that orbits an A-class or B-class Star. **Assuming Rayleigh Scattering occurs roughly the same way on this planet as it does on Earth, what colors would we see at Sunrise and Sunset?** I understand that what colours we see from our sun comes from the Rayleigh Scattering, but seeing as it's sci-fi I'm writing, I need a plausible colour scheme to use for my new planet. The Planet has a breathable atmosphere not too different to Earth, so for the sake of the argument, I'm assuming that the Rayleigh Scattering would occur roughly the same way, but my physics knowledge is sadly lacking in this area, and the Wikipedia article only refers to our own G-class Sun. On that note, would the Sky still appear Blue, from an A-class or B-class Star? Or would the Rayleigh scattering trigger a completely different colour of the sky? Is there no 'right answer' when it comes to what sunrise/sunset/sky would look like on a distant planet?


title: What path will an object in a cockpit take?

text: Situation: A fly is in the cockpit of a fighter jet, and flying directly in front of the pilot. The pilot becomes annoyed and decides to get rid of the fly by executing a sudden, high speed turn. The cockpit is so dark the fly cannot see any of the cockpit. will the fly continue to be in front of the pilot, or will it hit the side of the cockpit? If the pilot executes a slow turn will the result be different?


title: Are observables associated to spacetime regions?

text: In the Haag-Kastler approach to axiomatic quantum field theory, it is assumed that observables are 'associated' to spacetime regions. What this actually means is that there is a map $\mathcal{A}: R \mapsto \mathcal{A}(R)$, which associates to a given region $R$ the algebra of observables $\mathcal{A}(R)$ which one may measure in $R$ I'm wondering: Is this map in some sense 'invertible'? If you hand me an observable, can I associate to it a spacetime region in a unique fashion? Is there meaningful physics in this assignment?


title: Can a long pipe stop the flow of a liquid from a pump?

text: If a pump is discharging a fluid into a pipe, is it possible to add a long enough pipe such that the flow of the liquid will be stopped and none will come out of the open end of the pipe?


title: Please explain C14 half-life

text: I understand that C14 decays at a given rate. I also interpret this to mean that 100% of the atoms of C14 in an object will all decay at the same right, individually. So if I have 4 C14 atoms, will they all be gone in a full-life? or will two be 100% in a half-life while the other 2 are 0%? Please explain how the decay of C14 works.


title: How to measure the wavelengths of ultraviolet lines in the hydrogen spectrum?

text: how to measure the wavelengths of ultraviolet radiation isn't it invisible? it's possible to measure visible radiation but how to measure invisible radiation?


title: Concerning drag on a flow past a cylinder

text: I am wondering about the drag coefficient for a flow past a cylinder. I am reading this article. I understand why the drag is high to begin with (point 2), when the boundary layer separates and the recirculations appear, the pressure behind the cylinder (where the wakes are located) will drop, creating a drag. This is similar to what happens when vortices appear at the end of an airplane wing, the result is a drag force. However, I am wondering about the following:   1) Why does the drag decrease as the Re goes up?   2) Why does the drag coefficient take a dive at point 5   3) Why does it rise after point 5? The text doesn't really explain why the drag coefficient is increasing or decreasing.


title: Earthing or nothing

text: Sometimes, mostly in winter, when somebody touches the tap it passes current (especially when the hands are soaked in water or soap water). I read 3-4 years back in physics book that the tap circuit is connected to some copper plate which is dug inside the ground (called earthing). And then somebody suggested that if we don't touch the tap gently with fingers but like grab it with our hands (use all fingers), then you won't get current and surprisingly it did seem to work. Is it earthing and why does this current effect happen with tap... it doesn't happen anymore... but it was quite common to me in the past when I bathed. Is earthing and copper thing related to this? Copper thing seems quite far fetched and delusional, but can it be true? Or is there some other common system to get rid of this tap current in modern households?


title: Coleman-Mandula theorem in mathematical language

text: Every supersymmetry text starts off mentioning the Coleman-Mandula theorem. Often it is introduced using rather colloquial terminology. I was wondering if anyone knew a precise mathematical formulation of the theorem.


title: group velocity VS probability current

text: Think about an electron been accelerated from rest in a static electricfield. If we treat the problem classically, in which the electron is just a point charge. The velocity of the electron would increase linearly with respect to time. Now if we treat this problem quantum mechanically, in which the electron is represented by a wave packet (the field still classical). Assume we have solved the Schrodinger equation and have the time-dependent wave function $\psi(x,t)$, what should we calculate to represent the "velocity" of the electron? One possibility is to calculate the group velocity of the wave packet $v_g$. The other way is to calculate the probability current $$ j=\frac{\hbar}{2mi}\left[\psi^*\nabla\psi - \psi \nabla\psi^*\right]. $$ Are the group velocity of the wave packet and the probability current essentially have the same physical meaning? If they do, how to prove they are the same, and if they are different, what are the differences?


title: Singularity in Newton's gravitational law

text: If $r=0$ in the well know equation $F= G\dfrac{m_1\cdot m_2}{r^2}$, it will not follow that the force will be infinite? May someone please clarify it to me?


title: Separation of variables in various PDEs, physical meaning

text: The method of separation of variables produces an undetermined separation constant and a family of solutions indexed by the values of this constant. For instance, in the case of an infinitely long rod along the positive x axis (with suitable boundary conditions, like a fixed temperature at the beginning, and a given temp. distribution at initial time), the separation constant, $-k^2$, can vary continuously, and the solutions are of the form $$T_k(x,t)=C(k)\cdot \sin{kx} \cdot e^{-k^2\alpha t}$$ One is then supposed to integrate over $k$ to obtain the answer. In the case of a finitely long rod, the values of the constant are quantized and can be summed, rather than integrated. But when we're dealing with Schroinger's equation for a particle in a box, we are only interested in the eigenfunctions corresponding to the values of the separation constant, which we associate with energy. But the general solution would be a superposition of these wavefunctions. Suppose we're dealing with a 3D box of length $L$, then the eigenfunctions are: $$\psi_{k,\ell,m}(x,y,z)=\sqrt{\frac{8}{L^3}} \sin{\frac{\pi}{L}kx}\cdot\sin{\frac{\pi}{L}\ell y}\cdot\sin{\frac{\pi}{L}mz}, \quad k,\ell,m\in\mathbb{N}$$ My question: is there any physical significance to the function: $$\psi=\sum_k\sum_\ell\sum_m c_{k,\ell,m}\psi_{k,\ell,m}, $$ where $c_{k,\ell,m}$ are constant coefficients. Clearly this function is a solution to the Schrodinger equation, by the superposition principle. But does this function describe anything at all? Or is it that, unlike in the case of heat transfer, only the eigenfunctions matter?


title: Mass,Energy,Matter

text: In $E=mc^2$ what type of energy is $E$? For instance, you can find the kinetic energy of an electron by using $\frac{1}{2}mv^2$ but you can also find the energy from $E=mc^2$. How are those two different besides the values?


title: What's the total Cosmic Microwave Background energy?

text: This is a part of my wider attempts at accounting matter in the observable universe. The total light ever emitted by stars and other space objects is capped around 1% of baryonic mass (in energy equivalent). How much light is there in space and how heavy is it? How does the CMB compare to that? How would we calculate it?


title: What is "number degrees of freedom for frequency ν". Frequency is 1D right?

text: The book _QM Demystified_ states this about black body radiation spectrum: > An attempt to explain these results using classical theory was codified in > the Rayleigh-Jeans formula, which is an expression that attempts to give us > the energy density u(ν,T) of radiation in the cavity, where ν is frequency > and T is the temperature. Qualitatively, it is formed as a product of two > quantities: > > u = number degrees of freedom for frequency ν * average energy per degree of > freedom" The * means multiplication here. What does degree of freedom of frequency mean here?


title: shear and normal stresses

text: When we talk about shear stresses in a fluid, we find that the shear stress is given by $$\tau_{xy} = \mu(\partial_y u + \partial_x v) = \tau_{yx}$$ This relation we get when only looking at one side of our fluid-"cube". Now, in order to take into account the opposite side we assume that the fluid element is so small that the shear stress is constant, leading to the average $$\tau_{xy} = \frac{1}{2}2\mu(\partial_y u + \partial_x v) = \mu(\partial_y u + \partial_x v) = \tau_{yx}$$ Applying the same logic to the normal stresses gives me $$\tau_{xx} = \frac{1}{2}\mu(\partial_x u + \partial_x u) = \mu(\partial_x u)$$ However, in my textbook (White) it is given as $$\tau_{xx} = 2\mu(\partial_x u)$$ Where does this extra factor of 2 come from in the normal stress?