title: generation / destruction of fermions by phonons

text: my Hamiltonian consists of 1D free fermions coupled to a bosonic bath. The interaction is dictated both by scattering terms $H^{scatt}=\sum_{kq}\alpha^S_{kq}c^\dagger_kc_{k+q}X_q+h.c.$ as well as generation/destruction terms such as $H^{gd}=\sum_{kq}\alpha^{gd}_{kq}c^\dagger_kc^\dagger_{-k-q}X_q+h.c.$ Conventional second quantization convention is implied ($c$ are fermionic operators, $\alpha$ is just a momentum coupling matrix). I am setting up a BBGKY hyerarchy equation for the correlation functions to study the kinetics of this problem. Has anyone any reference about this? I see a lot for the case of scattering with phonons but the $H^{gd}$ is never there, but I suppose these kind of models could have been studied in chemical kinetics or superconductivity. I would like to see some example of master equation, or equation of motions with these processes taken into account...


title: Understanding of measurement in quantum mechanics?

text: I have a computer science background with basically zero physics background. I am trying to gain a 'high-level' understanding of quantum mechanics to aid me in some computer science work. Is my understanding correct here regarding a quantum register in a quantum computer - When a quantum register is read, the superpositioned states 'collapse' into a single state and we only know the probability that a certain outcome has occurred. I.e. if we have a state $|\psi \rangle= a|0\rangle + b|1\rangle$, then the process of reading a quantum register returns **2** values: The state $|0\rangle$ or $|1\rangle$, and the probability that this is the 'correct' state, which is calculated by taking $\sqrt{|a|^2 + |b|^2}$. I would like to be precise in my understanding, I'm not looking for 'thats kind of right', if it is incorrect I would appreciate it if you could tell me exactly what I have wrong.


title: Surviving under water in air bubble

text: An incredible news story today is about a man who survived for two days at the bottom of the sea (~30 m deep) in a capsized boat, in an air bubble that formed in a corner of the boat. He was eventually rescued by divers who came to retrieve dead bodies. Details here. Since gases diffuse through water (and are dissolved in it) the composition of air in the bubble should be close to the atmosphere outside, if the surface of the bubble is large enough; so the excessive carbon dioxide is removed and oxygen is brought in to support life of a human. Question: How large does the bubble have to be so that a person in it can have indefinite supply of breathable air?


title: Detecting absolute motion inside a box

text: This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ![CC license](http://i.stack.imgur.com/6dqR3.jpg) Rest frames are easy to understand. They are just for clarification. Lets move on to the moving frames. The velocity of the box is $0.1\ c$. Now a photon is emitted (I am not taking a light ray to avoid complication in discussion). After emission the box also moves a certain distance ahead. So the photon takes more than one second to reach the wall. But even the source moves that much distance ahead. When the light is reflected back, the source and the wall again move forward as the box is moving. But after reflection the wall has no role to play. We are concerned about the source. The source moves a certain distance ahead and therefore light takes less than one second to reach back. But the difference of the first case and the second case is not the same. To explain, I will give some equations. Moving frame 1: Velocity of the box: $0.1\ c = 30,000km/s$ Time taken by light to reach the wall $=\frac{330,000\ \text{km}}{300,000\ \text{kms}^{-1}}= 1.1s$ Distance moved ahead by the box from original position: $30,000\ \text{km}$ Moving frame 2: distance moved ahead by the box from original position $>30,000\ \text{km}$ as the box also moves ahead after reflection. let $d$ be the distance moved ahead by the box after reflection. Time taken by light to reach the source: $\frac{270,000\ \text{km}\ -\ d}{300,000\ \text{kms}^{-1}} <0.9s$ Therefore we see that this could possibly determine the absolute motion. So in total we see that the light will take lesser time to reach the source. Please correct me if I am wrong and give your opinion why is it so. **EDIT 2 for clarification** The box is the compartment in space in which you are moving and I am calculating the time the light takes to reach back the source. I am not even adding velocities. Please correct me and tell me where did I add velocities. For clarification just let me give a simple example. Suppose person A is standing still and B is running towards a light source. Obviously he will see the light before person A even though the speed would be the same. So, what I am doing over here is not increasing the speed of light, but instead decreasing the distance to be covered by it.


title: Neutral pions and chromodynamics

text: $\pi^0$ particles are either up-antiup or down-antidown (or strange- antistrange?) They must be opposite colors to preserve neutrality. Why don't the opposite quarks annihilate?


title: Is there a source that provides data for the temperature coefficient of resistivity at different temperatures?

text: I'm looking for a source where I can find the temperature coefficient of resistivity at different temperatures for pure metals. Tables are everywhere for 20$\,^{\circ}$C, but I'm having difficulties finding data for other temperatures. One resource I looked at (http://www.physicsforums.com/showthread.php?t=546194) provides a formula: $\alpha_T = \left(\frac{1}{\frac{1}{\alpha_0} + T}\right)$ I don't believe that's applicable to all materials, but is there a group of materials where that expression is true? * * * **[UPDATE]** @Trimok led me to the Bloch–Grüneisen formula $\rho(T)=\rho(0)+A\left(\frac{T}{\Theta_R}\right)^n\int_0^{\frac{\Theta_R}{T}}\frac{x^n}{(e^x-1)(1-e^{-x})}dx$ I can work with that, but there's a lot of parameters that I would need before solving it. Is there a source for $\rho\left(0\right)$, $A$, $\Theta_R$ (the Debye temperature), for different metals? Also which of the n values need to be considered?


title: How to get Gell-Mann matrices?

text: How to get Gell-Mann matrices $f_{i}$ (more or less strictly)? What are the requirements for getting them, excluding $||f_{i}|| = 1$, commutational law $[f_{i}, f_{j}] = if_{ijk}f_{k}$ and hermitian nature? Is that enough?


title: How an accelerated object sees another accelerated body in special relativity?

text: Assume two objects are moving with a constant acceleration $a_1$ and $a_2$, which are the measured accelerations by respective object (or constant force being applied to each of the objects). My problem is how one object sees the motion of the other one. I know that the accelerations are transformed according to the relation (Why proper acceleration is $du/dt$ and not $du/d\tau$?), $$ a = \frac{a'}{\gamma^3} $$ where $a'$ is the measured acceleration and $a$ is the acceleration in a inertial frame.


title: Path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $

text: How do I calculate path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $ where $t_i<t_1<t_f$? I am doing this by discretizing, the time intervals and adding a complete set of $|q_j t_j\rangle$ states at each point, then at the time $t_1$, one can add $p(t_1)|p^{\prime} t_1\rangle \langle p^{\prime} t_1|$, which is the momentum of the particle at time $t_1$. After taking the inner product with the position state at time $t_1$, and integrating I get $$\frac{1}{h} \int \mathcal{D(q)} \mathcal{D(p)} \int dp^{\prime} \frac{p^{\prime^2}}{2m} exp(-\frac{i}{\hbar}q_{t_1-1}p^{\prime}-(t_f-t_i)H(p^{\prime}, (\frac{q_{t_1-1}+q_{t_1}}{2})))exp(\frac{i}{\hbar}S)$$ This looks terribly ugly and wrong. How do I do it?


title: Modeling magnetic field shielding

text: I am wondering what is the best way to model magnetic and electric field shielding from a magnetic dipole in the near field? For example, let's say you have a coil of current carrying wire in the x-y plane which creates an AC magnetic field along the z-axis. I am interested in a model in which I could put in material parameters (such as $\sigma$, $\epsilon$, $\mu$) for a shielding plate located distance $r$ from the source. I tried using section 5.4 of an online electromagnetic book which talks about reflection, and transmission of of EM waves. I would estimate wave impedance as $Z=\omega\mu_0r$ which is the equation for near field magnetic source. I determine the intrinsic impedance of the shielding material as $\eta=\sqrt {\frac {j\omega\mu} {\sigma + j\omega\epsilon}}$. I want to try good conductors as well as ferrite so I'm not making any assumptions such as good conductor or loss-less medium. I implemented this but the result was not what I expected. I would expect highest energy reflection with the ferrite because it has low reluctance to magnetic fields and would guide the flux through it and return to source. However, a good conductor (e.g aluminum) had almost 100% energy reflection, but I was expecting the shielding mechanism of conductors would be all energy lost as absorption from eddy currents. Let me know your thoughts of whether this is a legit model; I can give more info about parameters/equations used if that's helpful.


title: Newton's First Law of Motion; Empirical Aspects

text: Newton's first law states that in an inertial frame, a body at rest continues to be at rest, and a body in constant rectilinear motion continues its motion, unless an external force is applied upon the bodies. My question is how far have these assertions been tested experimentally? More precisely, is there any need to test this statement, or is it taken as a "definition" of sorts? I assume the body at rest is a trivial case. On the other hand the case of the body in constant motion would be considerably harder to test, since no external force on a body is an idealization. But I am still curious whether there have been any attempts to test the case of the moving body.


title: Photon Escape Angle From Black Hole

text: Consider a photon source emitting photons near the surface of a Schwarzschild black hole. What angle, as a function of the source's radius from the event horizon, must the photons be emitted at such that they can escape to an observer at infinity?


title: How can one activate the decay of the quark b with PYTHIA event generator?

text: This is my problem and I hope finding a solution. > _In the simplest alternative, MSTJ(22) = 2, the comparison is based on the > average lifetime, or rather (c*tau "time life") , measured in mm. Thus if > the limit PARJ(71) is (the default) 10 mm, then decays of K0_S, Lambda, > Sigma−, Sigma+, Theta−, Theta+, Theta0 and Omega− are all switched off, but > charm and bottom still decay._ This is what I found in the manual of PYTHIA, I did this but the decay of b is not happened.   Knowing that the decay of b is activated by putting "MDCY(PYCOMP(5),1)=1".


title: Conditions for Conservation of energy law

text: In two-dimensional motion, which conditions are needed to be satisfied so the conservation of energy law holds? (for example, simple pendulum motion)


title: Why does elastic energy only depend on first derivatives?

text: Say we have an elastic material that is deformed with displacement function $u : \mathbb{R}^n \rightarrow \mathbb{R}^n$. It is reasonable to assume that the energy required for such a displacement is an integral over local properties of $u$: $$E = \int_S F(u_i, u_{i,j}, u_{i,jk}, \cdots)$$ Where $u_{i,jk\cdots z} = \frac{\partial^m u_i}{\partial x_j \partial x_k\cdots \partial x_z}$. It is clear that $F$ cannot depend on $u_i$, because the energy is translation invariant. As it turns out, for small deformations $F$ depends on all $u_{i,j} = \frac{\partial u_i}{\partial x_j}$ and does not depend on higher derivatives. Furthermore, $F$ is a quadratic in $u_{i,j}$, namely $F = \sum T_{ijkl} u_{i,j} u_{k,l}$ where $T_{ijkl}$ depends on the material. Is there a reason for this, or is this just an empirical fact? Is there a set of intuitive assumptions that lead to this form of $F$?


title: What are Jones matrices and how to derive them?

text: I'm coding a software for an optics lab I'm working in and I need to know how to derive expressions for Jones matrices for various polarizes. What does a Jones matrix represent and how would you derive them for say a linear polarizer with transmission axis oriented at an angle of $60$ deg with the vertical? Or even the simpler case of a half-wave plate with fast axis horizontal?


title: What exactly does $S$  represent in the CHSH inequality $-2\leq S\leq 2$?

text: What exactly does $S$ represent in the CHSH inequality $$-2~~\leq ~S~\leq ~2?$$ Sorry I've been reading for a couple days and I can't figure out what exactly $S$ is and the math is a bit over my head. Any help is much appreciated.


title: Mass, momentum and energy...How many equations for more then one elements?

text: Basically, for solving 1D flow equations, one uses the mass, momentum and energy equations (Also known as Euler equations). Say now I have $N$ elements in series, will I be using $3N$ equations?


title: Ising model Mean field theory and translational invariance

text: In the Ising model the mean value of any particular spin is: $$ m = \left<s_i\right> = \frac{ \sum_{s_i}e^{-\frac{H}{T} }s_i} { \sum_{s_i} e^{-\frac{H}{T} } } .$$ I read in several sources that due to "translational invariance" $m$ is "independent of the site label $i$". That means that all spins have the same average value. My question is whether this is an approximation or this is an actual fact? Why does translational invariance imply that all spins have the same average value? If we assume that there are no fluctuations then $m$ would be a constant throughout the lattice by assumption, not by "translational invariance" right? Again, I'm not sure what is meant by translational invariance here.


title: What's the mathematical background to the representation for Gaussian beams?

text: # Background A general optical system (not necessarily having an axis of rotational symmetry) can be represented, for small deviations from a base ray, by the matrix transfer equation, $$ \left[\begin{array}{c} n'L'\\\ n'M'\\\ x'\\\ y' \end{array}\right] = \left[\begin{array}{cc} B & -A\\\ -D & C \end{array}\right] \left[\begin{array}{c} nL\\\ nM\\\ x\\\ y \end{array}\right] = D(g) \left[\begin{array}{c} nL\\\ nM\\\ x\\\ y \end{array}\right] $$ where $L,M,N$ are the direction cosines of a ray, $n$ is refractive index, $x,y$ are coords on a reference plane, $A,B,C,D$ are $2\times 2$ matrices and a prime (') denotes the image space and unprimed quantities are in the object space. The sign convention for the matrix sub- blocks is from ``The Ray and Wave Theory of Lenses'' by A. Walther. The $4\times 4$ transfer matrices $D(g)$ are the defining represention of the symplectic group $Sp(4,R)$ carried on a 4-d vector space $V_{4}$ . They obey, $$ D(g)^{T} \left[\begin{array}{cc} 0 & 1\\\ -1 & 0 \end{array}\right] D(g) = \left[\begin{array}{cc} 0 & 1\\\ -1 & 0 \end{array}\right] $$ where the $0$ is $2\times 2$ and $1$ is the unit $2\times 2$ matrix. Thus one can say that geometric optics is the study of a finite dimensional representation of $Sp(4,R)$ and each optical system is a $g\in Sp(4,R)$. Furthermore, two optical systems $g$ followed by $h$ are equivalent to the single optical system $hg$. It turns out (see Guillemin and Sternberg ``Symplectic Techniques in Physics''), provided the optical system is lossless, that diffractive optics in the Fresnel approximation is the study of an infinite-dimensional projective representation of $Sp(4,R)$ carried on a Hilbert space. In this case, the complex amplitude $u(x,y)$ on a reference plane is a vector $|u\rangle$ and the transfer equation between object and images reference planes is now, $$ |u'\rangle=K(g)|u\rangle $$ where $K(g)$ is a kernel which is actually a projective representation of $Sp(4,R)$ carried on the Hilbert space. Note that, in a book on diffraction, like Walther's, the transfer equation would be appear as, $$ u'(x',y')=\int K(x',y'|x,y)u(x,y)dxdy $$ and the kernel $K(x'y'|x,y)$ depends on the matrices $A,B,C,D$ via a function called the eikonal. The details are not important for this question. # Question If one studies the diffraction of a Gaussian beam, $$ u(x,y)=\exp{\left\\{\frac{i}{2} \left[\begin{array}{cc} x & y \end{array}\right]\left(\frac{q}{n}\right)^{-1} \left[ \begin{array}{c} x \\\ y \end{array} \right]\right\\}} $$ by an optical system in the Fresnel approximation, then the output beam is also Gaussian and the relation between the $2\times 2$ input and output complex beam parameter matrices is: $$ \frac{q'}{n'}=\left(C\frac{q}{n}-D\right)\left(B-A\frac{q}{n}\right)^{-1} $$ This is another representation (realization) of $Sp(4,R)$ carried on the space of symmetric $2\times 2$ matrices like $q/n$. It's some sort of conformal transformation because, for cylindrical lenses, $q/n$ is a complex number and $A,B,C,D$ are real numbers, so the above equation is a conformal transformation. The existence of this representation was a complete surprise for me; it's clearly related to the infinite-dimensional projective representation of $Sp(4,R)$ because the derivation proceeds via Fresnel theory, but it's carried on the 3-d space of symmetric $2\times 2$ matrices whilst the projective representation has no irreducible subspaces other that the even and odd parity irreps. My question is, ``What is the mathematical background to the representation for Gaussian beams?''


title: How effectively does heat flow through copper wire?

text: If I have a line of copper wire (lets say 1 meter long, 1mm thick) and one end is a flattened disk of copper about the size of a quarter, and I apply a lot of heat to it (I'm talking 800 Celsius) will the entire line be heated to the same degree? I mean what temperature will the unheated end be after, say, a minute? Can it too reach 800 degrees over time? how much time? And lets assume it's in a vacuum so no air removes any of the heat the copper holds.


title: PhD Research Areas in String Theory

text: I'm thinking of applying to do a PhD in String Theory, starting in September 2013. I'm gradually learning more about the subject through external reading, but still most papers are impenetrable! Could anyone give me a description of the areas of current String Theory research that would be accessible for a doctoral student? Are there any particular open problems that might be worth getting to know? Also any general advice on how to choose a PhD topic would be most welcome! Many thanks in advance!


title: What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?

text: I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry. One alternative way of formulating it: I am looking for an equivalent of Weaire–Phelan structure that would be able to fill in a sphere, while stacked in layers around the central core. Another alternative way of formulating it: I am looking for a crystalline structure that would result in growth of spherical or (almost) spherical crystals. In case it is impossible, what would be the closest quasicristaline structure for this? Any pointers towards textbooks or publications or just intuitive explanations would be more then welcome.


title: Noether's theorem for more interesting transformations of the time co-ordinate

text: According to Wikipedia, Noether's theorem (for the mechanics of a point particle) says that if the following transformation is a symmetry of the Lagrangian $$t \to t + \epsilon T$$ $$q \to q + \epsilon Q$$ Then the following quantity is conserved $$\left( \frac{\partial L}{\partial \dot{q}}\dot{q} - L \right) T - \frac{\partial L}{\partial \dot{q}} Q$$ Now at this point we almost always consider either $T=1$ or $T=0$ --- we might consider some interesting transformation of the spatial co-ordinate, such as $\vec{Q} = \vec{n} \times \vec{q}$ for spatial rotations, but we rarely consider some interesting transformation of time. Suppose our Lagrangian is given by $$L = \frac{1}{2}m\dot{q}^2$$ i.e. a simple kinetic Lagrangian. Then can we not make the transformation $$t \to t' = t + \epsilon t = (1+\epsilon)t$$ $$q \to q' = q + \epsilon q = (1+\epsilon)q$$ i.e. $T=t$ and $Q=q$. This is the simplest example of a time transformation I could think of that wasn't the trivial $T=1$ or $T=0$. Then I would argue that our Lagrangian is invariant under this transformation, since $$\frac{d q'}{d t'} = \frac{d q'}{d q}\frac{d q}{d t}\frac{d t}{d t'} = (1+\epsilon) \frac{dq}{dt}(1+\epsilon)^{-1} = \frac{dq}{dt}$$ and so in the new co-ordinates, we have the same Lagrangian. Then from the expression at the top of this post, the quantity $$\left(\frac{1}{2}m\dot{q}^2\right)t - (m\dot{q})q$$ should be conserved. We can trivially show it isn't, however. Where is my error?


title: Time-Independent Gravitational Equation?

text: Is it possible to calculate gravitational induced position change without requiring the use of time (and therefore, acceleration) anywhere in the equation? If such an equation were to be discovered, would it be significant to cosmology/physics?


title: converting power spectrum to photon flux density

text: So I'm having trouble converting units and was hoping somebody could point out where I've gone wrong... It seems I'm missing something fundamental. a Power Spectrum has units $kW/m^2-\mu m$ for the y-axis and microns for the x-axis. I take it, for the $y$ axis that this actually means it has units $kW m^{-3} \mu m^{-1}$ instead of $kW m^{-3} \mu m$. a Photon Flux Density has units $10^{17} cm^{-2} s^{-1} eV^{-1}$ for the $y$ axis and photon energy ($eV$) for the x-axis. Here is my attempt to convert them... We know $W=\frac{J}{s}$, so we can write $$10^3 J s^{-1} m^{-2} \mu m^{-1}$$ and we know how to convert $m$ to $cm$, so $$10^3 J s^{-1} 10^{-4} cm^{-2} \mu m^{-1}$$ I interpret this to mean: so many joules hitting a certain area every second at a specific wavelength. Now we want to speak about the number of photons hitting a given area every second for a particular area and for a given photon energy. So we could multiply by the wavelength $\lambda$ ($\mu m$) to cancel out the extra reciprocal microns and we'd get, $$10^3 J s^{-1} 10^{-4} cm^{-2} \lambda$$ Now I know the energy of a photon can be given by $E=\frac{hc}{\lambda}$ and $J$ are units of energy, so $$10^3 \frac{hc}{\lambda (\mu m)} s^{-1} 10^{-4} cm^{-2} \lambda$$ and $hc =1.24 eV \mu m$ so, $$10^3 \frac{1.24 eV \mu m}{\lambda (\mu m)} s^{-1} 10^{-4} cm^{-2} \lambda$$ which I get to mean, $$10^3 1.24 eV s^{-1} 10^{-4} cm^{-2}$$ $$10^{-1} 1.24 eV s^{-1} cm^{-2}$$ which is almost what I wanted, except I'm missing a $10^{18}$ and my eV is not reciprocal. Can somebody help get me get this?! Alternatively I tried multiplying by $\frac{\lambda}{hc}$ (although I cannot justify why) and then we get, $$10^{-1} J s^{-1} cm^{-2} \mu m^{-1} \frac{\lambda}{hc}$$ Then I let $hc = 1.99 10^{-25} J m$ and we get, $$10^{-1} J s^{-1} cm^{-2} \mu m^{-1} \frac{\lambda (\mu m^{-1}}{1.99 10^{-25} J m}$$ Simplify because the joules cancel out and the microns, $$10^{24} s^{-1} cm^{-2} \frac{\lambda}{1.99 m}$$ Now after simplifying I'm left with $$\frac{\lambda 10^{24}}{1.99} s^{-1} cm^{-2} m^{-1}$$ The internet tells me $m^{-1} = 8.1 10^5 eV$ and after plugging in I get $$\frac{8.1 \lambda 10^{19}}{1.99} s^{-1} cm^{-2} eV$$ which is much closer but again the $eV$ are killing me. Help, please!


title: Creating entanglement by measuring in a certain basis

text: _This is one of the problems from Assignment 2 from CS191x at edx.org, so please do not post explicit answers._ > We have two qubits in the state |0+⟩ and we want to entangle them by > performing a partial measurement on the first qubit. Which of the following > measurements should we perform on the first qubit? _(I am not including possible answers as I want to understand it in general, not only this specific case)_ I am not sure how to determine the state after measuring one of the qubits. For the standard basis my reasoning goes like this: if we measure the first qubit in this base, its resulting state will be |0⟩ with the probability of 1. Because the state of two qubits is |0+⟩, we know for sure that the second qubit will then be in the state |+⟩ and therefore there is no entanglement. Firstly, I do not know if my reasoning above is correct at all. Secondly, how to determine the resulting state in a more general case, e.g. in the sign basis? (|+⟩, |-⟩).


title: What role does memory robots play in the many worlds interpretation?

text: Ron Maimon gave a very interesting answer to a question about the many worlds interpretation here. He mentions the essential role of memory robots in MWI, which is something I have _never ever_ heard any other MWI proponent mention at all. Are memory robots -- whatever they are -- absolutely necessary to make sense of MWI? If so, how come no one else talks about them? Do they have anything to do with Information Gathering and Utilizing Systems (IGUSes) in consistent histories?


title: How do I solve these integrals of wave function and operator?

text: 1. First integral $$\int \Psi^*({\bf r},t)\hat {\bf p} \Psi({\bf r},t)\, d^3r,$$ where the $\Psi({\bf r},t)=e^{i({\bf k}\cdot{\bf r}-\omega t)}\,\,\,$ and $\hat {\bf p}=-i\hbar \nabla$.   2. Second one $$\int \Psi^*({\bf r},t)\hat {\bf p}^2 \Psi({\bf r},t)\, d^3r,$$ where the $\Psi({\bf r},t)=e^{i({\bf k}\cdot{\bf r}-\omega t)}\,\,\,$ and $\hat {\bf p}^2=-\hbar^2 \nabla^2$.


title: Is color confinement detected?

text: I'm a graduate student studying QFT. I'm quite interested that is color confinement detected or proved? (both directly and indirectly) Or it is just an assumption?


title: Ontology of the quantum field

text: I'll use QED as an example, but my question is relevant to any quantum field theory. When we have a particle in QED, where is its charge contained in the field? Is the field itself charged? If so, wouldn't the whole universe be filled with a constant charge density? If not, where does the charge come from, a separate field? If a particle is a ripple in the QED field, how can the ripple be charged but not the field itself, and what determines how the charge is distributed among the field amplitude? This question is answered in quantum mechanics: we have point particles. But I find "particles as quanta of fields" confusing, because if the charge is contained in the field, and particles are just ripples in that field, then how is the charge of the ripple mapped to the ripple itself? Would a spread-out enough ripple have some small charge density filling a large region of space, or do we somehow map the charge of the ripple to a single point in space?


title: Sign convention for EMF

text: When we define the field generate by EMF, why there is not negative sign in $\mathcal{E} = \oint \vec{E} \cdot d\vec{l}$? Usually we talk about potential, there should be a negative sign, right?


title: C Method for Diffraction grating

text: Alright, so I am trying to find the efficiencies of a coated diffraction grating through the method in this paper. This is through a change of coordinate system. So I went through and derived all of the equations up until equation 26. I get lost at the Outgoing wave condition. I understand what he is doing, I just get confused as to how both equations 26 and 28 are true. Additionally, I do not see how he can solve equation 28. I am trying to do so in MatLab, and I only get errors saying that there are dimension mismatches. I would really appreciate any help! Thanks


title: In calculating work done by a constant force over a constant distance, why doesn't the subject's initial velocity matter?

text: Assume a point-mass $m$ is travelling in a straight line, and a force $F$ will act on $m$ (in the same direction as $m$'s velocity) over a constant distance $d$; why doesn't $m$'s velocity matter to the calculation of work done on $m$ by $F$? Work is defined such that, in this example, the work done by $F$ on $m$ is equal to $Fd$, but it seems that if $m$ were moving slower, it would spend more time in the field, allowing $F$ more time to act on $m$, thereby doing more work. In fact, if $m$'s velocity were very great, it would hardly spend time in $F$'s field at all (so very little work done). Maybe I misunderstand work; can someone address this confusion of mine?


title: Are there any established theories as to why dubnium-268 and 270 have such high stability for a trans-actinide?

text: Dubnium-268 has a half life of 29h and 270, 23.15h. I know of the island of stability but if dubnium is in it, the island is very small as only rutherfordium has isotopes that approach the same stability. Is there some special property of the two nuclides that stabilise them?


title: Gravitational Anomalies and Topological Order

text: I wonder the relation of gravitational anomaly and topological order. Specifically: 1) What is the definition of gravitational anomaly here? 2) How are they related?


title: What's wrong with this faster-than-light gedankenexperiment?

text: It is common wisdom - and mathematically proven - that quantum entanglement cannot be used to bypass the relativistic speed limit and transfer information faster than light. So there must be something wrong with the following gedankenexperiment, but I can't figure out what: Let there be a device which (nearly) simultaneously creates lots of entangled, coherent photon pairs and sends them to Alice and Bob, each of them receiving one photon of each pair. Both are far away from the light source and have placed screens into the - highly focused - light beam, so that they detect some small area of light on the screen. Now Alice wants to transfer one bit of information to Bob. If it is a 0, she does nothing. If it is a 1, she puts an appropriate double-slit plate into the light path, immediately before the photon bunch arrives. This will create an interference pattern on her screen, and entanglement will instantly replicate the photons' paths and such the pattern onto Bob's screen. So if he sees an interference pattern instead of a dot, he knows that it's a 1, and vice versa. Of course Bob's screen will not show an exact copy of what Alice sees: it will be olverlayed by noise, e.g. from photons which bounced off Alice's double- slit plate or decohered through environment interaction. Worst case a statistical accident may create a pattern out of a 0-bit which looks like the result of interference. But we may optimize the signal/noise ratio through the experimental setup, and besides of that _any_ real-world communication channel is subject to partial information loss (which must be compensated by error correction). So it seems like this experiment transfers information faster than light. What did I miss?


title: Bose-Einstein condensation in 3D

text: I have read in many books that BEC takes place in momentum space and in only 3-dimensions. What is meant by this statement?


title: How do we measure the physical field of a particle?

text: In the renormalization procedure of quantum field theories, say $\lambda \phi^4$ theory for simplicity, we use the physical mass $m$, the physical coupling constant $\lambda$ and the physical field $\phi$ to fix the bare quantities $m_0$, $\lambda_0$ and $\phi_0$. It is clear that the physical mass $m$ and the physical coupling constant $\lambda$ can be found from experiments (and using the S-matrix). But how does one "measure" the physical field $\phi$? **Edit:** I would like to (hopefully) clarify my question. My question is related to field renormalization $\phi_0(x)=\sqrt{Z_\phi}\phi(x)$, and how we decide what value $\phi$ should be. For the physical mass and coupling constant, we can perform experimental measurements to determine their fixed values but we don't seem to do this for the physical field (as far as I understand; I still need to properly interpret JeffDror's answer). **Are we basically looking at the divergence of Feynman diagrams and choose $Z_\phi$ such that we can absorb this divergence?** If this is true, then this would mean that the "physical" field is a badly chosen word and it would make more sense to call it the "renormalized" field?


title: Why does the guy moving on spaceship look younger in twin paradox?

text: If there is no particular absolute choice of frame of reference, the guy who sits on Earth is also moving away from the guy on spaceship perspective and hence time on Earth should also dilate when viewed from the guy on spaceship perspective. But why does the guy moving on spaceship look younger in twin paradox? What am I misunderstanding terribly? ADDED:: Is time dilation symmetric? If one frame of reference are moving with constant velocity w.r.t other, we have to transformation relations $$\Delta t = \frac{\Delta t'}{\sqrt{1 - \frac{v^2}{c^2}}}$$ Does each one of them see clock on other tick slowly than their own?


title: How to estimate the number of Cooper pairs in type I and type II superconductors, respectively?

text: When Al (type I) enters a superconductor state ( Meissner state), how many conduction electrons form Cooper pairs, or how many Cooper pairs exist in the Al ( may be number of Cooper pairs / Volume ) When Nb ( type II ) enters a superconductor state ( Vortex state), how many conduction electrons form Cooper pairs, or how many Cooper pairs exist in the Nb ( may be number of Cooper pairs / Volume ) Should the number of Cooper pairs in a type II superconductor be significantly less than that in a type I superconductor ?


title: Gravity and Mass

text: Two bodies of equal size and mass meet in space. My question is: will they attract each other equally or will their attraction cancel each other out?. Also: how long does it take for the two bodies to actually make contact with each other? - hours, days or maybe years?


title: What is the meaning of this String Theory Equation from CERN?

text: I have recently visited CERN, and in the Globe they showed an equation from string theory. My knowledge about it goes only as far as 'The elegant universe', so no mathematics, but i would say that the sketch beneath is about the string coupling constant. Could anyone please explain the equation to me? ![enter image description here](http://i.stack.imgur.com/wEu9H.jpg)


title: Gravitational inverse-square law

text: I was looking at the gravitational inverse-square law: $$ F_G = G \frac{Mm}{r^2} $$ This law comes from some experimental data? Why it is an exact inverse-square law? Could it be $$ F_G = G \frac{Mm}{r^{2.00000000000000001}} $$ or there is a mathematical method to find exactly this law?


title: Quantum mechanics, whats possible?

text: There is a thread in Physicsforums.com which states due to Quantum Mechanics, if you wait long enough diamonds will appear in your pocket, it also states its possible for all your atoms to spontaneously re-arrange themselves so you turn into a Boeing airplane. Surely this is fiction?


Is it possible to charge a capacitor to any potential? Does it depend on the dielectric placed between them? Or, are there other factors affecting it?


title: Center of Gravity vs Center of Mass

text: 1. To calculate the center of gravity of a distribution of mass, can I use gravitational potential (scalar) or must I use gravitational field (vector)?    2. And why, generally, the center of gravity goes to center of mass when the point where we calculate the potential goes to far away from mass distribution?


I'm confused by renormalization . If a lagrangian has a term with negative mass dimension , why can't the divergences be absorbed into lagrangian coefficients? What's the difference between divergences that can be corrected and those that can't


title: How do I visualize the non-coaxial rotation of this device?

text: The picture below shows an isolated system with a fairly massive wheel at one end, attached via its axle to a long shaft, like a bike tire on a bike frame, but the bike frame is merely a low mass 'truss.' At the other end of this long shaft is a mass of roughly the same magnitude as the wheel, so the center of gravity (CG) is roughly in the middle of the shaft. This mass is fixed to the shaft with no rotation possible. The assembly is floating motionless in 'space', with no contact to anything else. ![Diagram of apparatus](http://i.stack.imgur.com/KE7dZ.png) If a motor on the 'truss' causes the wheel to spin in one direction, the truss would begin to spin in the other direction about the common center of mass. The net angular momentum would thus be zero both before and after the spinning commences. The wheel and the truss would rotate in the same plane. The actual rotation rate of each part is dependent upon the individual masses, wheel radius, and the length of the shaft. It is getting complex, but so far easy enough to envision in general. Now, place into the 'truss' a mechanism that causes this long shaft to rotate on its long axis (which would be perpendicular to the spin axis) while it is still undergoing the above rotation relative to the wheel. Upon rotation at this new joint, a force is applied to the axle of the spinning wheel (and of course to the mass at the other end of the truss, too) causing each part to try to turn in the opposite direction. Given that the net angular momentum is still zero, the vector sum of the individual parts (the spinning wheel and the body as a whole rotating around its CG) must be equal and opposite. I cannot envision the result, however, nor do I have the background to derive the equations of motion of this 'whirly gig.' The best I can imagine is that the plane of overall rotation should change, with the plane of the wheel's rotation changing in the opposite direction. This would seem to result in a state where the wheel is no longer spinning in the same plane as the overall assembly, but that would seem unsustainable and perhaps unstable. How can the behavior of this system be understood?


title: how does a glow lamp work

text: First, what do you call this in English? ![http://www.dieter- heidorn.de/Physik/SS/K06_Elektrisches%20Feld/K01_Ladung_Strom/K11_Ladung/Ladung02.gif](http://i.stack.imgur.com/YyIyM.gif) Second, how does it work? Why do I have not only light at the gas barrier between the two wires? Thanks!


When to use $f$ and when $\nu$ signifying frequency? I guess that when you mean frequency of electromagnetic wave, you use $\nu$, and $f$ otherwise?


title: Is there a limit to the charge of a body?

text: Can a body be limitlessly charged? Suppose a sphere of radius $R$. Can it be charged limitlessly?


title: How can a Jones vector give linear polarization along an axis?

text: If we represent a Jones vector by two complex-valued exponentials, $J_1 = e^{i \phi_1}$ and $J_2 = e^{i \phi_2}$, how can this ever give a polarization along the x-axis? We write such a polarization as $J_1 = 1, J_2 = 0$, but the exponents used can never give a zero value. Nor can we simply use the real component, as the complex phase determines circular or elliptical polarization. Is it just a matter of rotating our basis for, say, $J_1 = 1, J_2 = 1$ to give a polarization along some new x-axis?


title: Why is a degree Celsius exactly the same as a Kelvin?

text: How on earth is it possible that the difference between two temperatures in Celsius and Kelvin is exactly the same. Given the historical definition of Celsius, I find it hard to believe that this is pure coincidence.


title: Why must the angular part of the Schrodinger Equation be an eigenfunction of L^2?

text: I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part and a radial part. When dealing with the angular part of $\psi$, the book claims that the angular part "must" be an eigenfunction of $L^2$ (the square of the angular momentum operator) and since the eigenfunctions of $L^2$ are the spherical harmonics $Y_{lm}$, then the angular part of $\psi$ is just the spherical harmonic equations.   I am confused as to why the angular part of $\psi$ must be an eigenfunction of $L^2$.


title: Does entropy alter the probability of independent events?

text: So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up: > Given a fair coin that has been tossed 100 times, _each time landing heads_ > , would it be more likely that that the next coin flip be tails or heads? I can see that since the event is independent by definition, then the probability would be even for both heads and tails: $$P(h | 100 h) = P(t | 100 h)$$ But would this differ in a quantum mechanical standpoint? I have a feeling that $P(h | 100 h) < P(t | 100 h)$ because of the push towards equilibrium in the entropy of the system. Am I wrong to think this way? * * * FOLLOW UP: (turning out to be more of a statistical problem possibly?) Something the around the "equilibrium only exists in the infinite-time limit" idea is what I'm getting hitched on. The proportion of head to tails is 1 to 1 as number of trails approach infinity (this is a fact correct?). Therefore, if this must be the case, mustn't there be an enacting "force" per say that causes this state of being to (admitted unreachable, but _technically eventual_ ) case? Or is this thought process just illegitimate simple because the state exist on at the infinity case?


title: Single photon's effect on conservation of momentum?

text: When your looking at basic Compton theory you find that if you shoot a stream of photons at a particle (usually atoms or electrons), then you have the basic laws of conservation of momentum. The photon acts like a particle, like a "billiard ball." The photon interacts with the said electron and the photon goes off in a new path described by $h/\lambda_2$ ($h$ being Planck's constant and $\lambda_1$ being the original wavelength of the photon). This wavelength is increased. Using a basic vector diagram with $h/\lambda_1$, $h/\lambda_2$ and $m\vec{v}$ for the particle you get basic conservation of momentum. My question is basically what happens when you are only using a single photon? I'm not aware of any experiments done with a single photon, so far this concept (Compton experiments) have only been done with multiple photons. The reason a single photon is important is because the energy of a photon is inversely proportional to the wavelength. The problem that I have with this is that $E = h\nu$. This is how we get our inverse wavelength in the formula (wavelength and frequency being inversely proportional). With a single photon you have no frequency, since you only have 1 event/photon. Thus how can you place Planck's constant over $\lambda$ to represent the energy of the photon, since there is no frequency?


title: Time Evolution of a Manifold Embedding

text: Given a smooth manifold $\mathcal{M}$ with a simplicial complex embedding $\mathsf{S}$, what specific tools or methods can be used to give an analysis of the time evolution of the manifold given some initial conditions? More specifically, if I have a gauge group $G_{\phi}$ acting on the simplicial complex with subgroups $S, SO(3), T$ representing scaling, rotation, and translation on the manifold, how can I introduce time into this picture? This is a general question that has been applied in the context of Causal Dynamical Triangulations, and I am essentially looking for a reference on how to get started reading about this field, and other questions relating manifold triangulations and time evolution.


title: What is the importance of studying degeneration on $M_g$

text: Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$. It seems to be important in physics to study the degeneration of certain functions on $\overline{M_g}$ as you approach its boundary. For which functions on $M_g$ is it interesting to physicists to study their degeneration as you approach the boundary? I know of theta functions, Green functions and delta invariants. Are there others? As in my other question, here is an article by Wentworth which I find interesting.


title: Question on friction

text: ![enter image description here](http://i.stack.imgur.com/2TNoo.png) Please look at the figure carefully. The question is written, and one has to match the two columns 1 and 2 given under "choices and explanation". Please tell me if I am really wrong, i.e. would you match C with both 1 and 3, or just 3. (my answer and the right answer is shown at the right hand side) Thanks!


title: Lagrangian for Euler Equations in general relativity

text: The stress energy tensor for relativistic dust $$ T_{\mu\nu} = \rho v_\mu v_\nu $$ follows from the action $$ S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x = -\int c \sqrt{p_\mu p^\mu} d^4 x $$ where $p^\mu=\rho v^\mu \sqrt{ -g }$ is the 4-momentum _density_. One uses the formula: $$ T_{\mu\nu} = - {2\over\sqrt{ -g }}{\delta S_M\over\delta g^{\mu\nu}}\quad\quad\quad\quad\quad\quad\quad(1) $$ And the derivation is given for example in this question that I asked before (or in the Dirac book cited therein): http://physics.stackexchange.com/questions/17604/lagrangian- for-relativistic-dust-derivation-questions Question 1: is there any Lagrangian (or action) that would give the following stress energy tensor for a perfect fluid: $$ T_{\mu\nu} = \left(\rho+{p\over c^2}\right) v_\mu v_\nu + p g_{\mu\nu} $$ ? Question 2: What about Navier Stokes equations? Question 3: If the answer is no to any of the questions above, can the equation (1) still be used as the definition of the stress energy tensor? Or should rather one use a definition that the stress energy tensor is whatever appears on the right hand side of the Einstein's equations (even if it can't be derived from an action)?


title: How is the energy distributed in a proton-antiprotion annihilation?

text: I know the products of the annihilation, but I don't know how much energy each particle has or gets. For example I know that 1876 MeV is released for each annihilation. Now, this energy is distributed among a number of pions, so how much energy does each pion get ? Also, this energy is distributed between kinetic and rest mass energy, how is it distributed ? and where does the kinetic energy go when the pions decay ? And what about the electron we get from the muon decay ? how much energy does it get and is this energy easy to obtain or it will just fly away similar to a neutrino ? I mean how far will the electron go in a medium until its energy is absorbed ? EDIT : I asked this question because I am confused where the kinetic energy of the particles go. Firstly, the neutral pion gets 390 MeV total energy, of which 135 MeV is the rest mass energy and 255 MeV is its kinetic energy. As some people said before, the decay of the neutral pion result in 2 gamma rays each with 67 MeV, which is only the rest mass energy over two, so where did the kinetic energy go ? shouldn't the pion have resulted in 2 gamma rays with 195 MeV each considering energy conservation ? Secondly, the charged pions. as well as the neutral pion, they get 395 MeV of energy too. When they decay, the product is a muon and a neutrino which I dont know how the energy is distributed here. Then the muon decays into an electron or a positron and 2 more neutrinos which I also don't know how much energy they get. Thirdly, the kinetic energy of the charged pions. How do the charged pions lose their kinetic energy ? and what will happen if the charged pion decayed before losing its kinetic energy ? All these three questions haven't been discussed in the related question, and thus this is not a duplicate.


title: Which citizen-science astrophysics and astronomy projects currently exist?

text: Most of you probably know of _Galaxy Zoo_ , a citizen-science project to classify galaxies with help of untrained hobby-researchers. In mathematics, the _Polymath Project_ is well known for its success. SETI@home, for example, is not _citizen science_ as you do no active research, only your computer is crowdsourced. Are there projects requiring more than simply visual classification of astronomical pictures?


title: Where does a star's angular momentum go as its spin slows down?

text: So we know that stars slow down as they age. But total angular momentum must be conserved. Where does that angular momentum go? The dissipation of Earth's tides _somehow_ transfers Earth's angular momentum to the moon (as shown in my answer at http://www.quora.com/Has-the-Earths- rotational-period-always-been-24-hours-If-not-what-was-it-before-and-what- caused-the-change). But where does a star's dissipation go?


title: Would it be economical to add a counterweight to rocket launches?

text: It seems a large amount of rocket fuel during launches is spent to get the mass moving; indeed according to QuickLaunch, Inc. it takes 40% of the rocket fuel to get to Mach 1.3. It seems as though the engines are firing quite a while before liftoff, and considering that the full launch weight of the space shuttle is 4.4 million pounds (~2 million kg). Would it be feasible to add a counterweight system to help it get started? It seems as though one could be built with a structure a few hundred meters above the launch vehicle, which could significantly reduce the launch weight and get the upward motion started sooner. What I'd imagine is four cables attached to the launch vehicle, running up to the structure and each having ~400,000kg weights attached. This would make the rockets only need to lift ~400,000kg for the first, say, 200m, which would lead to much greater acceleration for this span and it'd be to Mach 1.3 much sooner. Is this too hard to make? Would it have any noticeable effect on the fuel requirements, or would it be negligible? Is the acceleration already near the limits of the astronauts' bodies? Or would it just be one other thing that could fail? The reason I ask it just because of the seemingly ludicrous amount of weight that needs to be launched. Are there any other methods in the works to assist the launch besides rockets for manned vehicles? It doesn't seem space guns or sky ramps are ever planning on having humans in the launch vehicles.


title: What's the differences between pseudospin and spin?

text: It seems that they both transform as an U(2) group, but I've been told that the three components of real spin change signs under inversion while it is not the case for pseudospin. Could someone name all their similar and different properties? The more exhaustive, the better.


title: Can I determine whether it is night at a location by calculating only the sun's elevation?

text: There are many formulas for determining sunrise and sunset times for locations, but for my application I only need to know if it is day or night (given a time, latitude and longitude). After studying the terms azimuth, altitude/elevation, and zenith, I am curious if I can calculate the sun's elevation, and use that value to determine day/night status alone. As I understand it, any value below the horizon (taking into consideration the various values for twilight) should tell me that it is night. I should be able to use -6 for civil twilight, -12 for nautical twilight, etc. Do I need to worry about azimuth also?


title: Why are magnetic field lines perpendicular to the surface of a ferromagnetic material?

text: It is known that magnetic field lines become nearly perpendicular to the surface of a ferromagnetic material. The quantitative proof which uses the boundary condition requires that magnetization at the surface be zero. **Question:** _Why is magnetization at the surface of a ferromagnetic material zero? Also, can someone give a qualitative explanation for the approaching perpendicularness of magnetic field lines and the surface of a ferromagnetic material?_


title: Difference between gapless excitations and Goldstone bosons in Condensed matter physics

text: I have been looking around on the web and in books to clarify this, but can't find a good explanation describing relationship/difference between gapless modes/excitations and Goldsone modes/bosons in Condensed matter physics. Does the term "gapless modes" mean that no energy is required for these modes/excitations or that only an infinitesimal amount of energy is required for such excitations? If Goldstone modes/excitations require some(small) amount of energy (as mentioned in Ref:http://web.mit.edu/8.334/www/lectures/lec3.pdf), how can they ever be gapless? Does a previously gapless mode/excitation develop a gap or remain gapless if a continuous symmetry is spontaneously broken in a system?


title: Comparing LED light with fluorescence light, which one is better in terms of energy conservation?

text: Comparing LED light with fluorescence light, which one is better in terms of energy conservation and why? I want to switch to one of the choice for above for home lighting, so any advise would be greatly appreciated.


The abundance ratio of a nuclide is the ratio of the number of atoms of one isotope to the number of atoms of another isotope of the **same chemical element**. It may also refer to the ratio of one isotope to the total number of atoms in a single-element sample. this is an example of The abundance ratio: $$U_{92}^{235}=0.720$$%. $$U_{92}^{238}=99.275$$%.   1. how we can measure The abundance ratio of a nuclide?   2. are there any resource for the Abundance ratio of nuclear isotopes in early earth!?   3. How old is planet Earth !?( _Accurate_ )


title: Work done on an object from different frames

text: Consider this situation: A car is moving on a road and applies brakes. The road exerts a force $F$ on the car, due to which the car stops in $S$ meters. Clearly, the work done by the road on the car is $-FS$. But, according to Newton's third law, an equal force by the car acts on the road. And this force is also displaced by a magnitude $S$ (from the road's frame). So, does this mean, that the car does work on the road too? Also, from the car's viewpoint, the force is not displaced at all. So, from the car's frame, no work is being done. How come? Secondly, consider a boat of mass $m$ accelerating at $a$ with respect to the water. The work done by the boat's engine on the boat is $maS$. But from the bank, it can be seen that the water is accelerating at $a$ in the opposite direction. So, from the bank frame, no force acts on the boat, so no work is being done. How is this possible?


title: Can you equate the diffusivity constant in random walks with the one in Brownian motion (Einstein relation)?

text: In an unbiased random walk in one dimension, the coefficient of diffusion is $D = l^2/2\tau$, where $l$ is the size of the jump and $\tau$ is time taken for that jump. In simple Brownian motion, Einstein's relation says that $D = \mu kT$ where $\mu$ is the mobility, $k$ is the Boltzmann constant and $T$ is temperature. In both cases, it turns out: $$ \langle x^2 \rangle = 2Dt$$ So my question is, can we equate the two constants? So, can we say that: $l^2/2\tau = \mu kT$?


title: Where does energy in a field come from?

text: Let us consider for example Earth's gravitational field. If we put a ball somewhere in this field, the ball starts to accelerate due to the gravitational force exerted on it. I understand the explanation for this : "Gravitational potential energy (GPE) is converted into kinetic energy". But why is it that this GPE seems to exist only when I introduce the ball into the gravitational field? Am I creating this GPE somewhere? Also, for my second question : If the gravitational field does work in accelerating the ball, then won't it have to lose energy in order to do all this work? Where does all this energy required come from? From all this thinking I come to the conclusion that a field is some sort of wizardy with an infinite amount of energy that can be transferred to objects placed in it. But I am perpetually confused because for all my life, I've been taught that energy cannot be created. So where do all these energies come about, really?


title: Does the Higgs boson (or the 125 GeV boson, if it's not exactly the Higgs as predicted) occur in nature?

text: If the Higgs boson mediates mass interactions, do they exist in nature? Are there Higgs bosons flying around all the time? Or do they only exist for a tiny fraction of a second while they mediate mass? As I understand it, the bosons are all mediators of interactions. We know that photons, gluons, and the W-/Z- bosons exist. Photons persist for very long durations as they speed through the cosmos. Does the Higgs/mass-mediating boson do this? I'm sort of having trouble getting a grasp on at what point the mass boson would exist and how that would work in practical fact. Also, it's entirely possible that this is a nonsensical question based on me misunderstanding everything. :)


title: What do physical properties of materials trigger the capacitive touch screen?

text: I have watched some youtube videos about capacitive touch screen http://www.youtube.com/watch?v=ZHzaVzYEZbw http://www.youtube.com/watch?v=GmCE18RMEeQ The videos show that a conductor(finger), in which charges can be induced, can be used to trigger the capacitive touch screen. However, I tried to wear a plastic glove to hold a metal rod to touch the screen and no detection is triggered. I really want to know the physics theory about the capacitive sensing. Can someone tell me what **physical properties or shape** trigger the capacitive touch screen? Is there any examples that **something WITHOUT conducting to human body** can trigger the screen? (P.S. I have read other posts about capacitive touch screen here and do not find a good answer so this is not a duplicate)


title: Layman's method to sharpen a wire (STM-tip)

text: We use a platinum-irididum wire to fabricate our STM tips. And by "fabricate" I mean to cut it with really sharp pliers or scissors. Sometimes we get good tips but most of the time they are not usable especially when you need a high aspect ratio and a sharp tip with preferably only "one atom" where the tunneling current goes through. Therefore my question: How could one process a platinum-iridium wire to get a really sharp tip? (Besides using chemicals to etch it) Here are some characteristics of the pt80ir20 wire that we use: http://shjmjs.en.b2b168.com/shop/supply/13658861.html The melting point is around 1800 ° C. And by "sharp" and "high aspect ratio" I mean a geometry like this: ![enter image description here](http://i.stack.imgur.com/fP8qj.png)


title: spectral functions

text: Please, I would like to understand why you call the function $A(k,\omega)$ (here :The Spectral Function in Many-Body Physics and its Relation to Quasiparticles ) a spectral function? For me, as a mathematician, a spectral function is a function which writes : $F(S)=f( \lambda(S))$ where for example $S$ is a symmetric matrix and $\lambda(S)$ is the vector of eigenvalues of $S$. Thank you in advance, Sincerely.


title: Characteristic quantities in Fiber optics

text: I'm having trouble finding typical quantities in fiber optic communication. In particular, what kind of **powers** are generally used (or what is the minimum that fiber optics receivers can detect effectively)? What **frequencies** of light are generally used, and what are typical **sampling rates?**


title: Can a balloon be used as an anchor point for a pulley?

text: For a physics/ engineering contest, I want to use a large balloon as an anchor point for a pulley. This would allow me to raise and drop masses. However, in testing, when I pull on the pulley the balloon just lowers and when I stop pulling the string the balloon rises with the item in tow. My theory for why this didnt work has to do with the momentum of the balloon vs the device being lifted Is the balloon not large enough? Should i use multiple? Is this even possible? **Edit** Here is an illustration and a better description:![Balloon Anchor](http://i.stack.imgur.com/EiqiQ.png) If I would like to use a balloon to hold up a pulley to allow items to be lifted into the sky. In a real world test, when I pull the lifting rope (brown line). The balloon lowers. When I stop pulling, the balloon then lifts the payload back to the original position. **Edit 2** Some more observations that may help the discussion:   * There are guidelines that tether the balloon in place it would continue to rise if able.   * No matter how softly I pull the pulley line the balloon lowers.   * As noted in a comment below, I estimate the balloon is capable of lifting 4 to 6 lbs total and the payload is only 1/4 to 1/2 lbs   * The friction of the pulley is very small it is free spinning and the lines in this case are small strings Also, while all I have is my gut reaction from seeing and feeling the forces; I would like to direct the attention back towards the momentum and/or inertia of the balloon. It seems "easier" to move the balloon. It does return to its equilibrium, but seems easier to affect with smaller forces. Perhaps due to its small mass?


title: Lorentz boost matrix for an arbitrary direction in terms of rapidity

text: We have derived the Lorentz boost matrix for a boost in the x-direction in class, in terms of rapidity which from Wikipedia is: Assume boost is along a direction $\hat{n}=n_x \hat{i}+n_y \hat{j}+n_z \hat{k}$, ![enter image description here](http://i.stack.imgur.com/hfMhe.png) How do I generalise this to a boost in any arbitrary direction, and what is the result? Any help most appreciated.


title: Fermi and Boltzmann distribution of carriers in semiconductor

text: What are the requirements for describing charge carriers (e.g. electrons) in a semiconducting material by \- Fermi distribution \- Boltzmann distribution When do we apply the one or the other? If the explanation to this question is in Ashcroft/Mermin, reference to the relevant chapter would be appreciated. I don't agree with both commentators so far. * * * Edit Consider Eq. 21 in Sze, PHysics of Semiconductor Devices: $$n = N_C exp\left(-\frac{E_C-E_F}{kT}\right)$$ or Eq. 2.16 in Pierret, Semiconductor device fundamentals.


title: Relativistic kinematics of particle decay

text: Suppose a particle decays to three other particles. The masses of all particles are assumed to be known and we work in the rest frame of the parent particle. So there are 12 parameters for this because of the 4-momenta of the three daughter particles. Now the constraint of momentum conservation imposes 4 constraints and reduces the number of parameters to 8. Further, the energy- momentum relation for each particle imposes three more constraints and reduces the number of parameters to 5. Are there any other constraints that reduce the number of parameters to 2?


title: Is there any theory about extra-Universal place?

text: I mean you can probably imagine cells and extracellular space between them. In biology some things can go through the cell membrane in and out. What if universe/s are "similar" and some form of "energy" can leave the Universe and go to extra-universal place? And if it has certain amount new baby Universe is born? Are there some theories that operates with something I have speak above?


title: Are quarks the limits? The end of the fundamental science. For collisions on more higher energies will lead to black holes after all?

text: Are quarks the limit and the Plank scale is believed to be the limit of distance when the very concept of space and length cease to exist (10^-19) Any attempt to research the existence of shorter distances by performing collisions with higher energies will inevitably end up with black holes of larger and larger size **despite splitting the substance into smaller pieces**. The appearance of those black holes would herald the end to the important direction of science. And a new task would emerge - the research of the additional space dimensions? So is this view all true?


title: Waves travelling with water flow

text: Suppose I use a tool to create a circular wave in the river. If there are two fish swimming 1m from the source (2m from one another), they will both feel the wave at the same time. What will happen if the river flows from one fish to the other? How will it affect the waves?


title: What is the difference between infrared heat and "regular" heat?

text: In Feynman's terms temperature is the speed at which atoms are 'jiggling'. Now, let's suppose I've just eaten a sizable dinner, and my body temperature just got a tad up. Am I emitting more photons in the infrared spectrum, or are my atoms 'jiggling' faster and bouncing more of the air component atoms (nitrogen, oxygen etc.)? Or is it the same, and all heat energy transfer is mediated by photons? Surely not all heat is mediated by the IR spectrum of the light? Otherwise only objects made of materials able to absorb IR photons energy levels would heat up? Can't quite decide if it fits the scope of my question, but: where does heat reaching my skin from Sun come from? I plan to politely ignore answers 'from the Sun' :) I mean does it come from IR radiation? And more generally: why is heat commonly attributed to IR spectrum? I take heat is a form of energy, if so, why doesn't my yellow car heat me up 'by it's photons' - visible spectrum is supposed to be of higher frequency = energy than IR?


title: Ideal gas law, pressure increase and temperature

text: If I had a container, full with air, and I suddenly decreased the volume of the container, forcing the air into a smaller volume, will it be considered as compression, will it result in an increase in temperature, and why? P.S: the container is strong enough to bear high pressure and not to explode.


title: What is happening as our Universe is expanding? Is entropy increasing or decreasing?

text: Scientists say that entropy of our universe is increasing as it is expanding and our universe is cooling down gradually from the time of it's birth.If something is getting cooler and cooler then how can it become more random (entropy increase) with the passage of time.According to law of thermodynamics ,at absolute zero temperature entropy is zero.That means as we go down and down to the temperature scale entropy must decrease but why is it not happening in the case of our universe?


title: Photoelectric effect with protons

text: Is it possible to make a metal plate emit protons (not electrons) when it is illuminated with light? If possible, how?


title: Bogoliubov - de Gennes Hamiltonian and Zeeman energy

text: For my system I can write down the Hamiltonian in this form: $$ H = \begin{pmatrix} \epsilon_{1\downarrow}-\mu_{B}B & 0 & 0 & 0 \\\ 0 & \epsilon_{2\uparrow}+\mu_{B}B & 0 & 0 \\\ 0 & 0 & \epsilon_{1\uparrow}+\mu_{B}B & 0 \\\ 0 & 0 & 0 & \epsilon_{2\downarrow}-\mu_{B}B \end{pmatrix} $$ where $\mu_{B}B$ are the Zeeman split. Now I want to bring this system in contact with a superconductor and want to write down the Bogoliubov - de Gennes Hamiltonian. In my opinion the Bogoluibov - de Gennes Hamiltonian has this form since the Zeeman energy does not dependent that I have quasiparticle or holes: $$ \mathcal{H} = \begin{pmatrix} \epsilon_{1\downarrow}& 0 & 0 & 0 \\\ 0 & \epsilon_{2\uparrow} & 0 & 0 \\\ 0 & 0 & \epsilon_{1\uparrow} & 0 \\\ 0 & 0 & 0 & \epsilon_{2\downarrow} \end{pmatrix}\tau_{z} \+ \begin{pmatrix} -\mu_{B}B & 0 & 0 & 0 \\\ 0 & +\mu_{B}B & 0 & 0 \\\ 0 & 0 & +\mu_{B}B & 0 \\\ 0 & 0 & 0 & -\mu_{B}B \end{pmatrix}1_{\tau} + H_{\Delta}\tau_{x} $$ Without Zeeman term the problem is a standard textbook problem, since I have directly my Nambu spinor $\psi^{\dagger} = \left(c^{\dagger}_{1\downarrow},c^{\dagger}_{2\uparrow},c^{\dagger}_{1\uparrow},c^{\dagger}_{2\uparrow},c_{1\downarrow},c_{2\uparrow},c_{1\uparrow},c_{2\uparrow}\right)$ and can write down the Hamiltonian in the correct second quantization notation. But if I add the Zeeman energy in my second quantization Hamiltonian vanish my Zeeman term with this Nambu spinor. If a write in my Bogoliubov - de Gennes $$ \begin{pmatrix} -\mu_{B}B & 0 & 0 & 0 \\\ 0 & +\mu_{B}B & 0 & 0 \\\ 0 & 0 & +\mu_{B}B & 0 \\\ 0 & 0 & 0 & -\mu_{B}B \end{pmatrix}\tau_{z} $$ I get the correct results but this means that I will have a sign flip in my Bogoliubov - de Gennes Hamiltonian for quasiparticles an holes, which is in my opinion wrong! My question now is how I must changes my Nambu spinor so that my Zeeman term in my Hamiltonian will do not vanish or can I have a sign flip for quasiparticles and holes in the Zeeman energy?


title: Can a fly pierce itself onto a cactus needle?

text: Somebody on reddit posted a ridiculous picture today of a fly pierced onto a needle of a cactus: http://www.reddit.com/r/pics/comments/xarue/what_are_the_odds_of_this_accident/ ![](http://i.imgur.com/OKP8R.jpg) Whilst the OP claims the picture to be real, several people doubted the fly could ever reach enough momentum to actually pierce itself onto the cactus. Using estimates of the appropriate variables needed, could somebody calculate the plausibility of the OP's claim? How would one go about such a calculation? My hunch would be that it can be estimated using the fly's momentum but how can the required piercing force be calculated?


title: Charge-less, Mass-less, Spin Fields

text: after looking through a couple QFT texts it seems that all the spin-1/2 fields come associated with a charge of some sort. I was wondering if it's possible to write down a classical lagrangian (with Lorentz invariance) such that after quantization, the excitations of the field are merely spin-1/2 particles with no associated charges (electric, color) of any kind? That is,operators like $a^{\dagger}$ would only make single particle states with helicity $\pm \frac{1}{2}$ and no associated $U(n)$ or $SU(n)$ charges. Thanks.


title: In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?

text: Isham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is higher order typed intuitionistic logic. In their theory what role is played by intuitionistic logic? What are the types in their theory? I've also asked this question on Math.Overflow


title: Why is the valence band maximum at the gamma point in the bandstructure view of dispersion relation?

text: Why is the valence band maximum for most semiconductors at the gamma point in the bandstructure view of dispersion relation


title: Electric field. Linear charge density

text: I was wondering if anyone could help me out in this exercise I've been struggling to solve. A straight, nonconducting plastic wire $ 8.50 cm $ long carries a charge density of 175 $ nC/m$ distributed uniformly along its length. It is lying on a horizontal tabletop. Find the magnitude and direction of the electric field this wire produces at a point $ 6.00 cm $ directly above its midpoint. I can't use Gauss's law because we simply haven't been taught that. $$ E_y={KdQ \over r^2}sin \phi $$ I've tried using the equation above because there's not an electric field in the x-component, but I still get nowhere. I did use integration, but I still don't get the right answer I've got this: $$sin \phi={D \over r} $$ Where D is the distance from the midpoint of the wire to the point. $$ r^2=(x-{L \over 2})^2+D^2$$ Therefore: $$ E_y= \int {K\lambda D \over [(x-{L \over 2})^2+D^2]^{(3/2)} }$$ But when I solve that and evaluate from $0$ to ${L } $ I still don't get it right.


title: Are the field lines the same as the trajectories of a particle with initial velocity zero

text: Is it true that the field lines of an electric field are identical to the trajectories of a charged particle with initial velocity zero? If so, how can one prove it? The claim is from a german physics book from Nolting "Grundkurs theoretische Physik 3 - Elektrodynamik" page 51, let me quote: > Man führt Feldlinien ein und versteht darunter die Bahnen, auf denen sich > ein kleiner, **positiv** geladener, anfangs ruhender Körper aufgrund der > Coulomb-Kraft (2.11) bzw. (2.20) fortbewegen würde. In english: > One introduces field lines and means trajectories along which a small, > positively charged, initially resting body moves due to the Coulomb-foce > (2.11) resp. (2.20). 2.11 is just the coulomb law, 2.20 is $F = q E$. (If someone has a better translation, feel free to edit it). I don't see why this should be true. So it would be great to see a proof or a counterexample with solved equations of motion. For a magnetic field this claim is obviously wrong since the Lorentz Force depends linearly on the velocity. Are there other physical fields where the claim is analogously true? **Edit:** The answers show that the claim is not true in general but holds in the special case of a highly viscous medium. Is this also the case for moving charged cotton along the field lines in air, as shown in this animation: http://www.leifiphysik.de/web_ph09_g8/grundwissen/01e_feldlinien/01e_feldlinien.htm ? Do you have any references or more details for this viscous media limit? Do you have any computational counter example why it doesn't hold in general or a simulation which shows that?


title: How is a cathode ray tube different from beta minus radiation?

text: In beta minus the result is one neutron in the nucleus changing to a proton, plus an electron and an anti-neutrino being sent off. The antineutrino is indifferent to our health. So I guess what makes a beta source dangerous compared to a cathode ray tube must be a difference in the kinetic energy of the emitted electrons?


title: What does the dual of a tensor mean (e.g. dual stress tensor in relativistic ED)?

text: I know what the dual of a vector means (as a map to its field), and I am also aware of of the definition a dual of a tensor as, $$F^{*ij} = \frac{1}{2} \epsilon^{ijkl} F_{kl}\tag{1}$$ I just don't understand how to connect this to the definition of the dual of a vector. Or are they entirely different concepts? If they are different then why use the word dual for it? I know this is kind of mathematical or may be a stupid question, but I have a problem with understanding the need for dual of Dual Field strength Tensor in relativistic ED. I mean you could say that I am going to define another tensor using eq. (1) call it whatever we like.


title: Other kind of Brachistochrone problem

text: We know the Brachistochrone problem that to find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. I wonder if we use a line segment mass on a curve with the same problem. It is clear that the line segment mass will touch two point on the curve. Which curve equation must be for the least time in that case? I do not know how to start. Note: Line segment mass is released from point A and its finish place is origin (O). the line segment mass is homogen and lenght is $l$ and mass is $m$. no friction is in the system.Point $A(x_1,y_1)$ and Point $B(x_2,y_2)$ are given starting points. ![enter image description here](http://i.stack.imgur.com/P0naw.png) Thanks for answers


title: Particle number conservation equals $U(1)$-symmetry?

text: If have by now frequently read the above but never really understood it. It is said that the particle number conservations is related to the phase of the wave function, but how?


title: Qualitative discussion about entropy and disorder

text: Many discussions about entropy and disorder use examples of decks of cards, pages of books thrown in the air, two gases being mixed in a container, even the state of a nursery at the end of the day compared to the beginning of the day in order to explain the idea of order (and disorder). In all these examples it is pointed out that the disorder of the system increases, or that the system is in an ordered state and finishes in a disordered state after something has happened. Take the case of throwing the pages of the book in the air. You start with the pages numbered in sequence (I didn't want to use the for "order"), you throw them in the air, they land on the floor, you collect them up and notice the pages are not in sequence anymore. ANd the point is "They are not in the sequence _I_ call ordered. Nonetheless, they are in a new sequence." And, it appears to me that the probability to find the pages in this precise new sequence is equal to find them in the original sequence". In that sense, 'order' seems to be something that us humans define and it doesn't appear to be a property of the system. On the other hand, I can see that in the case of two gases mixing, empirically we find more states where the two types of molecules are occupying the entire volume of a container than one type of molecule in the left side and the other type in the right side of the container. Nonetheless, the precise state of each molecule, its position and therefore the entire state of the mixed up system is qualitative the same, isn't it? Isn't it equally difficult to make each molecule occupy that precise position in the mixed up state as in the unmixed state? Does this make sense? Thanks, Marcio


title: Action on Lard Oil

text: If water is mixed with lard oil and heated (creating some _super-critical_ liquid with water), how does this affect the volatility of the mixture in comparison with its _purity_..? So, My question is: What happens when a mixture of lard oil and water is compressed and then heated to over some $\approx800^o\text{C}$ almost instantaneously? **Note:** I'm no physicist or chemist, so simplicity would be appreciated :-)


title: Difference between spinor and vector field

text: How do we distinguish spinors and vector fields? I want to know it in terms of physics with mathematical argument.


title: Proving the existence of the magnetic potential

text: Suppose $\vec{B}$ is a differentiable vector field defined everywhere such that $\nabla\cdot \vec{B}=0$. Define $\vec{A}$ by the integral $$A_1=\int_0^1 \lambda(xB_2(\lambda x,\lambda y,\lambda z)- yB_3(\lambda x,\lambda y,\lambda z)) d\lambda$$ Together with its two cyclic permutations for $A_2,A_3$ I'm trying to work out two things here: $1.$ What is $\frac{d}{d\lambda}B_i(\lambda x,\lambda y,\lambda z)$ $2.$ How we can use $1.$ to determine $\frac{\partial A_2}{\partial x}-\frac{\partial A_1}{\partial y}=B_3$ From this we can deduce the existance of the magnetic potential by extending $2.$? This is what I have so far: Is $\frac{d}{d\lambda}B_i(\lambda x,\lambda y,\lambda z)=(x,y,x) \cdot \nabla B_i$? And can we bring the partial derivative on $A_i$ inside the integral? I have proceeded along these lines but have not found a way to substitute. Any help would be greatly appreciated!


title: The meaning of potential in Bohm-Aharonov experiment

text: The Bohm-Aharonov experiment involves a magnetic field inside a cylinder which is zero outside that cylinder. Nonetheless it affects the electrons moving outside the cylinder. The explanation for this (as far as I understand) is that even though the field is zero outside the cylinder, the _electromagnetic potential_ is not zero and can affect the electrons. In mathematical language, the EM field is the curvature of a connection (that plays the role of the EM potential) on the 3-dimensional space minus the cylinder. The curvature (and so the field) vanish but the connection is nonzero and has a _holonomy_ around the cylinder. (And apparently this experiment was the begining of physical gauge theory.) **Questions:**   1. What is the physical meaning of the EM potential in this case?    2. How is it related to the quantum theory?    3. Does it have anything to do with quantum fluctuations?


title: Quantum Box and Quantum Number

text: How many quantum numbers are needed to describe a stationary state of a particle in a multi-dimensional quantum box (say 73)?


title: How long does it takes for an object to slide on an incline ramp?

text: I hope I am asking this question in the correct site. Here is my question: if there is an incline at $70$ degrees, the object's friction is $\mu = 0.1$, and the incline is $1$ meter long, how long does it take for the object to reach the edge of the board? It has been a while since I have taken physics so I just need a little reminder. I need to write a python script to do all these calculations, and I can do that part -- I just need to know how to solve this problem.


title: Gravitational constant in higher dimensions?

text: From Newton's law of gravitation we know that $$F=G\frac{m_1m_2}{r^2}$$ where $G$ is gravitational constant. We can also see that it has dimensions $$[G]=\frac{[L]^3}{[M][T]^2}$$ and we have a good numerical estimate of its value ($G\simeq 6.67\times 10^{-11} N(m/kg)^2$). I've read (for instance in the paper I'm currently mostly interested in, Kerr/CFT correspondence) that in higher dimensions, there are 4 dimensional gravitational constant, and in the search for explanation of it, I've also found that in string theory we have gravitational constants of higher dimensions. But I haven't seen any formula that would give me mean to calculate it in higher dimensions. Is there such a thing, or is the definition of it theory dependent?


title: What causes the unexpected change in acceleration for flybys of spacecraft?

text: If the vehicle is not operating on RTG, then thermal recoils of photons shouldn't be considered as in the case of PIONEER. Then what actually accelerate the spacecraft from expected value (expected by Gravitational Slingshot) during swing by?


title: When can I use $\wedge$ instead of curl?

text: It seems in some circles the wedge product is used in preference to curl. I have a basic understanding of Green and Stokes' formula, I wish to use the $\wedge$ notation from now on. Can someone tell me if this is commonly done, and if so what is the underlying assumption of the surface. If it is not too much to ask, can someone show me how to write say Maxwell's equations using $\wedge$ instead of Curl


title: Continuous spectra of photons

text: I guess this is a basic quantum mechanics problem, but I'm not entirely sure of my answer. Suppose we have an electron in a hydrogen atom having the state \begin{equation} \frac{1}{\sqrt{x^2+(1-x)^2}}\left[x\ |4s\rangle + (1-x)\ |3p\rangle\right] \end{equation} Now, we change all of their energy levels according to Hund's rule. Without going into the details of which states the electron goes into, it suffices for us to say that we can write the change in energy in the form of, \begin{equation} \Delta E = \frac{x^2}{x^2+(1-x)^2}E_{4s\rightarrow??}+ \frac{(1-x)^2}{x^2+(1-x)^2}E_{3p\rightarrow??} \end{equation} Then it seems that by varying $x\in[0,1]$, we can have some kind of a continuous spectrum of energies being emitted. I am not doubting that if we only have the individual states, the change in energy is discrete, nor am I stating that from a state with a fixed $x$, arbitrary values of the change in energy can be obtained. The change in energy will be decided by the value of $x$. There are two ways in which I can think of exits to this problem, but I am unsure of either.   1. The change in energy levels each release a photon (or some part of?). So there are two photons (or some part of) released.   2. Electrons can't have such a kind of wave-function. What do you think?


title: Confusion with the torque

text: Consider an imaginary vertical plane. Now say, a body is falling freely (under earth's attraction). If you consider any axis that is perpendicular to that plane. We get a non-zero value for torque. Then why is it that body is not moving in a circular path about that axis?


title: Train motion... Push or Pull?

text: While arguing against my friend today about the turbulence appearing between train's wheels. I told that the train pushes air aside during its motion through the tracks. But, he rejected it. Then, what's happening in air (other than air drag) when a _fast moving_ heavy object slices through it? How does the motion of air look like in there?


title: Tunnel through Ceres

text: Question edited: If you dig a tunnel through a large asteroid like Ceres along its axis of rotation and jumped in then what would be the first thing to stop you from falling back and forth along the tunnel length ? Possibilities include: Dmitry Brant mentions gravitational waves and charged particles. John Rennie mentions drag from impure vacuum. Perturbations from other planets could shift axis of rotation causing you to hit the side.


title: Earth-Moon orbiting each other after being engulfed by Red Giant

text: Recently some exoplanets were discovered which are thought to be the leftover cores of giant planets that had survived a star becoming a Red Giant and then shrinking back to a subdwarf. If giant planet cores can last the lifetime of a Red Giant, then maybe smaller planets can survive at least for a while. When the Sun becomes Red Giant, if the Sun engulfs the Earth and Moon before they have evaporated, what will happen to the Earth-Moon orbit ? Will they be crashed into each other, or will they drift apart or will the orbit remain stable for a while before they are melted and evaporated away? Edit: Newly found planets are 'roasted remains' BBC News, 21 December 2011 Edit: More planetary systems around white dwarfs (WD 0421+162 and WD 0431+126) that shows signs of planets being consumed by the stars. http://news.discovery.com/space/alien-life-exoplanets/hubble-discovers-planet- graveyard-130509.htm


title: T-duality approaches

text: The textbook approach to explaining T-dualities is to show that a type of T-duality transformation "inverts the radius of the circle, that is, it maps $R\rightarrow\tilde{R} = \alpha'/R$ and it leaves the mass formula for the string invariant provided that the string winding number is exchanged with the Kaluza-Klein excitation number." 1 However, the broader classification of T-duality appears imply that theories are T-daul if there is any type of transformation that changes on theory into the other. So the question is whether there are other approaches to showing T-duality, or is there a "canonical" approach for T-duality. String Theory and M-Theory: A Modern Introduction [Hardcover] Katrin Becker (Author), Melanie Becker (Author), John H. Schwarz (Author)


title: Is there any thing other than time that "triggers" a radioactive atom to decay?

text: Say you have a vial of tritium and monitor their atomic decay with a geiger counter. How does an atom "know" when it's time to decay? It seems odd that all the tritium atoms are identical except with respect to their time of decay.


title: why cannot fermions have non-zero vacuum expectation value?

text: In quantum field theory, scalar can take non-zero vacuum expectation value(vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory take non-zero vacuum expectation value? What forbids fermions to take vevs?


title: What would be a proper set of subjects, along with their order, for someone interested in string theory?

text: If one wanted to study string theory, what subjects should they learn first and what order should the study them? I would imagine that there are opionions, but I suspect there is a natural order, or at least and heirarchy of subjects.


title: Mean optical depth in plane parallel atmospheres

text: I have the second edition of Houghton's "The Physics of Atmospheres". In section 2.2 he says one can do simple radiative transfer calculations in a plane parallel atmosphere by assuming that there are two fluxes, one going vertically up and one vertically down. In reality the radiation is going in all directions, but the two streams represent the amount integrated over the two respective hemispheres. Now in reality different rays will see a given layer of atmosphere as having different optical depths, depending on the angle a given ray makes with the normal. Houghton says that detailed calculations show that one can take this into account by replacing the true thickness of a given layer dz with 5/3 dz. This is my question-- Where does that 5/3 factor come from? When I do the calculation for an optically thin absorbing layer (as one would expect for something of infinitesmal thickness dz) I find that an initially isotropic stream (or rather, that half which is going either down or up) will have twice as much energy absorbed as would happen if all the radiation were travelling along a line normal to the layer. So I would have guessed you'd replace dz with 2 dz rather than 5/3 dz, but Houghton is the expert. Houghton uses this 5/3 factor several times in the book.


title: why do the electroweak vacuum have to be charge and color neutral?

text: My question is why the electroweak vacuum of the Standard Model have to electroweak charge and QCD color neutral? What goes wrong if electroweak vacuum has either non-zero charge or color quantum number?


title: Sign convention in optics

text: Why is the sign convention used in the derivation of the lens formula and yet used again when it is applied in numerical problems? Won't the whole idea of sign convention be eliminated if it is used twice?


title: What if exactly half the Earth's population jumped at one instant? + Secondary Question

text: I read somewhere that when you jump, the sole effect caused by your jump on the earth moves it about $10^{-18}m$ (I don't remember the figure exactly, but I think it was that). However - obviously - with so many people running, jumping, etc. on the whole surface of the earth, the whole effect is canceled out, so it's safe to say there is no net displacement caused by us. This got me to wonder, what if the whole population of one longitudinal hemisphere of the earth jumped at the exact same time - while the other half remained stationary - **_would we be able to notice any discernable displacement in the short time before we all land back to the ground?_** Let's consider the earth to have a perfect distribution of people on both hemispheres, and let's consider the people of the Eastern Hemisphere to jump. Now the people jumping along the Prime Meridian and the International Date Line (these two lines together form the circle that divides the earth into the West and Eastern Hemispheres) would produce no effect, since they would simply cancel each other out. However, the closer you go to $0°N, 90°E$ (the centre of the East Hemisphere), the component of force which adds up will keep increasing. So there will be a net force in the direction of the Western Hemisphere. I was wondering if it would be noticeable. ![enter image description here](http://i.stack.imgur.com/6Pk9u.gif) * * * Another question which just struck me: Out of all the satellites/rockets/space-shuttles we've sent out, have **_they_** caused any displacement on the earth? They are quite massive in comparison to _us_ (not the earth, of course), and have large speeds. Many of them are continuously moving further and further away from the earth - so there's no question of them falling back to earth and thus shifting it to its original position again. Will the momentum be enough to displace the earth?


title: Maxwell's Equations in curved spacetime

text: I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary derivatives with covariant derivatives. But I have read somewhere that this generalization is not unique and it is just the simplest one. Can anyone introduce some resources about this subject and how electromagnetism and Maxwell's equations are generalized to curved spacetime?


title: What bends fabric of space-time?

text: I know that mass can bend fabric of space-time, which causes gravity by making an object curve around a planet or star but is there anything else that can bend it? Other energy sources, forces anything?


title: Why is the value of thrust for a perfectly spherical event equal to ${\frac{1}{2}}$?

text: In a particle collision the _thrust_ is defined by: $$ T = max_{\hat{n}} \frac {\sum_i \left| \hat{p}_i . \hat{n}_i \right|}{\sum_i \left| \hat{p}_i \right|} $$ where $\hat{n}$ is the unit vector that maximizes the ratio of the sums ($\hat{n}$ is called the thrust axis) and the sum is over all the particles emerging from the collision. In some notes I have, it is stated simply that the value of thrust for a perfectly spherical event is ${\frac{1}{2}}$. Why is this?


title: Question about the Dirac notation for partial trace

text: I saw the following definition for the partial trace operator: > $\rho_A=\sum_k \langle e_k|\rho_{AB}|e_k\rangle$, where $e_k$ is basis for > the state space of system $B$. From what I know, in the Dirac notation, the meaning of $\langle v|A|u\rangle$ is the inner product of the vectors $|v\rangle$ and $A|u\rangle$, so I have two problems with this notation of the partial trace. First, how can an inner product be an operator? An inner product should be a complex number, so I guess that inner product represents an operator somhow. Second, what is the meaning of $\rho_{AB}|e_k\rangle$? $\rho_{AB}$ is a mapping on the space $A\otimes B$, but $e_k$ is a vector from the space $B$. So, I don't really know how to interpret the meaning of this notation.


title: Does Faraday cage block magnetic field?

text: I want to block magnetic field of the very strong magnet, can I put it inside faraday cage to block its magnetic field?


title: Expansion of the universe and strain

text: From cosmological models that involve expansion of the universe, can we not say that there are ever increasing tidal forces felt by solid bodies? If so, the material in solid bodies like metal blocks, glass rods, skeletal systems will tend to separate causing a strain on the body which counteracts the expansion If the tidal forces increase with time, will there not come a point in time, when the stress limit is reached and our bodies begin to shatter under intense tidal forces (similar to 'spaghettification')? If the above is true, using present cosmological data, has anyone calculated how long it will take before our bones shatter?


title: $Z_2 $ topological index in spin liquid

text: What is $Z_2 $ topological index in spin liquid system? How to understand its physical picture in condensed matter?


title: Is it the act of measuring a quantum particle that causes it to lose its uncertainty?

text: I have designed an experiment. Without going into detail it resolves around the double slit quantum eraser experiments. If we can infer the location of a particle without actually measuring it, does it remain in a quantum state? After all, we have not measured or detected that particle in any way. If not, it can not be the act of measuring it, but merely the fact we know about it that effects its quantum state. This does not fit any model I know of. If it is true that you do not need to measure or detect a particle to affect its state, what implications does that have for quantum mechanics?


title: Pull up and Pull down register

text: Currently I am working with `Pull up and pull down registers` and trying to understand what does it mean? But could not able to understand. I searched in Wikipedia but still confused.


title: Why does a gas inside a closed container experience atmosperic pressure when the gas itself is not in contact with the atmosphere?

text: I know this is a very basic (and probably stupid) question, but I have been confused about this for a long time.


title: What is meant by correlation propagation?

text: What is meant by correlation propagation in physics? I have an intuitive understanding but are there any introductory notes ( more mathematical oriented) and with some physical examples?


title: In solving the hydrogen atom, how to see intuitively in advance that the spin effects to the energy spectrum can be ignored?

text: When the hydrogen atom is solved in QM books spin is usually ignored because its effect is to add tiny piece to the energy. My question is, is there a way to see this in advance, to see that if we included the spin interaction pieces to the Hamiltonian that will contribute so little to the energy spectrum hence we can ignore it for the 1st approximation?


title: The limit of radio wave penetration

text: Why can I listen to my mobile phone's radio clearly inside the bus, inside the train, but not inside the elevator? Also, there is an interference of radio signal when the train is accelerating or decelerating. What is the reason behind this?


title: What does it mean if a = g in this situation?

text: I basically solved this problem, but I am unsure what the final equation actually means. > ![blocks on table](http://img560.imageshack.us/img560/9804/83508925.jpg) > > Write an expression for solving the mass of block C if mass B moves to the > right with an acceleration of $a$. Note that the coefficient of friction > between the table and mass B is $\mu$ and assume the mass of the string and > pulley are massless. > > _Hint:_ $m_C > m_A + m_B$ Not sure how to include my Free-Body Diagrams, but my final answer looks like $m_C = \frac{1}{g-a}\left (a\left ( m_A + m_B \right ) + g \left ( m_A + \mu m_b \right ) \right )$ Here is my question what happens if $a \to g$? It certainly can't mean mass C will become infinite. How would that even work? I also thought it might mean that the string might break but wouldn't that mean all strings tied to any block accelerating at g would break? Thanks


title: Einstein's Mass-Energy Equivalence versus Quantum Kinetic Energy

text: Using a naive view of Einstein's Energy Mass Equivalence $E=mc^2$ (where m is mass and c is the speed of light), it seems tempting to interpret this as a quantum mechanical version of the inherent kinetic energy for a collection of relativistic particles. If we assume that all quantum particles travel with constant velocity c through 4-dimensional spacetime, this means that if a particle has attained geometrical lightspeed, it's velocity in the time dimension must be zero. If we try to freeze a particle at some location, it will still move randomly in spacetime with velocity c, and consequently it becomes increasingly blurred, as we try to fix it's position by cooling it down. In this naive view, quantum uncertainty is related to the inherent kinetic energy of quantum particles. The expectation would then be that the kinetic energy equivalence of mass would be $\frac{1}{2} m c^2$. Is there any actual relation between the equations for mass-energy and kinetic energy, and if so what happens with the $\frac{1}{2}$ factor?