title: What truly is mass, and is there a direct way to measure it?

text: We know a mass of an object of one kilogram as an object that weighs W = mg = 9.8 N and we reference it to that, (when it should as a fundamental parameter describe weight not the opposite). But if we were to describe mass to an alien civilization on an alien planet we are exchanging knowledge with, by sending them a one kilogram object, according to their gravity they will measure it differently. Also their star could be curving space time in such a way, or their velocity according to SR will cause them to perceive mass on our planet -if they observe from away- differently. If we asked a crew on a space ship moving at a speed close to the speed of light wrt us, or moving in a gravitational field they don't know about, to measure the mass of our planet, they will get different results. On the same principle, we could be measuring the mass of far celestial objects like planets, differently. I perceive space time as full of curves and irregularities. We know the about some of these and we don't about others. I mean we know about the earth's gravity, the sun's but we ignore the effect of the galaxy and the cluster, dark matter, and who knows what else. Besides we change our position all the time with relation to these external factors that bend spacetime. So our measurements to an outside neutral observer, say these aliens could change. I've found definitions of mass like "the quantity of matter in an object" but that seems like the good old: mass = volume x density, but mass is the more fundamental quantity than either of them, with which theses parameters should be described by mass not the opposite, not to mention how relative these other quantities are, considering SR and GR. Or "The resistance of an object to acceleration" but again you have to describe how fast that object is moving and what spacetime it's in according to SR and GR. So what makes us so confident that mass is such a universal value, when we built everything on a concept referenced by our own gravity, and maybe our own reference frame? How do we describe mass to the aliens, who don't know about our (g)? How do we measure the mass of celestial objects say planets, by units like kilograms, and pounds, while they are not subject to the earth's gravity, (I'm well aware of the difference between weight and mass). I mean that's what they will weigh -ignoring their own gravity- if they were in our atmosphere on a huge scale? So what's the method? _**Bottom line_** Is there a direct way to measure mass like we do with other fundamental values like length and temperature, _other than_ using a scale or equations, i.e not depending on other physical parameters to describe it? \--Forgive the length..


title: Magnetic field of permanent magnet

text: Hi I am looking for some code to (computationally) calculate the magnetic field of a rectangular permanent magnet in 3D space. Preferably I could edit it to add in my own dimensions. Does anyone know of anything?


title: Why aren't two systems in thermal equilibrium the same as one system?

text: I am reading Molecular Driving Forces, 2nd ed., by Dill & Bromberg. On page 53, example 3.9, we consider why energy exchanges between two systems from the point of view of the 2nd law. We consider two separate systems. Each has ten particles, and each particle has two possible energy states. System A has total energy $U_{a}$ = 2, and $U_{b}$ = 4. Thus binomial statistics predicts the multiplicities of these systems: $W(U_{a})$ = $\frac{10!}{8!2!} = 45$ $W(U_{b})$ = $\frac{10!}{6!4!} = 210$ Now the confusing part, to me, is the math when these two systems come into thermal contact. Then the author asserts that the initial multiplicity is $W(U_\text{total})$ = $\frac{10!}{8!2!}\frac{10!}{6!4!}$ And that maximum multiplicity is found at $W(U_\text{total})$ = $\frac{10!}{7!3!}\frac{10!}{7!3!}$ = 14,400 But why consider the systems in this way, as opposed to thinking of a new system, with 20 particles, having $U_{a}$+$U_{b}$ = 6? Then we get $W(U_{a+b})$ = $\frac{20!}{14!6!}$ = 38760 ≠ $W(U_\text{total})$ I'm trying to develop a sense of the difference, I suppose, between two systems in thermal contact and one system. After they've equilibrated, how are they not treatable as one system? They clearly aren't, because if they were, then the total multiplicity of that one system must = the total multiplicity of the two systems A and B.


title: Does a cross really have a smaller area moment of inertia than a square of the same area?

text: I need to calculate the area moment of inertia of a cross for a homework assignment. The cross is a symmetric plus sign:                   _        | |     |==   ==|        | |         -      where the length/width of each arm is 1" (so the total area is 5 square in.). My understanding is that I can just separate the cross into three sections (left, middle, right), so the area moment of inertia would be $$ I = \sum \frac{bh^3}{12} = \frac{1\times 1^3 + 3\times 1^3 + 1\times 1^3}{12} = \frac{5}{12}$$ This is surprising to me, because a 2.2" x 2.2" square would have the same area but a much larger moment of inertia: $$ I = \frac{bh^3}{12} = \frac{(\sqrt{5})^4}{12} = 2.08$$ Since the arms of the cross span 3 inches, I would expect there to be more material further from the center, whereas the square only has a small amount of area in the corners that the cross doesn't have. Are these formulas correct or am I doing something wrong? Thanks in advance.


title: Vector representation of wavefunction in quantum mechanics?

text: I am new to quantum mechanics, and I just studied some parts of "wave mechanics" version of quantum mechanics. But I heard that wavefunction can be represented as vector in Hilbert space. In my eye, this seems almost improbable. How does this work? Can anyone present an example and how it gets converted to vector form? So I am referring to Dirac Bra-ket formulation of quantum mechanics.


title: Kinetic energy with respect to different reference frames

text: I'm having problems understanding the following situation. Suppose two 1-tonne cars are going with the same orientations but opposite senses, each 50 km/h with respect to the road. Then the total energy is $$\begin{eqnarray}E=E_1+E_2&=&\frac{1\mathrm t\times(50\mathrm{km}/\mathrm h)^2}2+\frac{1\mathrm t\times(50\mathrm{km}/\mathrm h)^2}2\\\&=&1\mathrm t\times(50\mathrm{km}/\mathrm h)^2\\\&=&2500\frac{\mathrm t\times\mathrm{km}^2}{\mathrm h^2}.\end{eqnarray}$$ Now if we look at it from the point of view of one of the cars, then the total energy is $$\begin{eqnarray}E=E_1+E_2&=&\frac{1\mathrm t\times(0\mathrm{km}/\mathrm h)^2}2+\frac{1\mathrm t\times(100\mathrm{km}/\mathrm h)^2}2\\\&=&\frac{1\mathrm t\times(100\mathrm{km}/\mathrm h)^2}2\\\&=&5000\frac{\mathrm t\times\mathrm{km}^2}{\mathrm h^2}.\end{eqnarray}.$$ I know that kinetic energy _is supposed_ to change when I change the frame of reference. But I understand that then there must be some other kind of energy to make up for it so that the energy in the system stays unchanged. But I don't see any other kind of energy here. I only see two total energies of the same system that seem to be different. Could you explain this to me? Please note that while I don't understand any physics, I do understand college level mathematics, so if necessary please use it. (I doubt anything more than high school maths should be needed here, but I want to say this just in case.)


title: Is there absolute proof that an object cannot exceed the speed of light?

text: Have any known experiments ruled out travelling faster than the speed of light? Or is this just a widely accepted theory?


title: Physical Interpretation of the Integrand of the Feynman Path Integral

text: In quantum mechanics, we think of the Feynman Path Integral $\int{D[x] e^{\frac{i}{\hbar}S}}$ (where $S$ is the classical action) as a probability amplitude (propagator) for getting from $x_1$ to $x_2$ in some time $T$. We interpret the expression $\int{D[x] e^{\frac{i}{\hbar}S}}$ as a sum over histories, weighted by $e^{\frac{i}{\hbar}S}$. Is there a physical interpretation for the weight $e^{\frac{i}{\hbar}S}$? It's certainly not a probability amplitude of any sort because it's modulus squared is one. My motivation for asking this question is that I'm trying to physically interpret the expression $\langle T \\{ \phi(x_1)...\phi(x_n) \\} \rangle = \frac{\int{D[x] e^{\frac{i}{\hbar}S}\phi(x_1)...\phi(x_n)}}{\int{D[x] e^{\frac{i}{\hbar}S}}}$.


title: Size of the Universe: Curved vs flat? Finite vs infinite?

text: I have recently heard the theory that the Universe may be smaller than observed but may be curved to the extent that light rays may have looped past us once already and hence appear to have originated from further away than the source actually is located. If this is the case, would we not see light in every direction due to the fact that empty space would simply allow us to see fully around the curved universe to ourselves or other luminous objects? Would this same problem not present if the Universe were infinite?


title: Color of a substance

text: A plant with green leaves viewed under red light would appear as which color?


title: Why does overclocking a CPU cause it to generate more heat?

text: It seems odd to me that overclocking a CPU causes it to consume more energy. The amount of energy flowing through the CPU should be related to the average number of 'gates' (or transistors) that are open, not how fast you open and close them. Does changing a transistor's state cause heat to be generated or is there another factor?


title: Speed of light originating from a star with gravitational pull close to black-hole strength?

text: Imagine you have a star which is on the brink of turning into a black hole. Lets say it is infinitely close to become a black hole, but not there yet. Since there is no event horizon, but a great gravity pull. Will the speed of light originating from this star be close to 0? A follow-up question: What will the speed of light be after it travels far enough from the star to escape its gravitational pull?


title: Can we squeeze atoms?

text: Lets consider few water molecules (or monoatomic noble gas or $H^+$ ions or electron gas) to be present inside a vessel, now if we enclose the vessel with certain hard material which could act as piston (assume that vessel is completely covered). Now, if we apply tremendous force on the piston (and no molecules are rushing out of the covering), can we watch the molecules to be squeezing? I have heard about particle accelerators, where we start with electrons or protons, accelerate them to high energy and smash into the target. In general, heavier the particle we want to produce, the higher must be energy of collision. It seems that keeping the high energy particles stationary and then squeezing them (if possible) with highly accelerated pistons from either side, is better than colliding high energy particles head-on. The problem in not using pistons, I must think, must be because of our inability to accelerate the massive pistons to a high extent as like accelerating particles itself. But, the head-on collision of pistons with high energy particles in between, will be better than head-on collision of particles itself, I think. In case of head on collision of particles I think, we can accelerate them to high extent, but we can't expect effective collision. _Balancing both mass and acceleration of piston, can we have the same result, as we get in particle accelerators?_ If we can, can we avoid constructing those large particle accelerators like Stanford linear accelerator center (see the picture)? _Can we create such piston squeezer? I know there might be some difficulties? What can we do to overcome it?_ ![enter image description here](http://i.stack.imgur.com/RLQ5A.jpg) Sometimes, I might have misunderstood, if so, pardon me and explain.


title: How to calculate Rest Mass practically with Standard Model?

text: With relativistic physics, we can apply force to see resistance against acceleration. It'd give us relativistic mass and we have well established formula to get to the Rest Mass as long as we know the velocity. In Standard Model, we have Higgs Mechanism to assign something Rest Mass. I was curious how to apply that practically.


Why can't the functional integral be derived in a mathematically rigorous way? What are the obstacles that we have to overcome in order to achieve that goal?


Are matter waves transverse and can they be polarized? What I know:I'm aware of the de Broglie matter waves hypothesis and de Broglie wavelength relation(at a very basic level as part of high school curriculum). But, it is not mentioned anywhere about whether they are transverse or longitudinal. If they were transverse they could be polarized but are they? I could understand that matter waves are not real waves and therefore there is no case of longitudinal or transverse. I know that the square of amplitude of the wave at a position gives the probability of finding the particle at that position but, why is then frequency defined for matter waves(in other words what is its use?)?


title: Does the phase difference between voltage and current in an LCR circuit exist throughout the circuit?

text: I know that in an purely inductive circuit the current lags behind voltage by $90^o$, in a purely capacitive circuit vice-versa and in an LCR circuit the current may lag or gain with respect to voltage depending on the value of capacitance and inductance. But, does this phase difference exist throughout the circuit? To clarify what I'm asking consider the figure below. Assume the circuit is not in resonance and their is some phase difference. But, does the same phase difference exist between the current and voltage across the resistor? Can I find the same phase difference between them if I take any point in the circuit? ![enter image description here](http://i.stack.imgur.com/oHfPH.gif)


title: Dark Energy Explanation Found

text: It's my sincere request to this Physics forum that if i am wrong (which has the least possibility atleast from my side) just reply "wrong" so that i can move on futher. I know personal theories are not allowed but i am not finding any place to get it checked. thanks DARK ENERGY The theory described below does not contain any self made false assumptions about anything but uses only one, most logical assumption about the potential energy of curved space. Let a particle of unit mass curve space according to general relativity.Now, if we suddenly evaporate it (i.e. convert it's mass into radiation), the curvature of space associated with it begins to die out.But what about the potential energy associated with the curved space after the mass is lost? We can better understand this with this example. We stretch a rubberband by applying a constant force (correspond to mg).Now, if we remove this force, the stretched rubberband tends to come to it's mean position.But, the potential energy due to initially stretched rubberband makes it go further from it's mean position making it vibrate along it's mean position. The same happens in space. Bodies cause the curvature of space which induces potential energy in space. So, when a body loses it's mass,the curvature associated with that mass does not just dies out but instead the space starts vibrating along it's mean shape i.e. the potential energy of the curved space associated with that mass makes the space vibrate along it's mean shape producing gravity - anti-gravity fields. But , if there is another body of mass m near it, the magnitude of anti-gravitational field is more in each oscilation as the other body tends to curve space (apply force i.e. mg) along it's direction. This is why the galaxies are moving away from each other.As the stars present in them lose their mass,anti-gravitational fields are produced along all directions making every galaxy move apart from each other. Therefore, the space is not expanding but instead the already curved space produces this effect as it starts vibrating along all directions when a body loses it's mass.


title: Qubit in Type 1.5 superconductor?

text: I'm interested in Type 1.5 superconductors, first proposed by Egor Babaev in 2002 and found in the laboratory in 2009 (magnesium dibromide). Such conductors favor small bundles of vortices. The most stable number of vortices in the bundle varies depending on conditions but is typically from 2 to 12. The vortices have fractional quanta. The bundle is sheathed by larger vortex. Lets suppose that we have a bundle of three. Would each vortex be an anyon, and the bundle be a qubit?


title: Finding the energy eigenvalues of Hydrogen using WKB approach

text: I need help to find the energy eigen values of Hydrogen atom using WKB approach. So far I know, the radial equation is given by $$\frac{1}{r^2} \frac{\partial }{\partial r} \left( r^2 \frac{\partial R(r)}{\partial r}\right) + \frac{2 \mu}{\hbar^2} \left( E - V(r) - \frac{\ell(\ell+1)\hbar^2}{2 \mu r^2}\right)R(r) = 0 \tag{1}$$ also I know the relation, for equation of the form $$u''(x) + k(x)^2 u(x) = 0 \tag{2}$$ the solution is of the form (for $E<V$) $$u(x) = \frac{C_1}{\sqrt{k(x)}} \sin \left( \int^x k(x) dx\right) + \frac{C_2}{\sqrt{k(x)}} \cos \left( \int^x k(x) dx\right)\tag{3}$$ as well as the relation $$\oint \hbar k(x) dx = \left( n + \frac 1 2 \right) \pi \hbar. \tag{4}$$ I have it's solution on note written in class but it's hardly understandable. How do I transform equation $(1)$ to equation $(2)$ and what do I use for the bounds of integration in equation $(4)$ to get the energy eigenvalue? I have done similar question for harmonic oscillator where the bounds of integration in equation $(4)$ is $\pm$ turning points (solution of $E(x) = V(x)$) but not sure about this one. ADDED:: Changing $R(r) = u(r)/r$ changes into $$ \frac{d^2u(r)}{dr^2} + \frac{2 \mu}{\hbar^2} \left( E - V(r) - \frac{\ell(\ell+1)\hbar^2}{2 \mu r^2}\right)u(r) = 0. \tag{5}$$ Changing $V = -e^2/r$ gives $$\int_{R_{min}}^{R_{max}} \sqrt{2 \mu \left( E + \frac{e^2}{r}- \frac{\ell(\ell+1)\hbar^2}{2 \mu r^2}\right)}dr = \left( n + \frac 1 2\right) \hbar \pi.\tag{6}$$ Now what do I choose my bounds for $r$? The final answer is given as $$E_n = - \frac 1 2 \cdot \frac{\mu e^4}{\hbar^2 (n + \ell+1)^2}.\tag{7}$$


title: Simple Commutator question

text: For some reason this is really tripping me up: $$[q_rq_sp_r,q_sp_rq_s]$$ Where $r$ and $s$ are different. Is this just zero because $p_r$ on $q_s =0$. I am trying to simplify this and I feel like 0 is too easy.


title: Speed of Light and Information

text: Einstein in his thought experiment(?) for the constancy of speed of light in vacuum in all frames reasoned , that if speed of light of vacuum isn't constant than you'll be able to perceive effect before action . But then this must happen in all mediums , but it doesn't ,that means if you live in a medium with high optical density , you can perceive effect before action ? How can this be justified in a medium but not in vacuum ? And supposedly if we weren't able to see and sound was our only source to get information , then shouldn't speed of sound too be a cosmic speed limit ?


title: Can Plasma Ignite?

text: This question on Scifi.se: Why does warp plasma burn green? mentions a fictional type of plasma called 'Warp Plasma' that is capable of igniting and when it does it sprays plasma flames/gas out of pipes as if it were oil or some other form of fuel. Wikipedia says that the sun consists of hot plasma interwoven with magnetic fields. I couldn't find anything about plasma ignition (This is what I originally thought might be a reason why stars are so bright). Is plasma capable of igniting?


title: Neutrinos and Speed of light

text: Einstein's Special Theory of relativity postulates that the speed of light is same for all frames. Suppose a neutrino is there moving at the speed of light. Then will that neutrino also be flowing with same speed for all frames or is this a special property of EM waves?


title: Excluding big bang itself, does spacetime have a boundary?

text: My understanding of big bang cosmology and General Relativity is that both matter and spacetime emerged together (I'm not considering time zero where there was a singularity). Does this mean that spacetime (say, away from the big bang event) must have a boundary? And what is its topology? By topology I mean without the metric.


title: Charge inside conductor

text: I know that the E field inside a conductor is zero. What happens if I put a source of charge inside the conductor? Say the conductor was spherical centered on the origin and there exists a charge at the origin. Then by Gauss's Law, there exists a non zero field inside the conductor. Or is it the case that even though this charge is within the sphere, it will redistribute evenly over the surface and hence the E field inside is zero? Many thanks


title: MRI's and Electromagnetic Radiation

text: If the waves in an MRI can go through our body, why is it that light with its magnetic fields gets stopped at our skin?


title: Rocket towing an object

text: I'm not sure if my question makes sense, but I don't know where to start. A crate of mass $m_2$ is connected by a massless rope of constant length $l$ to a rocket of mass $m_1$. We take into account gravity (the crate is initially hanging directly underneath), but the rocket has no vertical acceleration since it's acted upon by an upward force of $(m_1+m_2)*g$. We neglect air drag and treat the rocket and the crate it is towing as blocks of the same size. If a horizontal force $F$ acts upon the rocket, what happens to the crate? It's probably going to lag behind at a certain angle, but how can we find that angle? Is the situation different if there's no gravity? Edit: This link helped me answer my question: http://cnx.org/content/m14061/latest/?collection=col10322/1.83


title: P-T Phase diagram. Density of material at critical point

text: One of the questions I had while reading through some material was: Why is the density of a given volume of gas uniquely defined at the critical point, but not at the triple point? Is it because at the critical point, a substance will flow like a liquid but retains properties of gas? While at the triple point, any small fluctuation will drive the substance into one of the other well defined phases. Many thanks


title: Would a Nuclear bomb have any effect on the sun that could damage the earth?

text: I was asked this recently and wasn't sure. The power of the sun is much more powerful than that of a Nuclear explosion but the question was what is the worst that could happen, we are assuming a situation where the nuclear bomb wasn't itself immediately destroyed by proximity of the sun for whatever reason. So, for example, if it was near the surface, could that cause a massive sun spot or similar which could disrupt electronics b.t.w. my background isn't a physics one :-) thanks


title: is it possible to change the energy of a waveform like radio wave & turn it into microwave?

text: In the electromagnetic spectrum, the differences between all waveforms are the "frequency" & energy of the waveform. We are able to modify both of these parameters. So, is it possible to change a waveform from one to another? If so, how? In particular, is it possible to change a radio transmitter to a microwave emitter?


title: Direction of X-rays from x-ray tube

text: Typically anode of X-ray tube is at angle of ~45 degrees. Many images show that emitted X-rays are mostly perpendicular to electron direction. Is that correct? I had an impression that x-rays will be generated isotropically and only partially absorbed by heavy anode when flying in "wrong directions", into the anode. ![enter image description here](http://i.stack.imgur.com/iKmk8.jpg)


title: How to calculate these integrals about propagator of QFT analytically?

text: How to get these three analytical solutions? Thanks very much! $$ G_{ret}(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p \, \frac{e^{-ip(x-y)}}{(p_0+i\epsilon)^2 - \vec{p}^2 - m^2} = \left\\{ \begin{matrix} \frac{1}{2\pi} \delta(\tau_{xy}^2) - \frac{m J_1(m \tau_{xy})}{4 \pi \tau_{xy}} & \textrm{ if }\, y \prec x \\\ 0 & \textrm{otherwise} \end{matrix} \right .$$ Here $$\tau_{xy}:= \sqrt{ (x^0 - y^0)^2 - (\vec{x} - \vec{y})^2}$$ is the proper time from $x$ to $y$ and $J_1$ is a Bessel function of the first kind. The expression $y \prec x$ means $y$ causally precedes $x$ which, for Minkowski spacetime, means $y^0 < x^0$ and $\tau_{xy}^2 \geq 0$. $$G_{adv}(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p \, \frac{e^{-ip(x-y)}}{(p_0 - i\epsilon)^2 - \vec{p}^2 - m^2} = \left\\{ \begin{matrix} -\frac{1}{2\pi} \delta(\tau_{xy}^2) + \frac{m J_1(m \tau_{xy})}{4 \pi \tau_{xy}} & \textrm{ if }\, x \prec y \\\ 0 & \textrm{otherwise}. \end{matrix} \right.$$ $$ \ G_F(x,y) \ = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p \, \frac{e^{-ip(x-y)}}{p^2 - m^2 + i\epsilon} \ = \left \\{ \begin{matrix} -\frac{1}{4 \pi} \delta(s) + \frac{m}{8 \pi \sqrt{s}} H_1^{(1)}(m \sqrt{s}) & \textrm{ if }\, s \geq 0 \\\ -\frac{i m}{ 4 \pi^2 \sqrt{-s}} K_1(m \sqrt{-s}) & \textrm{if }\, s < 0\. \end{matrix} \right. $$ Here $s:= (x^0 - y^0)^2 - (\vec{x} - \vec{y})^2~$, where $x$ and $y$ are two points in Minkowski spacetime, and the dot in the exponent is a four-vector inner product. $H_1^{(1)}$ is a Hankel function and $K_1$ is a modified Bessel function.


title: Three integrals in Peskin's Textbook

text: Peskin's QFT textbook 1.page 14 $$\int_0 ^\infty \mathrm{d}p\ p \sin px \ e^{-it\sqrt{p^2 +m^2}}$$ when $x^2\gg t^2$, how do I apply the method of stationary phase to get the book's answer. 2.page 23 $$\int_{-\infty}^{\infty} \mathrm{d}p\frac{p\ e^{ipr}}{\sqrt{p^2+m^2}}$$ where $r>0$ 3.page 23 $$\int_{m}^{\infty}\mathrm{d}E \sqrt{E^2-m^2}e^{-iEt}$$ where $m>0$ I'm crazy about these integrals, but the textbook doesn't give the progress.


title: How symmetry is related to the degeneracy?

text: I have several questions about symmetry in quantum mechanics.   1. It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a symmetric group $G$, then the state space with the same energy eigenvalue will carry a representation of $G$. However, why this representation is usually irreducible?    2. Is it true that the representation of continuous symmetric group must be unitary and cannot be anti-unitary?    3. What is the difference between geometric symmetry and dynamical symmetry? By dynamical symmetry I mean for example the $\mathrm{SO}(4)$ symmetry of hydrogen. Some text refers dynamical symmetry to "internal" symmetry. How to state the definition of dynamical symmetry strictly?


title: Is taking the "square root" of the densitized inverse triad irregular in loop quantum gravity?

text: In loop quantum gravity, the canonical (Ashtekar) variables are chosen to be the densitized inverse triad $\mathbf{E}$ and some rotation connection field $\mathbf{A}$. To get the ordinary triad from $\mathbf{E}$, we need to take its "square root". But we know as long as the volume factor, i.e. the square root of the determinant of $\mathbf{E}$ is nonzero, we always have two solutions for the triad. They are related by a branch cut around $|\mathbf{E}| = 0$. We also know that if this determinant is negative, the corresponding triad will be _imaginary_! OK, you might now say there's no problem as long as we stick to solutions where $|\mathbf{E}|$ is always positive everywhere. But here is where another problem comes in. The state about which loop quantum gravity expansions are made is the state where $\mathbf{E}=0$ everywhere. Excitations over this state by Wilson loops contain wavefunctional components with negative determinants as frequently as we have components with positive determinants. Does that mean loop quantum gravity predicts imaginary distances, negative areas and imaginary volumes? And besides, aren't we expanding about a highly irregular solution? * * * Another related question is: People sometimes multiply the Hamiltonian constraint by the factor $\sqrt{| \mathbf{E} |}$, but this goes to zero whenever $| \mathbf{E} | = 0$, which actually _weakens_ the constraints by introducing additional solutions which were previously forbidden. Is such a procedure really justified?


title: Anodized aluminium reflectivity at 10.6 um

text: I wonder how I can model anodized aluminium reflectivity in ray tracing-based optical simulation. I know that the parts my company is using are anodized to get covered with a ~20 um (as specified) thick corundum layer. I would like to be able to properly model angular dependence of such a surface reflectivity. I am using Zemax, but please do not limit yourself to it. Any hint is welcome. The two options I can think of are 1) Create a model coating in Zemax by specifying reflectivity vs. angle. Can be done if I know the values. I could not find them so far. Could be measured as well but that's a major effort which I'd like to spare. 2) Specify a thin layer of corundum on top of a bulk aluminium part in Zemax. However I could not find the dispersion data for Al2O3 at 10.6 um and I cannot find anything in Zemax' material catalogues. Besides, I assume such a layer of 20 um thickness would act as a thin film resulting in AR or HR properties. But I don't think the anodization process is precise enough in terms of layer thickness so that I can rely on this side effect. Any help or comment is highly appreciated.


title: How does load affect frequency on the power grid?

text: This story about the use of battery/freewheel based Frequency Regulators confused me about how the 60hz frequency of the North American power grid was set--saying that it was kept at that frequency by balancing load and supply. I used to think that it was only voltage which was affected by this balance, and that the frequency was determined by the speed of the rotors in the generator. EG see Wikipedia's page on Alternator Synchronization. Can someone help me understand the physics behind this?


title: What are the arguments towards the Life-and-Entropy relation?

text: I've heard it from a few people, and I've seen it popup here in the site a couple of times. There seems to be speculation (and studies?) towards this idea, and this is what I've picked up so far:   * Living organisms are low entropy systems.   * The second law of thermodynamics is somehow strongly connected to the origin of life itself. This is a very interesting idea, unfortunately I've never seen anyone elaborate beyond that. I'd like to understand it a little better. Specifically:   * Why are the above statements true (neither is immediately obvious to me)?   * And what are the other arguments in favor of this theory? I'll accept both answers for and against this point of view, as long as it reasonably justifies _why_ the above statements are correct/false. _Note: I believe the thermodynamic definition of entropy is the one commonly used with these arguments. And I'm not sure what definition they use for life. TheWikipedia page is pretty vague on this._


title: Expectation/Probability that a certain event would occur?

text: I have this problem: A gas is composed of 1% ions that will eventually recombine in the gas and the gas will become neutral. I calculated the mean free path and the velocity of the particles (from the gas' energy), and from there I found the time in between collisions. But I want to find out the time in between collisions of only the 1% ions in the gas (not the 99% neutral atoms). How would I go about doing this? Thanks in advance!


title: Maxwell-Boltzmann distribution and total energy per unit volume

text: We know that $$n(E) ~=~ \frac {2 \pi (N/V)}{(\pi k_B T)^{3/2}} E^{1/2} e^{-E/(k_B T)} dE,$$ where $V$ is total volume. If then, how do we derive total energy per unit volume from this equation?


title: Could a tetraquark $q \bar{q} q \bar{q}$ be colorless?

text: CERN just posted this article where it informs that it was found an hadron which cannot be classified within the traditional quark model. What other models are there to explain this result? Or is it possible to introduce a correction to the quark model to explain such find?


title: When do stars become red giants?

text: I am a bit confused when do stars become red giants? Is it just after they have finished core H burning and the core contracts creating high temperatures which result in core He burning to occur which creates outward pressures pushing the outer lowers apart or something different? Also does core He burning and shell H burning (by burning I mean fusion) occur at the same time and if not which comes first?? Or am i totally wrong with all these points?


title: Behavior of Saha and Boltzmann

text: So I'm just wondering why the Saha and Boltzmann distributions behave differently as temperature increases? I know one is for ionization levels while the other is for energy levels but is that the answer?


title: Can doppler shift be used to find the MH370 black boxes?

text: The Australian ship Ocean Shield has detected multiple pings from the black boxes onboard the missing Malaysia Airline Flight 370, specifically on 4 lines of bearing according to this article. The same article also states that they need a few more lines of bearing in order to further narrow down the search area. So my question is pretty much as in the title - can they use doppler shift to help figure out where the pings are coming from? IIRC, they used the doppler shift from the satellite data to figure out that the aircraft was most likely on the southern of the two arcs that were proposed several weeks ago.


title: Why is QM maximally predictive?

text: Let's suppose I'm in the lab and I claim that I can predict _more_ than QM can, specifically, I can predict exactly at which moment in time a particle decays. You don't believe me (naturally) so I set up the experiment, provide a piece of paper with a time written on it, and start the clock. At the time I have written down, the particle decays. Exactly which of the six postulates of QM would this violate? As far as I can tell, it violates none of them so long as the results from multiple identical trials of this experiment reproduce the correct particle decay time distribution. (And yes, I'm aware of this paper http://arxiv.org/abs/1005.5173, but I would prefer a simpler explanation.)


title: Blocks stacked on an incline connected by rope around pulley

text: ![enter image description here](http://i.stack.imgur.com/UPKe6.png) > Two objects A and B, of masses 5 kg and 20 kg respectively, are connected by > a massless string passing over a frictionless pulley at the top of an > inclined plane, as shown in the figure. The coefficient of static friction > is mu_s = 0.4 between all surfaces (a) To what angle $\theta$ must the plane > be inclined for sliding to commence? (b) What is the tension in the rope, > and what are the magnitudes of the friction forces at this critical > inclination? (c) At an incline angle of 15$^\circ$, what is the tension in > the rope? (d) At an incline angle of 35$^\circ$, what is the tension in the > rope? I was able to solve (a) and (b) by drawing a free body diagram as shown: ![enter image description here](http://i.stack.imgur.com/VTsmW.png) Newton's Second Law, setting all accelerations to zero, implies the following relationships: $N_A = m_A g \cos(\theta)$ $T = m_A g \sin(\theta) + f_2$ $N_B = (m_B + m_A) g \cos(\theta)$ $T + f_1 + f_2 = m_B g \sin(\theta)$ The second equation can be substituted into the fourth equation to give \begin{equation} f_1 + 2f_2 = (m_B - m_A) g \sin(\theta) \;\;\;\; (1) \label{eq:1} \end{equation} Setting the friction forces to their maximum values $f_{1,{\rm max}} = \mu_s N_B = \mu_s (m_B + m_A) g \cos(\theta)$ and $f_{2,{\rm max}} = \mu_s N_A = \mu_s m_A g \cos(\theta)$ allows these equations to be solved for $\theta = 43^\circ$, $f_2 = 14.33$ N, $f_1 = 71.64$ N and $T = 47.76$ N. I am however a bit confused about parts (c) and (d) dealing with angles below 43$^\circ$. I have 5 unknowns: tension, two normal forces and two friction forces, but only four constraints from Newton's Second Law. Equivalently, referring to Eq. (1), the net applied force which the static friction must oppose is fixed, so $f_1+2f_2$ is known, but there is no additional constraint to determine how much $f_1$ opposes and how much $f_2$ opposes. There seems to be a degree of freedom in how $f_1$ and $f_2$ are determined, i.e. a free parameter. My attempt so far at this is to suppose that for very small inclines we might expect friction to hold the blocks stationary and thus the rope would be slack and the tension $T$ is eliminated from the equations. In this case the free body diagram would be drawn differently, because without the rope, the tendency is for block A to slide downwards across block B: ![enter image description here](http://i.stack.imgur.com/Xg0Wl.png) The maximum incline under these conditions is found by balancing forces: $m_A g \sin(\theta) = f_2 \le \mu_s m_A g \cos(\theta)$   $\Rightarrow \tan(\theta) \le \mu = 0.4$   $\Rightarrow \theta \le 21.8^\circ$ When the incline is increased above $21.8^\circ$, I am confused about what will happen. The blocks would slide down the slope, but the rope will tighten, and suddenly the tendency for the system would be for the heavier block B to accelerate down the slope, and the lighter block A to accelerate _up_ the slope (because block B pulls on it via the rope), resulting in a free body diagram as in my original figure. I still do not understand how to calculate tension and the two friction forces in this case. How do I determine the tension $T$ and friction forces $f_1$ and $f_2$ for incline angles between $21.8^\circ$ and $43^\circ$? For these inclines, there does not seem to be enough constraints to determine every quantity, see for example Eq. (1). Is there an additional constraint I haven't thought of, or have I perhaps drawn my free body diagram incorrectly?


title: Air Turbulence and DIY laminar flow hoods

text: So for years on the mycology, plant tissue culture, and DIY laboratory websites there has been this ongoing debate on how to achieve laminar flow in a home built laminar flow hood. Flow hood link! It is generally accepted that a squirrel blower is effective at creating this laminar flow using the set up in the image posted above. Many people are interested in using inline centrifugal fans because they are cheaper than squirrel blowers, more quiet, more energy efficient, and potentially more compact. The build for a laminar flow hood using these inline fans look, generally, like the two samples at the bottom of this link (http://www.fungifun.org/English/Flowhood#construction). The main question is whether these inline fans will produce laminar flow. The argument is that the air pushed by these fans is turbulent and so will exit the HEPA filter in a turbulent fashion. It seems to me that so long as the plenum is air tight besides the entry point(fan location) and exit point(HEPA filter), the plenum will achieve a static pressure (based upon the cfm of air driven by the fan and the resistance of the HEPA filter) and flow smoothly out of the HEPA. Would this be totally wrong? If so, is there a way to build the DIY flow hood to achieve a laminar flow using one of these inline centrifugal fans?


title: Why cant Electrostatic field lines form closed loops?

text: My physics textbook says "Electrostatic field lines do not form closed loops. This is a consequence of the conservative nature of electric field." But I cant quite understand. Can anyone elaborate? PS:- This question is answered. Please refer both the accepted answer and also the answer and the comments in Robin Ekman's answer for a complete understanding.


title: Pseudo scalar mass and Pure scalar mass

text: Since the only difference between pseudo scalar and a scalar term is just a change of sign under a parity inversion, is it possible that both of them be present in the same field and interact? For example let's say that the vector gauge field is copuling with some other field. And suppose I have a pseudoscalar mass term like $m\varepsilon^{\mu\nu\rho\sigma}\phi_{\mu\nu}\phi_{\rho\sigma}$ and pure scalar mass term $\frac{M}{16} \phi_{\mu\nu}\phi^{\mu\nu} $. In that case is it possible that both of them present in the same time in the field? Or there is any condition that they have to satisfy?


title: Does Quantum Mechanics assume space and time are continuous?

text: I was confused when I was listening to a Quantum Mechanics lecture online. Are space and time assumed to be continuous or discrete in Quantum Mechanics? I can see the question is vague, but this is so since I am confused.


title: Calculating Hubble Radius using relativistic effects

text: I am trying to calculate the Hubble Radius, or the distance from which an object will recede from an observer at the speed of light. I initially tried using $v=H_0d$ which gives $d=1.424\times10^{26}$ for $H_0 = 65km/s/Mpc$ however I have been told that a different equation should be used at relativistic speeds. After some research I have found the following formula: $z = \sqrt{\dfrac{c + v}{c - v}} - 1 \implies v = c \cdot \dfrac{(z+1)^2-1}{(z+1)^2+1}$ Therefore: $d = \dfrac{c}{H_0} \cdot \dfrac{(z+1)^2-1}{(z+1)^2+1}$ However, I have no idea how to get a decent answer out of this equation. Obviously $z \rightarrow \infty$ as $v \rightarrow c$ and so $d \rightarrow \infty$ also. Is this the expected result? How does one interpret this?


title: How do AM radio signals change with time of day?

text: I know that AM radio station signals fluctuate in quality with time of day because of changes in the ionosphere. How do these changes trend with time of day?


title: Physical meaning of taking twice the real part of a Fourier transform

text: In my previous question, Calculating the coherence length from a spectrum, it turned out that I can calculate the coherence length of my light source from the autocorrelation function, which can be obtained by taking the fourier transform of the spectrum, according to the Wiener-Khinchin theorem. In one of the answers, the answerer takes two times the real part of a Fourier transform. I wonder what the physical meaning of this is. This is the equation in question, slightly rewritten for clarity, where $\mathscr{G}(f)$ is the spectrum and $\Gamma(t)$ the autocorrelation function: $$\tilde{\Gamma}(t) = \int_{-\infty}^\infty e^{2\pi\,i\,f\,t} \mathscr{G}(f) \,df=2\,\mathrm{Re}\left(\int_{f_{min}}^{f_{max}} e^{2\pi\,i\,f\,t} \mathscr{G}(f) \,df\right)$$ I am also surprised that the answerer apparently claims that the part before the equals sign, without taking the real part is equal to the part after the equals sign, with taking the real part. Why is this? In practice, to me it seems that in the context taking the absolute values of the transform is much more useful, as it yields the envelope of the real part. However, I am curious about the meaning of the answer.


title: Physical Meaning of Linear dependence of vectors in quantum mechanics

text: I have got some questions regarding the mathematical concepts in Quantum Mechanics that I have listed below- 1) What is the physical meaning of linear dependence of vectors in Quantum Mechanics ? 2) Actually, what is so special about Hilbert space due to which wavefunctions are defined on it ?


title: What is Conductance?

text: What is conductance? I am being said that conductance is inverse of resistance?I do know that resistance is the opposition to the flow of current but do not get conductance? > I do know that:it is ease of flow current but my brain doesn't accept > it,don't know why Ain't it so important!Couldn't even find it on wikipedia.


title: Kaluza Klein theories, dilation field, and dimensional reduction

text: I am reading something about Kaluza Klein theories and compactification. I have some conceptual question: (1) Why do we call the fifth scalar field $\Phi$ the dilation field? Is there any scaling property for that? (2) What happens to this field after dimensional reduction? Many thanks if you can provide me with further reading material! :)


Is there a point interaction model of the electron? Is there a point interaction model of the electron? I imagine something like $\propto(\bar \psi\psi)^2$ (edited). Is such a thing in use? Since I expect some _but that's not renormalizable!_ -arguments: I think there are theories with scalar photons. Can you integrate out the massless photon completely? And that raises the question more generally: Does going from a renormalizable to an effective description theory change that property? * * * Edit: I just found the Four-fermion interactions. I guess that leaves the question if, or better how, these can result from swallowing the photon. Here is the question in that light: > Coming from QED, is there a point interaction model of the electron? PS: I like the last line of the article. Who would have seen that one coming :P


title: Potential vs Kinetic Energy of Particles in Gas

text: "In the gas phase, the molecules are freely moving particles traveling through space, where the kinetic energy associated with each particle is greater than the potential energy of intermolecular forces." Qualitatively, this makes perfect sense. The particles have are moving very quickly which trumps any attractive forces. However, I don't quite understand the energetics of such a situation. This motion is where the kinetic energy term comes from. On the other hand, the tendency for the particles to attract is represented by a potential energy term. Two particles that are attracted to one another in close proximity would have a positive potential energy, right? How do we know that the kinetic energy term has to be greater than the potential energy term? **EDIT IN RESPONSE TO ANSWER** Thought I would post this in case anyone else was confused. This is my rationalization of the answer. This has cleared up a lot for me. This also has to be why solids vibrate in place. For the following, assume two particles in one dimension. Assume the particles are at some finite distance from each other, each with no KE. Call this distance d. We can define the PE to be 0 at this distance, d. Since they attract each other, they fall towards one another. The attractive force is applied across the distance between them, hence work. The amount of work (or force * dist) to bring the particle to a certain velocity is its kinetic energy. In other words, all of the PE is converted to KE. Assuming the particles then “collide,” elastically of course, the particles reverse directions. They are now moving away, each with some KE. They still attract one another, however. The attractive force will apply itself across some distance. Well the amount of work to stop them will be equal to their KEs. This will happen at a distance at the distance d. At this point, there will not be enough KE to keep moving away from one another. They fall back towards one another and the process repeats. This is the vibration. In a gas, there is not enough attraction to stop the moving away from one another. In other words, the KE outweighs the PE.


title: What is the displacement of an accelerated and relativistic object?

text: Displacement in an accelerated classical object is: $$s=ut+\frac {at^2}{2}$$ What is the displacement of an accelerated relativistic object? In Newtonian mechanics there are two types of displacement.   1. Displacement of an object with velocity constant: $$s=ut$$   2. Displacement of an accelerated object with acceleration constant: $$s=ut+\frac {1}{2}at^2$$ This is not completely clear, but I think the second displacement should be something different in relativity. Is that true? What is the result of this integral in relativity? $$s=\int (u+at)dt$$ classicaly $$s=\int (u+at)dt=\int udt +a\int tdt=ut+a\frac {t^2}{2}+x_0$$ What is the relativistic one? more details: $$v=u+at$$ $$s\to displacement$$ $$a\to acceleration$$ $$u\to initial \,velocity$$ $$v\to final \,velocity$$


title: Mechanistic description of leverage

text: How would you describe how a lever is able to apply a large for to an object from only a small applied force _without_ recourse to conservation of energy? Is there a purely F=ma type derivation? For example, how would you do it for a simple truss system (e.g., triangular truss with one end fixed to a pivot) and for an elastic beam over a fulcrum?


title: How does wave function collapse when I measure position?

text: Text books say that when you measure a particle's position, its wave function collapses to one eigenstate, which is a delta function at that location. I'm confused here.   1. A measurement always have limited accuracy. Does the wave function collapse to exactly a eigenstate no matter what accuracy I have?   2. When a particle is in an eigenstate of position, I can represent the state in momentum basis, and calculate it's expected value (average) of kinetic energy. This gives me infinity. Can a particle ever be in such a state?


title: Purely mechanical description of how gravity causes a gyroscope to precess

text: I know the vector equation that relates torque to moment of inertia and angular momentum. What I want to know is what physical mechanisms actually occur to keep the gyroscope from falling. Where is the upward force coming from and how, mechanistically, does this get produced?


title: Why change in Capacitance?

text: I do know it that the overall **capacitance** decreases if two or more _capacitors_ are connected in series,but do not understand why? I do understand it mathematically but don't get the physics behind it.


title: Could one estimate the size of air-molecules based on analysis of the sound?

text: Say one knows air is composed of molecules (atoms). Could one estimate the size of molecules (atoms) by analysing the sound properties as one perceives them (clearness, speed, etc.)?


title: What does this quantum experiment says about quantum world?

text: I am complete noob so please bear with me. I always read that in quantum world things exists as probability and only become one when they are observed...or wave collapses into particle. But there was one recent experiment in which scientists observed the wave and it still showed interference pattern. So observing simply didn't collapse it. Side note: it makes no sense that quantum world should be able to distinguish that it's being observed by human or whether sensor alone.


title: Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

text: I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water requires $\log_2 e$ bits of information. Is there an intuitive reason why? Below is the calculation: Imagine a tank of water from which we are removing ions, which currently have concentration $c$. We move the ions to a reservoir of concentration $c_0$. Each ion can be considered to occupy a volume $1/c$, so the entropy change in moving an ion from our tank is $k_B\ln(c/c_0)$. As we empty the tank starting from $c = c_0$ to $c = 0$, the average entropy change per ion is $$\mathrm{d}\bar{S} = \frac{k_B}{c_0}\int_{c_0}^0 \ln(c/c_0)\mathrm{d}c =- k_B$$ Because the internal energy doesn't change, the free energy cost is $$N k_BT$$ to completely remove $N$ solutes.


title: Why does this automatic night light advertise money savings?

text: I just bought a night light to light the hallway since it receives no outside light. The one I bought advertises that it saves money because it turns on only during the night or (dark hours). I did the calculations and I am confused as to why it is even advertised because I did the calculations to find the cost per month to run it and as it turns out the money savings are absolutely miniscule. The power information on the night light is 120v, 60hz, and 0.15w. To find the cost to run it per month: 0.15w * 1kw/1000w * 24 hours * 30 days = 0.108 kwh per month. At a cost of 9 cents per kwh, the total cost comes to less than 1 cent per month. The fact that the night light is automatic does not make a big difference on my wallet--why with a dollar I could run it for 8.3 years. Am I missing something or is this just an example of advertising?


title: Statistical error in a regression

text: I measured some voltage values ($x$) and some corresponding frequencies ($y$). I know that the voltage can only be measured within an uncertainty $\Delta x$. And the uncertainty of $y$ shall be $\Delta y$. Now I'm interested in the slope of the regression line and analyze it using root (the statistics tool). I used $x$- and $y$ error bars. Root returns an Error on the slope ($\chi^2$-Method). Is this the final error on the slope or do I have to make some further propagation of errors?


Do particles and anti-particles attract each other? From the very basic understanding that they are created out of nothing mutually and collide to annihilate each other seems to indicate this happens due to an attraction. Is it a measurable force? Plus they are exactly alike except their opposite charge, which would indicate attraction, as this source indicates: http://www.thenakedscientists.com/forum/index.php?topic=36719.0 I'd like more information on this, if possible. For the record, I'm speaking about them under the construct of time. If you ignore the construct of time, both particles could actually be considered the same particle, one moving backwards through "time" in a loop that occurs "once". Ignore this if you do not know what I'm talking about, or feel free to correct me on it.


What is the precise statement of the OZI Rule? I've heard that a diagram is OZI suppressed if it can be "cut in two by cutting only gluon lines", but I don't really understand. For example, consider the decay $\phi \to K^+ K^-$, which is supposedly _not_ OZI suppressed. This diagram is from Griffiths: ![phi meson decays into a pair of pions](http://i.stack.imgur.com/uOjQR.png) Well, it seems to me that I can cut this diagram in half. I just have to insert the scissors in between the u and s quark on the bottom left, snip both the gluon lines, then exit between the u and s quark on the top right. Or are we not allowed to separate two quarks in the same hadron? What about a diagram where one of the quarks in a hadron emits a gluon and that gluon then decays to say a $\pi^0$? Would that be OZI suppressed?


As an undergrad I was often confused over people's bafflement with Schodinger's cat thought experiment. It seemed obvious to me that the term "observation" referred to the Geiger counter, not the person opening the box. Over time, I have come to realize that the Copenhagen interpretation actually _is_ ambiguous and that "observer" cannot be so easily defined. Nonetheless, an objective collapse theory (which is what I was unknowingly assuming) still seems to me the simplest explanation of wave collapse phenomena. I have read some of the objections cited in the Wikipedia article linked above, but it is still unclear to me why most physicists adopt the Copenhagen interpretation and reject objective collapse. For example, in this question on hidden observers, there was some discussion about the mechanism of wave collapse. It was suggested that perhaps the gravitational pull of a hidden observer would collapse the wave function. In response, it was pointed out that the gravitational pull would be negligible at the scales involved. Okay, then imagine the following: A hermetically sealed (i.e. isolated) box is balanced on a fulcrum. Inside the box is a radioactive isotope, a Geiger counter, and a trigger mechanism connected to a spring loaded with a mass on one side of the box. If the Geiger counter detects a decay, the trigger releases the spring and the mass shifts to the other side of the box. The shift in mass would, under observable conditions tilt the box on the fulcrum. According to the interpretation of Schrodinger's cat that I often hear (the cat is in a superposition) it seems that the box should slowly tilt over as the wave function of the system evolves with the half-life of the isotope. I can't imagine that anyone thinks this is a realistic expectation. I can see that people might object and say "But the contents of the box are interacting gravitationally with the outside system and observer so it is not really isolated!" Well, what of it? The same is true of the cat even if the interaction is less dramatic. The question, then, is: How isolated must a system be for it's wave function to be considered not collapsed?


title: Dyson fans in ceiling?

text: Will it be feasible to use Dyson fans in the ceiling since it has to draw air from the back to "push" towards the front?


title: Massless spin 1/2 particle

text: Could a massless spin 1/2 particle, or more generally massless half-integer spin particles exist? Does it make sense to say that they could be described for example by the Dirac equation by forgetting the mass term ?


title: Why do wheels appear to revolve opposite to the direction they are rotating?

text: When viewing cars that are driving along side of us, sometimes their wheels appear to be turning backwards even though they are traveling in the same direction as our car. Why do they look that way?


title: Special Relativity Second Postulate

text: That the speed of light is constant for all inertial frames is the second postulate of special relativity but this does not means that nothing can travel faster than light.   * so is it possible the point that nothing can travel faster than light was wrong?


title: Minkowski metric -- why does it follow from the constancy of the speed of light

text: In all the sources I’ve been able to find, the Minkowski metric appears ad hoc, or is defined analogously to the euclidean metric. I’d love to see an argument why this metric (time coordinates positive, space coordinates negative) must follow from the constancy of the speed of light. It is clear that the Minkowski metric is preserved under the hyperbolic transformation of space-time, but likely others are as well. Why this particular metric and not something else. Consider the determinant function of an n by n matrix. It has a god awful mathematical form involving the sum of n ! terms. Yet all you need to get the (unique) formula are a few postulates — the determinant of the identity matrix is 1, the determinant is a linear function of its rows (or its columns), interchanging any two rows of the determinant reverses the sign of the determinant, etc. etc. This basically determines the (unique) formula of the determinant. I’d really like to see the Minkowski metric come out of something like that.


title: Higgs mechanism and neutral fields

text: Consider a Lagrangian $L(\phi,A_{\mu})$ with $\phi$ being some scalar field and $A_{\mu}$ some dynamical U(1) gauge field that minimally couples to $\phi$. Under a global U(1) symmetry the field $\phi$ transforms as $$ \delta\phi=i\epsilon q \phi. $$ The field $\phi$ is said to be charged (with charge q) under the gauge field $A$. In a Higgs phase we have that $|\phi(x,t)|\neq 0$. In particular we can fix a gauge so that $|\phi(x,t)|=\Phi(x,t)$ is real. Then we consider small fluctuations $\Phi(x,t)=\Phi_{0}+\delta\Phi$ and integrate them out to obtain an effective theory in which the gauge field A is massive. My question: It seems to me as though the requirement that $\phi$ is charged enters when integrating out the small flunctuations, because if $\phi$ were neutral (i.e. q=0) there wouldn't be any flucutations that one can integrate out and hence one wouldn't obtain a massive term for the gauge field in the Lagrangian. Is this correct? If not where does the requirement for $\phi$ to be charged enter in the argument? And: Does the requirement for the matter field to be charged with respect to the corresponding gauge field carry over without difficulties to the non-abelian case? I am looking forward to your responses!


title: Calculate the effective linear attenuation coefficient of a megavoltage multi-energetic beam

text: Are you aware of a method or source for calculating the effective linear attenuation coefficient,$\mu_\text{eff}$, of a megavoltage multi-energetic beam ? For a mono-energetic beam one could use the half-value layer (HVL) formula $\mu = \frac{\ln 2}{\text{HVL}}$. Does it make sense to consider individual energy levels and their attenuation coefficient and get an average value? Like: \begin{align*} \mu_\text{eff} = \frac{1}{N}\sum_{j=1}^{N}\mu_j = \frac{1}{N}\sum_{j=1}^{N}\frac{\ln 2}{\text{HVL}_j} \end{align*} On second thoughts this doesn't seem right, because it doesn't take into account the contribution of each mono-energetic "sub-beam" (so to speak) to the multi-energetic "total-beam". It should be more like: \begin{align*} \mu_\text{eff} = \sum_j w_j \mu_j \end{align*}


title: Does a single electron moving at velocity $v$ have an associated magnetic field, ignoring intrinsic spin?

text: I have seen explanations of the magnetic field due to an electric current as being due to a Lorentz contraction of the moving electric charges. Would this explanation work for a single electron. There is still a current associated with a single moving electron.


title: Star visibility in outer space even during the day?

text: Say I am in a space shuttle and have reached outer space. Is it true that during the day it possible to see stars outside through the window? Do I have to wait until night? Why is this the case?


title: Energy expended in moving point charge in E field. Having trouble understanding an excerpt from E&M textbook

text: > To move charge from one point to another in an electric field, _the force > which we must apply is equal and opposite to the force due to the field._ > (Quoted from _Engineering Electromagnetics_ by Hayt.) Here is my concern: To move a charge, shouldn't the force that we must apply be just a little higher than the force exrted on the charge by the field? I know that electric field intensity is the amount of 'kick' a test charge feels when placed in that electric field. Now if I apply the SAME amount of force against the force due to E field, the charge, according to my understanding, will just stay there and won't move. If I apply a force just a little higher than force due to E field, only then the charge should move. Why does the text say that to MOVE charge in E field, we should apply force EQUAL to that of the force experienced by charge because of E field.


title: Understanding the argument that local U(1) leads to coupling of EM and matter

text: I'm trying to better understand the argument that U(1) local gauge invariance implies a coupling of EM and Dirac fields. I understand the math, but I'm not sure about the chain of logic. You start with $\mathcal{L}_\mathrm{Dirac} = \bar\psi ( i\hbar \partial_\mu - m)\psi $ and the following transformations: $$ \psi \rightarrow \psi' = e^{i\theta}\psi \qquad \left( \bar\psi \rightarrow \bar\psi' = \bar\psi e^{-i\theta} \right) \qquad (1)$$ $$ A_\mu \rightarrow A'_\mu + \partial_\mu \chi \qquad (2)$$ You often by applying (1) to $\mathcal{L}_\mathrm{Dirac}$, and note that to keep the form invariant, you have to change the partial derivative to the covariant derivative: $\partial_\mu \rightsquigarrow D_\mu = \partial_\mu - \frac{i}{e} A_\mu$. You do the calculation again, and then find $$\mathcal{L}' = \bar \psi\left( i \hbar \gamma^\mu (D_\mu - i \partial_\mu\theta + i\partial_\mu\chi) - m\right)\psi$$ Thus, to make $\mathcal{L}$ invariant under the transformations, $\theta = \chi$ (up to factors of $e$ and $\hbar$ that I missed). The phase of the electron wavefunction must in a way absorb the change of the four-potential given by the gauge transformation, or vice versa. I understand (2) comes from classical gauge freedom in electrodynamics. You are free to add a constant potential offset $\Phi_0$ to $\Phi$, or to add a divergence of a scalar field $\vec\nabla \chi$ to $\vec A$. Since $A_\mu = (\Phi, \vec A)$, it follows that (2) leaves the physics invariant. But where does (1) come from? Is this just the regular freedom of phase change you have with any wavefunction? If so, why doesn't the U(1) symmetry show up everywhere? Or does this come from _postulating_ a U(1) symmetry for $\psi$? If so, how is this motivated (other than "oh, it gives the right result")? For example, if I think (2) is better motivated, **is it possible to start with only (2) and possibly the covariant derivative, and get to (1)? In general, what assumptions can I put into the argument, and what can I get out of it?**


title: Collection Efficiency of Photon

text: I am currently reading this paper: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.116802#references In the second column of text in page 2, the author makes various claims about the number of photons detected and the collection efficiencies of different optical components. > 'we detect 2.6 million counts per second from the QD with excitation laser > power above QD saturation. The trion lifetime is 0.65 ns; i.e. the QD emits > ∼7.7 × 10$^8$ photons per second when driven well above saturation. Taking > into account the effect of the ∼90 ns dead time of our time-correlated > single photon counting module, our overall collection efficiency is 0.45%. > After correcting for the SSPD efficiency (≃40%), beam splitter (80%), and > polarizer (50%) losses as well as the fiber coupling efficiency (40%), we > conclude that 7.0% of the photons emitted by the QD are collected by the > objective.' QD - Quantum dot   SSPD - Superconducting single-photon detector TCSPC - time-correlated single photon counting While I understand that the dead time of 90ns means that for every photon detected, the instrument will not be able to detect any photons for the next 90ns, I do not understand how it factors into the calculation to arrive at the $0.45\%$ overall collection efficiency. The following is the steps that I did to try to arrive at the 0.45% collection efficiency: Given the trion lifetime, $\tau$ $= 0.65ns$   no. of photons from radiative recombination per second $= 1s/0.65ns$ $= 1.538*10^9 $   no. of photons emitted by the sample $= 1.538*10^9 * 0.5 = 7.7*10^8$ (value given in the paper)   The factor of half is due to the fact that there is a thin metal gate with a power reflectance $R < 0.5$ deposited on the top surface (page 1, second column).   From the different collection efficiencies of the optical components, the resultant efficiency is straightforward: $0.4*0.8*0.5*0.4 = 0.07$ i.e. $7\%$ (value given in the text) Therefore, of the emitted photons   $7.7*10^8*0.07 = 5.36*10^7$ photons get detected by the SSPD (not the TCSPC module). With these values I seem to be getting a much higher overall collection efficiency. Can anyone clarify the steps taken to arrive at the overall collection efficiency of $0.45\%$? Thank you very much.


title: Why dimensionality of the Electric Charge varies with the spacetime dimensions?

text: The point is: We can find via dimensional analysis that the electric charge dimensionality varies with the dimension of space-time. $$[\text{charge}] = eV^{(3-D)/2}$$(You can see below the way I did it) The question is: **Why it occur? What is the meaning of this?** * * * I'm using the Heaviside-Lorentz Units with Natural Units ($\hbar = c = 1$) so that everything has dimensions of energy (eV). $$[x] = [t] = eV^{-1}$$ $$[p] = [E] = eV$$ Using the action from Maxwell Theory $$ S = - \frac{1}{4} \int d^{1+D} x F^{\mu \nu} F_{\mu \nu}$$ And making a dimensional analysis, $$ [S] = [x]^{1+D} [F^{\mu \nu}]^2$$ $$ 1 = eV^{-D-1} [F^{\mu \nu}]^2$$ $$ [F^{\mu \nu}] = eV^{(D+1)/2}$$ Then, using the inomogeneous equation $$ \partial_\nu F^{\mu \nu} = J^\mu$$ Ang making an dimensional analysis $$ [\partial_\nu] [F^{\mu \nu}] = [J^\mu]$$ $$ eV eV^{(D+1)/2} = [J^\mu]$$ $$ [J^\mu] = eV^{(D+3)/2}$$ Now lets look the charg dimension. The relation of the charge with the (1+D) density current is $$[J^\mu] = \frac{[\text{charge}]}{[x]^D}$$ So, $$eV^{(D+3)/2} = eV^{D} [\text{charge}]$$ $$[\text{charge}] = eV^{(3-D)/2}$$ We get that only in 1+3 the charge is dimensionless. If we are at 1+1, and at 1+5 charge is just like time. * * * **Comment 1** At another place I was told that it (dimension of charge) have relation with the renormalizability of QED. And that the fact that charge is dimensionless only in 1+3 is related with Maxwell Equations being conformally invariant at 1+3.


title: What does John Conway and Simon Kochen's "Free Will" Theorem mean?

text: The way it is sometimes stated is that > if we have a certain amount of "free will", then, subject to certain > assumptions, so must some elementary particles."(Wikipedia) That is confusing to me, but it seems to be an amazing theorem. It has been interpreted as ruling out hidden variable theories, but there is still some dissent. Lubos has a good discussion of it on his blog in the birthday blog for John Horton Conway. I assume it means that the outcomes of microscopic measurements are not deterministic. What does the theorem assume and what does it prove?


title: How do you measure a particle's postion or momentum?

text: This question is about the Uncertainty Principle $$\sigma_x \sigma_p ~\ge ~\frac{\hbar}{2}.$$ Looking at the maths, I understant why the uncertainty in the poistion increases as the uncertainty in the momentum decreases and vice versa, but I don't understand it in terms of an experiment. For starter, **how do you measure a particle's position or momentum?** What is stopping me from making two simultaneous measurements, one for position and one for momentum? (I understand that the Uncertainty Principle is a natural phenomenon, not a limitation of our technology.)


title: Soliton Moduli Spaces and Homotopy Theory

text: The four-dimensional $SU(N)$ Yang-Mills Lagrangian is given by $$\mathcal{L}=\frac{1}{2e^2}\mathrm{Tr}F_{\mu\nu}F^{\mu\nu}$$ and gives rise to the Euclidean equations of motion $\mathcal{D}_\mu F^{\mu\nu}=0$ with covariant derivative $\mathcal{D}_\mu$. _Finite action_ solutions $A_\mu$ satisfy the condition that, $$A \to ig^{-1}\partial_\mu g$$ as we approach $\partial \mathbb{R}^4 \cong \mathbb{S}^3_{\infty}$, with $g$ an element of $SU(N)$. These provide a map from $\mathbb{S}^3_\infty$ to $SU(N)$, and are classified by homotopy theory. In Tong's lecture notes on solitons, he states without proof that the second Chern class, or Pontryagin number $k \in \mathbb{Z}$ is given by $$k = \frac{1}{24\pi^2}\int_{S^3_\infty}\mathrm{d}S^3_\mu \, \, \mathrm{Tr} \,(\partial_\nu g)g^{-1}(\partial_\rho g)g^{-1} (\partial_\sigma g)g^{-1}\epsilon^{\mu \nu \rho \sigma}$$ As I understand them, Chern classes are characteristic classes of bundles on manifolds; **in this case what bundle and manifold is $k$ associated with? How does one obtain $k$ in this case?** Tong states "The integer... counts how many times the group wraps itself around spatial $\mathbb{S}^3_\infty$." In addition, Tong states without rigorous proof the metric of the moduli space (the space of all solutions to the equations of motion which are self-dual): $$g_{\alpha \beta} = \frac{1}{2e^2} \int \mathrm{d}^4 x \mathrm{Tr} \, \, (\delta_\alpha A_\mu)(\delta_\beta A_\mu)$$ with $\delta_\alpha A_\mu = \partial A_\mu / \partial X^{\alpha} + \mathcal{D}_\mu \Omega_\alpha$ where $\Omega_\alpha$ is an infinitesimal transformation, and $X^{\alpha}$ are the collective coordinates. **How does one compute such a metric of a moduli space? Why should it be given by the sum of all zero modes?** **I would prefer an answer which utilizes arguments from differential geometry, and topology. Resource recommendations which are more rigorous or explicit would also be appreciated.**


title: Wave equation for de Sitter invariant Green's functions

text: In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields: $$(\square-m^2)G(x_1,x_2)=0 $$ can be rewritten, if the two point function only depends on the geodesic distance $Z_{12}=Z$ between the two points, to the following: $$\bigl((Z^2-1)\partial_Z^2+NZ\partial_Z+m^2 \bigr)G(Z)=0$$ I tried to trace back the references to the origin of this idea, but it leads to a dead end: a paper from 1968 by Geheniau and Schomblond in a (now) obscure journal from Belgium that I cannot find on the internet. Does anyone have an idea of how to recast the first equation as the second? My last question is slightly related. Any help would be much appreciated.


title: Do beam splitters work for very broad photons? (frequency bandwidth, spatial extent)

text: If I send a single photon through a usual beam splitter, is there a limit for the beam splitter to work properly related to the photons broadness in frequency or in space? For example a femto second photon. It has a spatial extent of about $10^{-7}\,\text m$ but a very broad frequency bandwidth of about $10^{15}\,\text{Hz}$. Since there a so many different frequencies I am wondering if I can naively assume that the beam splitter works properly. Maybe some expirienced experimenter can answer to that.


title: Quantum fluctuations in the non-relativistic limit

text: Is there any way to describe quantum fluctuations in ordinary quantum mechanics? For instance, a proton fluctuating into a proton-$\pi^0$ state and then back to a proton? What are the relevant equations in this case? I need only be qualitative so a mixture of field/QM (i.e. field theory in the non-relativistic limit) theory would suffice too.


title: Can't Prove formula from Sakurai's Modern QM @ Perturbation Theory

text: I am studying Perturbation Theory from J.J. Sakurai's textbook Modern Quantum Mechanics. I am having trouble proving formulas on page 299 (5.2.5) and (5.2.6) from the previous ones [mainly (5.2.4)]. Can anyone help? This is a problem of working with perturbation theory when the non-pperturbed state has degeneracy. I have scanned the page stating the framework of the problem (ignore my notes on right margin). To elaborate I do not get why $(E-H_0-\lambda P_1VP_1)$ is not singular. More importantly is the equation below correct and if so why: $$(E-\lambda P_1VP_1)|l>=E_D^{(0)}|l> $$ That is the core of my problem. If the above equation - in the framework of Sakurai's statement of the problem - is correct I can work out all the rest on my own. However I do not get why this equation would hold true. Regards, Karsus


title: what is strong nuclear force between proton and neutron in deuteron

text: The nucleus of deuterium, called a deuteron, contains one proton and one neutron. what is strong nuclear force between them!?


title: is there any uncertainty on the free particle with a definite momentum $\vec p$?

text: The probability amplitude for a free particle with momentum $\ p$ and energy $E$ is the complex wave function: $$\psi_{(\vec x , t)}=e^{i(\vec k\cdot \vec x -\omega t)}$$ is there any uncertainty on the free particle with a definite momentum $\vec p$!?


title: Is QCD free from all divergences?

text: On page 8 in http://arxiv.org/pdf/hep-th/9704139v1.pdf David Gross makes the following comment: "This theory [QCD] has no ultraviolet divergences at all. The local (bare) coupling vanishes, and the only inﬁnities that appear are due to the fact that one sometimes expresses observables measured at ﬁnite distances in terms of those measured at infinitely small distances. " 1) First of all, is this statement even correct? 2) Now my main question is: certainly, a naive application of the Feynman rules and regularization leads to non zero counterterms. (See chap 16 of Peskin). So what scheme could one work in such that the counterterms vanish?


title: What can drive the higgs mass in mSUGRA up?

text: As a test to familiarize myself with the program softsusy, I generated a spectrum for the following (already excluded, but once considered) mSUGRA point: $m_0 = 170\,\mathrm{GeV}$, $m_{1/2} = 190\,\mathrm{GeV}$, $\tan\beta = 3$, $\mathop{\mathrm{sign}}{\mu} = +1$ and $A_0 = 0$. The result is displayed in the picture below. While the mass hierarchy looks OK, I'm worried that the lightest scalar Higgs is around 100 GeV. Now, as we all know ;-), the Higgs lives around 125 GeV. Also, I understand that in leading order the lightest higgs should be around the Z mass, and that it gets a large correction from the top quark that pushes it upwards. What I'm wondering is now:   1. Is is really a feature of mSUGRA that the higgs is so light? Why have people been studying points like this, when this would have been ruled out by LEP? The $h_0$ should be sufficently similar to a "SM" Higgs, right?   2. If this is not a genuine feature, have I made a mistake? Is there a way to persuade softsusy to add higher order corrections that drive the mass up? (I'm already using the "Include 2-loop scalar mass squared/trilinear RGEs" option.) ![Spectrum generated by softsusy](http://i.stack.imgur.com/LJlYB.png)


title: Is it possible to define a notion of temperature in a microcanonical ensemble?

text: I am thinking of a mircrocanonical ensemble as a finite system for which the number of particles, volume and the total energy is fixed. Is there a more refined view of this? Can I think of temperature of this system as the average kinetic energy for all the particles? * * * To put the thing in a larger context - what is the implicit choice of ensemble when people define the entropy of a black-hole either as (1) horizon area or (2) via microstate counting or (3) macroscopically via quantum entropy function ? Naively it feels that for a black-hole entropy one must think of a microcanonical ensemble because its not clear to me as to with what "bath" will it be able to exchange anything to maintain any chemical potentials for the conserved charges, volume or energy...may be I am being too naive...


title: Prove a dielectric with infinite dielectric constant behaves as a conductor for static fields

text: I read the following problem: Prove that a dielectric medium for which $\varepsilon \to \infty$ behaves as a perfect conductor in the presence of static electric fields. So, the easy part is that the normal component of an electric field is cancelled when entering the medium, as in a conductor. We also know that the tangent component of the electric field is continuous through the media, but how can we prove it vanishes for this case? This is usually done for a conductor by saying that any tangent field on the surface would produce a flowing motion of charges, hence leading with a non-static situation, impliying that this component (and the normal also) vanish for a conductor. But I cannot see how to prove this for an infinite constant dielectric without using the previous argument (assuming a priori that it is a conductor with free movable charges), this would be circular reasoning. I could sum up the problem by asking: how do we prove that such infinite dielectric has an equipotential surface when exposed to static electric fields? or equivalently: how do we prove that the total field is actually normal to the surface of such dielectric? Thanks, any help is appreciated.


title: How come a whistling kettle starts whistling only when water boils, and not long before - due to hot air escaping under pressure?

text: A whistling kettle will start to whistle when the water boils and turns into a jet of steam which then exits the small aperture in the spout. But why doesn't this happen much earlier - when the air molecules in the kettle get heated up enough, shouldn't they also (due to the increased pressure) forcefully escape through the aperture? (Assumee that the kettle was half filled with water, and so the upper half was filled with air). This should happen long before boiling (which is when the water molecules gain enough momentum to escape the water surface). Yet in practice, the whistling only starts at the time the water boils - how come?


The title is the question: Would the Standard Model allow two energetic photons to form a particle-like, zero-spin resonance?


title: Why did we need relativity to derive $E=mc^2$?

text: Okay, so the way I understand one of the "derivations" of $E=mc^2$ is roughly as follows:   * We observe a light bulb floating in space. It appears motionless. It gives off a brief flash of light. We measure the frequency of this light, and conclude that the light bulb lost some amount of energy $E_1$.   * Next, we imagine flying by this light bulb at 90% the speed of light (or something similar), and again observe the flash. Due to the Relativistic Doppler Effect, the frequency of the light is decreased, and so we observe that the bulb only lost a smaller amount of energy $E_2$.   * Since the total amount of energy lost _must_ be the same in both reference frames, we conclude that the bulb must have lost kinetic energy in the moving reference frame. Kinetic energy is $\frac{1}{2}mv^2$. Since $v$ did not decrease, $m$ must have decreased. Thus, when bodies lose energy, they also lose mass. QED. So obviously it's a little more complicated than that, but my question is: why do we even need special relativity? Can't we replace "relativistic doppler effect" with "classical doppler effect" and still get a similar result? The exact relationship between $E$ and $m$ will change, but shouldn't the insight that _a relationship exists_ be accessible even with only classical physics?


title: Modes of a QFT and irreducible representation of the gauge group

text: This is in reference to the calculation in section 3.3 starting page 20 of this paper.   * I came across an argument which seems to say that the "constraint of Gauss's law" enforces gauge theory on compact spaces to be such that physical states over which the partition function sums over be gauge invariant.  I would like to hear of explanations of the above argument.   * Also the above seems to lead (quite non-obviously to me) to the conclusion that these physical states correspond to traces of products of operators acting on the Fock space vacuum. It is not clear to me as to how this trace is defined such that even after tracing it remains an operator.  {Very often one seems to want these operators to be in the "adjoint of" the gauge group. The meaning and motivation of this demand is not clear to me. (I am familiar with the notion of adjoint representation of Lie groups)}   * Related to the above is another claim I see which seems say that massless modes will be absent for any gauge group Yang-Mill's theory and any matter content if the theory is on a compact space. Is the above correct? Why (whether yes or no)?    * In such scenarios is the terminology of "basic excitations" of a theory the same thing as single particle states? How are these single particle states in general related to the physical states constructed above?  Which of these is what is referred to when people talk of "modes" of a QFT?   * If there is a gauge symmetry by definition it will commute with the Hamiltonian and hence the states of the theory at every energy level will form a representation of the gauge group. Can something be said about its reducibility or not?  The claim seems to be that if the there are say $n_E$ quanta at the energy level $E$ (transforming under say representation $R_E$ of the gauge group) then when counting its contribution to the partition function the boltzman factor has to further weighted by the number of $1$ dimensional representations ("singlets" ?) in the $n$-fold symmetric (for bosons) or the anti-symmetric (for fermions) tensor power of $R_E$. I would be glad to know of explanations of the above.


title: Is there an intuitive geometric view of the effects of Lorentz transformations?

text: Is there a _time + two spatial dimension_ representation of a Minkowski-space surface which could be constructed within our own (assumed Euclidean) 3D space such that geometric movement within the surface would intuitively demonstrate the “strange" effects of the Lorentz transformation (length contraction, time dilation)? Perhaps by making manifest the idea of a hyperbolic rotation (the rapidity)?


title: What are the current (popular(ish)) approaches to modelling the quantum nature of spacetime at the Planck scale?

text: My guess at a list of them would be: spin foams, casual sets, non-commutative geometry, Machian theories, twistor theory or strings and membranes existing in some higher-dimensional geometry... Firstly, what have I missed? Also, if there is a string theorist or similar on here that could briefly shed some light on what's involved with these approaches I'd be most grateful. [Editted/expanded from here on] OK so I'm not having much luck getting a response to this so I suppose I've not been clear enough. I'll try to expand a little: In early 2010 I attended this inagural lecture by string theorist- Prof. Mavromatos entitled 'MAGIC strings'. In it he proposes that some string theory models may violate Lorentz symmetry at the Planck scale resulting in a kind-of foamy spacetime that could be observed by differing arrival times of photons of different energies reaching us from distant astronomical sources. See http://www.kcl.ac.uk/news/events_details.php?year=2010&event_id=2178 or here for one of the papers: http://iopscience.iop.org/1742-6596/174/1/012016 Furthermore, as I mentioned in the comment below, Prof. Sir Roger Penrose mentions that Wheeler and others have strongely argued that if we could examine spacetime at the Planck scale we would see a tubulent chaotic situation (from quantum-mechanical vacuum fluctuation I suppose) or perhaps a discrete granular one. Penrose goes on to list some other approaches that may suggest how this discete stucture may manifest itself. Hence my list above. I have studied much QM, introductory QFT and the Standard Model as well as some basic GR but I have no formal experience of string theory. I therefore wondered if anyone here could jot down a sentace or two to explain what's involved with each of the above approaches and add to the list if I've overlooked some alternative popular(ish) approaches.


title: Why is Higgs Boson given the name "The God Particle"?

text: Higgs Boson (messenger particle of Higgs field) accounts for inertial mass, not gravitational mass. So, how could it account for formation of universe as we know it today? I think, gravity accounts for such formations.. not inertia. Is there a relation between both in Standard Model? Or, is there another way with which Higgs Boson contributed in the formation of everything?


title: How big would the impact of a nuclear warhead be?

text: I am writing a post-apocalyptic science-fiction story which includes the detonation of a nuclear warhead. In this context, What scientific information is available about the impact of a modern day nuclear warhead?


title: How are fictitious forces related to my feeling?

text: This question arises when I am studying fictitious forces in an undergrad introduction to physics course. Suppose I am standing in an elevator with an acceleration $a$ directed upward. From the ground viewpoint, with $N$ being the normal force on me, we have $N - mg = ma $ and so $N = mg + ma$. From my viewpoint, I feel two force: an upward force of $m(g+a)$ and a total downward force (gravity + fictitious force) of $m(g+a)$ too. If I were standing somewhere on a planet with gravitational acceleration $G=g+a$, then I feel these two forces too. That's why in the elevator I have the feeling of being on the planet with $G = g+a$. OK, so far so good. Now let's say I'm freefalling. From my viewpoint, I feel two force: an upward fictitious force of $mg$ and a downward gravitational force $mg$. The situation is pretty the same as if I were standing on the ground. But clearly I wouldn't feel that normal when freefalling; in fact I feel weightless. Why? Thanks for your help.


Why is work defined as force dot displacement? I know that it is defined like that based on the observational fact - we do more work when we apply greater force or move to a greater distance. But I wanted to know if there was a more physical reason to back this fundamental relation.


title: Can/has string theory solved cosmological constant problem?

text: Can someone explain to me what the KKLT paper says, and what has and hasn't it achieved regarding the ability to construct solutions with a small positive or negative cosmological constant in string theory?


title: What happens to the energy?

text: if we make a bell ring in a vacuum room for 5 mins. And then open the door, will be able to hear the sound? If no sounds vibrations are emitted to the environment what happens to the energy that would normally be carried away by the sound?


title: Sensitivity of eye

text: In which color human eye is most sensitive?


title: Dashed lines in Feynman diagram

text: In this article, in e.g. figure 2, what does these dashed lines across the Feynman diagram mean? ![](http://i.stack.imgur.com/gfKJf.png)


title: Are covariant vectors representable as row vectors and contravariant as column vectors

text: I would like to know what are the range of validity of the following statement: > Covariant vectors are representable as row vectors. Contravariant vectors > are representable as column vectors. For example we know that the gradient of a function is representable as row vector in ordinary space $ \mathbb{R}^3$ $\nabla f = \left [ \frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z} \right ]$ and an ordinary vector is a column vector $ \mathbf{x} = \left[ x_1, x_2, x_3 \right]^T$ I think that this continues to be valid in special relativity (Minkowski metric is flat), but I'm not sure about it in general relativity. Can you provide me some examples?


title: Why can't light pass through walls but sound can?

text: When I sit in a room I can hear voices coming from the adjacent room but the light in adjacent room does not enter my room i.e. sound waves travels through the wall but light waves can't. Why?


title: Effect of water on an image

text: ![enter image description here](http://i.stack.imgur.com/dZn1H.jpg) I am stuck on this question: "consider the image above, P is an opaque disc (lying in a glass beaker) illuminated from bellow by a source S. A converging lens L forms an image of this at Q. Explain qualitatively how the position and size of the image of the disc is changed when the beaker is filled with water." Here is my explanation (but I do not think it is right): The image Q will be unaffected by the water in the beaker (i.e. it will be the same size and position as the image when there is no water). This is because the rays (assuming S is large enough) that reach L from the disc P will be parallel to the normal of the water's surface when both entering and leaving it and thus no refraction of the rays occurs. This means that the rays reaching L are exactly the same as when no water was in the beaker. If this explanation is wrong please can you give me a HINT to the write answer rather then just the answer itself, thanks.


title: Probability using Klein-Gordon Equation

text: I read somewhere that the Klein-Gordon equation doesn't allow for conservation of probability. Can someone prove this mathematically?


title: Is quantum Hall current density local? (${\bf j}({\bf r}) = \sigma_H {\bf \hat n \times E}({\bf r}) $)

text: The good old Ohm's law $${\bf j}({\bf r}) = \sigma_O {\bf E}({\bf r})$$ if translated into words would be "the local current density is proportional to a local electric field." In a quantum Hall state (QHS), the linear response to an external electric field is given by the following $${\bf j} = \sigma_H \bf \hat n \times E$$ where $\bf \hat n$ is the surface normal. _**Is it also a local relation between applied field ${\bf E}({\bf r})$ and response current ${\bf j}({\bf r})$?_** If the electric field is non-zero inside the bulk, it means there must be current propagating inside the gapped bulk. I tend to understand it in an intuitive way. As you see in the picture, for a uniform electric field in $x$-direction, the chemical potential is raised up linearly in $x$ and it intersects levels in the bulk. The current in the bulk comes from the chiral edge modes and sink into edge back again. I don't know whether my picture is correct or not. ![As you see, for a uniform electric field in $x$-direction, the chemical potential is raised up linearly in $x$ and it intersects levels in the bulk.](http://i.stack.imgur.com/2edPK.png)


title: What are the solution spaces of Nonlinear Schrödinger equations?

text: As we know, the solution space of Schrödinger equation is a Hilbert space, however, what about it of Nonlinear Schrödinger equations such as $$i\partial_t\psi=-{1\over 2}\partial^2_x\psi+\kappa|\psi|^2 \psi$$?


title: Quantum causal structure

text: We take causal structure to be some relation defined over elements which are understood to be morphisms of some category. An example of such a relation is a domain, another is a directed acyclic graph. Yet another is a string diagram in a symmetric monoidal category. Panangaden and Martin showed that interval domains are categorically equivalent to (hyperbolic?) spacetimes. This makes the domain a perfect candidated for _classical_ relativistic causality. The planar graphs of the diagrammatical calculus are an enticing candidated for quantum causal structure. Then there is Hardy's causaloid. The classical causal structure seems very realist, as in we might believe in the existence of the set of events for a universe. I have offered the Fischer Impossibility result as a refutation of the naïve existence of this set. What are the best candidates for a quantum causal structure?


title: Matter vs. Antimatter shortly after Big Bang

text: I am not a physicist or astronomer in training at all, so this might be a dumb question with an obvious answer, but as I watched something the other day on matter & anti-matter, and the discussion was kind of put out there how the matter side won out even though the prevailing thought is that at the moment of the Big Bang the universe should have had equal amounts of matter and anti- matter. It then spoke of ideas that matter must have somehow won out since we obviously exist in a world of matter. After that I had the question why would matter need to win out for our universe to exist? Since we know a matter/anti- matter collision annihilates to pure energy, and we know $E=mc^2$, why isn't it possible that all original matter and anti-matter annihilated each other leaving all pure energy, which in turn and in time could form into matter?


title: Determination of displacement value in work formula

text: A net force will always create displacement which approaches infinity if left undisturbed. So how to fix a value of displacement in work formula? Isn't a mention time interval necessary? Or do we measure displacement only while force is acting on the body i.e the moment we stop applying force we also stop measuring displacement.


title: QED as a Wightman theory of observable fields?  With a collision theory?

text: [Note: I'm using QED as a simple example, despite having heard that it is unlikely to exist. I'm happy to confine the question to perturbation theory.] The quantized Aᵘ and ψ fields are non-unique and unobservable. So, two questions: A. Can we instead define QED as the Wightman theory of Fᵘᵛ, Jᵘ, Tᵘᵛ, and perhaps a handful of other observable, physically-meaningful fields? The problem here is to insure that the polynomial algebra of our observable fields is, when applied to the vacuum, dense in the zero-charge superselection sector. B. Is there a way to calculate cross sections that uses only these fields? This might involve something along the lines of Araki-Haag collision theory, but using the observable fields instead of largely-arbitrary "detector" elements. (And since we're in the zero-charge sector, some particles may have to be moved "behind the moon", as Haag has phrased it.) (Of course, the observable fields are _constructed_ using Aᵘ and ψ. But we aren't obliged to keep Aᵘ and ψ around after the observable fields have been constructed.) I suspect that the answers are: No one knows and no one cares. That's fine, of course. But if someone _does_ know, I'd like to know too. [I heartily apologize for repeatedly editting this question in order to narrow its focus.]


title: Are "typical" black holes rotating, or stationary?

text: From my (somewhat limited) understanding of GR I know that there are two different kinds of solutions that produce a black hole, some that rotate and some that do not. What I can't figure out from my reading so far is which of the two is considered "typical" (if either). That is, when we think we have detected a black hole in space, do we initially suspect that it's rotating or stationary? My naive assumption would be, since they form from collapsing _rotating_ stars, that most black holes would continue rotating after formation, increasing in speed as they decreased in volume. However, I see a lot of discussion about black holes that use Schwarzschild's equations, which describes a non-rotating object. Is this merely because those are easier to deal with and "close enough", or is it really believed that many black holes are non-rotating?


title: If the velocity vector of a moving particle is always perpendicular to the position vector, is the path a circle?

text: A Newtonian physics question: If the velocity vector of a moving particle is always perpendicular to the position vector, is the only possible path a circle? What if the magnitude of the velocity vector changes, what if it doesn't? EDIT: I meant to write "perpendicular" not "tangent" ANOTHER EDIT: UGH, I'm sorry, I meant to say this: If the velocity vector of a moving particle is always perpendicular to the position vector, is the only possible path a circle? What if the magnitude of the velocity vector changes?


How do we determine the temperature of a Black Hole? Since we cannot see a Black Hole, which I presume, is because it absorbs light, would it not also prevent radiation from escaping, making temperature determination difficult.