title: Lifetime of undiscovered element and its calculation

text: Reading about nuclear models, nuclear physics and the mythical ``stability island'' I just wondered about the next question: **How can the lifetime of any undiscovered superheavy element be calculated or estimated theoretically?** Moreover...Does it correspond to a numerical recipe or a theoretical closed approximated formula? Is the lifetime of superheavy atoms the same as that of the superheavy nuclei it has? Any good rereferences about this hard topic? For instance would be welcome! Comment: I would also be interested in how could someone calculate (if possible) the lifetime of, e.g., Ubh-310 from first principles with the aid of PC or grid computing...


title: Advanced Molten Salt Reactor - Is the concept of designing a reactor that uses spent nuclear fuel to generate power technically feasible?

text: I was going through the concept of designing a Nuclear Reactor that uses Spent Nuclear Fuel(SNF) to generate power as proposed by Transatomic Power . http://transatomicpower.com/white_papers/TAP_White_Paper.pdf **Is it possible to design such a Nuclear Reactor that uses spent nuclear fuel to generate power ?**


title: Can Mirror box simulate long light travel?

text: Imagine that there is a cube box that has mirrors all 6 faces in . If we use a strong laser and enter in the box from a small hole on the box. The laser light travels in the box long time that we can detect the laser via a detector on other hole of the box. 1) Is it possible to simulate the long light travel in it (for example a day or week)? 2) Is it possible to proof that there is no ether via that box? If we move the box in a fixed velocity what we can observe about receive time on detector. I ask a question first time in this website If it is asked question or not appropriate for your format sorry for that.


title: Mean kinetic energy according to the WKB approximation

text: > Show that in the WKB approximation, the mean kinetic energy $T_{n1}$ in a > bound state $\psi_n$ in a potential $V(x)$ is given by > > $\langle T_n \rangle = \frac{1}{2}\left(n+\frac{1}{2}\right) > \frac{dE_n}{dn}$ This is a homework problem and I'm having trouble understanding what it's asking.   * What does the notation $T_{n1}$ mean?   * What is the meaning of the expression $\frac{dE_n}{dn}$? Bound states should have discrete spectra. Could someone provide a clearer statement of this problem?


title: What equation describes the electrostatic potential in these circumstances?

text: I have a solver for Poisson's equation and it works nicely. It uses finite differences. It works in the presence of multiple dielectrics. It also solves the Poisson Boltzmann equation. That is, fixed charges with free moving charges, as in a molecule immersed in a solution with salt assuming that the molecule and liquid can be approximated as a continuum medium. Now, what happens if there are currents? this violates the assumption of equilibrium required for Poisson Boltzmann. I'm looking for the equation that describes this situation. I guess it should have the form $$ \nabla\cdot(\epsilon\nabla \phi) = -\rho_\text{fixed} + \text{<ions effect>} + \text{<current effect>} $$ I'm pretty sure this has already been studied. Can anyone direct me towards where to look for more detail? is there an equation with a name (like Poisson Boltzmann) for this?


title: Uniform distribution of charge on a plane and on a bar: conditions to have no motion of the bar

text: On the plane z=0 there is a superficial charge distribution such that $\sigma$ is constant. Near to the plane, there is a bar, charged uniform with total charge q. At the extremities the bar has two constraints, so it can't turn. If I want to find the constraints force and the force momentum needed to block the bar, can I consider the charge q as a single point charge and put it in the midpoint of the bar?


title: Transformation of Hamiltonian in Sun-Earth System

text: In Sun-Earth system, what transformation law allows me to find the Hamiltonian H in an arbitrary inertial system knowing the same in the center of mass?


title: Is spin just due to uncertainty in angular momentum?

text: I can't seem to think of any way to envision electron spin. Can it be thought of as the uncertainty in angular momentum?


title: Energy spent by motor in a period

text: Consider a single coil that is turning in a constant and uniform magnetic field thanks to a motor. The normal to the coil is given by: $${\bf u}(t)=\sin (\omega t){\bf u_x}+\cos(\omega t){\bf u_z}$$ How can we obtain the energy that the motor has to spend in a period $T=\frac{2\pi}{\omega}$? I have thought that it could be given by the integral of -$U_p$ ($U_p$ is the potential energy of the coil) from 0 to T (we should have to integrate because the normal vector to the coil depend on t, I have thought). But I'm almost sure that it is wrong.


title: In which field of mathematics do I learn path integrals?

text: I don't mean line integrals, I am talking about path integrals or functional integrals like the ones that Feynman introduced to quantum mechanics. And what are the prerequisites to this field of study?


title: When you measure position of an electron in a energy pure state, what happens to the energy?

text: When you measure the position of an electron that is in a pure energy state, what happens the energy becomes non-deterministic. That is future measurements of energy can only be predicted with respect to a probability distribution. This seemingly violates the conservation of energy since future measurements of energy may give different results. I assume here that the measurement process somehow adds some non-determinism or transfers energy to the measuring apparatus. But this is just a vague idea. How do you clearly explain this?


title: Is a "supercritical charge" in graphene similar to Hawking Radiation?

text: These papers describe a phenomenon referred to as "atomic collapse" and "supercritical charge" in graphene: Wang et al., Pereira et al. "Atomic collapse" appears when you have a large enough Coulomb potential in a system described by the Dirac Equation. In the case of graphene, a localized state is embedded in the continuum below the Dirac Point, causing an electron to fall into the state, leaving behind a hole. I was wondering whether something similar could happen for gravity. I know gravity is due to the curvature of spacetime rather than a Coulomb potential, but the phenomenon described by the papers cited above seem reminiscent of Hawking Radiation. Is "atomic collapse" the electromagnetic analog of Hawking Radiation?


title: Law of conservation of energy and kinetic energy: deformation of a spring

text: **Problem:**   _A block B of 1,5 kg is attached to the right of a spring (not deformed, with its right side attach to a wall) with a constant of $k = 80 N/m$ and, at rest, the block enter in collision with another identical block A. The block A moves to the left with a velocity of 5 m/s before the collision. Consider successively a restitution coefficient between the two blocks of $e = 1$ and $e = 0$. There is no friction in this problem.   a) the maximum deformation of the spring.   b) the final velocity of the block A._ * * * I have some difficulty to start this problem. I have an example with a block falling on a spring, but I have a hard time to apply it on a horizontal collision. I started by drawing a diagram of the two blocks before the collision. Block B is not moving and block A is going to the left. I also draw a diagram of the two blocks after the collision. The block B is going to the left and pushing the spring, and the block A is going to the right. (I'm going to use the french notation) Since the restitution coefficient is 1 (impact perfectly elastic), the two blocks will go in an opposite direction with the same velocity they had before the impact. So block A will go right at 5 m/s and B will stay at 0 m/s but the spring will be compress. Later, the block B will be push to the right with the elongation of the spring and then the two blocks will stick together and continue to the right with a restitution coefficient of 0 (impact perfectly plastic). **So, I understand what is happening, but I need some help for the steps to follow to resolve this problem. Can someone help me understand?** * * * **Note:** if you have some problem understanding the problem, it is probably because I translated it from a french book. We do not use the same exact term in french (for example, the exact translation from french of "velocity" is "speed"), so just ask for more informations.


title: Is everything made of massless particles?

text: Photons have no mass. Yet they interact gravitationally, as all energy does, with other energetic and massive particles. This means that if you put multiple photons in a system, you get something that appears to have mass, even though none of the constituent particles do have mass. That makes me wonder: Is mass really a fundamental part of reality? Couldn't it be that massive particles (protons/neutrons/electrons) are just composed of massless particles like photons knotted up, confined to a small area and whizzing around in very tight orbits? So everything is, in a sense, massless? The search for and discovery of the Higgs Boson suggests to me, in my limited understanding, that scientists believe mass is a fundamental property that some particles have. And also that mass is fundamentally different than other types of energy (though conversion is possible). Does all of this preclude a system like I describe?


title: Conservation of Angular Momentum, as related to a flywheel

text: Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled cylinder, assume a spoked bicycle wheel) rotating in the x-y plane, I'm trying to calculate the force generated in either direction along the z-axis. It seems to me, in line with Newton's first law of motion extended to rotational dynamics, what forces are physically being generated that prevent a rolling wheel from falling over?


title: Gravitational potential energy with regards to annihilation

text: Given particles A, B, C and D, where:   * A and B have an equivalent mass   * C and D have an equivalent mass, both larger than A (or B)   * D is the antiparticle of C. A and B start close to C, but with velocity, such that they have moved away from C, so their kinetic energy has been converted to GPE. If D then collides with C such that C and D annihilate, what is the fate of the GPE that A and B previously acquired?


title: Why can't I calculate center of mass via torque? Results off by a few percent

text: Why do I keep getting a slightly different result from the following two ways of determining the center of mass of a rigid, geometrically simple object? The object is a rectangular 5(x) by 7(y) sheet of uniform rigid material, with a 2(x) by 3(y) rectangle missing from the upper right corner. **Method 1)** The official formula in my textbook: x center of mass = ( m1x1 + m2x2 ) / ( m1 + m2 ) y center of mass = ( m1y1 + m2y2 ) / ( m1 + m2 ) This gives results of x = **2.18** and y = **3.09**. **Method 2)** A torque calculation that would seem more intuitive to me: The xy coordinate plane is parallel to floor and I watch it from above. Object is in the first quadrant (top right), touching the x and y axes. I imagine balancing the object on a razor blade parallel to the y-axis. I solve for x by assuming that the torques on the left and right side must cancel out. I rotate the razor blade so that it's parallel to the x-axis. I balance the object again. I solve for y by assuming again that the torques on each side must cancel out. This gives results of x = **2.07** and y = **2.9**. The difference between the results given by the two methods is small, but significant. What's going on? I checked my math several times and even tried a different problem with a simpler geometry. Again the results differed by a small but significant value. I'm fine with having to learn the textbook method, but would like to know why the torque approach gives results that are 3-5 % off.


title: How to calculate fluid(oil / hydrocarbon) loss under pressure

text: I'm trying to calculate the amount of fluid that would flow through an area dependant on the amount of pressure that there is. I'd also like to know the rate at which it would flow. Essentially I have a very basic model of a well drilling system. At the moment the variables / parameters for each of the objects in question are defined by the user but may be set to constants to enable testing. The assumptions I'm working on are: The viscosity of the oil / hydrocarbons is set to constant. Once drilled the area of the hole will not change (there will be no collapse etc). The well is never ending so constant pressure. If someone could point me in the right direction I'd be very thankful. Some of the assumptions may be way off so guidance in general is also appreciated, many thanks.


title: Where does the kinetic energy go?

text: A uniform cylinder was placed on a frictionless bearing and set to rotate about its vertical axis. After a cylinder has reached a specific state of rotation it is heated without any mechanical support from temperature $T$ to $T+\Delta T$. Angular momentum will be conserved but rotational kinetic energy will decrease as angular velocity decreases. What I fail to understand is where does this energy go?


title: Representation of a Signal and its evolution via Quantum System

text: I am a total beginner in the field of Quantum Mechanics. So, the question I am asking may be a silly one. So kindly give me possible answers or advice for modifications. Recently I am learning the concept of qubit. The quantum theory tells that a $n$-qubit system is represented by a unit vector in $(\mathbb{C^2})^{\bigotimes{n}}$ with some basis set. Now, we can also express a $2^n$ dimensional complex signal as a vector at any point of time, and with suitable normalization it is nothing but a qubit. Now, as far as I know, the evolution of a qubit is always dictated by a unitary operator, whereas, the evolution of a signal can be dictated by any arbitrary operator. So, is there any way, any sort of transformation that allows,given a signal and its evolution, to create its equivalent representation as an evolution of qubit, so that we can solve problems of signals using methods of Quantum Mechanics.


title: Difference: Fermi wave length vs. phase-breaking length?

text: I am reading a quantum transport book, where they often mention: phase breaking length and Fermi wavelength. I have looked up and found that: **Phase breaking length** = length over which electron remains its phase. **Fermi wavelength** = Wavelength associated with the maximum energy of electron (Fermi energy). This is often equal to the distance between 2 electrons. What I couldn't find, however (and in which I am interested) is: 1) _What is the difference between the Fermi wave length and the phase- breaking length?_ 2) _In which transport regimes do they play a role?_


title: Why does the water-pressure of my shower fall if I hold the shower head high?

text: I live in a very old house - build 1902 - in the 4th floor in the city of Karlsruhe (Germany). I have a shower and the gas-heater for the water is in it: ![enter image description here](http://i.stack.imgur.com/tpiBK.jpg) If I hold the shower head over some height (see image), the water pressure is suddenly reduced. Whats the reason for that? (I guess the way the pump works might be the reason.) ![enter image description here](http://i.stack.imgur.com/rvn6k.jpg)


title: Parallel circuits - Overall resistance decreases with additional resistor

text: Let's say that there is a parallel circuit with two identical resistors in parallel with each other. If a third resistor, identical to the other two, is added in parallel with the first two, the overall resistance decreases. Why does this overall resistance decrease?


title: Mathematical motivation of OPE?

text: In Peskin & Schroeder (and also Cheng which I have skimmed through) they motivate the Operator Product Expansion with a lot of words. Is there any way to motivate it mathematically, e.g. Taylor expansion or similar?


title: Does a point exist in the real world

text: In mathematics we can have an infinite number of points between two integers. This is really circular logic since a point is defined as infinitely small. Does a point exist anywhere in the physical world or is it simply a convenient mathematical abstraction with no place in reality. **Is space actually divided into infinitely small points? What about time?**


title: Is it possible that the universe in its entirety is discrete rather than continuous?

text: Since electric charge is comprised of discrete units and and mass is formed by discrete units is it possible that space-time itself is discrete as well?


title: Is everything in the universe discrete?

text: When beginning my education, I regarded nearly everything as continuous and analog in nature:   * Physical objects could have any mass on a continuous scale   * Light sources could emit any intensity of light on a continuous scale The more I learn, the more I find what I regarded as continuous is actually discrete:   * Physical objects are composed of discrete numbers of atomic and subatomic particles   * Light sources emit a discrete number of photons This trend of finding that things are actually discrete seems to be part of unraveling the properties of nature. The further you dig into something, the more you find the basic elements that comprise it. It seems strange to me that anything could be truly continuous in nature since such a thing could potentially store infinite information. Is there anything in the universe that we know with relative certainty is not discrete? **Edit:** This isn't really a duplicate of the question that is linked. That question is essentially asking, "does the Planck scale imply that space is discrete?" This is not the same as "is everything in the universe discrete?" I did not find the answer to my question there as the answers are addressing a different question.


title: Is time quantized? Is there a fundamental time unit that cannot be divided?

text: Is the present just a sharp line between the past and the future with no time at all, or is the present a short frozen unit of time? Could time be quantized into a fundamental units? Like Planck time or some other briefest unit of time? Does then time itself jump from one time unit to the next time unit, because there is nothing between? Could everything at the smallest timescale be a frozen 3D-picture, similar to the 2D-pictures in a motion picture? Could this reality be something like a 3D-motion picture with pictures shown with a time frequency? **Update:** I guess we will never know if time is quantized if we don't measure that it is quantized. Like if we find something with a high frequency that are affected by the frequency of the fundamental time units. There is one such observation of the redshifted light from galaxies which seem to cluster to specific bands in the energy spectrum: "The redshifted light we observe is consists of photons, discrete 'particles' of light energy. The energy of a photon is the product of a physical constant (Planck's constant) times the frequency of the light. Frequency is defined as the reciprocal of time, so if only certain redshifts are possible, then only certain energies are present, and hence only certain frequencies (or, equivalently, time intervals) are allowed. To the extent that redshifts of galaxies relate to the structure of time, then, it suggests an underlying quantization. "In our newest theoretical models we have learned to predict the energies involved. We find that the times involved are always certain special multiples of the 'Planck time,' the shortest time interval consistent with modern physical theories." http://www.scientificamerican.com/article.cfm?id=is-time- quantized-in-othe&page=2


title: Does the Planck scale imply that spacetime is discrete?

text: On a quantum scale the smallest unit is the Planck scale, which is a discrete measure. There several question that come to mind:   1. Does that mean that particles can only live in a discrete grid-like structure, i.e. have to "magically" jump from one pocket to the next? But where are they in between? Does that even give rise to the old paradox that movement as such is impossible (e.g. Zeno's paradox)?   2. Does the same hold true for time (i.e. that it is discrete) - with all the ensuing paradoxes?   3. Mathematically does it mean that you have to use difference equations instead of differential equations? (And sums instead of integrals?)   4. From the point of view of the space metric do you have to use a discrete metric (e.g. the Manhattan metric) instead of good old Pythagoras? Thank you for giving me some answers and/or references where I can turn to. **Update:** I just saw this call for papers - it seems to be quite a topic after all: _Is Reality Digital or Analog?_ FQXi Essay Contest, 2011. Call for papers (at Wayback Machine), All essays, Winners. One can find some pretty amazing papers over there.


title: Planck time, time or time interval?

text: Planck time is really a weird topic, if we try to find out that is it time or time interval. It is the time taken by light to travel a Planck LENGTH so it must be time interval. But we also know that Planck length is MOST FUNDAMENTAL and it can't be differentiated anymore. So what's the reality?


title: Is time continuous?

text: While working on physics simulation software, I noticed that I had implemented discrete time (the only type possible on computers). By that I mean that I had an update mechanism that advanced the simulation for a fixed amount of time repeatedly, emulating a changing system. I was a bit intrigued by the concept. Is the real world advancing continuously, or in really tiny, but discrete time intervals?


title: What were Feynman's objection(s) to a cubic lattice universe?

text: In this video of Feynman discussing the scientific method, starting at around eight minutes and 30 seconds, Feynman describes the proposition that space consists of a cubic lattice of points (as opposed to space being continuous). Feynman says "then we can prove that [the proposition] immediately is wrong," but he doesn't elaborate on the proof. > My question is: What are the objection(s) to a cubic lattice universe that > Feynman refers to in this video? I'm not looking for every possible objection to a cubic lattice universe. I'm wondering what in particular the (apparently immediate and obvious) objections are that made Feynman so dismissive of the idea.


title: What about continuity of Space and possible discreteness of Time?

text: Is time continuous or discrete? Is even this question a valid question? If you say, it all depends on resolution then assume the best possible resolution achievable. If it is discrete, then what about space? More specifically, what about space-time?


title: Conserved quantities in generalized n-body problem

text: Given a collection of point-particles, interacting through an attractive force $\sim \frac{1}{r^2}$. Knowing only $m_1a=\sum_i \frac{Gm_1m_i}{r^2}$ and initial conditions we can deduce the motion of the system. Consequently we can observe that three quantities remains constant A) center of mass of the system B) total energy C) angular momentum How can we derive these 3 facts directly from $m_1a=\frac{Gm_1m_2}{r^2}$ ? Are these quantities conserved for any attractive force $\sim\frac{1}{r^n}$ ? Given any monotonically decreasing force for $r$ in $(0,\infty)$, which are the conserved quantities?


title: Question about the Bernouilli equation

text: There are some things I encountered, studying the Bernouilly equation, that I don't understand. I was studying in the following book: http://www.unimasr.net/ums/upload/files/2012/Sep/UniMasr.com_919e27ecea47b46d74dd7e268097b653.pdf. At page 72-73 they derive the Bernouilli equation for the first time, from energy considerations. They state that it can be applied if the flow is steady, incompressible, inviscid, when there is no change in internal energy and no heat transfer is done (p.72 at the bottom). I understand this derivation, my problems arise when they derive the equation again at page 110-111, this time from the Navier-Stokes equation. I don't quite understand the derivation yet, but I am more confused about the outcome. It seems that the Bernouilli equation can now be applied under the four conditions they state (inviscid flow, steady flow, incompressible flow and the equation applies along a streamline) while it seems that there are no limitations to the internal energy of the flow and the heat transfer done. If I understand the last paragraph right, they state that the requirement that the flow is inviscid already comprises the claim that there is no change in internal energy ("the constant internal energy assumption and the inviscid flow assumption must be equivalent, as the other assumptions were the same", I don't really understand this reasoning, because the "inviscid flow assumption" was also already made in the previous derivation). Furthermore, if I follow the reasoning (so if I assume that inviscid flow indeed implies that there is no change in internal energy or if I assume that the Bernouilli equation can also be applied, without the assumption of "no change in internal energy") then example 4 at page 74 seems strange to me. It shows that in this situation the Bernouilli equation can't be applied directly (because headloss has to be included in the equation). However I think that we can easily repeat the derivation, assuming that the flow is inviscid (and assuming that the other conditions are satisfied), but this example shows that the internal energy increases, so inviscid flow can't imply "no change in internal energy". And the example also shows that the Bernouilli equation can't be applied, because head loss has to be considered (so this example seems to contradict the result at page 110-111). I hope someone can explain where my understanding is lacking, because this really confuses me about the conditions under which the Bernouilli equation can be applied. It would also be helpful, if someone could explain the derivation at p.110: what I don't understand is the definition of "streamline coordinates". Do they just take a random point on the streamline, where they place a cartesian coordinate system?


title: X-ray and neutron powder diffraction: peak broadening due to crystal size

text: When analysing powder diffraction patterns, the broadening of peaks can be used to estimate crystal sizes. Smaller crystal size gives larger broadening according to the Scherrer equation: $$ \beta = {{K\cdot\lambda}\over{D\cdot\cos \theta}}.$$ What is the physical origin of this effect? Edit: Added homework tag as this is related to my thesis on soil studies using diffraction methods.


title: Definition of complex permittivity

text: I'm not sure if this is the appropriate forum for my question as I actually am studying this as part of electrical engineering and I don't actually study physics. Nonetheless, I shall ask and if need be, move my question to another venue. My question is with regard to how complex permittivity is defined. According to my book $$ \begin{align*} \nabla \times \mathbf{\tilde{H}} &= \sigma \mathbf{\tilde{E}} + \jmath\omega\varepsilon \mathbf{\tilde{E}} \\\ &= (\sigma + \jmath\omega\varepsilon)\mathbf{\tilde{E}} \\\ &= \jmath\omega\underbrace{\left(\varepsilon - \jmath\frac{\sigma}{\omega}\right)}_{\varepsilon_c}\mathbf{\tilde{E}} \\\ &= \jmath\omega\varepsilon_c\mathbf{\tilde{E}} \end{align*} $$ ($\mathbf{\tilde{E}}$ and $\mathbf{\tilde{H}}$ are phasors.) I really do not understand why $\varepsilon_c \equiv \varepsilon - \jmath\frac{\sigma}{\omega}$ and not $\varepsilon_c \equiv \sigma + \jmath\omega\varepsilon$. What is the sense in creating a complex value, $\varepsilon_c$, and then multiplying by $\jmath\omega$ when you could just modify the definition of $\varepsilon_c$ such that $\nabla \times \mathbf{\tilde{H}} = \varepsilon_c \mathbf{\tilde{E}}$? I also have a conceptual question: From what I understand, $\epsilon$ determines the phase delay between the H and E fields. This phase delay, as far as I know, comes from the finite speed involved in 'rotating' the dipoles in the medium. When these dipoles are 'rotated' though, since they take a finite time to rotate, that implies to me that there are some sort of losses involved in rotating the dipoles. These losses, though, as far as I can tell, are not accounted for in $\varepsilon_c \equiv \varepsilon - \jmath\frac{\sigma}{\omega}$ (I figure the loss due to rotating the dipoles should be part of $\Im{\\{\varepsilon_c\\}}$ (from what I can tell, $\Im{\\{\varepsilon_c\\}}$ accounts for the loss and $\Re{\\{\varepsilon_c\\}}$ accounts for the phase delay); however, $\Im{\\{\varepsilon_c\\}}$ only seems to take into account frequency and loss from electorns crashing into atoms). Similarily, I would've thought that the loss that comes from electrons crashing into atoms (which $\sigma$ looks after), would also have the affect of at least somewhat slowing down the wave and causing lag. Basically, what I'm saying is, why aren't $\varepsilon$ and $\sigma$ also complex numbers? Or maybe they are... Thank you.


title: speed of sound and the potential energy of an ideal gas; Goldstein derivation

text: I am looking the derivation of the speed of sound in Goldstein's Classical Mechanics (sec. 11-3, pp. 356-358, 1st ed). In order to write down the Lagrangian, he needs the kinetic and potential energies. He gets the kinetic energy very easily as the sum of the kinetic energies of the individual particles (the sum going over to an integral in the limit). Let $\eta_i, i=1,2,3$ be the components of the displacement vector (each $\eta_i = \eta_i(x,y,z)$ being a function of position). So the kinetic energy density is ${\cal T}=(\mu_0/2) (\dot{\eta}_1^2+\dot{\eta}_2^2+\dot{\eta}_3^2)$, where $\mu_0$ is the equilibrium mass density. For the potential energy, he uses a thermodynamic argument, relying on the work done in a PV diagram, and using the equation $PV^\gamma = C$. His ultimate result, after several steps, is ${\cal V} = -P_0 \nabla\cdot\vec{\eta}+\frac{\gamma P_0}{2}(\nabla\cdot\vec{\eta})^2$ Here, $P_0$ is the equilibrium pressure, and $\gamma$ is the ratio of specific heats. He later shows that the term $P_0 \nabla\cdot\vec{\eta}$ has no effect on the equations of motion, and so he drops it. So his final formula for the Lagrangian density is: ${\cal L} = (1/2)(\mu_0\dot{\vec{\eta}}^2 - \gamma P_0(\nabla\cdot\vec{\eta})^2$ and the Lagrangian of course is the integral of this over all space. Now in the case of an ideal gas (or better yet, a perfect gas), my understanding is that the internal energy is _entirely kinetic_. Naively, the statistical model is a bunch of non-interacting point particles racing around, bouncing off the walls of the container. (For simplicity, ignore gravity.) This seems contradictory. Shouldn't we get the same results from a microscopic and a macroscopic viewpoint? To put it another way, this suggests that in a gas made up of non-interacting point particles, with no external forces except for the hard-wall forces, sound waves could not propagate (since the Lagrangian density would reduce to the kinetic part). That doesn't seem right.


title: Can we "fill" an atom with alpha particles?

text: The following passage has been extracted from the book "Modern's abc of Chemistry": > ..Heisenberg in 1927, put forward a principle known as Heisenberg's > uncertainty principle. It states that, it is not possible to measure > simultaneously both the position and momentum (or velocity) of a microscopic > particle, with absolute accuracy. Lets fill an isolated atom by subatomic "Rutherford projectiles"-alpha particles. I hope it is possible. This doesn't seem to be a limit of our technology. Isn't it? If we are successful in filling the an atom with alpha particles, we are decreasing the space for the electron and confining them to a least distance, isn't it? Doesn't this experiment, give us belief of measuring simultaneously both the position and momentum with little greater (or even complete) certainty than what predicted by Heisenberg's principle? This doesn't seem to allow us to fill an atom with alpha particles. So, can we fill an atom with alpha particles?


title: Dispersing ultrasound in a tube - patters

text: I am looking for patterns to efficiently disperse reflected ultrasound in the range of wavelengths 1mm to 4mm within the interior of a narrow tube (I do not want wall reflections). For various reasons absorption does not appear to be a solution. Thickness is also critical in that the surface must not be much more than 1mm deep. This is part of a setup for measuring absorption in gases using reflected pulses.


title: Torque definition and right hand rule not arbitrary

text: I have read the following: http://www.feynmanlectures.caltech.edu/I_20.html#Ch20-S1 The formula for $\tau_{xy}$ is derived in this chapter: http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-S2. In this derivation until equation 18.11 ($\Delta W=(xF_y-yF_x)\Delta\theta$) the term $xF_y-yF_x$ does not seem to be arbitrary. It would not make any sense the other way around like: $yF_x-xF_y$, because of the equations 18.6 ($\Delta x=-PQ\sin\theta=-r\,\Delta\theta\cdot(y/r)=-y\,\Delta\theta$) and 18.7 ($\Delta y=+x\,\Delta\theta$). Then $\tau_{yz}$ and $\tau_{zx}$ are derived (in the first link) by symmetry. $$\begin{alignedat}{6} &\tau_{xy}~&&=x&&F_y&&-y&&F_x&&,\\\\[.5ex] &\tau_{yz}~&&=y&&F_z&&-z&&F_y&&,\\\\[.5ex] &\tau_{zx}~&&=z&&F_x&&-x&&F_z&&. \end{alignedat}$$ * * * I have some ideas and wonder whether or not they are true: I have got the feeling that they are wrong but I have no idea why they should be wrong.   1. _So, since the formula for the torque in the $xy$-plane ($\tau_{xy}$) is not arbitrarily-derived, there is to torque $\tau_{yx}$, since $yF_x-xF_y$ would not be correct in equation 18.11._   2. In my first link, below equation 20.1 there are 2 pictures which shall demonstrate how the letters $x$, $y$ and $z$ can be interchanged. _How would that make sense?_ Since equations 18.6 and 18.7 are true, we "live" in a right-handed coordinate system and $\tau_{yx}$ would not make any sense.   3. Since $\tau_{yx}$ would not make any sense, the arguments in my first link down to equation 20.9 show that the right-hand rule is not arbitrary. What is wrong with my arguments? What does $\tau_{yx}$ mean?


How can we define U(1) local gauge transformation for Dirac spinor field?, like scalar fields?


title: Remotely changing superconductor levitation height?

text: I want to be able to modify the height of a quantum locked superconductor. My original plan was to levitate the superconductor over an electromagnet and modify the current to said magnet (increase the current for higher levitation height, decrease for lower). Further research has made it apparent to me that this won't work. Is there a way to change the levitation height of a superconductor short of mechanical interference within the system?


title: Balloon gas temperature experiment in water

text: In this problem set I have a passage that describes an experiment that looks at the changing temperature as an air filled balloon rises to the surface from the bottom of a water filled tank. The graph they provide shows that as the balloon rises to the surface the temperature of the air in the balloon decreases. (I'm paraphrasing a lot of the question because it's long and has a bunch of information that's not pertinent such as dimensions of the tank, dimensions of a valve that's not even used in any problem!!! etc.) I'm struggling with the idea of the temperature changing at all. From the answers from the problems it seems that the gas is doing work by expanding thereby losing internal energy and thus temperature. This to me makes sense, but I keep looking at the PV=nRT and thinking well wait, wouldn't the temperature just be fixed and the volume and pressure change correspondingly? Help getting through these basic concepts would be great! Also one of the problems I struggled with: Which of the following items of information would NOT help in predicting the results [shown in the graph]? A) The number of air molecules inside the balloon B) The thermal conductivity of the rubber (of the balloon) C) The variation with depth in the speed of the balloon D) The total mass of the water in the tank Answer is D I'm confused what the test makers were hinting at with C; if C could be included in your explanation of this experiment that would be great (does this somehow give the amount of internal energy lost??). I can't find other examples of this kind of experiment, is it a specific type? I.e. Does it have practical applications (even a name of like a standardized experiment similar to "pendulum motion" etc) or is it simply a conceptual check? Thanks! Update: http://s24.postimg.org/yzvb1ci5x/balloon_gas_temp_experiment.jpg


title: how long do large hadron collider experiments take?

text: This travel stackexchange answer has kinda got me wondering... how long do experiments involving the large hadron collider usually take? I'd expect you run it for a few seconds and bam - higgs boson detected or whatever. Maybe it'd take a few months to set the experiment up but once it's setup it doesn't seem like it'd take that much time at all to run the experiment? I mean, maybe you'd want to run it a few times to verify your results but if each run takes just a few seconds it seems like you could still be done with your multiple runs even in a single day. Any ideas?


title: How does the following commutator for measured observables and this operator relation imply the following relation?

text: $$ \hat{\Omega}_j{(\tilde{q}_j)}=\Omega_j(\tilde{q}_j-\hat{q}_j) $$ $$ [\hat{q}_j,\hat{q}_l]=ik_{jl} $$ Implies $$ [\hat{q}_j,\hat{\Omega}_l]= \frac{\partial\Omega_l(\tilde{q}_l-\hat{q}_l)}{\partial\hat{q}_l}.ik_{jl} $$


title: 1D Acoustical Relations beyond nearest neighbor couplings

text: Consider some 1D Lattice of atoms with nth neighbor coupling of strength k_{n}. I'm looking for the dispersion relation for acoustical phonons under these conditions. I start with the Lagrangian, $$L = K- V$$ $$L = \sum^{\infty}_{n} \frac{1}{2}m \dot{x}_{n}^{2} - \sum^{\infty}_{p=1} \frac{1}{2}k_{p} \\{(x_n-x_{n+p})^2 + (x_n - x_{n-p})^2\\}$$ Mass is the same for each atom. The Lagrange equation should be $$m \ddot{x}_{n}=\sum_{p=1} k_p(x_{n-p}+x_{x+p}-2x_n)$$ Now, if I use a travelling wave solution as an ansatz, I should get my dispersion relation as some infinite series. Is this correct? If so, help me out because I can't make it work. Thanks!


title: Disproving a refutation of quantum mechanics (QM) via a calculation of the ground state of the helium atom

text: This website http://www7b.biglobe.ne.jp/~kcy05t/ appears to refute Quantum mechanics using some proof. An important paper involved is this 'Calculation of Helium Ground State Energy by Bohr's Theory-Based Methods' http://arxiv.org/abs/0903.2546 (written by the website author) How to disprove the author's claims, assuming his refutation of QM is unacceptable/false. Note: I don't know if this question belongs here. Edit:It may take considerable effort to refute or support his claims.


title: How to check whether a given $W(x,p)$ represents a Wigner function of a physical state?

text: For simplicity let us consider one-dimensional quantum-mechanical systems only. Given any state $\rho\in\mathcal{B}(\mathcal{H})$ and its Wigner function $W_\rho(x,p)$, there are several properties it always satisfies,   * it is real-valued and bounded in absolute value by $2/\hbar$ from above,   * its marginals are well-behaved probability distributions,   * its overlap $\int W_\rho(x,p) W_\sigma(x,p) \mathrm{d}x\mathrm{d}p$ with the Wigner function of any other state $\sigma$ is nonnegative. Given an arbitrary function $W(x,p)$, we can reconstruct a state $\rho$ it corresponds to iff all of these conditions are met using the Weyl transform. If some properties are not satisfied, the resulting operator will be unphysical—non-Hermitian, unnormalized or non-positive. The question is how to check the conditions prior to the calculation. The first two are usually fairly easy to check but the latter involves going through all states of the system. Even if we restrict ourselves to pure states, this still iterates over all rays in an infinite-dimensional linear vector space and is as such usually done finding a proof tailored to the specific case. Is there a simpler (algorithmic) condition which can replace the third bullet above and implies its validity?


title: A question on partial trace and density matrix computation

text: Consider a Pure state of a two dimensional system $|\psi\rangle={1\over\sqrt{2}}(|e_1\rangle|e_1\rangle+|e_2\rangle|e_2\rangle)$ where $\\{|e_i\rangle\\}$ is an orthonormal basis. Could any one just confirm me whether the corresponding density matrix $\rho$ is defined as $|\psi\rangle\otimes |\psi\rangle$? If I am misunderstood could anyone tell me what will be the density matrix? also how to find the partial trace of $\rho$? I am bit lost to find the partial trace from the formuale $\sum_{i=1,2} (I\otimes\langle e_i|)\rho(I\times\langle e_i|)$ is $I$ a $2\times 2$ Identity matrix? Thanks for the help. Source: Quantum Computing:From Linear Algebra to Physical Realizations, Page-45


title: Absorption cross section and absorption coefficient

text: What is the absorption cross section, how is it measured? How to convert it to the absorption coefficient (measured in cm$^{-1}$)?


What is the relationship between earthquakes power and nuclear explosions? How to compared power of earthquake with nuclear explosion?


title: What if $\gamma$-rays in Electron microscope?

text: I was referring Electron microscopes and read that the electrons have wavelength way less than that of visible light. But, the question I can't find an answer was that, If gamma radiation has the smallest of wavelengths _of all_ , why can't it be used to reach to even finer details in microscopy?


title: Is Newtonian gravity consistent with an infinite universe?

text: Let us assume that we have have an infinite Newtonian space-time and the universe is uniformly filled with matter of constant density (no fluctuations whatsoever), all of it at rest. By symmetry, the stuff in this universe should not collapse or change position in any way if gravity is the only force acting on it. Now, consider Gauss theorem. It says that within a spherical system (it says more that that but this will suffice), the gravitational force felt by any point will be the same as if all matter between the center and the point were concentrated at the center. The matter outside the sphere does not contribute any force). Thus, in such a system, the matter (stuff, I do not say gas so we can consider it continuous) will collapse towards the center of the sphere. We can apply this argument to any arbitrary point in our previous infinite homogeneous universe, and conclude that matter will collapse towards that point (plus the point is arbitrary). So, why is Gauss's theorem is not valid in this case? I was signaled that this question is a duplicate and has been answered, however: The best I could get from the redirected question is this quote: "However, the mass can't be negative and the energy density is positive. This would force a violation of the translational symmetry in a uniform Newtonian Universe". It still doesn't give a satisfactory answer. For instance: how is that symmetry broken if we assume that there is no noise nor small density fluctuations in the system? How can you choose then the absolute "origin" that will break the symmetry? Still doesn't make sense to me.


title: What direction a flag on an object moving in the wind shows?

text: "The flag of a ship that is moving northward with 10 km/h, points exactly southwestward. The windsock at the lighthouse points under 30 relative to the western direction southward. Calculate the velocity of the wind at land and on board of the ship". I have done my homework and solved this problem, so this is not a homework question, but a conceptual one about flags. First, I have assumed that the ship velocity given in the problem is relative to the earth (that is the velocity as viewed by an observer on the earth). Second that the vector sum of the _the wind velocity_ and _the ship velocity relative to the wind_ equals to _the ship velocity relative to the earth_. These assumptions all make sense to me, while I am a bit uncertain about the third assumption I needed to do in order to solve the problem: the indication given by the flag on the ship! My understanding is that when you have a flag on an object moving in the wind, this flag - as seen from the earth - waves in the direction **opposite** of that of the velocity of the object **relative to the wind** (that is the velocity produced by the ship's engines in this case). My question: Could someone please explain if this correct and why it is so? In this problem this means that this latter velocity makes an angle of 45 degrees northeastward, the same angle made by the flag southwestward (which is the opposite direction in words). My results are: speed of the wind: 27.32 km/h relative to earth, but 33.46 km/h relative to the boat. The latter higher value I got makes sense, intuitively speaking, since the wind is a headwind, so it is stronger relative to the ship!


title: Necessary air pressure in flexible vessel to lift a certain mass

text: I have the following situation in mind: A big airtight bag of arbitrary shape with a person standing on it. The bag gets inflated with air to lift the person. Assuming that the bag is much larger than the persons footprint, how do I find the minimal overpressure in the bag that I need to lift the person of the ground? I was thinking of just dividing the normal force of the standing person by the footprint area, but I am not sure on that approach $$F_n = 80×9.81 = 784\text{ N}$$ $$P_n = \frac{784}{0.2×0.3} = 13066\text{ Pa}$$ I have the feeling that the bag dimensions play a role as well, as intuitively I would say that to do this, a small bag would work better than a big bag, but again I'm not sure...


title: Electrons drift velocity and capacitors

text: My friend said this to me and just want to make sure this is right " when we connect the a battery to a LED and the 2 poles are connected, electrons flow from the (-) to the (+) but with very low velocity, but when you do the same with a capacitor , once the 2 plates are connected electrons flow incredibly fast that's why it's discharged fairly quickly" is that true?


title: Compton scatering problem - How to solve this large problem faster using the momentum system?

text: I have encountered a hard exercise which i cannot quite solve. Could anyone help me with it? This is the exercise: > Lets say we have a photon whose energy $W_f$ is equal to the relativistic > energy of an electron $W_{e0}=m_e c^2$. What is the energy of a scaterred > photon $W_f'$ if after the "collision" the electron is moving in a direction > $\vartheta =40^\circ$ according to the original direction of a photon? * * * What i did first was to draw the image _(It is in Slovenian language so dont bother about what is written)_ : ![enter image description here](http://i.stack.imgur.com/5UCXT.png) Now i decided to first calculate the $\lambda$ of the incomming photon: \begin{align} W_f &= W_{0e}\\\ \frac{hc}{\lambda} &= m_e c^2\\\ \lambda &= \frac{hc}{m_e c^2}\\\ \substack{\text{this looks similar to the}\\\\\text{1st part of the Compton's law}} \longrightarrow \lambda &= \frac{h}{m_e c}\\\ \lambda &= \frac{6.626\times 10 ^{-34} Js}{9.109\times10^{-31}\cdot 2.99\times 10^8 \tfrac{m}{s}}\\\ \lambda &\approx 2.45pm \end{align} Now if i try to get the energy of a scattered photon i write down the conservation of energy: \begin{align} W_{before} &= W_{after}\\\ \frac{hc}{\lambda} + m_ec^2 &= \frac{hc}{\lambda'} + m_ec^2 + W_{ke}\\\ \frac{hc}{\lambda} &= \frac{hc}{\lambda'} + W_{ke}\\\ \end{align} This is one equation with two variables ($\lambda'$ and $W_{ke}$) so i am kinda stuck here and i need a new equation which must be a Compton's law. If i implement it i get: \begin{align} \frac{hc}{\lambda} &= \frac{hc}{\lambda'} + W_{ke}\\\ \frac{hc}{\lambda} &= \frac{hc}{\lambda + \Delta \lambda} + W_{ke}\\\ \frac{hc}{\lambda} &= \frac{hc}{\lambda + \tfrac{h}{m_ec}(1-\cos \phi)} + W_{ke}\\\ \end{align} Still i notice that i have 2 variables (now they are $\phi$ and $W_{ke}$). At this point i know i need 1 more equation. I presume it is from the momentum conservation so i write down the momentum conservation for direction $y$ and $x$: Direction $y$: \begin{align} p_{before} &= p_{after}\\\ 0 &= \frac{h}{\lambda'}\sin\phi - p_e \sin\vartheta\\\ p_e &= \frac{h}{\lambda'}\frac{\sin\phi}{\sin\vartheta} \end{align} Direction $x$: \begin{align} p_{before} &= p_{after}\\\ \frac{h}{\lambda} &= \frac{h}{\lambda'}\cos\phi + p_e \cos\vartheta\leftarrow \substack{\text{here i implement what i got from the }\\\\\text{conserv. of momentum in direction $y$}}\\\ \frac{h}{\lambda} &= \frac{h}{\lambda'}\cos\phi + \frac{h}{\lambda'}\frac{\sin\phi}{\sin\vartheta} \cos\vartheta\\\ \frac{1}{\lambda} &= \frac{1}{\lambda'} \left(\cos\phi + \frac{\sin\phi}{\tan\vartheta}\right)\\\ \lambda' &= \lambda \left(\cos\phi + \frac{\sin\phi}{\tan\vartheta}\right)\leftarrow\substack{\text{It seems to me that i could solve}\\\\\text{this for $\phi$ if i used Compton's law}}\\\ \lambda + \Delta \lambda &= \lambda \left(\cos\phi + \frac{\sin\phi}{\tan\vartheta}\right)\\\ \lambda + \tfrac{h}{m_e c} (1 - \cos\phi) &= \lambda \left(\cos\phi + \frac{\sin\phi}{\tan\vartheta}\right) \leftarrow \substack{\text{I got 1 equation for 1 variable $\phi$ but}\\\\\text{it gets complicated as you will see...}}\\\ 1 + \tfrac{h}{\lambda m_e c} (1-\cos \phi) &= \frac{\cos\phi \tan\vartheta + \sin\phi}{\tan\vartheta}\\\ \tan\vartheta + \tfrac{h}{\lambda m_e c}\tan\vartheta - \tfrac{h}{\lambda m_e c}\tan\vartheta \cos\phi &= \cos\phi \tan\vartheta + \sin \phi\\\ \tan\vartheta \left(1 + \tfrac{h}{\lambda m_e c} \right) &= \cos\phi \tan\vartheta \left(1 + \tfrac{h}{\lambda m_e c}\right) + \sin\phi\\\ \tan\vartheta \left(1 + \tfrac{h}{\lambda m_e c}\right) \left[1 - \cos\phi\right] &= \sin \phi\\\ \tan^2\vartheta \left(1 + \tfrac{h}{\lambda m_e c}\right)^2 \left[1 - \cos\phi\right]^2 &= \sin^2 \phi\\\ \tan^2\vartheta \left(1 + \tfrac{h}{\lambda m_e c}\right)^2 \left[1 - \cos\phi\right]^2 + \cos^2\phi&= \sin^2 \phi + \cos^2\phi\\\ \underbrace{\tan^2\vartheta \left(1 + \tfrac{h}{\lambda m_e c}\right)^2}_{\equiv \mathcal{A}} \left[1 - \cos\phi\right]^2 + \cos^2\phi&= 1 \leftarrow \substack{\text{i define a new variable $\mathcal{A}$}\\\\\text{for easier calculations}}\\\ \mathcal{A} \left[1 - 2\cos\phi + \cos^2\phi \right] + \cos^2 \phi - 1 &= 0\\\ \mathcal{A} - 2\mathcal{A} \cos\phi + \mathcal{A}\cos^2\phi + \cos^2 \phi - 1 &= 0\\\ (\mathcal{A}+1)\cos^2\phi - 2\mathcal{A} \cos\phi + (\mathcal{A} - 1) &= 0\leftarrow \substack{\text{in the end i get the quadratic equation}\\\\\text{which has a cosinus.}} \end{align} * * * **Question:** Is it possible to continue by solving this quadratic equation as a regular quadratic equation using the "completing the square method"? I mean like this: \begin{align} \underbrace{(\mathcal{A}+1)}_{\equiv A}\cos^2\phi + \underbrace{-2\mathcal{A}}_{\equiv B} \cos\phi + \underbrace{(\mathcal{A} - 1)}_{\equiv C} &= 0 \end{align} and finally: $$ \boxed{\cos \phi = \dfrac{-B \pm \sqrt{B^2 - 4AC}}{2A}}$$ Afterall if this is possible i get $\cos \phi$ and therefore $\phi$, $W_{ke}$ and finally $W_f'$. * * * EDIT: I did try to solve this using the quadratic equation and i got solution: \begin{align} \cos \phi &= \dfrac{-B \pm \sqrt{B^2 - 4AC}}{2A}\\\ \cos \phi &= \frac{2\mathcal{A} \pm \sqrt{4\mathcal{A}^2 - 4(\mathcal{A}+1)(\mathcal{A} - 1)}}{2 (\mathcal{A}+1)}\\\ \cos \phi &= \frac{2\mathcal{A} \pm \sqrt{4\mathcal{A}^2 - 4(\mathcal{A}^2-1)}}{2 (\mathcal{A}+1)}\\\ \cos \phi &= \frac{2\mathcal{A} \pm \sqrt{4\mathcal{A}^2 - 4\mathcal{A}^2 + 4}}{2 (\mathcal{A}+1)}\\\ \cos \phi &= \frac{2\mathcal{A} \pm \sqrt{4}}{2\mathcal{A}+2)}\\\ \cos \phi &= \frac{2\mathcal{A} \pm \sqrt{2}}{2\mathcal{A}+2)}\\\ \end{align} So if i apply "+" i get $\cos \phi = 1$ which is impossible for a photon to hold its original direction! But if i apply "-" and insert a variable $\mathcal{A}$ i get: \begin{align} \cos \phi = \frac{2 \cdot \tan^240^\circ \left(1 + \tfrac{6.626\times10^{-34}Js}{2.45\times10^{-12}m\cdot 9.109\times10^{-31}kg\cdot2.99\times10^{8}m/s}\right)^2 - 2}{2 \cdot \tan^240^\circ \left(1 + \tfrac{6.626\times10^{-34}Js}{2.45\times10^{-12}m\cdot 9.109\times10^{-31}kg\cdot2.99\times10^{8}m/s}\right)^2 + 2} = \frac{5.59 - 2}{5.59 + 2} = 0.47 \end{align} Now i can calculate: \begin{align} \phi&=\cos^{-1}0.47 = 61.74^\circ\\\ \Delta \lambda &= \frac{h}{m_e c} (1-\cos\phi) = 1.28pm\\\ \lambda' &= \lambda + \Delta \lambda = 3.73pm\\\ W_f' &= \frac{hc}{\lambda'} = 5.31\times10^{-14}J = 331.55 keV. \end{align} **And the result is correct according by my book. But this way of solving a problem is very long and in a case if i get it in my test i cannot solve it in time i think. So how can i solve it faster? In the comments it was mentioned that i should use the momentum coordinate system? How do i do that?**


title: Why does wet skin sunburn faster?

text: There is a popular belief that wet skin burns or tans faster. However, I've never heard a believable explanation of why this happens. The best explanation I've heard is that the water droplets on the skin act as a lens, focusing the sunlight onto your skin. I don't see how this would affect an overall burn, because the amount of sunlight reaching the skin is the same (ignoring reflection). Is this 'fact' true, and if so, what causes it?


title: characterization of potential

text: So i have a force field $F(x,y)$ and i have to find out wether it is a potential or not. My first idea was to calculate : $dU=Fdr$ (where $r$ is the radius vector) , to integrate on both sides and hence to see if $U$ is path dependent or not. That turned out to be right. I was thinking about another approach: we know that , if a potential exists then $F=-\nabla U$ So if $F$ is a potential it must be possible to find such a $U$ , wich in my case wasn't possible, hence $F$ is not a potential. My question: (1) Is the second approach right? (2) are there othere ways for solving this problem? Thanks in advance.


title: What are the problems in analyzing an experiment with non-ideal collisions?

text: For a two-dimensional collision experiment, I must explain in one of the questions the problems in analyzing a non-ideal two-dimensional collision. As the question states: > Suppose that the projectile marble and target marble do not collide with > their centers of mass equidistant from the floor, as shown in figure 8.4. > What problems in analyzing this experiment are cause by the non-ideal > collision? ![enter image description here](http://i.stack.imgur.com/1Pzya.jpg) I am not so sure that I have everything or if it is a valid awnser, but so far I have concluded the following: **The Problems in analyzing non-ideal collisions or any other non-ideal conditions lies with either the decrease of precision of data, accuracy of data, or both.** Note: For the sake of the quality of this post, I ask you to please feel free to make any edits so that people in the future can have this question answered. Also I thank everyone in advance for the contribution of this post.


title: Electric generators?

text: When a magnet passes through a copper coil and electricity is induced into the coil, is there a magnetic resistance on the magnet as it passes through the coil?


title: Speed Distribution

text: I came across a problem which reads: > The speed distribution function of a group of _N_ particles is given by:   >  $dN_v = kv\; dv\; (V>v>0)$   >  $dN_v = 0 \; (v>V) $   >  (a) Draw a graph of the distribution function.   >  (b) Find the constant _k_ in terms of _N_ and _V_.   >  (c) Compute the average speed, rms, speed and the most probable speed in > terms of _V_. Can anyone please help me solve it?


title: What are local electrons in a crystal?

text: I am reading Pekar's "Research in Electron Theory of Crystals" and I came across a passage I find a bit unclear: > The theory developed below takes into account the dielectric polarization of > a an ionic crystal by the electric field of the conduction electron. The > local polarization that results from this is related with the displacement > of the ions and consequently is inertial. It cannot follow the relatively > rapidly moving electron and therefore forms a potential well for the > electron. The depth of this potential well turns out to be sufficient for > discrete energy levels of the electron to exist in it. The electron, being > in a local state on one of these levels, can maintain with it sown field the > aforementioned local polarization of the crystal. Because of their inertia, > the ions are sensitive not to the instantaneous value of the electron field, > but to the average field. The latter can be calculated as the static field > of the $|\psi|^2$ cloud of the electron; it produces a static polarization > potential well, which in turn maintains the electron stationarily in a local > state. Such states of the crystal with the polarization potential well, > which in turn maintains the electron stationarily in the local state. Such > states of the crystal with a polarization potential well, in which the > electron is localized, were called by the author polarons Now, what exactly does he mean by local vs. conduction electrons? Are local electrons those that are not moving and are in the crystal? That doesn't seem right. What does it mean for an electron to be in a local state? (Also what does he mean by "inertial"?) IN fact, it would be nice if one explains this passage in understandable terms so that I can have some intuitive picture in mind.


title: Why are electric charges allowed to be so light but magnetic monopoles have to be so heavy?

text: My question is in two parts.   1. What is the origin of the electric field from an electric charge and why electron can have so small mass? While on the other hand for a magnetic monopole to create a magnetic field needs to be so heavy?    2. And if the magnetic monopole is a hadron what are the constituent elementary particles? What is balancing these energies so that the charges do not explode?  A simple undergrad level answer will do.


title: Zigzag flow of water along a vertical glass window

text: I've observed this behavior many times. When it rains, the rainwater will form vertical channels along a glass window. The flow of water is mostly confined within these vertical channels and the channels are (more or less) stable. But sometimes - and I suspect this happens when the flow intensity in one of the channels increases - the channel will switch from a vertical configuration into a zig-zag configuration. The zig-zag is composed of short segments running horizontally that are connected by semicircular (vertical) segments. The zig-zag is unstable and lasts only for 0.1 second or so. Then the channel reverts to its vertical configuration. I have made photographs of this behavior but I cannot find them now. I have seen similar patterns in the book "The self made tapestry" by Philip Ball, page 145. This shows growth instabilities in glass cracks. Is says "at higher speeds the crack becomes oscilatorry with a constant wavelength". This is what I see in the water flow. It feels counterintuitive. There must be a good explanation for this behavior. Can you point me to it? EDIT Here is a video .


title: Identifying fragments when there is a superposition of fragments in quantum Darwinism

text: In Zurek's theory of quantum Darwinism, information about the pointer states of a system imprint themselves upon fragments of the environment carrying records about the state of the system. Multipartite entanglement between the system and the many fragments effectively become classical correlations whenever one doesn't have access to all the fragments due to the monogamy of entanglement. So far, so good, but typically, the fragments are themselves in a superposition; a superposition of their locations, a superposition of the form of their encodings of their records, a superposition of existing and not existing, etc. This problem becomes especially acute whenever the density of record carrying fragments is very low, but still high enough to lead to decoherence. Even only two imprintings upon the environment are enough if the observer intercepts one of them while the other forever escapes him. Given this, how can one perform a proper quantum Darwinism analysis unless one already knew in advance where the record carrying fragments are and the form of their encoding? And to specify where the records are and how they are encoded, doesn't one have to resort to a decoherence analysis of the environment prior to that, and isn't that circular?


title: Multiplicity of eigenvalues of angular momentum

text: Reading Dirac's Principles of Quantum Mechanics, I encounter in § 36 (Properties of angular momentum) this fragment: ![enter image description here](http://i.stack.imgur.com/z9T4O.png) This is for a dynamical system with two angular momenta $\mathbf{m}_1$ and $\mathbf{m}_2$ that commute with one another, and $\mathbf{M}=\mathbf{m}_1+\mathbf{m}_2$. $k_1$ and $k_2$ are the magnitudes of $\mathbf{m}_1$ and $\mathbf{m}_2$, so the possible eigenvalues of $m_{1z}$ are $k_1$, $k_1-\hslash$, $k_1-2\hslash$, ..., $-k_1$, and similarly for $m_{2z}$ and $k_2$. The question is about the two $2k_2+1$ terms shown in the second line of eq (46). Shouldn't the last one be $2k_2+2$?


title: Second Law of Thermodynamics and the Arrow of Time: Why isn't time considered fundamental?

text: I've come across this explanation that the "arrow of time" is a consequence of the second law of thermodynamics, which says that the entropy of an isolated system is always increasing. The argument is that the past looks different from the future because of this increase in entropy. However, this still doesn't make time vanish, since a hypothetical clock could still be ticking in a completely uniform universe, but only this time there is no change in entropy because it is already at a maximum. In this maximum entropy universe, the past would look just like the future, but that need not mean that time isn't still flowing. It is just that we $\it{associate}$ the flow of time with a change that is recognizable. But after having watched a few episodes of Professor Brian Cox's Wonders of the Universe, I want to know the deeper reason behind why people make the entropy argument. I've heard Sean Carroll make a similar argument to a group of physicists, so I get the idea it is not just a sloppy popularization.


title: Insulators (also called Dielectrics) which cannot conduct Electricity

text: How Dielectrics as an Insulating materials transmit electric effect without Conducting Electricity ? How its Possible ??


title: What really is resistance? How does it generate heat?

text: OK I know that **R= V/I**. I also know that **R = ρl / A** But what I want to know is that what really causes resistance? Is resistance equivalent to force? or is it just a constant? Also, what causes conductors to heat up overtime when current flows through them? I know that the electrons lose energy and that energy gets converted to heat, but what causes them to lose this energy? Electrons don't collide with atoms or other electrons. **EDIT-1** Also, how does this lost energy gets converted to heat?


What's the most fundamental definition of temperature? Is it the definition concern about average energy, number of micro states, or what? By "fundamental", I mean "to be applied" in such general cases as Black Hole's Temperature, Accelerated Frame's Radiation,...


title: Determine stationary angular velocity of wheel with circuit in magnetic field

text: I have a wheel (free to spin around the $z-$axis) with four spokes that is connected by sliding contacts to a circuit with $U_0 = 0,72V$. Also, there is a B-Field parallel to the $z-$axis ![Imgur](http://i.imgur.com/aLF3N7S.jpg) For the induced electric potential I have: $$U_i = - \frac{1}{2}(R_{outer}^2 - R_{inner}^2)\omega B$$ (with $\omega$ = angular velocity) I'm now asked to find out the constant $\omega_0$ after the system is in a stationary state (moves with constant speed). The assignment points out to look at one mesh (with one spoke) on the wheel and to determine if Kirchhoffs second rule applies and if there is a current flowing in a mesh. The most obvious way I can think of would be (since $U_0$ should be equal in any spoke): $$U_0 - U_i = 0$$ and to solve for $\omega$. But elsewhere I was told that Kirchhoffs rules don't apply in systems with changing magnetic fields. Also I'm not sure if there still would be an emf induced in stationary conditions since the flow wouldn't change anymore then.


title: The acceleration vector of a simple pendulum

text: In this picture the acceleration vector $\vec{a}$ points upward when the pendulum is halfway Click To see animated GIF But according to this picture, the force acts tangentially: ![enter image description here](http://i.stack.imgur.com/qki27.png) Which means the acceleration should be tangential too, and never pointing upward? So whats right?


title: Instantaneous angular momentum of a disc

text: > _Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity > $v$. I want to calculate the instantaneous angular momentum with axis > through the edge of the disc (on the circumference)._ Angular momentum $= I \omega$. $I = \frac{1}{2}mr^2 + mr^2 = \frac{3}{2}mr^2$ by the parallel axis theorem. $\omega = \frac{v}{r}$. Therefore, angular momentum $= \frac{3mrv}{2}$. Alternatively, angular momentum $=p\times r= m r \times v = mrv$. Why do these two methods differ? Which, if any, are correct?


title: Why does space expansion not expand matter?

text: REFORMULATED: I have looked at the other questions (ie "why does space expansion affect matter") but can't find the answer I am looking for. My question: There is always mention of space expanding when we talk about the speed of galaxies relative to ours. Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object. If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it. I have a few potential answers for this, which raise their own problems:   1. Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance   2. Fundamental particles are curled up in additional dimensions ala string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying.   3. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me. I think some of the problems in this question verge into metaphysics, but I think from his (?) previous answer, Marek can probably explain the physical side of things a bit more thoroughly. I will leave it there cos anything else I write sounds rambling!


title: Expansion of the space-time metric

text: If the space-time metric is expanding with the expansion of the universe, if I could travel back in time, would I be less dense than the matter in that previous era?


title: Expansion of space

text: > **Possible Duplicate:**   >  spacetime expansion and universe expansion? So I've heard that space is expanding very quickly and that the redshift we see when we look at other galaxies is evidence of this. But why doesn't this expansion affect orbits of the planets in our solar system, for instance? I would think that the expansion of space is uniform through the universe...why doesn't it tear our bodies apart?


title: does space-time expansion affect on fundamental particle?

text: does space-time expansion affect on fundamental particle or point particle?


title: Expanding Universe and more

text: We all are pretty familiar with the Friedmann models of the expanding universe, but at present I would like to concentrate on the model where the universe goes on expanding with the lapse of time. We know that if we mark spots on a balloon and inflate it, distance between these spots increases gradually(with time, of course). We may draw an analogy that these spots represent the galaxies. Now imagine a space within one of these spots, whose dimensions is indeed less than that of the spot concerned. With time, the dimensions of this space goes on increasing with time. If we compare this space to the interstellar(as well as interplanetary) space, and by the process stated above, go on imagining spaces within the one imagined before, we arrive at a limit where the rate of dimension variation of the space with time becomes very small in magnitude. Here I ask my question: could it happen so that objects in the universe(even solids) are expanding at a rate so very feeble(much much smaller than even the rate at which the universe expands), because all objects, be they solid or any other physical form, constitute some space within this universe, on account of its existence, and can be designated as a space within the spot considered in our balloon model. It is indeed a mere whim of mine to compare a universe model with that of a balloon-spot model! Nonetheless, please remove my doubts upon this trifling matter, that has perplexed me a good deal.


title: Effect of Cosmological Expansion at the Atomic Level

text: > **Possible Duplicate:**   >  Why does space expansion not expand matter? Does cosmological expansion have any effects at the atomic level?


How does the gravity well change as space expands? If we assume that the Earth's gravitational field curves flat space to create a gravity well then how does the gravity well change as space expands also is the change in gravity well measurable.


title: Why space expansion affects matter?

text: If space itself is expanding, then why would it have any effect on matter (separates distant galaxies)?   * Space is "nothing", and if "nothing" becomes bigger "nothing" it's still a "nothing" that shouldn't interact with matter in any way (it doesn't have mass, energy, etc).   * Gravity doesn't have a cutoff distance afaik, so even the most distant galaxies should be attracted to each other. Gravity force would be very very tiny, but it would still dominate "nothing" from space expansion.   * Lets take inertia from Big Bang into account. Inertia would be the primary force that moves galaxies away comparing to their tiny gravity and even more tiny, if any, force of our "nothing" that is still expanding inbetween. Wouldn't expansion decelerate if driven mostly by inertia?


title: If the universe is expanding then why does the distance between Sun and the Earth is not expanding?

text: It has been proved that universe is expanding in the accelerating way. If that is true than the space between the Sun and the Earth must also be expanding. But it is not so, why?


title: How do we know space is expanding when we are part of space?

text: From what I understand space itself is expanding, and the Big Bang attempts to describe this expansion at the very early stages of the universe. This is usually described in a visual way as 2 dots on the surface of a balloon as the balloon is being inflated. We exist in space, so as space expands we are expanding too aren't we? If this is correct how do we know space is expanding at all? I'll attempt to explain further... 2 dots on a balloon with a ruler drawn between them measuring 1 cm. As the balloon expands, so do the dots, and the ruler, and it always says that the distance is 1 cm. From an observers point of view (somewhere away from the balloon) the dots, ruler, and ruler are all getting larger - but from the point of view on the balloons surface nothing has changed. Another way to describe this would be a man in a room, the room and everything in it (including the man) are getting bigger at the same rate. From the man's perspective nothing is changing but from outside the room - you can see everything is getting bigger. I guess what I am trying to say is that we are in the universe, and expanding at the same rate as it (aren't we?) so how do we know it's getting bigger?


title: What exactly is expanding when they say universe is expanding?

text: We know that universe is expanding and galaxies are moving away from each other. Does this mean the galaxies are also expanding in itself and therefore I guess growing larger in volume? Depending on the answer of that, does the solar system also expands?


title: Why doesn't everything expand when the universe expands?

text: Everybody has been taught at one point, "oh the universe expands, but that doesn't mean that everything is expanding uniformly, since that means we can't detect the expansion, but only that huge galaxies are moving away from each other". But I'm rather confused. Can't the expanding universe simply be thought as a coordinate axis that expands? The definition of "1" on the coordinate axis constantly expands? After all, spacetime itself is expanding, and not only "average distance of galaxies". So our Planck length would expand, light wavelengths expand, we expand, etc. But clearly this isn't happening. Of course, the handwavy explanation is "electromagnetism/gravity overcomes expansion at small scales", but the electromagnetic and gravity forces are defined in terms of constants relative to our "coordinate intervals", so if spacetime itself is expanding "under the feet" of gravity, shouldn't gravity not be able to do anything about it? We would also be unable to measure the expansion of spacetime since all of our measurement benchmarks and tools are also expanding. Clearly, this isn't happening. What is the _precise_ reason?


title: Are atoms getting weaker?

text: If the universe is expanding, it would make sense that the spaces between particles are getting bigger. If this is so, then the particles which make up atoms are also affected. Does that imply the spaces between the components of an atom will become large for the subatomic forces to hold? Are atoms getting weaker?


title: Cosmic Expansion - Why aren't we ripped off yet?

text: According to Hubble's law, the universe expands exponentially ever since the big bang.   1. If the space-time expands, what effects does it have upon us, (1.Earth, 2.solar system and 3. Milky Way).    2. What would be the fate of Gravitational force and other forces of nature if the expansion continues.    3. What happens to the dark energy and dark matter then?    4. Won't all the dark energy be used up in the acceleration process?


title: Expansion of Universe

text: > **Possible Duplicate:**   >  Why space expansion affects matter? If the Expansion is prevalent, i.e. it is observable and true then shouldn't that result in the expansion of the Milky Way galaxy, eventually our solar system would expand resulting in increase in the planetary distances (from the sun). Could the escape of Pluto be an example to this phenomena ? And is the Expansion resulting in increase in the sizes of the galactic objects ?


title: Spacial curvature and expanding space

text: If we take the analogy that in an empty space the space is just a flat sheet then if there is a single planet or a star then the flat sheet will curve below the planet leaving a curvature shaped like a hemisphere below the object, my question is, Does this curvature change as space expands?


title: Why doesn't Brooklyn expand? (Or "Is the expansion of the universe kinematic?")

text: > **Possible Duplicate:**   >  Why space expansion affects matter? Imagine two tiny spacecrafts that are moving with the Hubble flow and so are moving away from each other. Let's assume that they've been that way since the very early universe, never firing their engines, just drifting along their Hubble flow geodesics in a homogenous isotropic universe. They then momentarily fire their engines so that they "cancel" the Hubble flow and have a fixed proper separation. Will they now start drifting apart again (presumably due to expansion)? Or will they stay at fixed proper separation, and maybe very slowly move towards each other due to their mutual gravitational attraction? I guess this is another way of asking whether expansion is kinematic and hence can be forgotten (so that "Brooklyn isn't expanding" because gravitational collapse and structure formation have erased memory of the expansion). Or maybe someone will help me refine this question and make me realize I just haven't thought things through completely?


title: Space within galaxies. Is it stuck by the gravity of the galaxy or expanding and "slipping past"?

text: I understand that the inter-galactic space is expanding but galaxies themselves are not. What is happening to the space within a galaxy? Is it fixed by the gravity of the galaxy or is it expanding and moving out around it? Using the coins on a balloon analogy, is the balloon surface under the coins (galaxies) stuck to the coin and constrained or is it free to expand out, slipping underneath the coins leaving them in the same place (and the same size)?


title: spacetime expansion and universe expansion?

text: First of all, does the expansion of spacetime solely cause the expansion of universe? Secondly, if spacetime is the sole cause, do objects(matter with mass) themselves expand? Thirdly, by spacetime expansion, does time also expand? (at least in general relativity) Thanks.


title: How is the universe expanding?

text: > **Possible Duplicate:**   >  spacetime expansion and universe expansion? Is the space between planets is growing or the space between stars is growing or the space between galaxies is growing?


title: Expanding metre sticks

text: Given the Universe is expanding. Therefore everything within the U is expanding, in all dimensions, subatomic to cosmic. Then all metre sticks are expanding. The question: How can we measure U expansion with metre sticks that are also expanding? Alice only knew she had grown ten feet tall by comparing herself to her surroundings.


title: Do atoms expand with universe?

text: > **Possible Duplicate:**   >  Why space expansion affects matter?   >  Why does space expansion not expand matter? As we know, the universe is expanding, galaxies are away from each other. But what about atoms? Do they also in expanding? What's more, Bohr radius is $$a_0=\frac{\hbar}{m_e c \alpha}$$, if it is increasing, does it means $m_e$ is decreasing due to the density of Higgs field is getting thinner. or $c$ is decreasing or $\hbar$ is increasing?


title: How is it possible to measure expansion of universe

text: > **Possible Duplicate:**   >  Why does space expansion not expand matter? If according to Hubble's law space the expanding then shouldn't everything else along with the space expand and we should not be able to measure this expansion as our tools/measuring sticks would also expand in same proportion


title: What is the difference between matter & spacetime?

text: If the universe is expanding why doesn't the matter in it expand proportionally making it seem as if the universe is static? Alternatively, as spacetime expands why does it not just slide past matter leaving matter unmoved? What anchors the matter to a particular point in spacetime?


title: Phonons in non-crystalline media

text: Do sound waves in a gas consist of phonons? What about a glass? Or other non-crystalline materials such as quasicrystals? How does the lack of translational symmetry affect the quantization of the displacement field? All the answers so far have treated this question at a much more elementary level than I was expecting. I am already quite familiar with the properties of phonons in crystals. Therefore, do not explain the well-known derivations of the dispersion relation and second quantization of phonons in crystal lattices in your answer (and especially don't get them **wrong**!).


title: Find velocity and displacement from force equation

text: How to find velocity and displacement equations from a given force equation? For instance, it was given the following 1-D equation: $$F = b_1(v_1-v) - b_2 v$$ $v_1$, $b_1$ and $b_2$ are constants. I know that $F = ma = m\frac{\mathrm{d}v}{\mathrm{d}t}$, but I can't find how to integrate $F$. Is there any technique that can help me or my problem is just calculus?


title: Conceptual problems in nuclear physics for students?

text: Is there any good reference for conceptual problems for students which learn nuclear physics first time? I am not searching problems that involve difficult calculations. Quite the converse, they should be computational rather simple but conceptually difficult.


title: If there is a meltdown at the Fukushima reactors, would the control rods melt also?

text: According to the reports, the shutdown procedures at all the Fukushima reactors were successful, and all the control rods were fully inserted. So - if there was a meltdown, would the control rods also melt and blend into the resulting material (corium)? If so, would that have the effect of "diluting" the corium in radioactive terms and stabilising it to some extent? (I guess it would depend on the relative melting points of the fuel and the control rods: if the rods are of boron, the melting point is a lot higher than that of uranium.)


title: Why are solar eclipses more common in the southern hemisphere?

text: I've seen the claim that solar eclipses are more common in the southern hemisphere than the northern hemisphere and would like to understand why and if that is the case? Does it relate more to the position of the moon relative to the earth or more to how the earth rotates the sun or is this just hogwash? > http://science.slashdot.org/story/12/09/17/1152238/curiosity-rover-sees- > solar-eclipse-on-mars


title: How is tritium illumination possible without negative health effects?

text: Turns out there's tritium illumination \- a tiny very strong plastic tube will be covered in phosphor and filled with tritium. Tritium will undergo beta decay and a flow of electrons will cause the phosphor to glow. This gives enough light for illuminating hours marks on a wristwatch dial and the hands of the wristwatch for many years and is claimed to not pose health hazard. Now how it is possible to have energetic enough radioactive decay and no health hazard at the same time?


title: Negatve mass inside a black hole

text: With Hawking radiation, one half of virtual pair falls into horizon and this particle has negative energy. What would an observer inside horizon observe when seeing negative particles ? How do these negative particles interact with ordinary matter ?


title: Third principle of Nernst

text: ![enter image description here](http://i.stack.imgur.com/Bt418.png) I wonder how can I prove the fulfillment of the third principle of Nernst of a body that obeys the next expression.


title: Do gravitational waves travel on geodesics in GR? If yes, why?

text: I think, the answer is probably yes, but it can be answered by somebody who knows GR much better than I do. In case of a positive answer, can we say that gravitational radiation will be bent around graviting bodies exactly as light?


title: Can I throw a stone through my window without breaking the glass?

text: As far as I know, most of an atom is vacuum. Therefore, in theory, would it be possible for me to throw a tiny stone through my window without breaking it because no matter actually collides?


title: Magnetic flux and flow of electrons

text: What does change in magnetic flux mean? How can you change magnetic flux? How does a change in magnetic flux influence a current of electrons (electricity)?


title: What do subatomic particles look like for a 'speed of light - observer'?

text: Let's say that an observer is moving with the speed of light relatively to an atom that he wants to look into. He has equipment that precise that he can observe the atom and what is inside. From Einstein's theory we know that for light particles, everything else that moves with velocity smaller than the speed of light, 'looks like frozen, no move'. How would the elements inside the atom look?


title: Does the friction force change directions with a change in reference frame?

text: In a basic friction problem with Block A sliding on top of Block B, the direction of the friction force is usually explained as being simply the opposite of the direction of motion. So if Block A is sliding to the right, the friction force is pointing to the left. But this reasoning implicitly assumes that we are calculating friction force from the reference frame of Block B. What if we instead look at the problem from the reference frame of Block A? To Block A, it looks as if Block B is sliding to the left, so an observer on Block A would say that there is a friction force which, to oppose the direction of motion, points to the right. It seems counterintuitive and probably wrong for the direction of friction force to depend on reference frame like this. Where is the flaw in the reasoning above? Are the two reference frames described above not exactly equivalent in a way that leads to the force changing directions?


title: Does it make sense to continue searching for dark matter on Earth?

text: The Large Underground Xenon Detector (LUX) recently released results1 that they have found no signs of dark matter2 after a ~3 month search this spring and summer. The LUX group plans to spend all of 2014 looking for dark matter interactions with the liquid xenon. (I thought I read somewhere that they were planning on doubling the amount of xenon, but cannot find a link that confirms this). Early last year, researchers from Chile reported that there was no significant amount of dark matter in the solar vicinity3. They studied4 the motions of about 400 stars within 13,000 lightyears radius from the sun, and all the matter is accounted for in what we see: gas, dust, star, etc., and there's little room for dark matter. **Does it make sense to continue searching for dark matter via direct detection method when research suggests there's nothing to find in our solar vicinity?** **Would it make more sense to build more sensitive space-based detectors?** * * * 1 preprint, Akerib et al 2013 2 article, K Jepsen, Symmetry Magazine, 2013 3 article, ESO, Phys.Org, 2012 4 preprint, Mono Bidin et al 2012


title: Books for linear operator and spectral theory

text: I need some books to learn the basis of linear operator theory and the spectral theory with, if it's possible, physics application to quantum mechanics. Can somebody help me?


title: Some question about symplectic transformation

text: I read Arnold's book **Mathematical Methods of Classical Mechanics** and come across with three problems in page 229. > 1.Let $\lambda$ and $\bar{\lambda}$ be simple (multiplicity 1) eigenvalues > of a symplectic transformation $S$ with $|\lambda|=1$. Show that the two- > dimensional invariant plane $\pi_\lambda$ corresponding to > $\lambda,\bar{\lambda}$ is nonnull. > > 2.Let $\xi$ be a real vector of plane $\pi_\lambda$, where $Im~\lambda > 0$ > and $|\lambda| = 1$. The eigenvalue $\lambda$ is called positive if > $[S\xi,\xi] > 0$. Show that this definition does not depend on the choice of > $\xi \neq 0$ in the plane $\pi_\lambda$. > > 3.Show that $S$ is strong stable if and only if all the eigenvalues > $\lambda$ lie on the unit circle and are of definite sign. In my opinion, it will be difficult to deal with these question with the knowledge in this book.


1. What's the motivation behind the action principle?   2. Why does the action principle lead to Newtonian law?    3. If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and Hamilton principle from it?    4. Also does all Lagrangians obey $L=T-V$?    5. I think that it's related to the fact that the kinetic energy of the particle at all points on the path or it's travel time is as small as possible?    6. If so, How can we derive the principle of least action from this fact in detail?


title: Charge of an electrolytic capacitors

text: I can't understand the electrolytic capacitors, when a capacitor has a capacitance of 100 microfarads, does that mean that when it is charged with 100 volts will the charge of the plate be 0.01 coulomb? If there is a part of the plate with no isolation, then I touch it, I will be shocked with a charge of 0.01 coulomb and 100 volts?


title: $\left(H^\dagger H\right)^2$ is invariant under $U(1)\times SU(2)$?

text: Is it true that $\left(H^\dagger H\right)^2$ is invariant under $U\left(1\right) \times SU\left(2\right)$ where $H$ is the Higgs field $(1,2,1/2)$? Does this invariance imply that its hypercharge is invariant under $U\left(1\right)$ and its spin is invariant under $SU\left(2\right)$? . $$H = [H_+, H_0]$$ $$H_+ = [H_-]$$ but $$H_0 = [?]$$ $$H^\dagger H = [H_-][H_+] + [?][H_0]$$


title: What is the physical interpretation of the S-matrix in QFT?

text: A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers. Given a quantum field theory when can you define an S-matrix? Given an S-matrix when can you define a quantum field theory from it? (e.g. I have heard conformal field theories do not have S-matrices, is there a simple heuristic way to understand this? Also, I have heard that it is not possible to define a traditional S-matrix in AdS space.) How does one, in principle, completely specify the S-matrix of a physical theory and what information is encoded in it? (Do I have to give you both a list of all the stable bound states and single-particle states, as well as the probability amplitudes for scattering from initial and final states? or can I get a way with just telling you some single particle states and from poles in the scattering amplitudes deduce the existence of additional bound states?) Can two inequivalent QFT's give rise to the same S-matrix? E.g., from the S-matrix of the standard model can one, in principle, read off energy levels of the hydrogen atom and other atoms?


title: Can we have a black hole without a singularity?

text: Assuming we have a sufficiently small and massive object such that it's escape velocity is greater than the speed of light, isn't this a black hole? It has an event horizon that light cannot escape, time freezes at this event horizon, etc. However this object is not a singularity. If a large star's mass were compressed to the size of, say, a proton, it would certainly have these properties but it would still not be a singularity as a proton does have volume. The reason "physics breaks down" at singularities is because we cannot divide by zero, but as long as the proton-sized object has volume, physics won't "break down", yet we still have an event horizon and an object that is invisible (but not undetectable) from the outside. I have read the answers to this related question. I'm not sure if they don't address my specific question or if I don't understand the answers.


title: Meaning of the 'deep lattice limit' and 'shallow lattice limit'?

text: In condensed matter literature, at many places, the phrase 'deep lattice limit' is used. Please tell what is the deep lattice limit and the shallow lattice limit?


title: The Fraunhofer Measure

text: In a well known Maxwell paper he uses the units of wavelength which he calls the Fraunhofer Measure. He states it for the Fraunhofer D and F bands as $$\lambda_D = 2175 \text{ crazy units} = 589nm$$ $$\lambda_F = 1794 \text{ crazy units} = 486nm$$ So the conversion is: $$1nm \approx 3.69\text{ crazy units}$$ $$1 \text{ crazy unit} \approx 0.270nm$$ But what is the motivation for this?


I read that the number of atoms in the entire observable universe is estimated to be within the range of $10^{78}$ to $10^{82}$. Does the Universe have finite number of particles? If so, how could it be determined?


title: Einstein and vibrational energy of the atom and its way to QM

text: As suggested by one of the commentators on my last question, I am going through Bohr's Nobel prize lecture in order to understand how quantum mechanics was developed. The lecture describes Planck's observations on radiations. I'd like to know how it was concluded from these observations that energy can only change in discrete amounts and also the derivation of Planck's formula. The lecture then goes on to Einstein's idea about the restricting condition for vibrational energies of atoms and the specific heats of crystals. Can anyone describe exactly what Einstein's idea was about the specific heats of crystal, how that accentuated the concept of discrete energy variation and how it led to further development of QM?


title: What are "hidden valley sectors"?

text: In this end of the year article, Prof. Strassler mentioned that hidden valley sectors could lead to some still open loopholes concerning the experimental discovery of supersymmetry and other BSM physics at the LHC such as certain kinds of extra dimensions for example. He only explains that these hidden valley sectors are some kind of an extension of minimal supersymmetric models and he does not explain this further when I ask him in the comments. So I want to ask here: What exactly are these hidden valley sectors, and how are they related to some kinds of minimal supersymmetric models, such as the MSSM for example? Are they rather ad hoc additions to the minimal models or are they embeded in some theories valid at higher energies?


title: Latest advances in experimental quantum processors?

text: I'm and undergraduate student and I'm doing a report on Quantum computing. As a conclusion of my report I'd like to highlight the latest experimental advances in Quantum Computing, especially in methods like Ion trap and photon polarization. Most of the study I've made is on papers and documents dated 2000 or earlier, so I can't relay on them for this part. I've tried looking to the newest papers i could find online, but they're to specific and detailed and I'm not able to extrapolate something meaningful from them, given the small time I have. I just need to know how far have we come with coherence time, size of networks, number of gates applied et cetera.


title: How did L.H. Thomas derive his 1927 expressions for an electron with an axis?

text: I'm looking at the 1927 paper of Thomas, The Kinematics of an Electron with an Axis, where he shows that the instantaneous co-moving frame of an accelerating electron rotates and moves with some infinitesimal velocity. He states: > At $t=t_0$ let the electron have position $\mathbf{r}_0$ and velocity > $\mathbf{v}_0$, with $\beta_0=(1-{\mathbf{v}_0}^2/c^2)^{-\frac 1 2}$, in > $(\mathbf{r}, t)$. Then, by (2.1), that definite system of coordinates > $(\mathbf{R}_0, T_0)$ in which the electron is instantaneously at rest at > the origin and which is obtained from $(\mathbf{r},t)$ by a translation and > a Lorentz transformation without rotation is gven by > $$\begin{align*}\mathbf{R}_0 &= \mathbf{r} - \mathbf{r}_0 + (\beta_0 - > 1)\frac{ (\mathbf{r}-\mathbf{r}_0)\cdot > \mathbf{v}_0}{{\mathbf{v}_0}^2}\mathbf{v}_0-\beta_0 > \mathbf{v}_0(t-t_0)\tag{3.1a}\\\ T_0 &= \beta_0\left( t - t_0 - \frac > {(\mathbf{r} - \mathbf{r}_0)\cdot > \mathbf{v}_0}{c^2}\right)\tag{3.1b}\end{align*}$$ > > By eliminating $(\mathbf{r},t)$ from equations (3.1) and the similar > equations for $(\mathbf{R}_1, T_1)$,$$\begin{align*}\mathbf{R}_1 &= > \mathbf{R}_0 + \frac{(\beta_0 - 1)} {{\mathbf{v}_0}^2}(\mathbf{R}_0\times > (\mathbf{v}_0\times \mathbf{dv}_0)) - \beta_0 T_0(\mathbf{dv}_0 + (\beta_0 - > 1)\frac{(\mathbf{v}_0\cdot > \mathbf{dv}_0)}{{\mathbf{v}_0}^2}\mathbf{v}_0)\tag{a}\\\ T_1 &= T_0 - \frac > {\beta_0} c^2((\mathbf{R}_0\cdot(\mathbf{dv}_0 + (\beta_0 - > 1)\frac{(\mathbf{v}_0\cdot \mathbf{dv}_0)}{{\mathbf{v}_0}^2}\mathbf{v}_0))) > - d\tau_0\tag{3.3b} \end{align*}$$ What are the steps to get from (3.1) to (3.3)?


title: Old Russian Physics Papers?

text: Where can one find old Russian scientific papers in physics, say, in the Proceedings of the Russian Academy of Sciences or Zhurnal Eksperimentalnoy i Teoreticheskoy Fiziki? Can they be found online somewhere?


title: How to measure faster than light electric energy?

text: According to relativity,nothing can break light barrier.But a recent preprint shows energy transmission of commercial electric power (f=60Hz) is faster than light. (It is not the drift velocity of electrons because energy transport depends on the electromagnetic field instead of charged particles). Moreover, the speed increases as its frequency decreases so the value is infinity for a direct current (f=0).That is action at a distance (instantaneous interaction)! My question is whether it is possible to design a circuit to compare this speed with c in lab? For example,time-delay of an electromagnetic signal through a free space distance of 3m is $10^{-8}\text{ s}$. As to direct current along a copper wire, however, there should be no delay. Is the difference detectable? I'm interested to the experiment because it is of substantial significance to measure the rate of electric power for electrical engineering not matter the result can exceed c or not.