title: Didn't we mess up with the temperature?

text: The following passage has been extracted from the book "The Feynman Lectures on Physics-Vol l": > The mean kinetic energy is a property only of the "temperature." Being a > property of the "temperature," and _not of the gas_ , we can use it as a > definition of the temperature. The mean kinetic energy of a molecule is thus > some function of the temperature. But who is tell us what scale to use to > use for the temperature? We may arbitrarily _define_ the scale of the > temperature so that the mean energy is linearly proportional to the > temperature. The best way to do it would be to call the mean energy itself > "the temperature." That would be the simplest possible function. > Unfortunately, the scale of temperature has been chosen differently, so > instead of calling it temperature directly we use a constant conversion > factor between the energy of a molecule and a degree of absolute temperature > called a degree kelvin. > > **The constant of proportionality is $k=1.38\times10^{-23}$ joule for every > degree. So if T is a absolute temperature, our definition says that the mean > kinetic energy is $(3/2) kt$** (The $3/2$ is put in as a matter of > convenience, so as to get rid of it somewhere else.) * * * From the above passage, at absolute zero, by definition, mean kinetic energy of a molecule should be zero-"completely frozen." There is a giant principle which stands against the view of atoms getting completely frozen; the following passage from the same book introduces the principle: > As we decrease the temperature, the vibration decreases and decreases until, > at absolute zero, there is a minimum amount of vibration that the atoms can > have, but not zero..... > > Remember that when a crystal is cooled to absolute zero, we said that the > atoms do not stop moving, they still jiggle. Why? If they stopped moving, we > would know where they were and that they had zero motion, and that is > against the uncertainty principle. We cannot know where they are and how > fast they are moving, so they must be continually wiggling in there! * * * Aren't the above two passages in contradiction with each other? Didn't we mess up with temperature?


title: What temperatures can be reached in an air-to-air thermocompressor nozzle and why?

text: People are generally of the opinion that the boiler injector cannot be redesigned to run on air. In other words, an air-to-air thermocompressor that puts fresh air into a tank without a mechanical pump. Assuming there is a large quantity of high pressure air available to drive the injector, what is the procedure to determine the pressure, volume and temperature necessary to entrain large quantities of atmosphere or some other lower pressure air and put it into a 200 psi tank? It has been suggested that the boiler injector is a bad analogy since the drive air cannot condense in the nozzle as it does in the boiler injector. If I knew how to compute obtainable temperatures, I would have a better idea whether or not air could condense for a split second so its latent heat could contribute to resisting the tank pressure. As I understand it, the pressure will become velocity in the converging nozzle due to expansion and some of the pressure will come back in the diverging nozzle. According to PV/T = constant, there's no problem getting to -320 deg. F. with high pressure air, say 1000 psi or whatever, but this doesn't take flow or dynamics into account and I don't know where to start. So far this question is stumping people and search engines, so I am thinking the answer is unknown. Even if there is no way for air to condense in a nozzle (which I doubt), I still need to know how to estimate the requirements of a conventional (non- condensing) air-to-air thermocompressor.


title: Friction on roads

text: I have a question with which I am having trouble. A 71m radius curve is banked for a design speed of 91km/h. Given a coefficient of static friction of 0.32, what is the range of speeds in which a car can safely make the turn? I'm confused. Do I not need to know the mass of the vehicle for this question, so that I can calculate the forces etc and find how much force I need/how much force is available?


title: The formal solution of the Schrodinger equation

text: Let's have Schrodinger equation (or some equation in Schrodinger form) $$ \tag 1 i \partial_{0} \Psi ~=~ \hat{H} \Psi . $$ One likes to write that it has formal solution $$ \tag 2 \Psi (t) ~=~ \exp\left[-i \int \limits_{0}^{t} \hat{H}(t^{\prime}) dt^{\prime}\right]\Psi (0). $$ But usually the solution of $(1)$ is given by the method of successive approximations in a form $$ \tag 3 \Psi (t) ~=~ \hat {T}\exp\left[-i \int \limits_{0}^{t} \hat{H}(t^{\prime}) dt^{\prime}\right]\Psi (0), $$ where $\hat {T}$ is time-ordering operator. It seems that $(3)$ doesn't coincide with $(2)$, but formally $(2)$ is good: it satisfies $(1)$ and initial conditions. So where is the mistake?


title: path planning with invasive measurements

text: My background is not science, and I hope the question I am about to ask doesn't look like a homework kind of a thing! Anyway, I will try my best to make the point clear. imagine there is a lake, and a boat equipped with a sensor on that lake. boat can move freely in a contained rectangular shape region on the lake, namely $ 0 < x < 1 \mbox{ and } 0 < y < 1 $ . the sensor installed on the boat takes measurements at times $ t_0, t_1, … $ with constant frequency. Each time sensor shoots a bunch of rays downward (in the shape of a thin cone, like a flashlight) and receives their reflection off the seabed and then sensor returns two numbers; first one indicates the depth of lake at that point and second one indicates something about some quality of soil that makes the seabed at that point. Because the measurements are noisy (we assume distance measurement is perfect, but the measurement about the chemicals found in the seabed is noisy) one can imaging that by taking multiple measurements at a single point $(x_t,y_t)$ and refining those measurements using come filtering method (e.g. Extended Kalman Filter, or some other method) he can increase the certainty about those measurements. $s(x,y) = f(x,y)+noise(x,y)$ (where 'f' is the true value and 's' is sensors measurement about soil quality) Now the problem is a path planning problem. We want to know how the boat should explore the lake in the next N seconds (it takes N seconds for the sensor to take say 100 samples). But there are two other factors to take into account. First; somehow we have a means of estimating the measurements of sensor if the sensor was to be turned off, taken to a random point $(x_r,y_r)$, turned on and take only one measurement. So we have s*(x,y) which has been proven to be a good estimate of s(x,y). We can use S* in our path planning phase. Second; one can imagine that measurements will not be independent and there is correlation between measurements. This correlation is stronger between nearby point (where $ \|(x_1-x_2,y_1-y_2)\|$ is small ) but points that are far apart are less correlated. Also one would imaging that at point where water is shallow and seabed is close to water level, a small movement of boat will result in more varying measurements, while in places where water is quite deep, even if the boat moves a bit, measurement will not change much. (like when I look at a mountain far away, if I move a few meters I still see the same image, but if I am looking at something close to me, moving a few meters will result in different view point). I must say the important measurement for me is the one about soil quality, and distance measurement is only provided to help finding the correlation between measurements made at nearby points, as mentioned above. I don't know how the measurements are correlated, I can just make some guesses based on the argument above. At time $t=t_0$, boat is at point $(x_0,y_0)$ and all I am given is the tool S*(x,y). and I want to do the path planning for the next N seconds. I will appreciate any suggestion/help and please let me know if any part of problem is unclear, I know without proper graphs,etc. it is not easy to explain the idea. My own attempt to solve the problem is as follows: make a regular grid of $m \times n$ on $ 0<x<1 $ and $ 0<y<1 $ and restrict the boat to always be positioned on one of these points. so path planning is on discrete space now. calculate s*(x,y) for all grid points. (Safely assume $(x_0,y_0)$ is also on one of the grid points). S* tells me estimate measurements at $ x,y$ . Because I know the noise model and the filtering scheme that will be used to refine the measurements, I can calculate how many bits of information (reduction of differential entropy) I will gain if I take two or more consecutive measurements from same position. Also by introducing a non-informative prior probability (uniform distribution) over all possible values, it is possible to calculate how much information can be gained by taking a single measurement at a new position. I define the path planning problem as one of maximising the overall information gain while amount of work (number of samples taken) is fixed. Also samples have to be taken either from same position as previous one (boat stationary) or from a position next the previous sampling location (boat moving, but it's speed is limited so measurements have to be made on neighbouring points on the grid). Now the question is, if I take a measurement at a point $p_1$, how informative a measurement at a neighbouring point $p_2$ will be, knowing that these two points are somehow correlated. Now this is were I am stuck! I thought maybe some techniques such as mean field theory or variational methods can help me model the correlation between the points and therefore figure out how redundant a measurement on a point will be if a measurement has been made on at least one of its neighbours. But I can not figure out how to go forward from here. It would be great if anyone can help me with this problem, or direct me to the right place to ask it.


title: Quantum Anomalies in Non-Gauge Theories?

text: I'm reading about quantum anomalies in QFT and all the examples seem to arise in gauge theories. Is it true that theories without a local gauge invariance don't have quantum anomalies? I can't think of examples of symmetry violation in any non-gauge theories, particularly the free theories. Then again, there might be a well-known example I'm not aware of!


title: Can Smoothed-Particle Hydrodynamics (SPH) be used to simulate porous media flow and deformation?

text: I am trying to use Smoothed-Particle Hydrodynamics (SPH) to study fluid flow in and around porous media. The aim is to observe how it causes erosion and failure. For this, from my understanding, there needs to be a proper consideration of all the processes at all scales. However, with SPH when problems of bigger scales are considered, i believe there is an averaging over increasing spatial scales and thus loss of information of processes happening in the sub-particle scale. Ex: if the discretization is such that each particle represents 5 liters of fluid or 1 cubic meter of porous media, aren't the processes within these volumes lost to us? Even though they may be considered at the equation level, aren't they difficult to visualize? To summarize, the use of SPH is primarily to model a continuum using particle discretization, but if it is so coarse such that averaging effects from continuum mechanics need to be considered to account for sub-particle contributions, isn't it redundant to still be using this method for the problem?


title: Why is velocity normally distributed in a gas, but not energy?

text: If one looks at a cubic box of gaseous atoms all initially flying in the same direction at the same speed (but flying at an angle to the walls, so as not to reflect up-and-down against the box walls forever), they will collide with the walls and each other, their previously uniform velocities becoming messed up randomly until they are distributed according to a Maxwell-Boltzmann distribution, which is a normal distribution. Looking at the set-up as a random-generator, this can be considered an application of the central limit theorem, which says that the mean of a large number of random variables will end up being normally distributed. My question: Why doesn't the same reasoning hold for energy? Aren't the energies of the atoms in such a box also random variables? However, the energies follows the Boltzmann distribution, which isn't a normal distribution. Of course, the relationship between speed and energy prohibits both energy and speed being distributed normally, but doesn't this finding contradict the central limit theorem?


title: Is a black hole a perfect black body?

text: A black body absorbs all light/radiation in its reach. According to basic laws of physics, the more energy a body absorbs the more it can emit. Therefore, a black body absorbs all energy directed at it and also emits all energy that's been absorbed. A black hole is known to absorb all sorts of every (light, radiation..). If it absorbs -all- energy around it, it should in addition emit all energy it has absorbed. But due to its vast gravity noting can "escape", and therefore nothing is actually emitted. Is a black hole still considered a perfect black body? Disclaimer: I am no physicists, I am a senior year high school student with an interest for physics. I don't know the preferred terminology of things, especially not in English (2nd language), so if anything is unclear I will explain in comments below.


title: Explicit form of $\gamma^\mu \partial_\mu$ in the Dirac equation

text: I'm in an introductory particle physics class, and in performing manipulations on the Dirac equation, my instructor expands the $\gamma^\mu \partial_\mu$ term as: $$\gamma^\mu \partial_\mu = \gamma^0 \frac{\partial}{\partial t} + \vec{\gamma}\cdot \vec{\nabla}$$ where $\vec{\gamma} = (\gamma^1,\gamma^2,\gamma^3)$, but to my knowledge, $$\gamma^\mu \partial_\mu = \gamma^\mu \eta_{\mu \nu} \partial^\nu = \gamma^0\frac{\partial}{\partial t} - \vec{\gamma} \cdot \vec{\nabla}$$ using the convention $\eta_{\mu \nu}=\operatorname{diag}(+,-,-,-)$. Am I missing something here?


title: Poles bit in a propagator

text: Hi I am trying to derive the K-G propagator and am stuck on the bit where Cauchy's Integral formula is needed i.e evaluating from $$\int \frac{d^{3}p}{(2\pi)^3}\left\lbrace\frac{1}{2E_{p}}e^{-ip.(x-y)}|_{p^{o}=E_{p}}+\frac{1}{-2E_{p}}e^{-ip.(x-y)}|_{p^{o}=-E_{p}}\right\rbrace $$ to $$\int \frac{d^{3}p}{(2\pi)^3}\int \frac{dp^{0}}{i2\pi}\frac{-1}{P^{2}-m^{2}}e^{-ip.(x-y)} $$ I understand that the formula $g(z_{0})=\frac{1}{2\pi i}\int \frac{g(z)}{z-z_{0}}dz$ must be used but I just don't see how the solution can be found,


title: How to calculate air resistance of penny dropped from Empire State Building?

text: If a penny is dropped from the Empire State Building, then its speed, without taking air resistance into consideration, is $\sqrt{\left(32\frac{\textrm{ft}}{\textrm{s}^2}\right)(1454\textrm{ ft})}=216.3\frac{\textrm{ft}}{\textrm{s}}$, or $147.5\frac{\textrm{mi}}{\textrm{h}}$. What would the calculation be to take into account air resistance?


title: How to calculate the heat transfer rate between the liquid and the gas?

text: Let water (liquid) be in a chamber (with no heat transfer to the walls). The gas is the residual space above the liquid, meaning that the contact surface is the surface of the water. Given the gas and the liquid are at a certain pressure, but the temperature of the gas and the liquid differ. How can I find the heat transfer rate for this problem?


title: energy efficiency, transformation from chemical to thermal energy, for district heating plants

text: If I have a system in which I introduce 100e.u.F (energy units) derived from chemical energy (i.e. fuel) and generate thermal energy to heat water what are e.u. absorbed by water? I.e. the efficiency of the transformation? Basically I would like to know the average/general efficiency of energy transformation for a district heating plant. Considered that the only energy input is fuel and the only energy output is heat (no electricity)? What are the energy loss? Thanks, Luther


title: Can the mass of longitudinal and transverse W bosons be measured separately?

text: Some higgsless unified models of particle physics predict that the mass of longitudinally polarized W bosons and the mass of transversely polarized W bosons are different. In those models, a difference in masses is also predicted to appear for the Z boson. Is there a way that the existing data from the LHC, the LEP or the Tevatron can be used to check this prediction? Or maybe it has already been checked?


title: Dimensional Analysis with $\alpha$, $\beta$, and $\gamma$ Powers

text: In Prof. Walter Lewin's Dimensional Analysis lecture, he stated that: $$t ~\propto~ h^α m^β g^γ$$ ($\alpha$, $\beta$ and $\gamma$ all to some power of their unit). Why does he put $h$, $m$ and $g$ to some power of $\alpha$, $\beta$ and $\gamma$?


title: Binary star system - Revolution around Primary vs Companion

text: How likely is it in a binary or multi-star system for a non-star celestial body to revolve around the primary star rather than the companion star?


title: Why do Nuclei lose mass?

text: When it comes to things like gravity and the electromagnetic force, masses aren't reduced-but with nuclei the mass difference is noticeable. What about nuclear forces makes them capable of putting mass into binding energy?


title: Infinite universe - Jumping to pointless conclusions

text: I watched an episode of thee BBC Horizon series titled 'To infinity and beyond'. In this program a number of respected physicists and mathematicians were talking about the nature of infinity and an infinite universe. They argued that if the universe is infact infinite then every possibility must play out somewhere, even going so far as to get a physicist to calculate how far you would have to travel to find an exact replica of the earth. They also used the classic example of infinite monkeys producing the works of Shakespeare. Now to me the monkey example makes sense considering that the works of Shakespeare are finite and so are the number of possibile outcomes of a monkey mashing away at a keyboard for a given period of time (although very large still finite). But the logic of applying this to the universe seems flawed to me, surely in the context of the universe the possibilities are also infinite as it is with a sequence of numbers. the numbers 1,2,3,4... go on infinitely without repeating themselves so to say because something is infinite every possibility must play out seems to me incorrect. Now perhaps you could argue that a finite number of atoms can only assemble themselves in a finite number of ways - again I can see this although I am not entirely sure that two lots of atoms arranged in the same way are necessarily the same since we currently rely on probablity calculations to predict the outcome of subatomic processes (this could arguably be due to slight variations at a more fundamental level...) but even if this were true. They went further to suggest that in an infinite universe there is an exact copy of you or I doing exactly the same thing and indeed every possible thing. Now it seems to me at this point things have become ridiculous, even by the time you have calculated the possibility of an exact atomic copy, the number of possible interactions I could have at any time with the universe, their affects on my atomic makeup and indeed future interactions, surely at this point we are dealing with infinite possibilites. Any feedback on any of these points welcome but my central assumption here is this: Infinite possibilities will not play out even over an infinite period of time. Is this correct?


title: Mermin-Wagner theorem in the presence of hard-core interactions

text: It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with hard-core interactions; for example to conclude that genuine crystal phases for a system of hard disks (with possible additional interactions) cannot exist in 2 dimensions. If this particular claim has been proved rigorously a few years ago (see this paper), it is known in general that the presence of hard-core interactions can lead to phases with broken continuous symmetry (a specific example is given below). To keep things simple, let me focus on nearest-neighbor spin models on the square lattice, with spins taking values in the unit circle. So let us consider a formal Hamiltonian of the form $$ \sum_{i\sim j} V(S_i,S_j), $$ with $V$ is a continuous function, assumed to be invariant under the action of $SO(2)$: $V(r_\theta S_i, r_\theta S_j) = V(S_i,S_j)$, where $r_\theta$ rotates the spin by an angle $\theta$. In that case, it is known that all pure phases of the model are invariant under the action of $SO(2)$. (Note that we do not even require $V$ to be smooth, so that the usual, both heuristic and rigorous, arguments relying on a Taylor expansion and a spin-wave argument do not apply immediately; that one can do so was proved here). Substantially more general results are actually known, but this will suffice for my question. What I am interested in is what happens for models of this type in the presence of hard-core interactions. No general results are known, and the situation is proved to be subtle. Indeed, consider for example the Patrascioiu-Seiler model, in which $$ V(S_i,S_j) = \begin{cases} -S_i\cdot S_j & \text{if }|\delta(S_i,S_j)|\leq\delta_0,\\\ +\infty & \text{otherwise,} \end{cases} $$ where $\delta(S_i,S_j)$ denotes the angle between the spins $S_i$ and $S_j$, and $\delta_0>0$ is some parameter. In other words, this model coincides with the classical XY model apart from the additional constraint that neighboring spins cannot differ too much. For this model, it is proved here that, when $\delta_0<\pi/4$, there exist (non-degenerate) phases in which rotation invariance is broken. Nevertheless, one expects that phases obtained, say, by taking the thermodynamic limit along square boxes with free, periodic or constant boundary conditions should be rotation invariant. So, now, **here is my question** : Are there any heuristic physical arguments supporting the validity of a version of the "Mermin-Wagner theorem" in such situations? All the heuristic arguments I know of fail in such a context. Having good heuristic arguments might help a lot in extending the rigorous proofs to cover such situations. **Edit:** Let me precise my question, as the (quite long) discussion with Ron Maimon below shows that I haven't stated it in a clear enough way. I am _not_ interested in a discussion of why the counter-example given above leads to a violation of MW theorem and whether it is physically realistic (as far as I am concerned, its main relevance was to show that one has to make _some_ assumptions on the interaction $V$ in order to have rotation invariance of all infinite-volume Gibbs states, and this is exactly what this example does). What I am really interested in is the following: does there exist heuristic (but formulated in a mathematical way, not just some vague remarks) arguments with which physicists can derive the MW theorem in the presence of hard-core interactions? I would even be interested in arguments that apply in the absence of hard-core interactions, but when $V$ is not differentiable (even though this case is treated rigorously in the reference given above).


From the book Introduction to Classical Mechanics With Problems and Solutions by David Morin, page 236 states: > Noether's Theorem: For each symmetry of the Lagrangian, there is a conserved > quantity. Whereas the Wikipedia page states: > Noether's (first) theorem states that any differentiable symmetry of the > action of a physical system has a corresponding conservation law Does the action and Lagrangian have identical symmetries and conserved quantities?


title: Equivalent temperature: laser and cell containing Rb

text: What's the meaning of "equivalent temperature" related to a cell containing rubidium and crossed by laser?


title: If you could reverse gravity, what velocity would you achieve on leaving Earth?

text: If you could reverse gravity, to make it repulsive instead of attractive, what velocity would you achieve on leaving Earth? A simple question really, but I have completely forgot how to calculate this sort of thing. Also after leaving Earth, if you could reverse the Sun's gravity (on yourself) what velocity could you achieve leaving the solar system?


title: Do gases have a general upper limit of density?

text: Is there some limit for the density of gases, at which no change in condition could make it more dense without making it fluid, or solid - or something 'in between'?


title: Is $\langle k \vert k_1k_2\rangle=0$

text: Using that $$ \vert k_1k_2\rangle = a^\dagger({\bf k_1})a^\dagger({\bf k_2})\vert 0 \rangle$$ and the commutation relations $$[a({\bf k}),a^\dagger({\bf k'})]=(2\pi)^32\omega\delta^3(\bf {k}- \bf {k'})$$ what would then be for instance $$\langle k\vert k_1k_2\rangle=?$$


title: Eigenenergies and eigenkets given the Hamiltonian

text: For a two level system the Hamiltonian is: $$ H=a(|1\rangle \langle1|-|2\rangle\langle2|+|1\rangle\langle2|+|2\rangle\langle1|) $$ where $a$ is a number with the dimension of an energy. I need to find the energy eigenvalues and the corresponding eigenkets (as a combination of $|1\rangle$ and $|2\rangle$). I used: $$ H |ψ\rangle=E|ψ\rangle $$ And using the fact that : $|a\rangle = \sum_i c_i |a_i\rangle$ I wrote $|ψ\rangle$ as a combination of the two system kets $|ψ\rangle=c_1|1\rangle + c_2|2\rangle$ ($c_1$,$c_2$ are complex numbers). so $$\begin{aligned} H|ψ\rangle =& a(|1\rangle\langle1|-|2\rangle\langle2|+|1\rangle\langle2|+|2\rangle\langle1|)\cdot(c_1|1\rangle+c_2|2\rangle) \\\ =& a(c1|1\rangle-c_2|2\rangle+c_2|1\rangle c_1|2\rangle)=a ((c1+c2)|1\rangle+(c1-c2)|2\rangle) \\\ =& E|ψ\rangle. \end{aligned}$$ How do I continue?


title: Renormalization of the R-charge?

text: In general I would like to know as to known or what is/are the standard references about R-charge renormalization in supersymmetric theories. When does it do so and what is expected or known to be interesting.   * A little more specifically I want to know whether something is particularly special if the R-charge of the scalar chiral superfield in some theory is seen to be flowing to values greater than 1/2 under the flow.    * And if the R-charge of the scalar chiral superfield is flowing to values less than half then what does it physically imply? I have at times seen a vague argument along this line that if it is flowing to 0 asymptotically then that means that the theory is developing a continuum spectrum in that limit - which is supposed to be more surprising if the theory was defined on a compact space(-time?) to start with. But I don't understand the above argument any much more and would like to know of precise statements/derivations/references - and hopefully pedagogic ones from where a beginner in the field can learn!


title: Electron Relaxation/Polarization for and n-type Semiconductor

text: Please help me understand the following (general) statement, referring to electrons in a full valence band of an n-type semiconductor: "An electron filling up the last empty state in the valence band will in doing so prevent the other valence electrons from reducing their energy through polarization and relaxation around the impurity center" I don't understand what is meant by the last part of this. I know that in a full band, electrons have no empty state to move into, but I don't know what is meant by polarization and relaxation "around the impurity." The impurity referred to is a donor (n-type SC). Another statement (which I think is basically the same) says: "In the case of a completely filled valence band, no (impurity, I assume) scattering can take place, because all states are occupied. Now, if a hole is created at, for example, the top of the valence band, the remaining valence electrons will relax around the impurity ions... this new flexibility of the system makes the system lower in its energy." What does this mean "relax around impurity ions"? To sum it up, what I'm not understanding here is: a) what is meant by "relax around the impurity" (I have no idea what they mean by "relax"), and b) reducing energy by polarization or relaxation (What/how/why? What do they mean by polarization?) Edit: I spoke with a professor about this, and I _think_ that this all has to do with screening. In other words, if there are empty states in the valence band, the charge density is modified to a new equilibrium to screen the impurity, "relaxing" around the impurity. I think the point on polarization follows the same logic (screening). Any input on my thoughts would be appreciated.


title: How did Lord Rayleigh derive/determine the phase function for his scattering model?

text: I've been researching the question for quite some time, as I understand it the phase function is actually an approximation due to the particle-wave duality inherent in participating media such as the atmosphere or anything else. As they are reemitted from particles, some EM waves mingle with their neighbours and amplify or kill off each other, therefore general approximate lobes are constructed from empirical data. The Rayleigh scattering phase function is symmetrical as defined: $$\Phi_R(\theta) ~=~ \frac{1}{4\pi}\frac{3}{4}(1 + \cos^2\theta).$$ However, I have no idea where this came from. I tried researching different phase functions, even those more modern from Henyey and Greenstein in 1941. But they just stated it is an approximation and gave the final form with no details. Could someone show me, please?


title: Did Planck said that his theory is distinct from Zeno's paradoxes?

text: I remember once reading that Planck or some other prominent figure in quantum physics said that the theory (probably Planck length or Planck time in particular) is not about the thing what Zeno's paradoxes, in particular about motion, tries to point out. Unfortunately I cannot remember where did I read it. As I am interested in why exactly did he think that these problems are not, or not very closely, connected, I would like to find a citation on this (should it exist). They seem quite closely resembling each other for some and there must be reasons to consider for the contrary. Should such a quote exist, could anyone provide me with a source so I can verify its genuineness and unfold the claim?


title: Aharonov-Casher effect for charged particles

text: All the explanations of the Aharonov-Casher effect seem to imply it only "works" for neutral particles with a magnetic moment. This seems to stem from the duality of the A-C effect with the more known Aharonov-Bohm effect. The particle being neutral is also mentioned in the original paper. Is it strictly necessary to consider the A-C particle to be neutral? Can't the A-B and A-C phases just add up in the case of an electron in an electromagnetic field? I know for sure that in e.g. the Pauli-Breit Hamiltonian (a non-relativistic limit of the Dirac Hamiltonian) contains a $\boldsymbol \mu\times\boldsymbol E$ A-C term, together with the $\boldsymbol A\cdot \boldsymbol p$ A-B term.


title: Free fall time with non uniform acceleration and some initial velocity

text: Free-fall time for two objects on a radial path (starting from rest) is given by: $t(y)=\sqrt\frac{y_0^3}{2u}\biggl(\sqrt{\frac{y} {y_0} \bigl({1} -\frac{y}{y_0}}\bigr) + \arccos\sqrt\frac{y}{y_0}\biggr)$ Where: $t$ is the time after the start of the fall $y$ is the distance between the centers of the bodies $y_0$ is the initial value of $y$ $u$ = $G(m_1 + m_2$) is the standard gravitational parameter. The solution of this equation of motion yields time as a function of separation. See also this Phys.SE and links therein. * * * Question: Now let's say these objects start with some **initial velocity**. How would you incorporate some initial $v$ into these calculations?


title: Properties of an object whose collision with Earth would completely disintegrate Earth

text: This picture got me thinking, whether such collision would be possible, and would it really look like that from the moon. What would be the properties (mass, size, velocity etc.) of an object, whose collision with Earth would completely destroy it in the manner of that picture? That is, after the collision, a large portion (if not most) of Earth would continue straight along the same path as that of the colliding object, but from the opposite side of the planet. If such an event were to happen, would the sight in that picture be an accurate depiction when observed from the surface of the moon?


title: Black hole (classical or quantum?)

text: Theoretically we can convert a body into black hole by compressing its mass below some radius (known as Schwarzschild Radius). Suppose such object after becoming black hole has a radius which is comparable to atom and nucleus radius. Now my question is: what happens if we run this object into double slit experiment setup (single black hole at a time)? Shall we get interference pattern on the detector wall because its radius is in quantum domain (say we somehow know when on detector screen this black hole will hit) or simple-particle pattern (i.e. classical way) because of the mass associated with that black hole? If you have a really tiny black hole, will it behave as a classical particle, or will it exhibit quantum behavior?


title: Effect of water pressure on sinking objects

text: As I understand, water pressure increases as we go towards bottom of the ocean. So if an object* is thrown into water and it starts sinking with some speed, does the sinking object's acceleration increase with increasing pressure? Also does water solidify under very high pressure and if so is that high pressure achieved at the ocean bottom? If so, would a sinking object stop sinking and rest on the "solidified" water, if we have a deep enough ocean?   * e.g. black box of a submerged plane Edit: I have accepted best current answer, if you think you can write a better answer, please do so.


title: Squinting at light sources

text: I am sure it's just your eyelashes creating a filtering effects, but if you look a a bright(ish) light source such as a lightbulb while squinting, if looks like you are seeing straight light rays emitting from the lightbulb, I assume you can't see an individual ray of light like this?


title: binding energy of a nucleus is positive?

text: I have found from this link http://hyperphysics.phy- astr.gsu.edu/hbase/nucene/nucbin.html that: Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it. The difference is a measure of the nuclear binding energy which holds the nucleus together. This binding energy can be calculated from the Einstein relationship: Nuclear binding energy = Δmc2 Now from the above it seems that the nuclear binding energy should be positive to compensate the energy difference between between the mass of the protons and neutron and the mass of a nucleus. But my question is how the binding energy can be positive if this binds the nucleons by **attractive** force? I have also gone through this The "binding energy" of bonded particles adds mass? , but didn't get my question resolved.


title: Is 4-volume element a scalar or a pseudoscalar in special relativity?

text: In general relativity 4-volume element $\mathrm{d}^4 x = \mathrm{d} x^0\mathrm{d} x^1 \mathrm{d} x^2\mathrm{d} x^3$ is clearly a pseudoscalar (or scalar density) of weight 1 since it transforms as $\mathrm{d}^4 x \to \mathrm{d}^4 x' = J \,\mathrm{d}^4 x$, with $J$ Jacobian determinant of the coordinates transformation. In special relativity we consider only Lorentz transformations, which have $J = \pm 1$, so shouldn't $\mathrm{d}^4 x$ be a pseudoscalar also in special relativity? Landau states ("The Classical Theory of Fields", § 6) that «the element is a scalar: it is obvious that the volume of a portion of four-space is unchanged by a rotation of the coordinate system», but this doesn't proof that $\mathrm{d}^4 x$ is a scalar rather than a pseudoscalar since a pseudoscalar looks like a scalar under a proper rotation of the coordinate system ($J = 1$), differences arise only for an axis inversion ($J = -1$).


title: What is a clock?

text: Relationalists love to define time operationally as what clocks measure, but this begs the question of what counts as a clock. Clearly, it's a measuring instrument and what it measures is supposedly time. We need to avoid circular definitions of time. There are many possible measuring devices, and most don't measure time. Which of them counts as a clock? To which one has to answer it has to give a linear real number as a pointer reading, it orders events correlationally, etc etc has all the properties we demand of time. This is circular.


title: How does the view of night sky change as the Sun orbits around the Milky Way?

text: I know that the Sun and hence the Solar System orbits around the galactic center of the Milky Way. Does this rotation cause any visible change in the night sky? I know that human life span is negligble compared to the time it takes the Sun to go around the galaxy, but will we ever see any change in the night sky if we record the the observations over few generations? Will we ever see a new start or constellations? Or a different view as we go around the Milky Way? I am assuming (and hoping), given enough time to make considerable progress of the Sun around the Milky Way, there has to be some change, we may get to see another galaxy or something :) Now, don't tell me that the Milky Way itself is going around something even bigger :) (I am glad I found this site, there was a question that I always wanted to ask but did not know where.)


title: Best observing techniques for a Total Lunar Eclipse?

text: Is there any good tricks to observing a total lunar eclipse that I should be aware of? Just wanting to know what to do to be prepared for the upcoming one, but please post in general for future viewers of this question.


title: How do I use this 'Horizon Observatory'?

text: Just around the corner, we have one of these: ![image](http://i.stack.imgur.com/MoTiY.jpg) It's at the Halde Hoheward (article in the German wikipedia), and it's called a 'Horizon Observatory' by the people who built it. How does it work exactly, and how do I use it? A note: clearly, I need help with this question. Any edits will be much appreciated. :-)


title: What are the differences in using an eyepiece with a barlow instead of a shorter eyepiece?

text: I intend to start making visual observations, and I want to know more about the difference between using barlow lenses and one or two eyepieces and using a complete kit of eyepieces, both for planetary and deep space objects.


title: Physical intepretation of nodes in quantum mechanics

text: I am taking my second course in QM, and my head is starting to spin as it probably should. But I would very much like to clear up my head about a few details regarding the wave function. As I know it is impossible to predict where particles are and one can only give a probability of where it _should_ be. The simplest case is a "frictionless" particle "bouncing" back and forth inside a infinite square well. Eg a particle in the following potential $$ V(x) = \left( \begin{array}{cc} 0 \ , & \text{for} \ 0 \leq x \leq a \\\ \infty \ , & \text{elsewhere} \end{array} \right) $$ Which gives rise to the following normalized solution $$ \psi_n(x) = \sqrt{\frac{2}{a}} \sin\left( \frac{\pi n}{a}x \right) $$ My problem is what the **nodes** in the square function represents. If I draw $|\Psi_2(x,0)|^2=|\psi_2(x)|^2$ I obtain a graph similar to the one below. ![enter image description here](http://i.stack.imgur.com/5Z2US.png) What is the physical explenation that finding the particle around a small region around $a/2$ is close to zero? Or why is it so much less likely to find it near $a/2$ than $a/4$? Eg why is $$ P(a/2 -\varepsilon \leq X \leq a/2+\varepsilon) = \int_{a/2-\varepsilon}^{a/2+\varepsilon} \left| \psi_2(x) \right|^2 \,\mathrm{d}x \sim 0 $$ for small $\varepsilon$


title: What would happen if a supermassive blackhole at the center of a galaxy evaporates?

text: Well the title says it all but I will just explain it in detail a bit. We know that a blackhole eventually has to evaporate due to the hawking radiation. It is also said that the blackholes at the center of galaxies are the galaxies' source of energy. So what would happen if that blackhole evaporates?


title: Calculate 2D density of states from 3D density of states

text: I have a 3D DOS which is calculated by this formula: $$D(E) = \sum_n\int\frac{\mathrm d^3k}{(2π)^3}\delta(E−\epsilon_n(k)) $$ I do not have any analytical expression for kinetic energy. Is there any way to achieve 2D density of states jut by having 3D density of states. thank you very much.


title: Does gravity cause spacetime to bend?

text: Does gravity cause spacetime to bend even though space has no mass?


title: Planck time, distance, mass? Why do we take those values?

text: Say we want to make an educated guess for critical values of time, distance and mass, where quantum gravity effects are supposed to be non-negligible. These values are given the prefix "Planck-". Now, the way that they are "derived" is to take the speed of light $c$, Planck's constant $h$ and the gravitational constant $G$. Their units contain mass [$\mathrm{kg}$], distance [$\mathrm{m}$] and time [$\mathrm{s}$]. So say we want to get the Planck distance $d_\text{Pl}$, then we just make the ansatz $$c^A h^B G^C = d_\text{Pl}$$ where $A$,$B$,$C$ are unknown exponents that are determined by equaling the dimensions on both sides of the equation (3 unknowns: $A$,$B$,$C$ and 3 units: $\mathrm{kg}$,$\mathrm{m}$,$\mathrm{s}$). This determines $d_\text{Pl}$ uniquely. The analogous ansatz is made for the Planck time and mass. My question: Why do we think that this gives us a valid guess on the regime for quantum gravity?


title: Alpha-stable isotopes

text: Why some isotopes with positive alpha-decay energy are stable? For example, alpha-decay energy of stable 194Pt is about 1.5 MeV. But there is no stable isotopes with positive beta-decay energy. For example, half life of 197Pt with beta-decay energy 0.7 MeV is 19 hours


title: A question about canonical momentum and arbitrariness for potential in magnetism

text: The following question confuses me: > There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle > is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, > and speed $v$ along the $x$ axis. It is very convenient to restrict our > discuss in two dimension plane, the $x$-$y$ plane. Find the particle > coordinate when its speed is along $y$ axis. ![enter image description here](http://i.stack.imgur.com/ekxeJ.png) I want to apply the canonical momentum to find the point. The canonical momentum, $P=p+qA$, is a conservation quantity when the particle moves. I let the potential $A=(0,- \frac{1}{2} \beta x^2)$ satisfied $B=\nabla \times A$ and the Coulomb's gauge $\nabla \cdot A = 0$, hence the original canonical momentum is $(mv,0)$, and the canonical momentum is always equal to $(mv,0)$. When the particle is along the y axis, the momentum of the particle is $(0,mv)$, so the potential must be satisfied $qA=P-p=(mv,-mv)$. Here, I am in trouble. I cannot solve the point where the potential $A$ equals to $(mv,-mv)$, unless I choose another expression for potential. I am confused about the expression of potential. It should be arbitrary for physics, but here, it is not. If I choose $A=(a \beta xy,b \beta x^2)$ and $2b-a=-1$, there is a freedom degree to set the value of $a$ or $b$, and the point that I have to find is not fixed. I want to know why here the potential cannot be arbitrarily set its value. Could someone help me?


title: Fine grained vs. coarse grained measurements and MWI

text: Alright, so it is my understanding that the idea that measuring systems do a coarse grained measurement which give the appearance of decoherence. I understand that the claim implicit there is that decoherence does not actually occur. I also understand that MWI requires decoherence. To what extent is the above true and does it pose a problem for MWI?


title: Normal ordering and path integrals

text: What is the manifestation of normal ordering for creation/annihilation operators in the path-integral formalism?


title: What are the demographics of stars visible to the naked eye?

text: Of the stars that can be seen with the naked eye, what are the distributions of each type? For example, how many are main sequence? how many are Super Red giants/white dwarfs/neutron stars...etc. What's the distribution by mass and distance?


title: Why is it that angular acceleration is constant in different instantaneous reference frames?

text: Take the following example: A rod (of length L and mass m) is held horizontally at both ends by supports. One is instantaneously removed. The specific problem is to prove that the force on the other support drops from mg/2 to mg/4, which I proved by first considering the centre of mass as the instantaneous reference frame, and thus considering a rotation around the support. Resolving angular forces: (F = Force at pivot, I = Moment of Inertia = m(L^2)/12, ω = angular velocity)                FL/2 = I * dω/dt      FL/2 = m(L^2)/12 * dω/dt      F = mL/6 * dw/dt   (1)      Now taking the instantaneous reference frame around the pivot: (I = M(L^2)/3, ω' = angular velocity, force at CoM = mg)               mg * L/2 = I * dω'/dt     mgL/2 = mL2/3 * dw'/dt      dw'/dt = 3g/2L    (2)      The desired solution can be found by substituting (2) into (1), i.e. by equating dw'/dt and dw/dt. Why is it that this can be done?


title: Quantum Mechanics and the Airy Function, the physics of the turning point

text: I'm working with the Airy function, and the book states at $x=0$ is a turning point, and there are two very different behaviors on either side. In general what a does a turning point mean in differential equations? A point where the highest order derivative in the equation equals zero? The book says this makes sense, oscillatory and decaying on either side of the turning point. But if $E>$ turning point it decays, that's the opposite case of the finite square well right? if $E<$ potential then it decays. What does it physically mean to have a turning point there, and why is it oscillatory when $E$ is greater than the turning point? This is so unintuitive, these potentials confuse me.


title: Coulomb interaction as virtual particles exchange?

text: I've been reading about virtual particle exchanges in physics books and in Physics SA posts, where a particle interpretation of gravity and Coulomb interaction is established. The Feynman Diagram picture (combined with the snowball picture that a fellow contributor provided in a related post) serves to account for the repulsion part: _grosso modo_ two particles in motion, a virtual photon/graviton, momentum change induces opposite motions ($\Delta \vec p \ $ and $ \ -\Delta \vec p$). Still, how can we account for the attraction (as a layman's analogy if not in formalism)?


title: Can Noether's theorem be understood intuitively?

text: Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. However I don't know of any, do you? Independence of time <=> energy conservation.   Independence of position <=> momentum conservation.   Independence of direction <=> angular momentum conservation. I know that the mathematics leads in the direction of Lie-algebra and such but I would like to discuss whether this theorem can be understood from a non- mathematical point of view also.


title: Why does light refract if photons are not bound by an axle?

text: In the classic metaphor, a light beam bends for the same reason that a wagon getting one wheel stuck in the sand does...the wheels travel at uneven speeds, and the wheel on the smoother surface travels faster. But the key to the wagon scenario is the axle - if the two wheels were not bound, the faster wheel would sail on, heedless of the other wheel's difficulty. So, if the metaphor is useful at all, there is an axle force binding the photos in a beam of light, which causes it to turn when it hits a different medium non-perpendicularly. Or is this just a bad metaphor for the rubes?


title: What principles does an air glider use?

text: I just saw this video which was kind of nifty. What principles govern this? Is it simply that 700 lbs of air pressure are exerted from that little 1 HP blower? What would you have to take into consideration to adopt the same principles to move something like a car on a turntable? Is moving something with air more economical than moving it by other means? I'm just thinking out loud...


title: Physical vapor deposition of SiO2

text: Could you suggest any if it's possible to deposit a layer of SiO2 via PVD? Why doesn't it widely used? Is that correct that I need ~1600C in vacuum? Could you suggest any books/papers about that? Unfortunately cannot tag this properly :-)


title: Open/Closed Branes

text: Hello this is my first question. For an open string you can pick different boundary conditions for the endpoints along different directions of space time. For example, you can choose Dirichlet conditions in some directions and Neumann along others. This gives us D-branes. My question is, why can't you choose Neumann b.c. along some directions, and closed string b.c. along some others? Is there some easy way to see this is nonsense?


title: Lean angle of a turning bicycle

text: I'm asked to derive a relationship for the leaning angle of a bicycle with the following specs:   * Center of gravity for bike and rider is a distance $L$ above the ground when vertical, and the total mass of bike and rider is $M$.   * The wheel radius is $r$ and the wheel mass is $m$   * The radius of curvature for the turn is $R$, the speed is $v$ I am to show that $$\tan \theta = \frac{v^2}{R} \frac{2mr + ML}{MLg}$$ but I am unsure. If I take $M$ to be the total mass, including the wheels, then I would guess that the condition is that centrifugal force and gravity act in such a way that the total torque is zero, i.e. $$M g L \sin \theta = M \frac{v^2}{R} \cos \theta L$. But then the mass of the wheels and their radius doesn't enter. If, on the other hand, I exclude the wheels from $M$, wouldn't I still have to add them to both sides, i.e. $$(MgL + 2mgr) \sin \theta = \frac{v^2}{R} \cos \theta (ML + 2mr)$$ or where does the extra term 2mr come from?


title: Where's the best place to add weight to a Pinewood Derby car?

text: A little background: a Pinewood Derby car is a small wooden car that races down an inclined track, powered only by gravity. You are allowed to add weight to the car up to a certain limit. Here is a recommendation to add the weight to the upper back of the car, to maximize the potential energy. My own gut feel is to add it so that the weight is evenly distributed between all 4 wheels. I'd like some advice that is well grounded in science.


title: does current product push or pull effect

text: Since i was a child i was told that current has pushing or pulling effect. However, i never got a dc shock and i don't remember ac shock (i got it very long before). The day before yesterday, an experienced electrician told me that dc has pulling effect ( most of the batteries supply only 12V it's not so much to worry but if supplied with very high voltage it is very deadly comparison to ac and) and ac has pushing effect. Logically i can't find any explanations. electricity is just flow of charge, and in our body, we have more electrons than protons (from C-14 decay) but still very less than enough to give shock or pushing or pulling effect.


title: Size of our inflationary bubble

text: Once again, an attempt to connect popular and real science. I have read that inflation implies our universe should look flat, or really close to flat, because our observable universe is only a really small part of a much larger "inflationary bubble". So, we are like people who can see only a very small patch of the Earth and think its flat. See, for example:   * http://www.astro.ucla.edu/~wright/CMB-MN-03/inflating_bubble.html   * http://nedwww.ipac.caltech.edu/level5/Guth/Guth5.html In that case, do we have any theoretical or empirical estimates of how large our inflationary bubble is compared to the observable universe ? I read an article by Andrei Linde in Scientific American saying that the size of the bubble could be $10^{10^{12}}$ metres (1 followed by a trillion zeros). Is this generally accepted ?


title: Suvat equations in reverse direction

text: This might be a basic question, but please help me out. I have an object traveling in the positive direction with a velocity $v$ and I wish to apply a constant acceleration so that the final velocity is equal in magnitude but opposite in direction (i.e. $-v$). I do not know the time, but know the distance over which I want to do this, the equation to use would be $v^2=u^2+2as$. But then, $(-v)^2=v^2+2as$, so $v^2-v^2=2as$ and so I get an $a=0$ which is obviously incorrect. This stems from the fact that $s=\frac{(u+v)}{2}t$, so $s=\frac{v-v}{2}t$ and you can see where this is going. What would be the best way to do this?


title: Speed of liquid being blocked at end of pipe

text: How fast would water go if at the end of of a 1 inch diameter pipe was closed by a valve? The system is as follows: 5 meter high source of water that feeds a 1 in pipe. The pipe goes straight down from the middle of a 25 square meter box. (1 high x 5 wide x 5 deep) At the end of of the pipe, a valve is attached. The valve is opened instantly. So far I have worked out the velocity of the water as if there were no blockage. $v = (2gh)^{1/2}$ $v = 9.9 m/sec$ Does the presence of the blockage change the velocity of the system when it is removed? Diagram: ![5 meters high, 4 meters of pipe.](http://i.stack.imgur.com/Iv1Vj.jpg) Sorry for poor quality, in a hurry because of school


title: Is it necessary to use decay width calculated at the same order as the scattering process?

text: I would like to calculate higher order corrections to a process for which there is an intermediate resonance which subsequently decays into lighter states. I am confused about how to treat the width of the resonance. Is it correct to say that in order to preserve unitarity, the order at which the decay width of the resonance is calculated should match the order of the process I'd like to calculate? So an LO cross section requires LO decay width, etc.


title: What is the purpose of the factor $N/L$ in the magnetic field of a solenoid?

text: I am supposed to find the expression of the magnetic field on the axis of a solenoid of radius $a$, length $L$, and with $N$ the number of turns. So in order to find $dB$ (to integrate over dx), I was expecting something like this : $dB = \dfrac{\mu_0 I a^2}{2 r^3} dx$, where $r$ is the length between a random point A and the turn considered, but it turns out in the solution that the expression is something like : $dB = \dfrac{\mu_0 I a^2}{2 r^3}\cdot \dfrac{N}{L} dx$ And I really don't understand what is this $\frac{N}{L}$ factor doing here :/


title: Is there a finite frequency of physical interactions?

text: If particles use gauge bosons to convey information about various forces then is there something like a finite "refresh rate" at which they update information about themselves?


title: Do I need the exact velocity when experimenting with sliding coins?

text: I'm doing a home experiment but it's not going very well. I'm pushing coins on a table. I'm taking the time for how long it takes coin A to hit coin B and then I divide it by the time between them to find the velocity of coin A. I say that the velocity times the mass of coin A should equal the velocity of coin B times its mass plus the velocity of coin A times it's mass (after). My calculation isn't making any sense. Is this experiment not possible with friction on the table? Do I need the exact velocity when it hits?


title: could we obtain the potential (in one dimension) from the Gutzwiller trace?

text: to solve and obtain the potential of a 1-D Hamiltonian we must solve an integral equation $$ N(E)= A \int_{0}^{E}\frac{V^{-1}(x)}{\sqrt{E-x}}$$ fro a some constant 'A' , then my question is since the approximated espectral fucntion $$ N(E)= <N(E)>\+ \sum_{p.p.o}A_{p}e^{\frac{iS(E)}{\hbar}}+c.c $$ with $ <N(E)>$ meaning the WKB approximation (smooth) to the spectra staircase and p.p.o means summation over the periodic orbits with $ S(E)= \sqrt{2m} l_{p.o}$ the action over the closed orbits , then can i from the Gutzwiller trace formula recover the potential ? this is my ansatz http://vixra.org/pdf/1301.0078v3.pdf which i think is valid at least for one dimension


title: WKB expression for Dirac equation?

text: given the one dimensional Schroedinger equation $$ - \frac{\hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}\Psi(x)+ V(x) \Psi(x) =E_{n}\Psi (x) $$ the WKB method for the energies is $$ (n+1)2\pi \hbar =\int_{a}^{b}\sqrt{E_{n}-V(x)}dx$$ with 'a' and 'b' being turning points my question is what is the WKB aproximation for the Dirac equation in one or two dimension $$ \left(\beta mc^2 + \sum_{k = 1}^3 \alpha_k p_k \, c\right) \psi (\mathbf{x},t)+V(x)\Psi(x,t) = i \hbar \frac{\partial\psi(\mathbf{x},t) }{\partial t} $$


title: If time slows down when you move faster, does this give you an "effective speed" different from your proper speed?

text: Suppose you're travelling at 0.9c toward the sun, and you tag past the Earth and start a clock. Would Lorentz contraction/time dilation cause you to get to the sun faster than (about) 9 minutes (measured in your own reference frame)? If so, does this allow us to create a measure of "effective Newtonian speed" by dividing the distance you would have travelled without Lorentz contraction by the time it took you to reach the Sun from the earth? If not, why, and is there any thought experiment that demonstrates this? (I know that it would take 9 minutes from the point of view of somebody actually _at_ the Sun.) * * * A little research on Wikipedia about "faster-than-light travel" reveals what what I'm talking about is known as four velocity.


title: How to add magnitude data in an ENU coordiante system

text: I have water velocity data taken in an ENU (East, North, UP) or XYZ coordinate system. The data is contained in 3 columns like this:               E   N   U     1   3   .1     2   5   .2     2   6   .1     -1  4   .1     -2  4   .1      So the first column represents velocity (in m/s) in the East (or X) direction (negative numbers represent velocity in the West (or -X) direction. The second column indicates velocity in the North (or Y) direction. And the 3rd column represents velocity in the Up (or Z direction). The data is scalar, but I'm assuming I want to end up with speed and directional data. For ease of understanding, if I were to just consider 2 dimensional data (ignore the Z or up data), is it acceptable to add the E and N data to get useful magnitude and directional data? For example if in the last row East is -2 and North is 4. So I've got 2 m/s West and 4 m/s North. But does the number 2 (-2 + 4) mean anything? Or do I need to use $a^2 +b^2= c^2 = 4 +16= 20 \rightarrow \sqrt{20}= 4.47$ But If I were to do this, then I loose the - sign (West direction) information, and it would not have mattered if the data was originally West (-2) or East (2). In the end, I'm looking to get useable data on current speed. But I'm not even sure if the end result of this kind of data should be (A) magnitude + direction (ie 2m/s at 20 degrees) or just (B) a single number that is only a combined magnitude with no reference to direction(ie 2m/s). I know for my calculations I do need an absolute magnitude that would represent current speed (option B) but am not sure how to calculate this.


title: Computing with qubits

text: We have a qubit in the state $|\psi \rangle= √3/2 |0\rangle + 1/2 |1\rangle$, which we want to measure in the $cos \theta\ |\theta\rangle + sin \theta |1\rangle, sin \theta |\theta\rangle - cos θ |1\rangle$ basis. In order for the two possible outcomes to be equiprobable, what should be the value of $\theta$ in degrees?


title: Newton's law of cooling: changing temperature of environment

text: > _A metal ball having temperature of $80^\circ C$ is placed into $m$ grams of > water at $0^\circ C$. After ten minutes, it was found that the temperature > of ball and water are $60^\circ C$ and $20^\circ C$ respectively. After that > the ball (at $60^\circ C$) is placed into another $m$ grams of water at > $0^\circ C$. Find the temperature after $10$ minutes._ I tried approaching this by Modification of Newton's Law of Cooling with two initial conditions, I was able to eliminate the constants of integration I am not being able to eliminate the heat transfer coefficient with latter two initial conditions, I am not being able to (Mathematica returns no solution). How do I determinate the temperature after $10$ minutes? Is it not possible to eliminate coefficient of heat transfer with initial conditions?


title: Do multiple permanent magnets aggregated together approach the same strength as a single magnet of the same size?

text: Here's an applied physics question. ;) If I buy some cube or sphere magnets like these, can I aggregate them together to create a stronger magnet (almost as strong as a single magnet)?


title: Voltage and resistance in series connection

text: In a series connection with n elements it is true that (voltage): $$V = V_1 + V_2 + ... +V_n$$ and (resistance): $$R = R_1 + R_2 + ... +R_n$$ If I know one of these I can infer the other. But is it possible to prove any of them without the other?


title: Convergance of a system to Boltzmann distribution

text: Consider a system with finite-dimension state X and energy E(X), with dynamics which follow the Langevin equation $\frac{dX}{dt}=-\nabla_X{E(X)}+\eta(t)$ where $\eta$ is white noise $<\eta_i(t)\eta_j(s)>=2T\delta(t,s)\delta_{ij}$. I'm interested in the conditions under which it is safe to assume the distribution of the system states will converge to Boltzmann distribution $P(X)=\frac{1}{Z}e^{-E(X)/T}$. I'm aware only of the need to assume that the energy is bounded, but I would like to know if there is some systematic analysis on the conditions under which the Boltzmann distribution is a good description of such system. Thank you! EDITED: removed the need for high-dimension of X


title: How do I find work done by friction over a curve represented by a polynomial?

text: I am facing a problem in Physics. Problem: What will be the work done by the frictional force over a polynomial curve if a body is sliding on this polynomial($a+bx+cx^2+dx^3+\ldots$) curve from rest from the height $h_1$ to height $h_2$ (where $h_1 > h_2$). I tried to solve this as follows: frictional force $F = k mg \cos\theta$, where $mg \cos\theta$ is normal force at that point. $k$ is coefficient of friction Total work done=Line Integration over the polynomial(dot product of F and displacement). But to go ahead from this point,i do not know.


title: Why does a point charge generate an electric field and why is an electric field represented by this formula?

text: Why does a point charge generate an electric field and why is an electric field represented by this formula $$E ~=~ \frac{q}{4 \pi \epsilon r^2},$$ where $\epsilon$ is permittivity of free space and $r$ is the distance from point charge $q$? Can this equation somehow be mathematically derived?


title: Is it possible to find out the distance traveled by a car if the force applied on it is given?

text: Say you have car which produces $F$ amount of force which is transferred to the wheels directly. Now assuming that there is air friction which is causing a retarding force proportional to the velocity of the car. I need to calculate the distance that is traveled by the car at any particular instance of time. What I have done so far - $$x = \frac{(F\cdot t - m\cdot v)}{u}$$ where: $x$ - distance traveled, $F$ - Force supplied to the wheels, $m$ - mass of the car, $v$ - velocity of the car, $t$ - time, $u$ - coefficient of air friction. As you can see unless i know the velocity of the car, I can not tell the distance that was traveled. Which proves that we can never determine the distance traveled by the car if we only know the force applied by the engine.


title: Redirecting light beams from beam splitters

text: I'm doing a project where I am taking a laser beam and sending it through a beam splitter. As I understand, approximately 50% of the light will go pass through and 50% will be reflected. So this means that half of the total energy of the beam will go one way, and the other half will go the other. The intensity must be halved right? I want to be able to keep on dividing it so that I keep getting twice the amount of laser beams that I have before that are 1/2 the intensity. I want to intersect all the laser beams together at a single point like a gamma knife. I want to demonstrate the gamma knife idea with the aid of some medium, and show that a point of light will be where the intersection is. My question is, will a point of light be present? Will I be successful in doing this? http://en.wikipedia.org/wiki/Radiosurgery What arrangement of mirrors will allow for me to direct all the beams to an intersection point? Is it possible to use one beam splitter and lots of mirrors to repeatedly send it through the same beam splitter so that I won't have to buy multiple beams splitters? Of course I want to use the least amount of mirrors and beam splitters to save money... Can you guys help me think of the arrangement of mirrors to achieve this?


title: Limit on space-time dimension from susy

text: I read an argument saying that it would be impossible to write down a super- symmetric theory in more than 11 dimensions, this limit coming from the dimension of the Clifford algebra that goes as $2^{\frac{N}{2}}$ or $2^{\frac{N-1}{2}}$ for $N$ even or odd, respectively. I haven't studied a lot of susy and I don't see how it wouldn't be possible to create a super-symmetric multiplet in higher dimensions as long as we add enough scalar fields (${\cal{N}} =1$ in my example) to match the fermionic degrees of freedom.


title: What is the 'apparent horizon' of a black hole?

text: The Wikipedia article is full of general relativistic and differential geometry jargon, and its accuracy is questionable. So, without such (or explaining said jargon without more jargon), what is the 'apparent horizon' of a black hole?


title: Riddle: can you swim faster upstream than downstream (with respect to the water)?

text: A friend of mine posed a riddle to me: A man swims upstream in a river, which is flowing at an unknown rate. He is wearing swimming goggles. At a certain point he loses his goggles. 10 minutes later he realizes he lost them, so he immediately turns around and swims back downstream to get them. When he finds his goggles, floating in the water, he finds himself at a point 500 meters downstream from the point where he lost his goggles (with respect to the ground, of course, not the water). Question: At what speed (km/h) is the river flowing?                \-------------- SPOILER -------------   My solution is one and a half kilometres per hour, but another friend does not agree with me, he says swimming upstream is more efficient (with respect to the water) than swimming downstream. Is he correct? If so, why?


title: Does the moon affect the Earth's climate?

text: So, this morning I was talking to a friend about astronomical observations, and he told me that lately there has only been good weather when there was a full moon in the sky, which was a shame. I jokingly said: 'maybe there's a correlation!', but then I started thinking: wait, if the moon can affect the oceans, why shouldn't it also make an impact on the atmosphere, which is just another fluid. So... are there atmospheric tides? Does the moon affect the weather or the climate in a significant way?


title: Does electric charge affect space time fabric?

text: I am confused with this question. Does electric charge affect the space time fabric? If so, why? Also if electric charge does not affect the space time fabric, how can we interpret the origin of the electric field around a charge?


title: Collision between 2d circle and flat surface

text: First of all I want to preface this post by saying that I am absolutely terrible at maths, my level of geometry equals being able to discern a circle from a rectangle but that's about it, as for trigonometry I know nil. I'm making a Pong game, and I have coded everything but the collision logic and also of course calculation of ball velocity and trajectory based on the angle of the ball. The problem right now is that I just don't know how to proceed now, I realize that I have to do some kind of trigonometry to modify the angle of the ball upon impact, but it would be great if someone could point me in a more specific direction because trigonometry is a pretty big and vast field.. Also keeping in mind that my math skills are.. Quite basic..


title: The definition of Gauge Fluctuation

text: What is the definition of Gauge Fluctuation? For example, in Z2 lattice gauge theory. Thanks.


title: Is the historical method of teaching physics a "legitimate, sure and fruitful method of preparing a student to receive a physical hypothesis"?

text: The French physicist, historian, and philosopher of physics, Pierre Duhem, wrote: > The legitimate, sure and fruitful method of preparing a student to receive a > physical hypothesis is the _historical method._ To retrace the > transformations through which the empirical matter accrued while the > theoretical form was first sketched; to describe the long collaboration by > means of which common sense and deductive logic analyzed this matter and > modeled that form until one was exactly adapted to the other: that is the > best way, surely even _the only way,_ to give to those studying physics a > correct and clear view of the very complex and living organization of this > science [emphasis added] (Duhem, P.: 1905/1954, ‘ _The Aim and Structure of > Physical Theory’, _Princeton University Press, Princeton, NJ, p. 268). Ernst Mach also advocated the history and philosophy of science (HPS) teaching method: > A person who has read and understand the Greek and Roman authors has _felt_ > and _experienced_ more than one who is restricted to the impression of the > present. He sees how men, placed in different circumstances, judge quiet > differently of the same things from what we do today. His own judgments will > be rendered thus more independent (Mach, E.: 1886/1986, ‘On instruction the > Classics and the Sciences’, In: ‘ _Popular Scientific Lectures’,_ Open Court > Publishing Company, La Sale, IL., p. 347). Igal Galili, author of "Experts’ Views on Using History and Philosophy of Science in the Practice of Physics Instruction," wrote to me that the historical method "presents a great controversy in university physics textbooks of physics."      Arnold B. Arons, in his _Teaching Introductory Physics_, opposes the HPS teaching method; he thinks something "goes wrong if you suspend judgment (page I-229) in order to retrace historical footsteps."      Why is this? Do you agree or disagree? **Is the historical method a "legitimate, sure and fruitful method of preparing a student to receive a physical hypothesis"?**      Thanks in advance for any insight on this


title: Why does heterodyne laser Doppler vibrometry require a modulating frequency shift?

text: On the wikipedia article (and other texts such as Optical Inspections of Microsystems) for laser Doppler vibrometry, it states that a modulating frequency must be added such that the detector can measure the interference signal with frequency $f_b + f_d$. Why couldn't you remove the modulating frequency $f_b$ and interfere the two beams with frequencies $f_0$ and $f_0+f_d$ to produce a signal with frequency $f_d$ at the detector? I haven't been able to find any reasoning on the subject. My first idea was that the Doppler frequency might fall inside the laser's spectral linewidth and thus not be resolvable, but for a stabilized low-power CW laser (linewidth on the order of KHz) and a typical $f_d$ in the tens of MHz range I don't see this being an issue.


title: In what sense is SUSY a spacetime symmetry?

text: Clearly the SUSY anti-commutation relations involve momentum, and thus the generator of translations in spacetime: $\\{ Q_\alpha, \bar{Q}_{\dot{\beta}} \\} = 2 (\sigma^\mu)_{\alpha \dot{\beta}} P_\mu $ So I would say that naively SUSY has 'something to do with spacetime' since the any idiot can simply see the $ P_\mu $ in the above as I just have. But at a deeper level is there a relation between, say, the $Q$ and $\bar{Q}$ and spacetime? Alternatively, without writing down the above relation, how can we see that SUSY has something to do with spacetime? Thanks.


title: What does AdS/CFT have to say about quantum gravity in our world?

text: The Ads side of the AdS/CFT correspondence is a model of quantum gravity in 5 dimensional antidesitter space. What can it say about quantum gravity in our 4-spacetime dimensions? Or is it just a toy model to better our understanding of quantum gravity as a whole?


title: Work done against a resistive force

text: My past year exam paper had a question about work done against the resistive force, where the answer key said it was resistive force * distance. As I understand it, work done is a measure of impact a force has on an object, but why is the resistive force, which is in the opposite direction of the direction of motion used?


title: Angular momentum and gyro effect on twin wheels

text: Suppose there are two twin wheels fixed on a vertical rod (z-axis, _with a handlebar, like a bike_ ) by an horizontal spinning axle (x-axis) so that the rotation plane is in the y-axis. The wheels are connected in some way so that setting one spinning will make the other spin in the opposite direction. Suppose the wheels are spinning: their angular momenta are exactly the same, but point in opposite directions. If we rotate the handlebar to the left ( _or the right_ ) the wheels will try to precess in opposite directions, therefore they will mutually cancel out. But, if we tilt the handlebar (and the rod) out of the vertical to the right/left, what happens? Both the wheels will oppose the change in the rotation plan ( _for opposite reasons but they will oppose it_ ). I would say that the stabilizing gyro effect will be doubled because it takes no work to change the direction of a gyro if and **only if** it is allowed to precess: when you prevent precession the gyro offers a strong resistance. Edit: I do not know if the fact that the wheels are side by side on the x-axis )and not above each other, on the z-axis) changes the conclusion they reached here or if those answers are wrong altogether, but in the example I have described there should be some resistance anyway (if not exactly double). Can you give a detailed description of what happens here?


title: In what sense can an object in outer space be "on fire"?

text: The famous "Tears in rain" soliloquy in _Blade Runner_ goes like this: > I've... seen things you people wouldn't believe... [contemptuous laugh] > Attack ships on fire off the shoulder of Orion. I watched c-beams glitter in > the dark near the Tannhäuser Gate. All those... moments... will be lost in > time, like [small cough] tears... in... rain. Time... to die... In what sense can attack ships be "on fire" in space? I would think that lack of oxygen would externally-visible keep combustion as we know it on Earth from going on more than momentarily, but perhaps I'm wrong. Or maybe there's some other phenomenon we would describe as "on fire." Could some sort of a nuclear reaction be described as "on fire"?


title: Galaxy velocity curve

text: When deriving the relation between velocity of a star and its distance $r$ from the center of the galaxy, one assumes that the masses outside $r$ have no contribution and those inside $r$ give a force the same as if they were all at the center, similar to the shell theorem. My question is, the shell theorem holds for spherically symmetric distribution. Why we can use it for galaxies, which are disks?


title: Grounded conducting sphere inside uniform electric field

text: The problem of a grounded conducting sphere inside a uniform $E$ field in the $z$ direction can be solved by imagining the field be produced by a pair of charges $Q$ and $-Q$ put on the $z$ axis, taking the limit that the charges are very very far away, $Q\rightarrow\infty$, and using the image method. Under this limit, the field produce by $Q$ and $-Q$ will be uniform in the vicinity of the sphere. My question is, why we need two charges? A single charge $Q$ can also produce a uniform $E$ field under the same limit.


title: How was the Michael Jackson hologram accomplished?

text: There have been a few presentations now in which a live stage performance was simulated by what was described as a hologram. The most recent example of this was the Michael Jackson "appearance". How are these done? The classic hologram I am familiar with uses only one wavelength of laser light and constructs an interference pattern on a photographic plate, where it is recorded. When the same light source illuminates the developed plate, the interference pattern effectively reconstitutes the original light paths to reproduce the effect of looking through a window (the plate) to view the original object as if it was illuminated in monochromatic light (that of the laser). The stage presentations obviously differ in that they are in full colour, and they are moving in real time... not to mention the overall physical size. So, what's different about the way these presentations are prepared and executed that allows them to render in such a life-size and life-like manner? Are they truly holograms? Do they employ the same principles of physics as a "classic" hologram? Are they actually something entirely different and only incorrectly labelled as holograms?


title: Vibrations at Absolute Zero

text: Is matter still vibrating at absolute zero temperature? If it isn't, wouldn't we then be able to know both its position and momentum?


title: Why do we see the sun's light color different from the moon's light color?

text: Why do we see the color of the sun's light as red or orange, while we see the moon's light as white, although it's reflected from the sun?


title: ED-XRF Detector Operation

text: ED-XRF detector operates by detecting the photons that hit it's semiconductor surface and measure the energy of the fluorescent photons by measuring the current that was generated by photon. The value of the current is proportional to the energy of the photon which is defined by an atom that has generated this fluorescent photon. What I don't understand is, how does detector knows whether it was hit by a single photon with energy of, lets say, 2 keV or by two photons with energies of 1 keV each that has arrived simultaneously and resulted in the same total current. The energy values of the photons are purely hypothetical. I know that detectors have some maximum counts/second values, but two simultaneous photons must be a common occurrence. So my question is, how can ED-XRF detector distinguish between one photon and multiple photons hitting its surface simultaneously.


title: Could airport security devices detect differences between printed and written documents?

text: If airport security scanners of any kind (xray, thermal, whatever else they use) looked at two items:   * A printed paper textbook   * The same printed paper textbook into which we have inserted a regular folded US letter-sized paper with something written on it with a pencil, pen, marker, etc. Could the security be able to detect the difference between the two?


title: Integrals over grassmann numbers

text: I want to prove an identity from Peskin&Schroeder, namely that $$\left(\prod\limits_i^{} \int d \theta^*_i d\theta_i\right) \theta_m^* \theta_l \exp(\theta_j^* B_{jk} \theta_k)=\det(B) B^{-1}_{ml}$$ $B$ is a hermiteam $N\times N$ matrix and $N$ should be even. $\theta_j$ and $\theta_j^*$ are $N$ complex grassmann numbers. I would like to do it similar to the case of complex and not grassmann gaussian integrals, where you artificially introduce a term in the exponential and then differentiate. I could prove, that $$\left(\prod\limits_i^{} \int d \theta^*_i d\theta_i\right)\exp(\theta_j^* B_{jk} \theta_k+\eta_j^* \theta_j+\theta_j^*\eta_j)=\det(B)\exp(-\eta_j^*B_{jk}^{-1}\eta_k)$$ where $\eta$ and $\theta$ are (complex) grassmann numbers.If they were just complex variables, the rest would be clear. I could get the first equation differentiating the second with respect to $\eta_m$ and $\eta_l^*$ and then let $\eta=\eta^*=0$. The problem is, that for a grassman number the exponential is $e^\theta=1+\theta$ since all higher order terms cancel. For a sum like we have here, there should also be terms of second order, but nevertheless the exponential is not reproduced by differentiation. Can I nevertheless obtain the wished result in that way? It looks quite promising, I just don't see, how to come from the second equation (left side) to the first equation (left side). It should work with differentiating, but I don't see why.


title: Charging using a CRT TV set

text: I was doing an experiment with my CRT TV where I put aluminum foil on the screen wire it to a can and open the TV and a ring between 2 can will swing if I ground the other can. http://scitoys.com/scitoys/scitoys/electro/electro4.html#franklin Anyway I tried something out, I used the same way to charge a metal sphere while the tv was on, the sphere was charged and everything seemed to be alright only when removed the wire (connecting the sphere and the foil) from the foil on the TV the sphere lost its charge, why is that? If the charge just decayed, is that normal to decay so fast (in less than a minute) while it is not grounded?


title: How an-isotropic magneto resistance(AMR) changes as film thickness increases?

text: As the film thickness increases, an-isotropic magneto resistance(AMR) changes in the presence of external magnetic field because of spin orbit interaction. But i don't know how it is responsible for change in AMR from starting to the end of film growth. I know this question is a bit stupid but neither my teacher nor the textbook are very helpful, and I would really appreciate any help. Many thanks!


title: What is the amplifying medium in a laser diode?

text: I know it seems like a trivial question, but I can't seem to find the answer anywhere. So - what is the amplifying medium in a laser diode? Meaning: In a classical laser resonator, there a substance (like HeNe gas) which undergoes a population inversion to allow lasing. Every source I've read describes how a laser diode produces photons via recombination, and has metallic walls to allow photons to bounce back and forth inside the cavity, but no mention of an amplifying medium.


title: What determines the direction of precession of a gyroscope?

text: I understand how torque mathematically causes a change to the direction of angular momentum, thus precessing the gyroscope. However, the direction, either clockwise or counterclockwise, of this precession seems to me a bit arbitrary beyond mathematical definitions. (What if torque were defined by a "left hand rule", for example?). What's the fundamental physical reason that the precession of a gyroscope would be directed in a certain direction? Related question.


title: The speed of light also applies for 'distance' materials?

text: The question is hard for me to put into one sentence so please try to completely read the example: If I had a stick that is 1000KM long and I would push it forward with 1 millimeter in lets say... 10ms(I have completely no idea how long it would take)but let's say I was about to turn on a switch that is 1000KM + 1 millimeter away from me, how long would it take for me to see the light that is next to the switch to turn on? Basically the answer would be a calculation based on the distance the light needs to travel in order for it to reach me + that one millisecond. But I cannot understand that that calculation does not consider anything about the stick being pushed, if the stick was 1 meter and I would perform the same action the calculation would be the same, resulting in the fact that the stick can have any length no matter how far it would still turn on that light as fast as it would if it was 1 meter long or 1000KM long. Something in my logic way of thinking is telling me that the stick must be slowed down based on the speed of light. If you can provide an answer to the next example I would fully understand this paradox: If I have a stick that is 1000KM long and pushing it forward just a little would cause the light in my tower to turn on, 1000KM further away someone is waiting on my push and has the end of the stick placed on the switch of hes light tower. What would the someone see happening if I push that stick ? There are 3 answers possible:   1. He(the someone, the 2nd person) will see hes light turn on and then the other.   2. He would see both lights turn on simontaniously. (my answer, considering the speed of light delay on the moving stick)   3. He would see the other light turn on 1st and than his. (very unlikely) The the answer I need is either 1 or 2. I do not understand why it would be 1 but I would love to accept it, in order to accept it I need someone to explain to me why 1 is the answer. Thank you so much for reading my question and/or leaving a comment or answer ! Diede.


title: Power Spectral Density of constant speed data in a car

text: I recently calculated the PSD of the vibration data in a car at constant speed. I would like to know what this means and what if I calculate PSD of the vibration data in a car for the total journey with varying speeds? What do both PSDs signify?


title: Why we don't see long range airborne CO2 lasers?

text: I wonder, why http://en.wikipedia.org/wiki/Boeing_YAL-1 is not CO2 one? Are the issues with air transparency at 10um? Or it's impossible to focus on large distances due to diffraction?


title: Why didn't Newton have a cosmological constant

text: Einstein initially added the Cosmological Constant because (if I get this right) it seemed to him that the universe should be static. I agree that back then this would have been an obvious assumption. I'm curious now, before Hubble, where there any opinions/debates about whether the universe would be expanding or contracting? Kind regards, Thomas


title: Applicability of Baxter's method for IRF models

text: In a interaction-round-a-face model of $n^2$ particles in a lattice, a weight $W(a,b,c,d)$ is assigned to each face in the lattice based on the spins $a,b,c,d$ (listed say from the bottom-left corner in counter-clockwise fashion) of the particles at the corners of the face. Based on this, a partition function is formed $Z=\sum\prod W(a,b,c,d)$, where the the sum is over all possible spins of all particles and the product is over all the faces in the lattice. The well-known text _Exactly Solved Models in Statistical Mechanics_ by Baxter shows how to obtain exact solutions for $Z$ in a couple cases, like the six-vertex model and the eight-vertex model, using "commuting transfer matrices." In reading Baxter's book, I am uncertain of the applicability of this method. For instance, I am working on a particular application where particles in a square lattice can have either up spin (+1) or down spin (-1) and the weight of any face $W(a,b,c,d)=1$ unless all four spins around the face alternate, in which case $W(1,-1,1,-1)=W(-1,1,-1,1)=4$. (The boundary condition here is that the all the spins on the boundary must be up.) Does anyone know if the commuting-transfer-matrix method (or any other method) should yield an exact solution for this particular weighting of the spins? More generally, should the commuting-transfer-matrix method yield exact solutions for _any_ weighting of the spins (even in the two-spin case)?


title: Giant string in space

text: I saw an interview with Ed Witten, where he said one way to confirm string- theory is to observe a giant string floating in space, left over from the Big- Bang. How does one observe such a string, does it have thickness? Is this string any different then the strings that (hypothetically) make up elementary particles? What is required to produce such a large string, why is this string so much bigger then others? What happends if one tries to interact with this string, can one stretch/cut it etc? Can we have a stable mega-string on earth, and can it be used for anything?


title: How to approach this kind of task about kinetic energy?

text: The bullet with mass $$m_{ball}=0.2 kg$$ travels with speed $$v=2 \frac{m}{s}$$ and hits Plasticine sphere with mass $$m_{sphere}=2.5 kg$$ and get stuck. I need to find the amount of heat ejected. How to approach this task? Probably it's about kinetic energy transforming to heat; and the law of conservation of momentum.


title: Would warp bubbles emit gravitational Cerenkov radiation in general relativity?

text: Inspired by the gravtiomagnetic analogy, I would expect that just as a charged tachyon would emit normal (electromagetic) Cerenkov radiation, any mass- carrying warp drive would emit gravitational Cerenkov radiation. The gravitomagnetic approximation may well break down near the mass, but "sufficiently far" from it, this would still be valid. Is that correct? Specifically, let's suppose there is a moving closed surface S, such that on and outside S the gravitomagnetic equations are approximately valid (no assumptions about interior), such that it moves with a velocity greater than $c$, and such that it "carries mass", in the sense that the closed surface intergral of the gravitational field strength around S is negative (net inward gravitational field). In general relativity, is this situation even possible? If so, would it emit gravitational radiation? If so, how fast would it lose energy (mass)? I am motivated by the recent media hype around the Alcubierre metric. Nevertheless, it is a general question applying to any proposed "moving warp bubble" solution of general relativity. (As opposed to, say, a pair of "stargates", or a "warp corridor", or whatever -- if a mass $M$ travels through a stargate, it might be that the gate through which it enters could get heavier by $M$, and the gate through which it leaves could get lighter by $M$. Then this particular question wouldn't arise.)


title: Refractive Index formula for denser to rarer medium

text: I learnt that the formula for refractive index when light travels from rarer to denser medium is **(sin i / sin r)** where i = angle of incidence r = angle of refraction Is the same formula used for calculating refractive index when light travels from denser to rarer medium ?? or is it, **(sin r /sin i)**


title: Has the use of the holographic principle of string theory in condensed matter physics silenced the skeptics?

text: It seems to me that the use of string theory in calculations of strongly- interacting matter in condensed matter physics is an example of the theory being on the right track. And then there's the application of string theory to black holes. Have these quieted the skeptics? If not, what's the deal? Could a theory be used in making accurate calculations and still be wrong? Aren't the odds of that happening rather small?


title: Where does electricity go from a solar panel that is not plugged in to anything?

text: I found a similar question here on this site, but my question is slightly different. If a solar panel is exposed to sunlight but is not plugged in to anything--dc load, inverter, etc--where does that electricity go? In this example, I'm assuming the solar exposure is still freeing electrons, but where do they go? Thanks!


title: Temperature as frequency spectrum of stress-energy tensor?

text: I am currently learning general relativity, and in the textbooks that I am reading, temperature seems to be treated as a scalar field, extraneous to the geometry of spacetime. This is puzzling me, because I would naively believe that purely geometric data, namely the stress-energy tensor, should be enough to determine temperature, from the following consideration: In cold matter, nearby particles are moving at low speeds relative to each other, and thus the stress-energy tensor must vary "slowly" across that matter, i.e. it must be "low-frequency"; in hot matter, nearby particles are moving at higher speeds relative to each other, which means that four-momentum varies significantly from one particle to the next, i.e. the stress-energy tensor must vary "quickly" across that distribution of matter, i.e. it must be "high-frequency". So it occurred to me that perhaps temperature might be just a crude measure of how "high-frequency" the stress-energy tensor field is, across a small region of spacetime around a given event? Note that this wouldn't contradict statements about how no "new" scalar field can constructed from spacetime geometry, because these statements are about purely local constructions (e.g. contract the Ricci curvature tensor at each point to define scalar curvature), and the construction that I am talking about here is not purely local, as one needs to perform frequency analysis of the stress-energy tensor over a small region of spacetime to define how "high- frequency" it is. Accordingly, temperature is not purely local, since in a region of spacetime small enough to contain only one particle, temperature should be undefined (correct?). Could anyone here either point out the first mistake in my reasoning here, or mention some literature that I should read on this topic? In particular, I don't really know precisely how to make sense of "the frequency spectrum of the stress-energy tensor over a region of spacetime", or even what kind of mathematical object that would be, and would be very interested to read any text clarifying that. My other question, then, would be: if temperature is just a crude measure of how high frequencies some kind of spectrum of the stress-energy tensor contains, then there must exist situations where talking of temperature as a scalar is inappropriate, and one has to account for a "superposition of temperatures"? I suppose that the implicit approximation usually made is to account only for the highest frequency in the stress-energy spectrum as temperature, but surely if there is another, slightly lower frequency with a sufficiently higher amplitude there, it should be able to have significant temperature-like effects to forbid ignoring it as a temperature?


title: What keeps a gas giant from falling in on itself?

text: There is not enough gravity at the center to start nuclear fusion, but it seems that there would be plenty enough to collapse the planet.


title: What is the physical property of metal nanoparticles?

text: I am a Math student but now I have to deal with gold nanoparticles in aqueous solution. Now I was wondering whether the physical properties of gold nanoparticles are the same as the properties of gold itself(whereby I mean a huge amount of gold) or do they rather behave like single gold atoms? Further I was wondering about the following: If gold particles are swimming around in aqueous solution: What sort of forces do we have or to be more precise: What is the most important term in the interaction betweeen gold(nanoparticle)-water, water-water(i guess this is dipole-dipole and H-bonding) and gold(nanoparticle)-gold(nanoparticle)?


title: What is the concept behind ...?

text: Could someone kindly explain the concept behind this statement " Vector A is perpendicular to both Vector B and Vector C. So Vector A is parallel to VectorB x Vector C " Is there any rule like if a vector is perpendicular to two other vectors, then it is parallel to their products?


title: Compatibility of effects implies compatibility of POVM's?

text: Let $A = \\{A_1 ,\ldots , A_n\\}$ and $B = \\{B_1 \ldots , B_n\\}$ be two POVM's. Suppose every pair $(A_1, B_1)$ is jointly measurable as a couple of effects. Does this imply the joint-measurability of $A$ and $B$?


title: Varying vibration frequencies

text: Im currently testing vibrations through materials. I have a vibration motor that runs 200hz. Problem; the pressure I apply to the motor change the frequencies I pick up. Why? Example: If I use a clamp to attach the motor to whatever Im testing, i measure 200hz. If I use manual pressure, the force I apply heavily influence the measured frequency. It was my understanding that a change in pressure would only influence the measured energy/amplitude of the signal, not lowering the frequency. Especially when testing softer materials or composites of materials. Sometimes I get measures that are 1/3 of input frequency. Any ideas?


title: Electric Field in Conductor Zero?

text: My textbook claims that the electric field in a conductor is zero in a static condition, as otherwise, a current would flow. But what if I go infinitely close to a proton; there will be an electric field right? Is my idea wrong or is the textbook flawed?


1. What is the force between two magnetic dipoles?   2. If I have two current loops parallel to each other with currents $I_1$ and $I_2$ and radii $R_1$ and $R_2$ a distance $z$ from each other, what is the force between them?   3. What would change if they were two solenoids instead of current loops?   4. Would the same hold if it was two magnets?    5. Or a magnet and a solenoid?


title: What would the spectral distribution of a greenbody look like?

text: Suppose you had a body that behaved like a blackbody for all wavelengths except some range that we would call "green". For those wavelengths it reflects all radiation incident upon it. Am I just talking about anything that has the color green, or would such an object be somehow more exotic? When heated, how would its spectral distribution compare to that of a blackbody?