title: Why is this not a violation of parity invarance for EM

text: I read that Wu's experiment illustrates that parity violation is possible for weak processes. In that experiment, when Co-60 undergoes beta decay, the emitted electrons come out opposite to the direction of nuclear spin. The mirror image process does not occur. I also read that parity is conserved for EM and strong processes. But consider the following from EM. Say I have a positively-charged particle moving to the right, and the magnetic field is into the page. Then force on the particle is up (i.e. the particle is accelerated upwards initially). And here, the mirror image also does not occur! The mirror image (the mirror I am thinking of lies in the plane that cuts your head between the eyes) would be moving left, magnetic field into page, acceleration still pwards - but EM would predict that the acceleration is supposed to be downwards!! Why isn't this an example of parity violation?


title: How to calculate net power output of heated, expanding air?

text: I'm interested in designing and building a Stirling engine which uses air that has been heated, which expands and then acts upon a piston producing power. There is a fixed amount of air inside the sealed 2" cylinder, and a relatively stable heat supply. The piston compresses cool air and is powered by the expanding, heated air. Two questions here:   1. How to find the power needed to compress air inside the 2" diameter cylinder to different depths?   2. Depending on the amount of compression produced by the piston, how does that affect the rate of expansion of the heated air? If the power needed to compress the air to a certain pressure exceeds the net power output of the expanding air, then the engine won't function. So, I need to calculate the stroke of the piston inside the cylinder to a depth that the engine can use efficiently. Thanks.


title: Doppler broadening: time scale to frequency scale

text: ![enter image description here](http://i.stack.imgur.com/h8s8B.png) Consider a cell containing Rubidium and enlight it with a laser. Connect the system with an oscilloscope and give a triangular wave as input (so you can know when the Rubidium is resonant). This is the signal that you see downward. You can see the output in the upper signal. It is given by the difference between input signal and the signal received by the photodiode... Looking at the spectral line relative to D2 rubidium transition, the oscilloscope gives me this picture. I need a pragmatic hint. I have to measure the Doppler broadening so I need to convert time scale to frequency scale. How can I do that? Thanks a lot!


title: How to convert physical ligth quantities (frequency, intencity, spectrum) to RGB and back?

text: Suppose I would like to have maximally physical image format. Which quantities should I store in the pixel? Obviously, it should be frequency spectrum, i.e. table with frequency vs. WHAT? How to convert RGB values to any sort of physical quantities and vise versa?


title: electromagnetic waves accelerating reference frame

text: A charge is at rest in an inertial reference frame. Consider this situation from the point of view of an observer who is accelerating relative to the charge. Would the observer observe electromagnetic waves generated by the charge?


title: Is there Phase difference between voltages at end points of a long AC Power line

text: I found this explanation somewhere: Since wavelength=c/freq so in a AC power line of 50 Hz, wavelength=(3*10^8)/50 = 6000 Km, so voltage phase reverses after 6000 Km in a ac Power line. Now this would have been correct if it was a 50 Hz E.M. Transmission line, but does the same occur in metal wire with A.C. ? Clearly the power transmission through the wire would not be through E.M. waves. I am also confused if a wave phenomenon does occur in a AC wire or not. If it occurs then how (in terms of flow of electrons) and at what speed/wavelength ?


title: Energy stored in a capacitor in an RC circuit

text: Suppose we have a capacitor of capacitance $C$ and a cell of emf $E$, why is the maximum energy stored in a capacitor equal to $\tfrac{1}{2}CE^2$? I feel confused because, the potential difference against the capacitor will be less than the emf of the cell because of the potential drop across the resistor. What is the flaw in my thinking?


title: Pauli matrices product identity

text: How to prove the identity $$ \tilde {\sigma}_{\alpha}\sigma_{\beta}\tilde {\sigma}_{\gamma} = g_{\alpha \beta}\tilde {\sigma}_{\gamma} + g_{\alpha \gamma}\tilde {\sigma}_{\beta} - g_{\beta \gamma} \tilde {\sigma}_{\alpha} + i\varepsilon_{\alpha \beta \gamma \delta}\tilde {\sigma}^{\delta}, \qquad (1) $$ where $$ \sigma_{\alpha} = (\hat {\mathbf E}, \sigma ), \quad \tilde {\sigma}_{\beta} = (\hat {\mathbf E}, -\sigma ), \quad \varepsilon_{\alpha \beta \gamma \delta } = -\varepsilon_{\beta \alpha \gamma \delta} = ..., \quad \varepsilon_{0123} = 1, \quad g_{\alpha \beta} = diag(1, -1, -1, -1)? $$ I tried to do this by constructing the relation $$ \sigma_{\alpha}\tilde {\sigma}_{\beta} = g_{\alpha \beta}\sigma_{0} + i\varepsilon_{0\alpha \beta \gamma}\sigma^{\gamma} - \delta^{0}_{\alpha}(\delta^{0}_{\beta}\sigma_{0} - \tilde {\sigma}_{\beta}) - \delta^{0}_{\beta}(\delta^{0}_{\alpha}\sigma_{0} - \sigma_{\alpha}), $$ where first summand corresponds to $\alpha = \beta$, the second - to $\alpha , \beta \neq 0$, the third - to $\alpha = 0, \beta \neq 0$, the last - to $\beta = 0, \alpha \neq 0$, and $\sigma^{\mu} = g^{\mu \nu}\sigma_{\nu}$. But I can't get the answer in a compact form of $(1)$ by using my construction. In particular, I don't understand how $\varepsilon_{\alpha \beta \gamma \delta}$ is appeared in the final answer. An edit. I proved it, but the proof is terrible.


title: Hamiltonian with position spin coupling

text: I am solving a Hamiltonian including a term $(x\cdot S)^2$. The Hamiltonian is like this form: \begin{equation} H=L\cdot S+(x\cdot S)^2 \end{equation} where $L$ is angular momentum operator and $S$ is spin operator. The eigenvalue for $L^2$ and $S^2$ are $l(l+1)$ and $s(s+1)$. If the Hamiltonian only has the first term, it is just spin orbital coupling and it is easy to solve. The total $J=L+S$, $L^2$ and $S^2$ are quantum number. However, when we consider the second term position and spin coupling $(x\cdot S)^2$, it becomes much harder. The total $J$ is still a quantum number. We have $[(x\cdot S)^2, J]=0$. However, $[(x\cdot S)^2,L^2]≠0$, $L$ is not a quantum number anymore. Anybody have ideas on how to solve this Hamiltonian?


title: Why is the surface of Venus so hot?

text: Whenever I have seen Venus described, its high surface temperature is attributed to an intense greenhouse effect. This seems to make sense, as its atmosphere is roughly 96% CO2. But on Earth, the greenhouse effect works because the atmosphere is (mostly) transparent to sunlight, but (somewhat) opaque to longer wavelength light radiated back from the surface. The atmosphere of Venus would be very opaque to longer wavelength light from the surface, just like Earth (at least around the CO2 absorption bands). But isn't Venus also very cloudy and largely opaque to visible light? If the solar radiation that reaches the surface is limited, wouldn't this also limit the ability of the CO2 to "trap" heat? The atmospheric pressure at the surface of Venus is much higher than it is at the surface of Earth. Isn't this a more straight-forward explanation for much of the high temperature?


title: Self-adjoint differential operators

text: I'm having a hard time understanding the deal with self-adjoint differential opertors  used to solve a set of two coupled 2nd order PDEs. The thing is, that the solution of the PDEs becomes numerically unstable and I've heared that this is due to the fact, that the used operators were not self-adjoint and the energy is not preserved in this case. The two coupled 2nd order PDEs are: $$\frac{\partial ^2p}{\partial t^2}=V_{px}^2 {H_2} p + \alpha V_{pz}^2 {H_1} q + V_{sz}^2{H_1}(p - \alpha q) + S\tag{1}$$ $$\frac{\partial ^2q}{\partial t^2}=\frac{V_{pn}^2}{\alpha}{H_2} p + V_{pz}^2 {H_1} q - V_{sz}^2{H_2} \left(\frac{1}{\alpha}p - q \right) + S\tag{2}$$ where p is the pressure wave field and q is an auxiliary wave field, $S$ is the Source term $V_{px}$ and $V_{sz}$ are seismic velocities into the x - or z-direction respectively, $\alpha = 1$ and $H_1$ and $H_2$ are the rotated differential operators: \begin{eqnarray} {H_1}& =& \sin ^2 \theta \cos ^2 \phi \frac{\partial ^2}{\partial x ^2}+\sin ^2 \theta \sin ^2 \phi \frac{\partial ^2}{\partial y ^2} + \cos ^2 \theta \frac{\partial ^2}{\partial z ^2}+\\\ &&\sin ^2 \theta \sin 2 \phi \frac{\partial ^2}{\partial x \partial z} + \sin 2 \theta \sin \phi \frac{\partial ^2}{\partial x \partial y}+ \sin 2 \theta \cos \phi \frac{\partial ^2}{\partial x \partial y}\end{eqnarray} $$ {H_2} = \frac{\partial ^2}{\partial x ^2}+\frac{\partial ^2}{\partial y ^2}+\frac{\partial ^2}{\partial z ^2} - {H_1}. $$ where $\phi$ is an azimuth angle and $\theta$ is a tilt angle. In this case I am solving for the solution of a pressure wavefield. **EDIT** Is there a physical explanation for self-adjoint operators? The paper I am referring to can be found here were equation 14 and 15 resemble my postet equations.


title: Hohmann transfer orbit questions

text: So, I have a couple questions about transfer orbits. As I understand it, an object's, say a satellite, orbit is basically tied to it velocity relative to the object, the planet, that it is orbiting. The basic premise is that you have the satellite in a circular orbit of X radius, going speed v. Now, if the satellite decelerates, it reduces its velocity. Since the new velocity is not enough to maintain its original orbit, the satellite will "fall" towards the planet. Now, even though the satellite was (say) originally at the proper velocity for the new lower orbit due to the deceleration, by the time it actually arrives at the new orbit, its velocity likely changed, due to the different acceleration vector of the planet, the vector causing the actual fall. Even if it was at the proper velocity, it's actual vector would like be wrong, it would no longer be tangential to the planet, it would likely be steeper. This would effectively cause the satellite to fall right through the lower orbit and keep accelerating toward the planet. Minimally it would not be in the stable orbit desired. So, this is why there is a second acceleration/deceleration necessary to correct the satellites velocity and perhaps it vector once it reaches the new orbit. Of course, the opposite all applies if trying to get to a higher orbit. My question is during the initial deceleration, is that simply applied opposite the current orbital velocity vector? And when the satellite arrives at the new orbit, what direction is the correctional acceleration/deceleration made? Is it the difference of the desired tangential direction that it wants to go and the current direction it is going? or simply opposite its current vector? I understand that the point of the Hohmann transfer orbits is to use as little velocity change (and thus fuel) as possible, but can an orbital transfer be faster or slower if you're willing to burn more fuel to affect the velocity change? Will a slower satellite "fall faster" than a faster one? Intuitively that makes sense to me, but at the same time there's the concept that no matter how fast the bullet, it hits the ground at the same time, it just travels farther. So I'm not sure. On the other hand, if you apply more thrust and you're trying to lift to a higher orbit, that seems directly related to the amount of thrust you're willing to use. Is this how the transfer orbits work? There's the math and formulas to calculate the delta v necessary on both ends of the transfer, but I'm just trying to visualize the process. Finally, if you had unlimited fuel, and time was more a consideration, would you even bother with this process versus something more "point and shoot, turn and burn"?


title: Direction of Time on Event Horizon

text: Does the axis of Time point into a black hole or away from? Can you give a reference paper?


title: So what is happening in this angular kinematics equation?

text: > The wheel of a car has a radius of 20 cm. It initially rotates at 120 rpm. > In the next minute it makes 90 revolutions. What is the angular > acceleration? So the answer is solved by using one of the angular kinematic equations. More specifically delta theta. The problem I am having trouble understanding is the answer which probably stems from my poor fundamentals. The answer is: (90x2pi) = 4pi(60) + 1/2 (alpha) (60)^2 So where does 90x2pi come from?


title: What is the observable Earth we can see?

text: Yes I know we can see the whole earth, but how far can we see left to right waving out the limitations of sight. Because it's impossible to see the whole earth right? because it's spherical? So is there some kind of equation to work this out?


title: Which laws of physics apply when creating a soap blaster with pressurized air?

text: I want to create a soap blaster using:   1. a 1" hose with 8 bar compressed air   2. a non pressured container of soap and water mix   3. **without** the use a pressurized tank I.e. something like this sand blaster: ![enter image description here](http://i.stack.imgur.com/khJu3.jpg) where the sand is picked up from the vacuum of the air flow. The question is really which laws of physics apply in this creation and how can I calculate the dimensions for my soap blaster with the maximum allowed pickup of soap mixture at the lowest noise level?


title: What is the invariant associated with the symmetry of boosts?

text: Noether's Theorem states that if a Lagrangian is symmetric for a certain transformation, this leads to an invariant: Symmetry of translation gives momentum conservation, Symmetry of time gives Energy conservation etc. The Galilean principle stating that all reference frames that move with constant speed relative to each other are equivalent is also a symmetry principle: Setting up a physical system that is identical to the original except for a constant velocity (boost) added will have the same behaviour. Shouldn't there be an invariant associated with this symmetry? If yes, what is that invariant?


title: Noether's charge due to lorentz transformation

text: > **Possible Duplicate:**   >  What conservation law corresponds to Lorentz boosts? For a relativistic free particle, What is the Noether charge generated due to Lorentz transformations? What is conserved quantity associated with boosts?


title: Resistance and current

text: I'm not a current student at any school, but I am learning a new profession, and some of it is a basic understanding of elecrticity. I have some knowledge, but definitely not enough, and I have had to self teach most of what I know using old textbooks that I have found added to some military experience in ths subject. anyways I'm trying to teach myself how to calculate current through resistors, but I'm having trouble setting up and working through word problems. I know this may seem simple to most people on here, and I apologize for that, but sucking at something is the first step at being sorta good at something. Examples A 242Ω resistor is in parallel with a 180Ω resistor, and a 240Ω resistor is in series with the combination. A current of 22mA flows through the 242Ω resistor. The current through the 180Ω resistor is ___ _mA. Two 24Ω resistors are in parallel, and a 43Ω resistor is in series with the combination. When 78V is applied to the three resistors, the voltage drop across the 24Ω resistor is___volts.


title: Pair production of neutrinos

text: I learned that neutrinos have a much lower energy than electrons. Pair production of electrons occurs when the photon energy is above 2 times the energy of an electron. So I am wondering if pair production of neutrinos wouldn't be even more common and occur at much lower energy levels?


title: Double Slit Problem, Waves and Optics

text: Given d(slit separation)= $0.158\:\rm{mm}$, $\lambda _{red}= 665\:\rm{nm}$, $\lambda _{g/y}= 565nm$, L(distance from screen)= $2.24\:\rm{m}$ What is the distance between the third order red and green/yellow fringes? I am using the equation $X _{3}= \frac{m \lambda L}{d}$ (just to find the distance to the third red fringe). My teacher told me this equation is approximate, but I think this is beyond simple approximation error... I keep getting the answer $2.8284 \times 10^{7}\:\rm{m}$. This seems unreasonable; what am I doing wrong? $\:\rm{m} = \:\rm{mm}\times10^{-13}, \:\rm{m}= \:\rm{nm}\times10^{-9}$, right?


title: How much time does it takes an electron to tunnel through a barrier?

text: I know that in quantum mechanics there is no "time operator", so such a question is ill-posed. Anyway if the tunneling is instantaneous, this would imply an information transmission faster than $c$. On the other hand, how could someone define such a "time"?


title: Observing the exponential growth of Hilbert space?

text: One of the weirdest things about quantum mechanics (QM) is the exponential growth of the dimensions of Hilbert space with increasing number of particles. This was already discussed by Born and Schrodinger but here's a recent reference: http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4770v2.pdf and another one: http://www.scottaaronson.com/papers/are.pdf Another difference between quantum mechanics and classical physics is that QM is discrete.   A good example is the line spectrum of hydrogen. Is there any good observational example which demonstrates the exponential growth of Hilbert space dimensions?   Even for low numbers?   (Does it perhaps show up in the line spectrum of a three or four valent atom?)


title: Electric potential and maximum charge on a conductor

text: Does increasing the amount of electric charge on a conductor cause an increase in its _electric potential_ to a point at which it becomes maximum; where it can hold no more extra charge? Is it true? How? I read it from a book while studying _capacitance_. Does this idea sound _foolish_?


title: Sign convention with the $AdS$ metric

text: One would say that $AdS_n$ satisfies the equations for the scalar curvature (R) and Ricci tensor ($R_{\mu \nu}$), $R = - \frac{n(n-1)}{L^2}$ and $R_{ab} = - \frac{n-1}{L^2}g_{ab}$.   * But do the signs in the above depend on the sign of the metric convention?  * * * I am confused when I look at these two metrics,   * $ds_1^2 = \frac{r^2}{Q^2}dt^2 - \frac{Q^2}{r^2}dr^2$   * $ds_2^2 = \left ( 1 - \frac{\Lambda r^2}{3} \right ) dt^2 - \frac{ dr^2 } { \left ( 1 - \frac{\Lambda r^2}{3} \right ) }$ Are both the above valid metrics of $AdS_2$? (with what sign of $\Lambda$?) For the first one has, $R = 2/Q^2$ and $R_{ab} = \frac{1}{Q^2}g_{ab}$ For the second one has $R = - \frac{2\Lambda}{3}$ and $R_{ab} = -\frac{\Lambda}{3}g_{ab}$ Now I am not sure how to consistently define $L>0$ for these two metrics using the same formula for both!


title: What's the conserved quantities correspond to the generator of conformal transformation

text: What's the conserved quantity corresponding to the generator of conformal transformations?


title: How to do Legendre transformations on a S=S(U,V) P,V,T system?

text: **Problem** : For a $P,V,T$ system with constant mass,entropy can be considered a function of $U,V$, i.e. $S=S(U,V)$. The goal is to derive the rest of the thermodynamic functions via Legendre transformations. **Attempted answer** : I start with the 1st law of thermodynamics $dU = TdS - PdV$, which I solve for $dS$: \begin{equation}dS=(1/T)dU+(P/T)dV\end{equation} Let, $Y\equiv S,C_1\equiv 1/T,X_1\equiv U, C_2\equiv P/T, X_2\equiv V$. The first Legendre transformation and the associated differential are: \begin{equation}\widetilde{T1} = Y - C_1 X_1 = S - (1/T)U\end{equation} \begin{equation}d\widetilde{T1} = dS - (1/T)dU + (1/T^2)UdT = (P/T)dV +(U/T^2)dT\end{equation} Therefore $\widetilde{T1} = \widetilde{T1}(V,T)$. Does this seem correct to you ?   1. Do I stop here for $\widetilde{T_1}$ or is there more to do?   2. What are the natural variables for $\widetilde{T_1}$? I am a little concerned due to the fact that $T$ is intensive variable and if I recollect correctly, the natural variables are always extensive.


title: Why is there a gap in porkchop plots?

text: On a porkchop plot for a given departure date (X axis), why are there two local energy minimums along the arrival date (Y-axis) for a transfer between Earth and Mars? The Hohmann transfer orbit seems to have one optimal solution, but the plot's two minimums seem fairly distinct in time but similar in energy; 15.0 to 15.5 and 15.5 to 16.0 in terms of C3L (something I only vaguely understand; KSP mostly deals in delta-V) ![Earth to Mars porkchop plot](http://i.stack.imgur.com/rer1W.png) A NASA page about sending spacecraft to Mars refers to "Type 1" and "Type 2" transfer orbits, which clashes with a perhaps simple view that there should be a singular optimal Hohmann transfer orbit; the smallest ellipse tangent to two orbits. Granted, the planets' orbits are not perfectly circular, but the different transit times (red contours) for local minimums differ by almost a factor of two! (about 200 days and about 400 days) I'm not sure if I'm reading the plot correctly though, as there is a disconnect between the given Earth- Mars plot, and the prose on the page as well, which talks about 7 month (~200 day) or 10 month (~300 day) transfers.


I think I remember a talk where a professor said that Vesta is a particularly important asteroid because its gravity is strong enough to perturb other asteroids. In spite of Vesta's size, this effect might be so strong that some smaller asteroids might be kicked out of their orbits - making their way to Jupiter, or to the inner solar system. Can Vesta dominate the orbits of other asteroids? All related to the one question, there are particular points I'm interested in:   * if so, how often, presumably?   * is there a preferred direction (inwards / outwards)?    * has the perturbation rate been constant over geologic timescales?   * do the "victims" stay in the plane of the ecliptic?    * did someone model such processes? I currently think the whole process is chaotic - essentially unpredictable.


When trying to find the Fourier transform of the Coulomb potential $$V(\mathbf{r})=-\frac{e^2}{r}$$ one is faced with the problem that the resulting integral is divergent. Usually, it is then argued to introduce a screening factor $e^{-\mu r}$ and take the limit $\lim_{\mu \to 0}$ at the end of the calculation. This always seemed somewhat ad hoc to me, and I would like to know what the mathematical justification for this procedure is. I could imagine the answer to be along the lines of: well, the Coulomb potential doesn't have a _proper_ FT, but it has a _weak_ FT defined like this … Edit: Let me try another formulation: What would a mathematician (being unaware of any physical meanings) do when asked to find the Fourier transform of the Coulomb potential?


title: Exact diagonalization to resolve ground state degeneracies

text: I am studying a perturbed Toric Code model that is not analytically solvable. On a torus the ground state degeneracy of the unperturbed model is 4. Once we turn on the perturbation there is a change in the ground state degeneracy. I would like to detect this change in ground state degeneracy numerically using exact diagonalization techniques. On my computer I have stored the action of the Hamiltonian on a set of basis states. So if you give me some state $\left|\psi\right\rangle$ I can give you $\hat{H}\left|\psi\right\rangle$ in terms of the basis states. Now I used this information to compute the spectrum using the Lanczos algorithm and the Jacobi-Davidson algorithm. While the spectrum itself is correctly reproduced neither of these algorithms reproduces the degeneracy of the ground state correctly - not even in the unperturbed case. Hence the following question: What are common exact diagonalization algorithms for this type of many-body system that correctly resolve the degeneracy of the ground state? I am looking forward to your responses!


title: Internal Inspection other than X-ray

text: I'm looking for the contactless methods to collect the information of the body construction especially skeletal structure to calculate in the computer model . Are there physical methods to inspect internal side of the body other than X-ray and no any exposure of radiation ? For example, echo , MRI and so on .


title: Why is the Heisenberg Uncertainty Principle not obvious give the conservation of mass- energy?

text: A photons energy is given by $E=h *f$ and momentum $p=E/c$ (spin?) but the photon has no (rest) mass! Therefore it is the ultimate probing tool for looking at any mass position and velocity because mass transfer is not involved only momentum.But to calculate/ measure the particles exact position by scattering a photon from the mass into a detector dictates some of the photons momentum has been transferred to the mass i.e. the mass has to move (is disturbed from it initial position by some delta). This is intuitively obvious ;I would like to see how Heisenberg quantified(proved) this uncertainty hopefully without referring to an ansatz wave function.


title: Know altitude and speed of an object in orbit, with true anomaly

text: I'm quite stuck with this problem. I know that I have an object in orbit. I know the eccentricity of that orbit, as well as the semi-major axis of the orbit. Giving a true anomaly, how do I find the speed and altitude of that object? The true anomaly is the angle between the line made with the focus of the ellipse and the position of the object. Thank you! P.S. I'm more looking for a general help, more than a specific answer. That's why I didn't give any numbers.


title: T-Duality between Type HE String theory and Type HO string theory

text: My question is regarding T-Duality between the 2 Type H string theories. I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so $$\operatorname{T}:{{\cal P}}_{{\mathop{\rm GSO}\nolimits} }^ - \leftrightarrow {{\cal P}}_{{\mathop{\rm GSO}\nolimits} }^ + $$ Since the Type IIB String theory employs the same GSO Projections on the left and right movers while Since the Type IIA String theory employs the different GSO Projections on the left and right movers, the 2 theories are T-Dual to each other. However, when one considers T-Dualities on the Type HE string theory and the Type HO String theories, why are they T-Dual to each other? I presume that maybe T-Duality switches $\operatorname{Spin}(32)/\mathbb Z^2$ and $E(8)\times E(8)$, so therefore, the theories to T-Dual to each other. But if so, then why? Why does T-Duality switch $\operatorname{Spin}(32)/\mathbb Z^2$ and $E(8)\times E(8)$? Thanks in advance.


title: What is a correct and simple definition of quantum physics?

text: Is it correct to define Quantum Physics as the study of Physics in sub-atomic scale? Does Quantum Physics studies something else other than sub-atomic phenomena? This may be a very stupid question but realize that I am **!!!VERY NOOB!!!** at Physics.


title: Is the cooling rate of a (very) cold object, sitting next to an AC higher or lower?

text: In more detail: If i have two soda cans, both are cooled to exactly 4 degrees celsius, And i put one in a 25 degrees room, and the other next to an AC vent set to 16 degrees. After three minutes, which one should be colder than the other and why? Edit: To clarify - if I have a cold soda can, should I place it near the AC vent or not (if I like my drink cold)? Which location will cause faster heating?


title: Does (it make sense to say that ) the universe has a center?

text: I was reading this page: http://www.guardian.co.uk/science/2011/oct/23/brian-cox-jeff-forshaw-answers and I found this sentence by Brian Cox: > That seems to imply that everything is flying away from us and we're > therefore somehow in a privileged position; that isn't true. The way it's > often described is if you imagine some bread with raisins in it that you're > baking in the oven and as you heat it, it expands. On any particular raisin, > if you look, you can see all the other raisins receding from it. So it's > space that stretching, it's not that everything's flying away. I already heard this raisins analogy, but it never persuaded me: I understand that the "big bang" is more like a "big stretch", and I see how every 2 observers in the universe are being distanced farther and farther away (regardless of their position) Yet one of the Big Bang ideas is that the universe isn't anymore considered infinite and completely homogeneous But the fact that the universe is finite, while inflating to me implicates that it should have some kind of bounds (not that we can reach these "bounds", since our distance to them is getting bigger, but they should still exist) (And the fact that it's spreading inhomogeneous mass and energy over big distances, is thus making it more homogeneous, but this doesn't probably matter) So: the very idea of a big bang seems to me in contradiction to the assertion that there's no such thing as a "center of the universe": If it has a finite mass and some kind of bounds, then it should also have a barycenter. And if we consider the bread with raisins analogy: the bread has a center from which it's expanding Surely, the universe isn't homogeneous (like the distribution of the raisins), and so, in its hypothetical center, there may not be actually anything... but I think (even if it's really unlikely) it should still be theoretically possible to have a raisin in the exact centre of the bread


title: How to derive "Anti-Lagrangian" $L_4$ and $L_5$ points

text: In this paper on co-orbital dynamics the authors discover, numerically, "Anti- Lagrangian" solutions to the restricted 3 body problem. These Anti-Lagrange $L_4$ and $L_5$ points are 120 degrees ahead and behind the planet (if I understand correctly). It is possible, as Lagrange demonstrated, to prove that the usual $L_4$ and $L_5$ points are stable solutions to the restricted circular 3 body problem. But how can you prove that these new-fangled Anti-Lagrangian $L_4$ and $L_5$ points are stable solutions? The method used by Lagrange will not result in such a proof.


title: What happens to temperature when pressure is constant in a cylindrical piston of saturated liquid ammonia?

text: Let's say I have a cylindrical piston containing saturated liquid ammonia that is fitted with an electrical heater and a paddle wheel for stirring at an initial pressure and an initial temperature. When the gas expands, some of it evaporates to form a two phase, liquid-vapor solution inside the system. By the way, this process occurs at a constant pressure. My real question is, what happens to the temperature as the pressure is constant and the volume increases, also causing the specific volume to increase. I would assume the temperature increases, but when I look at the steam table, there is only one temperature corresponding to the pressure. For example, if the initial temperature is 20C, the initial pressure is 8.57bar. If that pressure is constant so the final pressure is 8.57bar, the steam table still says the temperature is 20C. Why is this? Because I was just looking at the ideal gas equation and it essentially says temperature increases as volume increases. But can I use this intuition with the ideal gas law when the system is 2 phase?


title: Lagrangian density of an interacting real scalar field theory

text: Srednicki writes the Lagrangian density of an interacting scalar field theory as $$ \mathcal{L} = -\frac{1}{2} Z_\phi \partial^\mu \phi \partial_\mu \phi -\frac{1}{2} Z_m m^2 \phi^2 + \frac{1}{6} Z_g g \phi^3 + Y\phi $$ He claims that $Y=O(g)$ and $Z_i=1+O(g^2)$. What is the basis of this claim? Why do we ignore the $Y_0$ in the expansion of $Y(g)$: $$Y(g) = Y_0 + Y_1 g + Y_2 g^2 + \cdots \cdots $$ and again why do we take the $Z_0 = 1$ in the expansion of $Z_i(g)$: $$Z(g) = Z_0 + Z_1 g + Z_2 g^2 + \cdots \cdots $$ Why $Z_1 = 0$ ? Are there any references where $\phi^3$ diagrammatics is explained clearly?


title: How does one measure space-like geodesics? Or: What is the physical interpretation of space-like geodesics?

text: In general relativity, time-like geodesics are the trajectories of free- falling test particles, parametrized by proper time. Thus, they are easy to interpret in physical terms and are easy to measure (at least in principle). Is there a similar interpretation/measurement for space-like geodesics? For example, how do I measure the shortest path between two space-like separated points? What is the interpretation of such a path (apart from it being a geodesic)? My first guess is that the answer will involve a static picture (with no change in time), e.g. how elastic springs stretch between two fixed points. The problem with this picture is that the curves the springs bend along depend on the stiffness of the spring. (I believe one gets a geodesic when the stiffness is infinite, but this is no effect one would be able to measure for everyday gravitational fields.) **Addition:** As VM9 pointed out below, I should fix something like a space (a space-like hypersurface) before talking about the geodesic distance. So, let me define space-like geodesic for my purpose as follows, which will be a local notion: Take an observer, which simply shall be a time-like vector $u$ at an event $P$ of space-time $M$. Let $V$ be the orthogonal complement of $u$ (a three-dimensional space of space-like directions at $P$). Let $\Sigma$ be the image of a small neighborhood of $0$ in $V$ under the exponential mapping (that is the set of events that are connected to $P$ by small geodesics that are orthogonal to $u$ at $P$). It is that space-like submanifold my observer is interested in. How can one physically measure lengthes in $\Sigma$? While every measurement process takes time as VM9 pointed out as well, let's assume that time flies rather slowly ($c \to \infty$) so that one could work, for example, in Gaussian coordinates (synchronous coordinates) with respect to $\Sigma$.


title: Finding possible values of $L_x$ given $L^2$

text: Here's a homework problem I'm working on. I am not asking for the answer, but any guidance or comments on the approach are appreciated. > Given that a measurement of $L^2$ for a free particle has resulted in the > value $6\hbar^2$, what are the possible results for a measurement of $L_x$? I've been following the approach given on pp. 378-380 in Liboff (4th ed.). I've made it as far as expressing the eigenfunctions of $L_x$ as sums of the eigenfunctions of $L^2$... Here's what I've got: $$\begin{align*} X_1 &= \frac{1}{2}\left(|2,2\rangle - |2,1\rangle + |2,-1\rangle - |2,-2\rangle\right)\\\ X_2 = -X1 &= -\frac{1}{2}\left(|2,2\rangle - |2,1\rangle + |2,-1\rangle - |2,-2\rangle\right)\\\ X_3 &= \frac{1}{2}\left(\sqrt{\frac{3}{2}}|2,2\rangle - |2,0\rangle + \sqrt{\frac{3}{2}}|2,-2\rangle\right)\\\ X_4 = -X3 &= -\frac{1}{2}\left(\sqrt{\frac{3}{2}}|2,2\rangle - |2,0\rangle + \sqrt{\frac{3}{2}}|2,-2\rangle\right)\\\ X_5 &= \frac{1}{2}(|2,2\rangle + |2,1\rangle - |2,-1\rangle - |2,-2\rangle)\\\ X_6 = -X_5 &= -\frac{1}{2}\left(|2,2\rangle + |2,1\rangle - |2,-1\rangle - |2,-2\rangle\right) \end{align*}$$ The next step appears to be to express $L^2$ as sums of the eigenfunctions of $L_x$, which does not seem possible. It was a lot of algebra, matrices, determinants, etc. to get to this point so it is certainly possible that I've miscalculated something accidentally, but does anyone see anything fundamentally wrong here with this approach? And/or is there a simpler way?


title: How efficient is a desktop computer?

text: As I understand it (and admittedly it's a weak grasp), a computer processes information irreversibly (AND gates, for example), and therefore has some minimum entropy increase associated with its computations. The true entropy increase is much greater, and comes from the conversion of electrical energy to heat. How efficient is a typical desktop computer when viewed in this light? Make any assumptions you find useful about the energy use, computations per second, temperature of the room, etc.


title: How does one measure the frequency of a laser?

text: I am taking a short introduction course on lasers. I never knew that the frequency of a laser is so high for a given wavelength (e.g. 780nm). I am wondering how people can measure the frequency of the laser. Do they downconvert the frequency of the light so that we could measure it with scope?


title: Mathematically possible vs physically probable outcomes

text: A good buddy of mine and I have had a friendly debate about the origins of the current state of our universe (namely; Earth and life on Earth) and have fundamentally disagreed in our stances with respect to probabability, infinity in time and space and possible/probable event outcomes. He maintains the position that given a set of possibilities and enough trials, each outcome _must_ have occured; which is his reasoning for why life must exist. I do not necessarily take issue with this particular concept, as given an infinite amount of time and states of matter life is bound to come from one of those states. In our discussions, however, we have been using a specific example in which I disagree vehemently with his stance. The example: > If you throw a handfull of sand in the air an infinite number of times, and > that sand lands on a flat surface, every configuration _will_ happen > (according to his position). For instance, the sand landing in a pattern > which spells your name out is a mathematically possible outcome, and will > therefore happen given enough trials. To counter his stance on this example, I took the position that there is a mathematical (but not physical) possibility that every grain of sand lands in the same one inch square of the surface; but I maintain that even though it is a mathematically possible outcome it will never happen because of the way the physical world works - that sand will be roughly evenly distributed for each throw, even if over an infinite number of trials, assuming consistent and fair trials (ie, no God or other being moving grains of sand). I submit that even though it is a mathematical possibility, you'll never see your name spelled out in block letter English anywhere in the universe without the influence of intelligence, even if you were able to attempt a verification for this - he disagrees. I held him liable for mathematical/physical proof of reasoning for his stance and he has taken to dismissing me as ignorant of probability and infinity. Can anyone provide some good reasoning for either side of this argument? I realize that either is an impossible stance to prove, since we can't verify our positions, but any well-reasoned insight will be appreciated. A similar question, with an answer I found to be relatively useful: Infinite universe - Jumping to pointless conclusions **EDIT:** After reading some of the comments and answers here it has become apparent that I may have misrepresented my ultimate question. I realize that given a non-zero probability and an infinite number of trials, the mathematical probability of encountering the event described by said probability converges to 1. Some have taken the position that there is no disconnect between a mathematical probability and the likelihood (read: possibility) of a physical event happening. To simplify the argument, the surface can be thought of as a grid - in which case every single configuration has some mathematical probability associated with it. My stance regards certain configurations as physically impossible, however, which is the reasoning behind my one-inch-square analogy. Can anyone show clear reasoning (and sources!) for their belief that it is possible to toss a handful of sand into a one inch square?


title: Losing mass in space

text: So I came across a question while studying laws of motion. Roughly, this is how it goes: There are two astronauts in a space shuttle, who together have mass 200 kg. If by doing exercise, they manage to lose 80 kg, what will be the percentage increase in speed of the shuttle. The question is pretty straight forward, if thought about directly. However, my instant reaction was that by conservation of mass, the mass that the astronauts lose will still be contained within the space ship in the form of water, CO2, etc. So technically there won't be any change in mass, thus no change in speed. I would like to know if this assumption is correct and in what forms is the mass we lose released.


title: Does rotational energy have effect on gravity/metric?

text: Intuitively, if energy can be stored in rotational motion, it has to obey $E=mc^2$. Does rotation of typical stellar-sized objects - BHs, pulsars, binaries - have measurable effect on their overall gravity? (I'm not talking about nearby effects, like frame dragging described by Kerr metric, the effect on measurements from the Earth is of interest)


title: counting refractive index of a plano convex lens

text: suppose that, there is a plano convex lens and its thickness is 5.00cm. If you watch it straight from the convex side, it seems that its of 4.4 cm. What is the refractive index of this lens?


title: insufficient electrons in a conductor

text: We all know that if an electric field is applied across an isolated conductor, then charges are induced at either surface such that the net electric field inside becomes zero. Now if the applied electric field is so strong that there are not sufficient free electrons in the metal to move and cause the required surface charge seperation. Then will the conductor now behave as a non- conductor(i suppose so) or will it ionise nearby gas and extract electrons from it .


title: Why the electric field inside a conductor is zero?

text: In electromagnetism books, such as Griffiths or the like, when they talk about the properties of conductors in case of electrostatics they say that the electric field inside a conductor is zero.


title: In electrostatics, why the electric field inside a conductor is zero?

text: In electromagnetism books, such as Griffiths or the like, when they talk about the properties of conductors in case of electrostatics they say that the electric field inside a conductor is zero. I have 2 questions:   1. We know that conductors (metallic) have free electrons which randomly moves in all directions, so how come we can talk about electrostatics which by definition means stationary charges?   2. When the textbooks try to show why the electric field inside a conductor is zero they say let us put our conductor in an electric field. What happens then is that there will be an induced surface charge density which consequently induces an electric field within the conductor such that the total electric field within the conductor will be zero. That is perfectly understood, but my problem is the following: the original claim was that the electric field within a conductor is 0, not the electric field after putting the conductor in an external electric field it became zero. I do not understand the logic!


title: Including air resistance, what is the escape velocity from Earth?

text: Including air resistance, what is the escape velocity from the surface of the earth for a free-flying trajectile?


title: Can polarization effect the coherence length?

text: I'm taking an optics lab in which I'm required to construct an interferometer, and measure the wavelength of a laser, and the coherence length of the light emitted from a candle fire. Now, I've been hinted by my instructor that when working with mirrors (which are present in an interferometer), it is best to make sure that the laser is polarized to either "P" or "S" polarization - otherwise, the mirrors might give an elliptic component to the polarization, which in turn will spoil the measurment, due to interference effects. **So now comes the question: should the light from the candle be polarized as well??** I have a reason to suspect that polarizing it will improve the coherence length, and on the other hand, I'm pretty sure that elliptical polarization will take effect if the light remains untouched. What is your opinion on this dilemma?? Thanks!!


title: Pressure vs wind speed, on a rectangular surface

text: How do I go about finding the pressure exerted on a rectangular surface in a free flowing air stream? I wouldn't imagine that this is directly related to the airspeed / surface area, but have no idea where to start. Is there even an equation, or does one need to do some kind of FEA? For instance a 1.2m x 2.4m metal sheet suspended some distance above ground level, if I have a gust of wind at 8m/s (directly perpendicular to the sheet), what is the average pressure across the face of sheet?


title: Conservation of energy (or lack thereof) in Doppler cooling

text: I did not find my question answered elsewhere, so here it is. I'm doing a project in my first optics course, and we are reading a bit about Doppler cooling. I understand that a laser is tuned to a frequency where the photon energy $E_p = h \nu$ corresponds to an energy slightly below the energy $E_{abs}$ required to excite the gas atoms, and that an atom moving towards the laser at a high speed (relative to rest of the gas) will experience a blueshift that allows the atom to absorb the photon, thus slowing down the atom. I also understand that the photon is re-emitted in a random direction, which of course means that the atom's velocity in the direction of the laser will be decreased. What I'm not sure I understand is how the re-emission of the photon doesn't just bring the atom back to the same kinetic energy (but with a different direction of motion). I have not been able to find a source explaining this, but here's my own attempt at an explanation (which I am not sure is correct, which is why I am asking here): The absorbed photon has an energy (in the frame of the laboratory) of $E_1 = h \nu_1$ which is slightly less than the absorption energy $E_{abs}$. But after the absorption the atom's speed is reduced, thus the photon will be emitted with a different frequency $\nu_2$ (in the frame of the laboratory). Since the speed of the atom (relative to the frame of the laboratory) has been reduced by the absorption, the energy $E_2$ of the emitted photon will be closer to $E_{abs}$, thus $|E_{abs} - E_2| > |E_{abs} - E_1|$ (the last step of the explanation only works if the atom's speed perpendicular to the laser is not greater than the speed parallel to the laser for most atoms, but since the laser is tuned to only hit the fast moving atoms, this seems improbable enough to not invalidate the explanation). Is this explanation correct or have I made mistake? I have taken a special relativity course but no quantum mechanics yet, so please keep the quantum mechanics to a minimum if possible.


title: Probabilistic quantum cloning

text: I have a question with regard to probabilistic quantum cloning - see for example http://prl.aps.org/abstract/PRL/v80/i22/p4999_1. It does seems like I can use the proof for no-cloning theorem to disproof the existence of equation (7) in the paper quant-ph/9704020. Do you think this is true? Suppose probabilistic quantum cloning is actually possible, now according to the current papers, if the cloning process fails, the state that we intend to clone would be destroyed. Looking at the equation in the original paper, however, it does seem that a repair or a reverse operation might be possible in the event of a failure. More specifically, in the paper quant-ph/9704020, if I replace the $\left|\phi\right>$ state in Equation (7) with say, $\left|\psi_T\right>\left|0\right>$ where $\left|\psi_T\right>$ is a state orthogonal to the input state $\left|\psi\right>$, the proof would work just as fine. Do you think this is true? If this is true, a repair would be possible in case of cloning failure. The process would still be probabilistic, but I can repeat till it is successful. I do hope for some feedback from experts out there. Thanks!


title: Modeling of exact stick-slip-friction using Linear complementarity problems (LCP)

text: Within my master's thesis, I try to model a machine elements and have to model the exact slipping and exact sticking between the bodies. So I noticed that such problems can be formulated as a LCP. However I have difficulties at finding any literature where the usage is described well with examples.. I would like to have something like a 1-DOF model such a box on a plane pulled with a spring and friction modeled with coulomb or so. I would be very grateful of mentioning any literature/sites which can bring me further. I am really desperate at implementing the coulomb friction..


title: How to Analyze Applied Forces/Torques of System With Multiple Massless/Frictionless Pulleys of Different Radii

text: I have been reviewing the basics of mechanics in preparation of studying Spivak's text book on mechanics (I am from a more mathematical background and I am taking an advanced analytical mechanics course next quarter which is using this text). I recently came across a problem in a text different from the one that I am using (University Physics), and I was having difficulty understanding how to approach it, and indeed even understanding the details of the situation (the problem is stated with little detail). Unfortunately, my text does not seem to cover anything like it, in the exercises or otherwise. > _Imagine a flat surface inclined at 45 degrees. A 1500 kg block is placed on > the incline, and it is (according to the figure) attached directly to a > pulley of radius $r$. The pulley itself has a cable rolling over it which > extends along the incline with one end connected to the surface and the > other end connected to a larger pulley of radius $3r$, but at a point of > contact which is only $r$ from the center. Another block of unknown mass $m$ > is attached to the larger pulley at the edge ($3r$ from the center) and is > allowed to hang. We are asked to compute the mass $m$ of the hanging block > required to counteract the motion of the block of mass 1500 kg. (The > physical situation [I will try to update this with a picture as soon as I > can] is basically just like the traditional one pulley/two-block system on > an incline first encountered with problems involving Newton's laws; except > here there are two pulleys involved as described above)._ To be perfectly honest, I am really not at all sure what is going on in this problem. If we take the axis of rotation to be the center of the larger pulley, then it is clear the second block imparts a torque of $3rmg\sin\left(\frac{\pi}{4}\right)$ and a tension on the cable is just $mg$. It seems to be the block on the incline imparts no torque since its action is directed parallel to the radial coordinate of the axis (if we are taking the natural coordinate system with axes perpendicular and parallel to the axis of rotation). What is the significance of the smaller pulley to which the mass is attached?


title: Dalitz plot analysis

text: I have seen a few Dalitz plots so far and tried to understand how they are useful. So one of the advantages of these plot is that the non-uniformity in the plots can tell something about the intermediate states that we cannot detect. My question is how do you extract the mass of these resonant particles from such plots? What additional information would you need?


title: Active speakers picking up cellular tower waves?

text: Since a week or so a constant high pitch sound (~4khz) emanates from my active monitor speakers. After eliminating any ground or power source issues I noticed, that the sound rises in volume whenever I open my window - which is exactly between my speakers and an array of cellular antennas on the opposite building. I recall there were new antennas added a few weeks ago. Our public database shows that there are over 20 transmitters on there, with 3 pointing exactly in my direction. **Question** : Can HF-EMWs produce such a sound in an audio amplifier or through it's connectors (it's not the cables or whatever comes through them)?


title: Why FQHE need a lower energy state?

text: There are a lot papers explaining why Laughlin's wavefunction are energetically favorable, but seldom explain why a lower energy state could explain the plateau at $\nu=1/3$. I met at several places claims like: a lower energy state at $\nu=1/3$ will pin the electron density at $\nu=1/3$. But why is that? And what actually it means? when we move $\nu$ from $1/3$ what happens? electrons adjust there distance or new particle been added? And is this a phase transition? Hope someone familiar this field could give me some help, thanks!


title: Why does an airliner burn more fuel at lower altitudes?

text: At lower altitude an aeroplane usually has more lift. However an aeroplane flying at low altitudes (with gear/flaps up) at low velocity burns the same amount of fuel it would flying much faster at a higher altitude. Why?


title: Does the Pauli exclusion principle instantaneously affect distant electrons?

text: According to Brian Cox in his _A night with the Stars_ lecture$^1$, the Pauli exclusion principle means that no electron in the universe can have the same energy state as any other electron in the universe, and that if he does something to change the energy state of one group of electrons (rubbing a diamond to heat it up in his demo) then that must cause other electrons somewhere in the universe to change their energy states as the states of the electrons in the diamond change. But when does this change occur? Surely if the electrons are separated by a significant gap then the change cannot be instant because information can only travel at the speed of light. Wouldn't that mean that if you changed the energy state of one electron to be the same as another electron that was some distance away, then surely the two electrons would be in the same state until the information that one other electron is in the same state reaches the other electron. Or can information be transferred instantly from one place to another? If it can, then doesn't that mean it's not bound by the same laws as the rest of the universe? \-- $^1$: The Youtube link keeps breaking, so here is a search on Youtube for Brian Cox' _A Night with the Stars_ lecture.


title: How to debunk 'The Electric Universe'?

text: My father is a generally intelligent person, however he has latched onto a theory which I believe to be completely incorrect. He doesn't believe in gravity, but rather subscribes to an 'Electrical Theory of the Universe', see the website The Electric Universe. I've looked into it enough to realize that it flies completely in the face of current physics models, but I'm not qualified to debunk it. I know it's almost certainly incorrect - extraordinary claims requiring extraordinary evidence and all - but I can't demonstrate it. So my question is this: Are there any observable behaviors which are inconsistent with the theory's predictions, or are there any demonstrable disproofs for this theory? What evidence can I present against it? Edit: Sorry for the delay in this, but here's a link to a series of Youtube videos on the electrical theory of the universe (which seems to be the term used by it's proponents, alternatively called the plasma theory). 6-part Youtube video:   * Part 1   * Part 2   * Part 3   * Part 4   * Part 5   * Part 6


title: Why electric field has a major role in vision?

text: Although the electromagnetic wave is made op of both electric and magnetic fields the electric field contributes much in vision and is thus, called the light vector. But, why is it that the electric field has a major role?


title: what is a difference in the width of the spinning bar?

text: The bar with length l, density r, diametr d, Young's modulus E, Poisson's ratio mu, is spinning around the cross-section, what is the change in the width of this bar?


title: LHC Experiments for finding parallel universes?

text: I watched this video featuring Michio Kaku explaining parallel universes. In the last two minutes he said that experiments in the LHC could reveal that there might be parallel universes and then he stops. What experiment was he talking about? And how would that be possible?


title: Correction to Period of a Pendulum

text: In one derivation of the corrected period of a pendulum, we started off like so: The mass has a height $y$ given by $l(1-\cos \theta )$. $E = K + E \rightarrow \frac{1}{2}ml^2 \dot{\theta}^2 + mgl(1-\cos \theta)$ The next step introduces $\theta _0$, and I've got no idea where this came from. $$\frac{1}{2}ml^2 \dot{\theta}^2 + mgl(1-\cos \theta)= mgl(1-\cos \theta _0)$$ Now we just solve for $\dot{\theta}$ and solve the DE.W I'm interested in the theta side of the equation. $$\int \frac{d\theta}{\sqrt{\cos \theta - \cos \theta _0 }}$$ We go through a bunch of subs and changes of vairble to arrive at $$\int ^{2\pi} _0 \frac{du}{\sqrt{1-K^2 \sin ^2 u }}$$ So my two questions are   * Why are we involving two $\theta$ values? The text didn't make it clear why we needed an extra $\theta _0$. It appears that $mgl(1-\cos \theta _0)$ is the total energy of the system. Our total energy cannot surpass the initial gravitational potential energy, this is clear. My only thought as to what $\theta$ means is the instantaneous position of the angle.    * My text mentioned that this is an elliptical integral. Mathematically speaking, what _is_ an elliptical integral? Can this integral be solved exactly, or does it always require approximations from the expansion?


title: How realistic is the game "A slower speed of light"?

text: The game "A slower speed of light" from MIT claims to simulate effects of special relativity: > Visual effects of special relativity gradually become apparent to the > player, increasing the challenge of gameplay. These effects, rendered in > realtime to vertex accuracy, include the Doppler effect (red- and blue- > shifting of visible light, and the shifting of infrared and ultraviolet > light into the visible spectrum); the searchlight effect (increased > brightness in the direction of travel); time dilation (differences in the > perceived passage of time from the player and the outside world); Lorentz > transformation (warping of space at near-light speeds); and the runtime > effect (the ability to see objects as they were in the past, due to the > travel time of light). But does restricting the render engine to special relativity not miss out several effects that might happen close to the speed of light? Especially I'm thinking about effects related to inertia and acceleration/rotation of the observer. So are there any important effects missing which would make the game a even more realistic simulation of the movement close to the speed of light?


title: Will ideal gas law apply to plasma?

text: I have read that plasma is a state of matter that resembles gas but it consists of ions and electrons coexisting. So my question is : If plasma is just ionized gas, will ideal gas law apply for it ?


title: Spinors Under Spatial Reflection

text: ![enter image description here](http://i.stack.imgur.com/GkwGl.jpg) How eq(4.4) is a solution of eq(4.3)


title: Stern Gerlach experiment - only two discrete beams?

text: The Stern Gerlach experiment was meant to prove the orbital quantization of electrons where there should be +ml,0,-ml states. So for l=2, there should be 5 beams. But they saw 2 beams, which was shown to be due to the 2 states of spin. Now, because of the addition of the spin magnetic moment, shouldn't there be now 10 beams?(2 additional states for each the 5 orbital states). What happened to the orbital magnetic contribution?


title: Does a static electric field and the conservation of momentum give rise to a relationship between $E$, $t$, and some path $s$?

text: For a static electric field $E$ the conservation of energy gives rise to $$\oint E\cdot ds =0$$ Is there an analogous mathematical expression the conservation of momentum gives rise to?


title: The shape of the earth$\ldots$

text: ....is an oblate spheroid because centrifugal force stretches the tropical regions to a point farther from the center than they would be if the planet did not rotate. So we all learned in childhood, and it seems perfectly obvious. However... I am at $45^\circ$ north latitude. Does that mean   * An angle with vertex at the center of the earth and one ray pointing toward the equator at the same longitude as mine, and one ray pointing toward me, is $45^\circ$ (that would mean I'm closer to the north pole than to the equator, measured along the surface, as becomes obvious if you think about really extreme oblateness); or   * The normal to the ground where I stand makes a $45^\circ$ angle with the normal to the ground at the equator at the same latitude (this puts me closer to the equator than to the north pole); or   * something else? If for the sake of simplicity we assume the earth is a fluid of uniform density, it seems one's potential energy relative to the center of the earth would be the same at all points on the surface.   * Would the force of gravity at my location, assuming no rotation, be directly toward the center? Would it be just as strong as if the whole mass of the earth were at the center and my location is just as far from the center as it is now?   * Would the sum of the force of gravity (toward the center or in whichever direction it is) and the centrifugal force (away from the axis) be normal to the surface at my location?   * Given all this, how does one find the exact shape?   * How well does that shape in this idealized problem match that of the actual earth?


title: Is eternal inflation and the multiverse compatible with causal patch complementarity?

text: The argument for eternal inflation is we have some patch of metastable vacuum with positive cosmological constant, and so it expands exponentially a la de Sitter. Most of the patch decays to something which expands more slowly, but only a tiny fraction continues to expand at that fast exponential rate. The magic of exponentiality is despite only being a tiny fraction, it still dominates, and this process continues forever. OK, but add in causal patch complementarity, and well, only the causal patch counts, right? The fraction counting is no longer admissible because we can only measure the fraction within the causal patch, and any observer will always exit the inflationary phase with probability 1. What gives? The spatial multiverse presupposes there is such a thing as outside the patch. Is that a no no? The multiverse of different string compactifications, well, how many of them are there inside a causal patch simultaneously? As for many worlds multiverses, is many worlds even true?


title: Why did Schrodinger never budge on the meaning of $|\Psi|^2$

text: Schrodinger believed that the phisical interpretation of the wavefunction $\Psi$ was the vibration amplitude and $ |\Psi|^2 $ was the electric charge density. While no-one disagrees with his interpretation of $\Psi$, many physicists believed Schrodinger was wrong about about $|\Psi|^2$ and argued that $|\Psi|^2$ is a probability. Schrodinger never accepted this view, but registered his "concern an disappointment" that this "transcendental, almost psychical interpretation" had become "universally accepted dogma." Why did Schrodinger forever think that $|\Psi|^2$ was the electric charge density and not a probability?


title: A wonky gravitational potential and its critical points

text: I have tough problem I am not sure how to solve: For this question, we are confined to a plane. Consider a gravitational field that is proportional to $\frac{1}{r^3}$ instead of $\frac{1}{r^2}$, and consider its potential which is then proportional to $\frac{1}{r^2}$. Suppose that I put $n$ identical point masses in this plane, all at different locations and let $U(x,y)$ be the potential function. > What can we say about the critical points of $U(x,y)$? Specifically, can we > show that the number of critical points is always $\leq n$? Thank you for your help! **Remark:** By critical point, I mean the usual definition in vector calculus, that is a place where both partial derivatives are zero.


title: Torque vs Moment

text: I was wondering, why in Newtonian physics torque is called "torque" while in static mechanics they call it "moment"? I prefer by far the term "torque", for not only it sounds strong, but also instead of moment, the correct synonym of torque is moment of force.


title: how does dynamic casimir effect generate correlated photons

text: There is a recent paper on arxiv receiving lot of acclaim http://arxiv.org/abs/1105.4714 The authors experimentally show that moving a mirror of a cavity at high speeds produces light from high vacuum. The usual doubts about the experimental techniques seem to be very clearly addressed and reviewed (as per Fred Capasso's comments) http://www.nature.com/news/2011/110603/full/news.2011.346.html) My question is : Can someone explain how correlated/squeezed photons are generated in this process ? I can get a feel for how a moving mirror can generate real photons by imparting energy to the vacuum (correct me if this is not consistent with the detailed theory). But, I don't see how photons are generated in pairs. Could someone describe the parametric process happening here ?


title: Landau's ambiguous statement about the existence of inertial frames

text: Landau writes "It is found, however, that a frame of reference can always be chosen in which space is homogeneous and isotropic and time is homogeneous." Does he mean that we can prove the existence of an inertial frame or does he want to say that it is assumed by doing enough number of experiments? Can we start with some axioms and definitions of properties of space and time and then deduce the existence of such a frame in which space is homogeneous and isotropic and time is homogeneous?


title: Does magnetism affect corrosion?

text: Supposing there is an iron nail that is left to rust, if we compare the time it takes to rust with that of a magnetized iron nail, will there be any difference in the time of corrosion (assuming other environmental factors are constant)?


title: Black hole related questions

text: Well I have a couple of questions regarding Black holes so here they are, 1.Shouldn't they be called black spheres?(holes are in 2D right?) 2.What will happen if black holes collide?(If they can) 3.Will they have the "information" of what they have eaten? 4.What's a white hole? (i'm only 16, so sorry if these seem stupid)


title: Why is quantum mechanics based on probability theory?

text: What makes us formulate quantum mechanics based on probability theory? Isn't the real quantum world based on unknown laws to us? Is it possible that results of an experiment will be measurable in another way but not expected value?


title: What would be the effect of a slant barrel on the trajectory of a bullet?

text: Let's say I saw the barrel of a gun with a 45° angle, what would be the effect on the trajectory of a bullet fired through that barrel ? Would the bullet be less stable (I guess), would it make the gun fire with an angle, and would that be toward the "small" end ?


title: Steam bath physics

text: In the steam bath at the health club, why is the "steam" thicker first thing in the morning before it has been used all day and the walls are "hotter"?


title: How do we know that $\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue $W$?

text: I am kind of new to this eigenvalue, eigenfunction and operator things, but I have come across this quote many times: > $\psi$ is the eigenfunction of an operator $\hat{H}$ with eigenvalue $W$. First I need some explanation on how do we know this? All I know about operator $\hat{H}$ so far is this equation where $\langle W \rangle$ is an energy expected value: \begin{align} \langle W \rangle &= \int \limits_{-\infty}^{\infty} \overline{\Psi}\, \left(- \frac{\hbar^2}{2m} \frac{d^2}{d \, x^2} + W_p\right) \Psi \, d x \end{align} From which it follows that $\hat{H} = - \frac{\hbar^2}{2m} \frac{d^2}{d \, x^2} + W_p$. * * * **Additional question:** I know how to derive relation $\hat{H}\hat{a} = (W - \hbar \omega)\hat{a} \psi$ for which they state that: > $\hat{a} \psi$ is an eigenfunction of operator$\hat{H}$ with eigenvalue > $(W-\hbar \omega)$. I also know how to derive relation $\hat{H}\hat{a}^\dagger = (W + \hbar \omega)\hat{a}^\dagger \psi$ for which they state that: > $\hat{a}^\dagger \psi$ is an eigenfunction of operator$\hat{H}$ with > eigenvalue $(W+\hbar \omega)$. How do we know this?


title: metric extension outside the light cone

text: Could anyone explain what "extending the solution" beyond the past light cone means? Say, for example, if I have a metric (no coordinate singularities), how can I extend it to the outside of the past light cone? Up to know, I only could find the extension argument in the context of Schwarzschild solution, where it seemed to be simply the procedure of removing a coordinate singularity. So what if I don't have a coordinate singularity, how do I show the extension of my solution? What mathematical techniques does "extending the solution" imply?


title: Resource about Supercontinuum Generation in Fibers

text: I would like to consult a nice reference that explains the theoretical background of SC generation in optical fibers in detail but more or less self- contained. I would also like to have your opinions on nonlinear optic books that present material at introductory level. Thanks in advance


title: Does greater number of lines of force around the magnet imply greater magnetic field strength around it?

text: ![enter image description here](http://i.stack.imgur.com/LKYC5.png) If we sprinkle iron fillings on a sheet of glass placed over a short bar magnet. The arrangement of iron fillings will be similar to the one shown above. > Why do some of the iron fillings arrange in a particular pattern when > sprinkled around a magnet, instead of getting attached to the magnet?   >  All the filings are resting on a surface where there is friction. If the > force due to the magnet does not exceed this friction, the filings won't > accelerate to the magnet (only the closest ones experiencing the largest > forces do). Iron is also ferromagnetic, which means it can concentrate > magnetic fields. So filings that are too far to be affected by the magnet > itself can be attracted to adjacent filings which are concentrating the > magnetic field better. This is why most of the filings seem to be more > attracted to each other than the magnet itself. But essentially all the > magnetic field is caused by the magnet. After this good answer by gregsan to the above question, I got a doubt here. Considering gregsan reason to be true, for gaps between the fillings around the magnet. I thought, if the reason for gaps in between the fillings is due greater field strength at those gaps (caused by displacement of fillings towards the magnet), and if the reason for those lines in between the gaps is due to lesser magnetic field at those locations (causing the fillings to remain at those same position). I thought iron fillings lines around the magnet exist if magnet can't exert more force to accelerate them against the frictional force, on the other hand in the gaps, fillings are more accelerated towards the magnet, so they get attached to the magnet causing gaps. Now, I assumed the lines around the magnet to be the locations where force due to magnet is less. So, if more is the lines around the magnet, greater will be locations where force due to magnet is less. Considering this, I thought, greater number of lines of force indicate less intensity of magnetic field around the magnet, but I have been taught in my school that, field strength to be more if greater is the lines of force around the magnet. Is it that magnetic field strength will be concentrated more at a shorter distance, if lines of force is more? I don't know whether I have misunderstood the answer of gregsan or is there any reason which would account for greater number of lines around the powerful magnet? If any is the case, please explain.


title: Negative potential energy of gravity

text: Does the negative potential energy in the gravitational field have to be considered in calculating the total mass of the system in question (because of $E=mc^2$)? If so it seems to me that the adding this negative energy to the calculation would slightly diminish the strength of the gravitational force over long distances.


title: Why does the Kruskal diagram extend to all 4 quadrants?

text: Why is it that the Kruskal diagram is always seen extended to all 4 quadrants when the definitions of the $U,V$ coordinates don't seem to suggest that the coordinates are not defined in, say, the 3rd quadrant. I can see that combining the definitions give equations that seem to allow that, but shouldn't the individual definitions of $U,V$ matter...? Physically, does it make sense?


What is the difference between spin glass and spin liquid? Do they both originate from frustration?


title: Calculate fluid pressure loss due to hole leakage

text: I have a cylindrical pipe of internal diameter of around 5mm, with pressurised fluid flowing though it. If I have holes at the wall of the pipe, how do I calculate the pressure loss due to water leaking out through those holes?


title: Harmonic oscillator and Lorentz symmetry

text: There is a analog between harmonic oscillator $x=\frac{1}{\sqrt{2\omega}}(a+a^\dagger)$ and quantum field $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, which is used to quantize the field operator. However, one thing confuse me is about the coefficient $\frac{1}{\sqrt{2\omega}}$. For field operator, this comes from Lorentz invariance, just because we have integrated time t. However, for harmonic oscillator, there seems no apparent Lorentz symmetry give me this. Is there any hidden symmetry behind the harmonic oscillator?


title: The strong Markov property of Gibbs measures in 2D Ising Model

text: My background is that of a mathematician. I have a question about the two Dimensional Ising Model. I think the terminology I use is similar to the physical. I'm trying to understand the following passage in the article on the arXiv about strong Markov property in two-dimensional Ising model. > The strong Markov property of Gibbs measures, stating that > $\mu(\cdot\,|\mathcal{F}_{\Gamma^c})(\omega) =\mu_{\Gamma(\omega)}^\omega$ > for $\mu$-almost all $\omega$ when $\Gamma$ is any finite random subset of > $\mathbb{Z}^2$ which is em determined from outside, in that > $\\{\Gamma=\Lambda\\}\in\mathcal{F}_{\Lambda^c}$ for all finite $\Lambda$, > and $\mathcal{F}_{\Gamma^c}$ is the $\sigma$-algebra of all events $A$ > outside $\Gamma$, in the sense that $A\cap > \\{\Gamma=\Lambda\\}\in\mathcal{F}_{\Lambda^c}$ for all finite $\Lambda$. > (Using the conventions $\mu_{\emptyset}^\omega=\delta_\omega$ and > $\mathcal{F}_{\emptyset^c}=\mathcal{F}$ we can in fact allow that $\Gamma$ > takes the value $\emptyset$.) For a proof   >  one simply splits $\Omega$ into the disjoint sets $\\{\Gamma=\Lambda\\}$ > for finite $\Lambda$. Could someone explain to me clearly an intuition about this property Strong Two-dimensional Ising model and the respective proof?


title: Long-Life High Altitude Balloon

text: Normally high-altitude balloon experiments end with the balloon popping and the payload falling back down to be reclaimed. But if a second balloon was attached to the payload, one which was only partially inflated at launch, then could you keep the balloon aloft for a very long period of time? A sort of extremely-cheap very-low-orbit satellite. And if so, then does anyone do this?


title: Does the attached "poster" work as a hook into the arXiv paper cited, "Nonlinear Wightman fields"?

text: "Nonlinear Wightman fields" are my current response to a wish to do interacting quantum field theory differently, no matter how successful what we currently do may be. The following image of a single page "poster" attempts to get across why I think the mathematics is interesting, with the intention that an ordinary physicist would find the hook curious enough to look at the 22 page arXiv paper. The mathematics of section IV of that paper is really as simple as "use the Hadamard product of matrices" to construct something nontrivial that might have more relevance to Physics than the Wightman axioms have had since they were created more than 50 years ago. This is at the same time familiar stuff and far up a different mountain, so there is some hope at the same time as there is concern that physicists generally will not understand the motivation or that I've made a mistake in the mathematics. [Note that the image itself is legible even if what is displayed inline is marginal.] ![Nonlinear Wightman fields -- a poster](http://i.stack.imgur.com/hzGN8.jpg) The paper this cites is something of an outcome from the thinking that led to my question "Does renormalization make quantum fields into (slightly) nonlinear functionals of test functions?", 18 months ago, when I was using PhysicsSE quite actively as a way to help my research. Some of the content of the arXiv paper may also be found in a much rawer form as an entry in this year's FQXi essay competition (so raw that I can't recommend that you chase the link). People who've been on PhysicsSE long enough may remember my attempts, for over a year, to use PhysicsSE as a tool for research, which I eventually felt to be counterproductive because it led to too little long-term thinking, and also because I felt unable to do much to help people whose research directions were different from mine. I will submit the arXiv paper to a journal, probably JMathPhys, fairly soon, where it will hopefully generate a worthwhile critique either of the whole or of parts, but I would prefer to iron out kinks in the presentation or in the mathematics before doing so (or, if someone is kind enough to make a killing remark about the mathematics, you could save the editors or referees of JMathPhys or of some other journal some trouble). As an aside, anyone who takes the time to read sections II and III of the arXiv paper will find calculations and an unconventional perspective on interacting quantum field theory that I would expect anyone who has thought for a while about foundational issues in QFT to find curious and perhaps useful.


title: A point in multiple magnetic fields

text: Given two parallel wires carrying a current (e.g. 2 and 3 Amperes) and the distance between them, 5 cm, how do I determine the magnitude of the magnetic field at a point M mid-distance between the wires (2.5 cm from each)? The wires are located in a vacuum with ${\mu}=4\pi10^{-7}$. If I use the formula $$B=\frac{\mu*I}{2*\pi*r}$$ and calculate the magnetic field for both currents/wires, how do I find the resulting magnetic field? How do I do that, assuming the wires are perpendicular and in the same plane? How does this generalise to more than two wires?


title: Keeping air in a giant gravitationally-bound space balloon

text: Let's say a space-faring society wants to make a space station that has a large volume filled with air (or other gas), but no gravity. Using normal pressure tanks will require gathering an amount of material proportional to the volume, which is a ratio set by the tensile strength and desired pressure. It's likely that some other method for containing gas would be more economic for anything over a certain volume. Could you confine a large volume of air in space using self-gravitation to hold the container together? Well obviously you can. Consider: a spherical volume of air surrounded by a solid sphere of matter through which the air cannot leak or diffuse and the pressure balances the gravity of the walls. Think of a big balloon ball in space, or alternatively, injecting the middle of the moon with air until it starts expanding. A hollow planet, if you will. There will be little gravity within the air because the walls don't contribute to the gravity inside and air has a low density. So here is what I'd like to ask:   * For a given pressure, what surface mass density ($kg/m^2$) would you need? What would the wall thickness be?   * Going by the amount of material required, at what size would this approach be more economic?   * How stable would this thing be?   * Hypothetically, could you use the same principles to drape a airtight tarp over Mars and keep atmosphere from leaking out? It would be the surface mass density that determines the altitude at which it rests, right? Disclosure type statements: I can do a lot of the calcs for this myself, but I don't want to because I have doubts about certain parts and I want to avoid influencing other people with my potentially incorrect thought process. If you look at my Physics SE activity, you might notice that I'm fascinated by self-gravitation problems. I came up with this question reading Keeping air in a well.


title: Is there a small enough planet or asteroid you can orbit by jumping?

text: I just had this idea of orbiting a planet just by jumping and then flying upon it on its orbit kind of like superman. So, Would it be theoretically possible or is there a chance of that small body to be & remain its unity? ![Orbiting an asteroid by jumping](http://i.stack.imgur.com/MNhD5.jpg)


title: Mass-Spring Damper system - moving surface

text: I need help with a physics problem, I don't know much about dampers, how can this be solved? ![spring](http://i.imgur.com/ybpcQ.png) we have $y_0(x)=\mu\sin(\Omega x)$ We arrive at this equation for motion (where we define $b$ and $w_0$ ourselves, and $z=y(t)-y_0(t)$) $$\displaystyle\frac{d^2z}{dt^2} + b\displaystyle\frac{dz}{dt} +w_0^2z = \mu\Omega^2U^2\sin(\Omega Ut)$$ Can someone show me the steps in between for determining this equation of motion **EDIT:** What I have is (with $y(ii)$ meaning second derivative of $y$, and $y(i)$ first): $$m(y(ii)-y_0(ii))=-K(y-y_0)-C(y(i)-y_0(i))$$ which simplifies as $$(y(ii)-y0(ii))+\frac{c}{m}(y(i)-y_0(i))+\frac{k}{m}(y-y_0)=0$$ which $\implies$ $z(ii)+bz(i)+w_0^2z=0$ (which is wrong) Maybe I could be shown a proper free body diagram by someone if my idea of the forces are wrong?


title: Quantum harmonic oscillator

text: I read somewhere that a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM (quantum harmonic oscillator). It was given that the amplitude of this SHM is quantized, and each quantum signifies a particle. (i.e. if the ball rolls with minimum amplitude, there are no particles in that point of space. If it has the next amplitude, then there is one particle and so on). What I don't get is how this analogy relates to quantum fields which are not exactly quantized at every point of space. For example, a single electron has a wavefunction spread out over some space. At every point in this space, we can say that "there is a fraction of the electron over here". But, If I model this as a bunch of oscillators, I can't have a fraction of an electron as the amplitude of SHM, as its supposed to be quantized. I'm quite sure there's a flaw in my interpretation, but I can't figure it out. Could someone give a more detailed explanation of quantum harmonic oscillators? Note that I do not understand the mathematics behind quantum mechanics, so though I don't need layman's terms, I would rather stay away from the equations.


title: What happens to angular momentum when matter is converted to energy?

text: Let's say a spinning star radiates mass-energy only from it's pole regions. How does the loss of mass-energy effect the angular momentum of the star?


title: Meaning of negative frequency of sound wave

text: Suppose that Alice and Bob are both holding speakers emitting sound at a frequency $f$. Alice is stationary while Bob is moving towards Alice at twice the speed of sound. In the case of Alice, if I forget for a minute that she is holding a speaker herself, and just think about the Doppler effect from Bob moving towards her, I get $$f_{\text{effective}}=f\frac{1}{1-\frac{2v_a}{v_a}}=-f$$ I do not know what "negative" frequencies mean in the context of sound waves, and so I do not really know how to describe what Alice will hear as Bob becomes very close to her. I also do not know how the fact that she is emitting sound at a frequency $f$ will affect, if at all, what she hears. And, from Bob's perspective, I get $f_{\text{effective}}=3f$, which is a bit more meaningful, but does not factor in the fact that Bob is emitting sound himself. Any clarification is appreciated.


title: Different degrees of freedom with RGB, CMYK and Frequency

text: Ok, so I understand the eye has 3 different types of receptors and I've seen the process of converting from RGB to CMYK. However if in physics I can specify a color using a single number (its frequency) why do computers need 3 (RGB) or 4 (CMYK) numbers to specify the same color? Is there some kind of disagreement in the amount of degrees of freedom involved? Thanks a lot.


title: Does String Theory explain wave-particle duality?

text: Does string theory explain the weird things that happens at the quantum level, especially wave-particle duality?


title: electromagnetic induction. Does charge matter?

text: Just wondering. I know a negative electric charge moving though a coil will induce a voltage in the coil. My question is, would a positive charge, say an ion beam, moving though a coil also induce a voltage?


title: Alternate layman's metaphors for illustrating curved space-time

text: The metaphor of a surface (typically a pool table or a trampoline) distorted by a massive object is commonly used as a metaphor for illustrating gravitationally induced space-time curvature. But as has been pointed out here and elsewhere, this explanation seems (to a layman like me, at least), to be "hopelessly circular", and in the end contributes little to an understanding of how modern theories of gravitation work. Are there other (or additional) metaphors that might be helpful in illustrating to lay readers (a) what motivates modern gravitational theory and (b) why it has greater explanatory power than Newtonian gravitation?


title: Theoretical basis for black hole evaporation

text: What is the basis for black hole evaporation? I understand that Hawking-radiation is emitted at the event horizon, a theoretical result originating in General Relativity and Quantum Field Theory, but it seems to me that additionaly one has to assert an integral conservation law for mass/energy, ie. for a sphere surrounding the black hole. Does such a conservation law hold for the simplest case of a Schwarzschild metric? I am grateful for any related classic paper references. **EDIT:** The usual heuristic for understanding Hawking-radiation is: virtual pair, one falls in, one goes out; the ones going out are called Hawking- radiation. But what about the ones going in? Naively, it seems there should also be Hawking-radiation going inward, which would actually increase the black hole's mass.


title: What is the relation between retarded potential and the Lorentz transformation of EM fields?

text: In Griffiths' ED book he derives the field of a moving charge by two ways:   1. LW retarded potential.   2. Lorentz transformation of EM fields. (eq10.68 and eq12.92 and the discussion that follows,3rd edition) Now my question is: _fundamentally_ , what is the relation between the potential retardation and the L transformation of the EM fields? Can we totally replace the function of one by the other? Can we derive one formula from the other?


title: Why closed bottle change its weight when I put effervescence tablet?

text: I use several shape, several type of material (glass, metal, plastic), I use two different balances with 0.01g of accuracy. I put oil on gasket, and put upside down (like that I can see if water escape). But always it's the same result, when I put one, two or more effervescence tablets, the weight decrease: one tablet => -0.03g two tablets => -0.06g three tablets => -0.09g Sure the difference is not big. But if I put an object without effervescence tablet, the weight is always the same (move sometimes +0.01 or -0.01g but never more). The time for decreasing is about 2 minutes so it's not enough for change something from temperature I think especially with glass container. So, maybe someone has done this experimentation before and know where is my error ? Or maybe someone can test and try this experimentation ? @Luboš Motl: "Recall that the air density is about 1.3 grams per cubic centimeters", you're sure ? it's not 0.0013 ? Yes, I have the same values for glass (2 mm of thickness and one of 3 mm of glass) with a metal cover of 0.8 mm of metal. I done about more than 100 measures. After 2 minutes, the tablet is full dissolved in water and weight move very few after (-0.01g next 2 minutes) but never more. Maybe I found: when bubbles move up in water, they have gas in it (CO2), this gas move up with a speed, so there is a quantity of movement, the weight losses is the sum of mass of bubbles multiply by speed. Like quantity of movement is conserved, the weight don't change. It's possible to use the formula of Newton: force=2mv if top speed is 0.25 m/s the weight losses is 2*0.3/1000*0.25/10 = 0.015 g with 0.3 g of CO2, image show speed that I found on Internet. If it's that, the weight must change with a ball full of air (ping-pong ball) in water. But the CO2 in a tablet is very powerfull, 0.3g give 0.187 liter of CO2, even the ball move faster the volume is not great in a bottle. The ball must be down before close the container. And the gas must relax when the ball reached surface. Is it possible it is the rotation of Earth that change the pressure in water due to the centripetal forces ? This give -0.03N for each kg of water. Good day


title: Riemann tensor notation and Christoffel symbol notation

text: In paper by Barnich and Brandt Covariant theory of asymptotic symmetries, conservation laws and central charges they defined the Riemann tensor like this: $$R_{\rho\mu\nu}^{\quad \ \ \lambda}~=~\partial_\rho \Gamma_{\mu\nu}^{\ \ \ \ \ \lambda}+\Gamma_{\rho\sigma}^{\ \ \ \ \ \lambda}\Gamma_{\mu\nu}^{\ \ \ \ \ \sigma}-(\rho\leftrightarrow\mu).$$ Now I have taken the 'normal' definition of Riemann tensor and raised the first index, and lowered the last one, and if I do the same with original (lower the first one and raise the last one) I get the same expression, which means that this is ok. But, why such definition? And does that mean that the Christoffel symbols have different definition compared to usual? I mean raised first and lowered last index.


title: Convergence and well-definedness of Lorentzian path integrals

text: Wick rotation of quantum field theories to Euclidean path integrals with a nonnegative measure everywhere is a wonderful tool. Not so with Lorentzian path integrals. Events far separated in coordinates can have zero or arbitrarily tiny interval separation in relativity. Ultraviolet divergences crop up for infrared separations at arbitrarily high boosts. The integrand becomes highly oscillatory phasewise around null separations. Absolute convergence is nonexistent, only mere convergence which is so sensitive to integral reorderings it raises warning flags. Changing the regulator or the order of limits can change the answer drastically. Are such path integrals even well-defined?


title: Where does the rubber go when a tire wears down?

text: Every year millions of car tires are worn down on our highways, yet the roads are not all black from the rubber, neither are the sides of the roads black. Where does all the rubber go?


title: Desperately Need Help with Grade 9 Static Electricity

text: I am preparing to teach Grade 9 Static Electricity next week and am going crazy trying to figure out what is happening in one of my experiments. I have a short piece of PVC pipe, 4 inches diameter, and I rub it with wool to charge it negatively. I can observe excellent repulsion when I touch it with my foil bit (dangling from a thread). Here is the problem: I am holding down the PVC pipe down on a wooden base with two brass-plated wood screws, and these screws somehow collect an INSANE amount of positive charge, even when I am very careful not to touch them with the wool. The foil bit is strongly attracted to the screws, and when it touches them it bounces off more violently than anything I've seen in any of my other static electricity experiments. Can anybody explain what I am seeing?


title: Correct way to calculate torque produced by axle

text: For my electrical engineering course, we had to build a simple DC motor that can lift a coin. I have tested the motor, and here are the results:   * rotational speed (no load): 3630 RPM (380 rad/sec)   * Current with load (9g): 3A (limited)   * Current with no load: 0.7A   * Maximum weight lifted: 0.1422 N   * Max voltage 12V I now want to plot a torque-speed curve and calculate its efficiency. My problem is that the weight it lifted is a force quantity. To convert it to a torque quantity, I multiply by the axle radius (6mm) which gives 0.00085 Nm. This seems wrong to me becausekjg when I calculate the efficiency $\epsilon = \frac{\omega \tau}{VI}$ I get $\epsilon = 0.9 \% $ which seems extremely low. Is this the correct way to calculate the torque produced by an axle when lifting a load?


title: Systems with different particle statistics

text: Is there a way to describe interactions between systems with particles of different species, that is to say with different statistics? For example: I am placing a boson next to a free fermion gas. How can I write down interaction Hamiltonians that make sense? By interaction Hamiltonians I mean Hamiltonians that contain products of fermion and boson operators? Somewhat I am puzzled with this question, since both the boson and fermion operators act on different Hilbert spaces. Might bosonization or fermionization a solution (at least for 1D systems)? Best.


title: Iterated dimensional regularization

text: Given a 2-loop divergent integral $\int F(q,p)\,\mathrm{d}p\mathrm{d}q$, can it be solved iteratively? I mean   1. I integrate over $p$ keeping $q$ constant   2. Then I integrate over $q$ In both iterated integrals I use dimensional regularization. Can it be solved iteratively? I presented a paper to a teacher of mine about regularization of integrals using the Zeta regularization. He told me that for one dimensional integrals (or one loop integrals) it was fine, but that my method could not handle multi loop integrals. I argue back that you could apply the regularization method by introducing a regulator of the form $$(a+qi)^{-s}$$ I could make the integral on each variable by iterated regularization, that is applying the algorithm iteratively. EDIT: i think they have cheated me :) making up excuses not to put me atention by the way , how can i insert math codes on my posts ?? is just setting `$` at the beginning and the end of the equation ?? * * * ## Edit: 19th of July thanks :) your answer was quite useful :) however can I not insert a term $(qi+a)^{-s} $ on each variable and then apply the regularization iteratively ?? I say so because I made a paper http://vixra.org/abs/1009.0047 to regularize integrals using the regulator $(q+1)^{-1}$ and tried to extend it to several variables, however that was my doubt, if i could apply my regularization scheme to every variable :) thanks again I mean for a one dimensional integral $\int dx (x+a)^{m-s}$, I know how to regularize it by using the Euler-Maclaurin summation formula plus the Riemann Zeta function $ \zeta (s-m)$ Then for multiloop integrals, I had thought that i could introduce the $s$-regulators (x+a)^{-s}(y+a)^{-s}.. and so on on each variable, and then apply iterated integration... :) so this is a resume of my method.. a) i know how to use Zeta regularization to get finite values for the integral $ \int dx(x+a)^{m-s} $ in terms of the Riemann Zeta function $ \zeta (s-k) $ with k=-1,0,1,....,m b) for a more general 1-dimensional integral $ \int dx f(x)(x+a)^{-s}$ i add substract a Polynomial $K(x+a)(x+a)^{-s} $ to get a finite part and then regularize the divergent integrals $dx(x+a)^{m-s} $ c) for a more complicate 2-loop integral $ \iint dpdq F(q,p)(p+a)^{-s}(q+a)^{-s} $ to obtain a regularization of it i do the sema method , first on 'p' considering 'q' a constant and i treat it as a one dimensional integral over 'p' and then over 'q' by substracting a Polynoamials $ K(q,p+a)(p+a)^{-s} $ and so on


title: What is the fundamental reason of the fermion doubling?

text: Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds themselves with an additional amount (precisely $2^d$) of fermionic fields. One can fix this by considering different discretizations of the action that make unwanted fields decouple in the continuum limit. The downside is that the additional terms have to spoil some nice features of the theory (chiral symmetry, locality, lattice symmetry, ...). Now, I wonder what is the true reason for the appearance of new fields. Is it the fermionic nature of the theory? (In other words, is a similar problem ruled out for bosonic fields?) And do all (naive?) fermionic theories (that is, independent of the continuum form of the action) suffer from this problem? More generally, how can one tell _a priori_ what will the field content of a lattice theory in the continuum limit be? Or is the field content fundamentally a continuum limit property that has to be calculated?


title: Nature of Microscopic space-time

text: I am going through the introductory chapter's of Schwinger's Source theory. He writes, > It [Source Theory] is a phenomenological theory, designed to describe the > observed particles. No speculations about the inner structure of the > particles are introduced. No abstract definition of particle is devised. The > theory is thereby firmly grounded in space-time, where the experimenter > manipulates his tools, **but the question of ultimate limitation to > microscopic space-time description is left open, with the decision reserved > to experiments. Correspondingly, no Operator-fields are used.** Now in this regard, I would want to know how operator fields answer the question of ultimate limitations to microscopic space-time (If they are related to each other)? **EDIT 1 :** It just struck me that the limitation could be due to canonical commutation between field operators and their conjugates. However, I don't see how to formalize a restriction using this commutation.