title: What is the exact relationship between scale invariance and renormalizability of a theory?

text: I have often read that renormalizability and scale invariance are somehow related. For example in this tutorial on page 12 in the first sentence of point (7), self similarity (= scale invariance ?) is referred to as the non- perturbative equivalent of renormalizability. I don't understand what this exactly means. Can one say that all renormalizable theories are scale invariant but the converse, that every scale invariant theory is renormalizable too, is not true? I'm quite confused and I'd be happy if somebody could (in some detail) explain to me what the exact relationship between scale invariance and renormalizability is.


title: Download only physics and maths wikipedia pages for offline use

text: There are tools for downloading the entire wikipedia database (above 8 Gb without pictures), but I would like to download only physics and maths pages, to view them offline. Wikipedia pages have a tree structure in categories, so it should be possible. Please see here http://en.m.wikipedia.org/wiki/Wikipedia:Database_download#section_1   "To download a subset of the database in XML format, such as a specific category or a list of articles see(...)" and a link to some other page from which, after many efforts, I could surely get what I want. I am just wondering if anyone has already done it and can save me/us the effort with a few "how to" guidelines. I know wikipedia seems for many of you not much an orthodox source, but it is usually an excellent introduction to areas that are not in your main line of research/study. I miss it very often while commuting.


title: On characteristic X-ray spectra and relative intensity

text: I am looking at the following image (from http://www.schoolphysics.co.uk/age16-19/Atomic%20physics/X%20rays/text/X_ray_spectra/index.html): ![enter image description here](http://i.stack.imgur.com/Z270f.gif) and I want to know, of the two curves, which one represents the element with the higher atomic number. That is, I understand that X-rays are scattered and that the peaks are characteristic of a material. What I am less clear on i why one curve should be above another relative to their atomic numbers (I am going to assume the cutoff voltage on the left is identical even though in this picture it isn't). The reason I am confused is that I am told that that $\frac{1}{\sqrt{\lambda}} \propto Z$ which is all very well, but on this graph it would seem to indicate that the upper line is a heavier (higher Z) material. Is hat the case, or is intensity actually proportional to $\frac{1}{\sqrt{\lambda}}$ as well? I would have thought the lower curve would be a higher Z since it usually take less energy to knock electrons off of elements further up the periodic table. Anyhow, what clarification might be offered is appreciated.


title: Calculating Resultant Force and Torque

text: I'm working on a sandbox game that allows the player to build a spacecraft and attach thrusters in arbitrary locations on the hull of the spacecraft. The game is set completely in 2D. (I'm a programmer, not a physicist, so I apologize if my terminology is all wrong). I have need to actually calculate my own physics. Say the player makes a simple spacecraft as follows: A===O===A where "A" are the thrusters pointing down, "O" is the cockpit and just so happens to be the center of mass as well, and "=======" is just some metal bar joining everything together. We can completely ignore the existence of any gravity. Both thrusters are identical and, when turned on, produce an upward force of F at the point of the thrusters. The torque about the CoM for the left one completely cancels out the torque of the right one - hence the net torque is zero. The resultant force at the CoM (I believe) is 2*F up. Therefore, the ship accelerates up - there is no sideways acceleration and no torque to cause the craft to rotate. What if only the right-side thruster is fired while the left one is left off? There would be a net anti-clockwise torque on the craft but I believe there is also some resultant force on the CoM as well? Torque I know how to calculate, but what about this resultant force vector? I'm trying to relate this to the experience of flicking the tip of a pen resting on a table top. There would be torque because I observe the pen spinning, but there would also be some resultant force because the pen is also sliding down the table. Thanks!


title: what are dimensions?

text: First, discrete examples. In a computer screen I can specify any "2D" point with just one single number (pixel order starting count from first at upper left, and going on, left2right and up2down like reading till last one at right bottom corner) Then I don't need two numbers to specify position, just one. Same can extend to other "dimensions" I can use same trick to describe a point inside a discrete cube, once have covered a screen like "area" descend a plane level plane               0 .....5     6 .....10     11.....15      then a cube (made of above planes)               0  ____ 15     16 ____ 31     32 ____ 47      so a single number can map any point in a 3d discrete cube what about continuous one? same thing using differential dx instead of discrete points or planes, and that's all (of course as differential is not well defined as discrete this won't be so easy) Anyway my question is: **what is a good definition of dimention that avoid these tricks? there is one?** Finally another way to take 3d to 1D, is a reversible transformation like this 3d point = (x,y,z) W = x + y * 2^20000 + z * 2^40000 the only "restriction" for this method is that equivalent 3d coords should be lesser than 2^20000, a very easy thing, at least in the known universe even in Plank's units (20000 and 40000 could of course be changed for lesser numbers, but I like concrete examples)


title: When periodic solutions are combined with timelessness, do we get closed timelike curves?

text: In quantum gravity, ADM wavefunctional solutions have to satisfy the Wheeler- DeWitt equation. This leads to timelessness. What happens if we have a time periodic solution? In classical general relativity, a time periodic solution just means that and no more. But when combined with a timeless wavefunctional, if the same configuration occurs twice or more often, the coefficient of the configuration component in the wavefunctional has to be exactly the same both times around, both in magnitude and in phase. That is because we have no disambiguating clock external to the timeless wavefunctional, which is not multivalued. But this is exactly the description of a closed timelike curve. Assume space is compact so we do not have to worry about asymptotic infinity.


title: What is escape velocity? In reality, how can something no longer be under the gravitational influence of something else?

text: Isn't G a continuous function and although you leave the immediate vicinity of the earth with an escape velocity won't it always exert a force, however small it may be. Won't that force eventually pull the object back to the earth (assuming the absence of other objects)


title: How can I prevent being zapped by static electricity every time I touch a doorknob or handle in the office?

text: I don't know what it is about this office, but it seems everything I touch (doorknob, bathroom faucet, edge of kitchen sink in the break room), I get zapped by static electricity. It's getting old. I feel like that scene in Office Space. I've worked in other offices and it's not nearly this crazy. This has been going on for months so it's not the weather. Why does this happen and is there any way I can defend against this evil?


title: What is the laplace transform of a single mass?

text: I'm trying to get a transfer function of `F=ma` in the Laplace domain. This should be simple, but yet I'm confused. The transfer function is displacement over force. So, I have two approaches.   1. First approach: integrate w.r.t. time twice, and laplace transform of that. $$\ddot{x}=F \\\ \dot{x}=Ft+c_1 \\\ x=\dfrac{1}{2}Ft^2+c_1t+c_2$$ which makes for a transfer function with $c_1$ and $c_2$ zero: $$h(t)=\frac{x}{F}=\frac{1}{2}t^2$$ The right hand side has a Laplace transform of $$H(s)=\frac{1}{s^3}$$   2. Laplace transform of double integration, which is simply $$H(s)=\frac{1}{s^2}$$ I have heard that the second one is correct, but why is the first one not correct?


title: Nonlinear anomalous Hall effect

text: Has there been any research on anomalous Hall effect which would observe or predict a non-constant dependence of the AHE conductivity on the applied electric field?


title: Finding the minimum radius of the pivoted disc

text: Here is a question based on Simple Harmonic Motion that I tackled just now. However I think I am having an approach to tackle this but I am not sure about it. > **Ouestion** : _A uniform disc of radius $R$ is pivoted about point $P$ such > that it is free to oscillate in the vertical plane. Distance between the > pivot and centre of disc $x$, such that the time period of oscillation is > minimum._ ![enter image description here](http://i.stack.imgur.com/ekARf.png) So till yet I know that for a circular disc like this one, we have _time period_ , $$T=2\pi\sqrt{\frac{I}{\kappa}}$$ where $I$ is moment of inertia of the disc and $\kappa$ is the torsional constant. So after substituting the values knowing that $\kappa=\frac{\tau}{\theta}$ and $I=mr^2$ I have, $$T=2\pi\sqrt{\frac{mr^2\theta}{\tau}}$$ Now next to this I am thinking of finding the minima of this function so that I can get the least value of r. However I am still not sure that this will help me in anyway. Also I want to know that if we can differentiate this function to get minimum value of $r$ then do we really need to substitute $\tau$ as $\tau=r\cdot F$.


title: Evaluating low-temperature dependence of the BCS gap function

text: How does one go about evaluating the behavior of the BCS gap $ \Delta = \Delta(T) $ for $ T \to 0^+ $ under the weak coupling approximation $ \Delta/\hbar\omega_D \ll 1 $? In Fetter & Walecka, _Quantum theory of Many-Particle Systems_ , Prob. 13.9 it is said that the starting point is $$\tag{1} \ln\frac{\Delta_0}{\Delta} = 2\int_0^{\hbar\omega_D}{\frac{\mathrm d\xi}{\sqrt{\xi^2+\Delta^2}}\frac{1}{e^{\beta\sqrt{\xi^2+\Delta^2}}+1}}, $$ which I have no problem deriving from the theory, but I can't find a way to actually evaluate this integral even under the approximations $ \hbar\omega_D \to \infty $, $ \Delta \approx \Delta_0 $ (in the RHS) and $ \beta\Delta \to \infty $. [Of course $ \beta = (k_BT)^{-1} $ and $ \Delta_0 = \Delta(T = 0)$.] I have tried several approaches, used different Taylor-expansions and changes of variables, but I am simply stuck. For the record, the expected behavior is supposed to be $$\tag{2} \Delta(T) \sim \Delta_0\left(1 - \sqrt{\frac{2\pi}{\beta\Delta_0}}e^{-\beta\Delta_0}\right) .$$ EDIT: Just leaving it here for the posterity. I found a more complete way to tackle this integral; specifically, under the WC approximation one has $$ \int_0^{+\infty}{\frac{\mathrm d x}{\sqrt{x^2 + 1}}\frac{e^{-\beta\Delta\sqrt{x^2 + 1}}}{1 + e^{-\beta\Delta\sqrt{x^2 + 1}}}} = \int_1^{+\infty}{\frac{\mathrm d y}{\sqrt{y^2 - 1}}\frac{e^{-\beta\Delta y}}{1 + e^{-\beta\Delta y}}} = $$ $$ = \sum_{k=1}^{+\infty}\int_1^{+\infty}{\frac{\mathrm d y}{\sqrt{y^2 - 1}} (-1)^{k+1}e^{-k\beta\Delta y}} = \sum_{k=1}^{+\infty}(-1)^{k+1}\int_0^{+\infty}{\mathrm d t\; e^{-k\beta\Delta \cosh{t}}} = \sum_{k=1}^{+\infty}(-1)^{k+1} K_0(k\beta\Delta), $$ $ K_0 $ being the 0-order modified Bessel function of the second kind, whose asymptotic behavior is known and may be used to solve the problem in a relatively clean way (and even find the corrections at higher orders, which are $ \in O(e^{-\beta\Delta}(\beta\Delta)^{-k - 1/2}) $. Cf. Abrikosov, Gorkov, Dzyaloshinski, _Methods of Quantum Field Theory in Statistical Phyisics_ , 1963. Pagg. 303-304.


title: Can horizontally and vertically polarized light combine to become circularly/elliptically polarized light?

text: Well, we know that circularly/elliptically polarized light is made up from orthogonal components. So is it possible then to create circularly/elliptically polarized light by combining horizontally and vertically polarized light? It seems to make perfect sense to me. EDIT: Clarification: I mean by creating circularly/elliptically polarized light in the laboratory (though beam-splitters ?, I don't know) by combining different light beams of horizontally/vertically polarized light.


title: Is any one compact dimension for one particle the same as for another particle?

text: In the 3+1 dimensions of everyday life and GR particles can share the same extended dimensions. Probably all particles share the same 3+1 dimensions. In string theory compact dimensions seem to be limited to each individual particle. Is there any meaningful, or otherwise, sense in which the compact dimensions of one instance of a particle are shared with, or the same as, the compact dimensions of another instance of the same type, or a different type, of particle ? Is there anyway that these compact dimensions interact ? If not, what purpose do they serve ?


title: Could Legolas actually see that far?

text: The video “How Far Can Legolas See?” by MinutePhysics recently went viral. The video states that although Legolas would in principle be able to count $105$ horsemen $24\text{ km}$ away, he shouldn't have been able to tell that their leader was very tall. ![enter image description here](http://i.stack.imgur.com/ZpHOj.jpg) I understand that the main goal of MinutePhysics is mostly educational, and for that reason it assumes a simplified model for seeing. But if we consider a more detailed model for vision, it appears to me that even with human-size eyeballs and pupils$^\dagger$, one might actually be able to (in principle) distinguish smaller angles than the well known angular resolution: $$\theta \approx 1.22 \frac \lambda D$$ So here's my question—using the facts that:   * Elves have two eyes (which might be useful as in e.g. the Very Large Array).   * Eyes can dynamically move and change the size of their pupils. And assuming that:   * Legolas could do intensive image processing.   * The density of photoreceptor cells in Legolas's retina is not a limiting factor here.   * Elves are pretty much limited to visible light just as humans are.   * They had the cleanest air possible on Earth on that day. How well could Legolas see those horsemen? * * * $^\dagger$ I'm not sure if this is an accurate description of elves in Tolkien's fantasy


title: Perfect pinhole diffraction pattern with sharp fringes using a 632nm laser

text: I'm trying to produce a diffraction pattern with pinhole using a laser of 632nm wavelength .The pinholes' diameter are ranging from 10um , 25um , 50 um , 0.1mm and so on . I also have good lenses for collimation and focusing. What is of importance to me is to generate distinguishable bands in a way that I can make sure there exist no photons in dark band and the fringes are perfect borders between light and dark bands. At the moment what I can observe is such a pattern .   http://www.pictureshoster.com/files/ihyxqb9relj0tv9mbab6.png You can also have a look at setup which I used .   http://www.pictureshoster.com/files/y0iqmqttzzc4y8n2y6mq.jpg As you see there aren't perfect circles over there and borders have some aberrations! Is there any way to produce sharp fringes of diffraction pattern ?


title: A Cosmological horizon at the Hubble radius?

text: I have calculated that if one extends a rigid ruler into space by a fixed proper distance $D$ then a clock at the end of the ruler, running on proper time $\tau$, will run more slowly than time $t$ at the origin by a time dilation factor: $$\frac{dt}{d\tau} = \frac{1}{\sqrt{1 - H^2 D^2 / c^2}}$$ where $H$ is the Hubble parameter. If one substitutes in Hubble's law, $v = H D$ (the theoretical law which is exact), one finds the following satisfying result that $$\frac{dt}{d\tau} = \frac{1}{\sqrt{1 - v^2 / c^2}}.$$ Although this looks like a result from special relativity I derived it by combining the FRW metric line element and an equation for the path of the end of the ruler, $\chi = D / R(t)$, where $\chi$ is the radial comoving coordinate of the end of the ruler, $D$ is a fixed proper distance and $R(t)$ is the scalefactor. Does this prove that there is a cosmological horizon at the Hubble radius $D=c/H$ where the proper time $\tau$ slows down to a stop compared to our time $t$? This seems to be a general result which is true regardless of cosmological model. Details of Calculation The general FRW metric is given by: $$ds^2 = -c^2 dt^2 + R(t)^2\left[d\chi^2+S^2_k(\chi)d\psi^2 \right]$$ where $d\psi^2 = d\theta^2 + \sin^2 \theta d\phi^2$ and $S_k(\chi)=\sin \chi$,$\chi$ or $\sinh \chi$ for closed ($k=+1$), flat ($k=0$) or open ($k=-1$) universes respectively. The scale factor $R(t)$ has units of length. Consider a ruler of fixed proper length $D$ extending out radially from our position at the origin. The path of the far end of the ruler in comoving coordinates is $$\chi = \frac{D}{R(t)}$$ Differentiating this equation by proper time $\tau$ gives us: $$\frac{d\chi}{d\tau} = - \frac{D}{R^2} \frac{dR}{dt} \frac{dt}{d\tau}.$$ Using the FRW metric we can find a differential equation for the path of the far end of the ruler. We substitute in $ds^2=-c^2d\tau^2$ (end of ruler has a time-like path), $d\psi=0$ (the ruler is radial) and divide through by $d\tau^2$ to obtain: $$c^2\left(\frac{dt}{d\tau}\right)^2 - R(t)^2 \left(\frac{d\chi}{d\tau}\right)^2 = c^2.$$ Substituting the expression for $d\chi/d\tau$ into the above equation we find: $$c^2\left(\frac{dt}{d\tau}\right)^2 - D^2 \left(\frac{\dot R}{R}\right)^2 \left(\frac{dt}{d\tau}\right)^2 = c^2.$$ Using the definition of the Hubble parameter $H=\dot{R}/R$ we finally obtain: $$\frac{dt}{d\tau} = \frac{1}{\sqrt{1 - H^2 D^2 / c^2}}.$$


title: Topological insulators - Surface states have a phase?

text: When I look at the circle of the Dirac cone around the Dirac point of, let's say, $Bi_2Se_3$, then the electron winds around and it is true that it goes from momentum $-k$ and spin-up to $+k$ and spin-down. Now how can I use this fact to show that the Berry phase of $\pi$ arises? When the electron completes one circle it did go from $k$ to $k$ and from spin-up to spin-up. So basically nothing changed...? Picture that shows the Dirac cone in the Brillouin zone and the spin on the left hand side: ![enter image description here](http://i.stack.imgur.com/x5e3U.jpg)


title: Are these data enough to solve this simulataneity problem

text: observers: **S** and **S** '. S stands **in midway** between two events (say, 2 flashes) located **20 metres apart**. He sees two flashes occurring **simultaneously**. **S'** notes a **20ns difference** in them. **S'** is moving along x axis with uniform velocity What is this velocity in S frame? delta t equation leads to a 4th degree polynomial equation of v, so I must be wrong. Please help.


title: Plasma Propulsion system - Maximum Velocity

text: What is the maximum velocity that can be achieved using plasma propulsion if we could make a propulsion system as powerful as lightning ?


title: Educational physics stories with a funny punchline

text: As a physicist, when I'm giving lectures or during colloquiums, I usually find it necessary to have some appropriate and related jokes in hand. All of the best teachers have some, and they use them when they have to; so I think that it is a necessity of good teaching. On the math side we have this gem(although being closed and reopened several times); however on the physics side I couldn't find much. Hopefully this topic will help me and many others with this regard.


title: RC Parallel Circuits

text: I am trying to solve the following exercise: * * * A capacitor 27 and $\mu$F is connected to a battery of 21 V through a resistance of 14 M$\Omega$. 1) What 's the charge on his parallel-plate? 2) To reduce such a charge of 16%, I connect a wire in parallel with the condenser. What will be now the ddp across the parallel-plate capacitor? 3) What resistance the new wire must present to ensure this outcome? Solutions: q = 576$\mu$C; $V_c$ = 17.64 V; $R_2$ = 2.666667K$\Omega$ * * * I succeeded to find the solution for the question 1) and 2) but not the 3). Here is what I tried: the picture should be like this: ![enter image description here](http://i.stack.imgur.com/YVOob.jpg) $R_1$ = 14 M$\Omega$ $V_f$ = 21 V c = 27 $\mu$F * * * q = c * $V_f$ = 576 $\mu$ C $V_c$ = $\frac{q}{c}$* (1 - 16/100) = 17.64 V $R_2$ resistance in parallel to the capacitor (1) $R_2$ * I = $V_c$ (2) $V_f$ = ( $R_2$ + $R_1$ ) * I I tried to solve (1) and (2) to find the $R_2$ but the result I found is different from the solution. Any hints? Thanks.


title: If aerographite is lighter than air, why doesn't it float?

text: Air is 6 times denser than aerographite but looking at pictures or videos presenting the material, I see it resting on tables rather than raising to the ceiling.   Also, since the material is made of carbon nanotubes, I assume there are empty spaces between those tubes. Why are those spaces not occupied by air?


title: complex numbers in optics

text: I have recently studied optics. But I feel having missed something important: how can amplitudes of light waves be complex numbers? I suppose this is quite fundamental, but I do not find the answer in my course ... Thanks, Isaac


title: Difference between short impact and sustained pressure

text: If I press the wall (with my hand) I feel a little pressure at my hand and I move away from it. If I hit the wall (lets say using the same amount of energy for total work) I feel pain in my hand. Why is it? Is it because time of impact is shorter? Would I move away from the wall in second case if standing on perfectly frictionless ground?


title: Equation of motion for average acceleration

text: I am trying to solve the following: > _A man of mass 83 kg jumps down to a concrete patio from a window ledge only > 0.48 m above the ground. He neglects to bend his knees on landing, so that > his motion is arrested in a distance of about 2.2 cm. What is the average > acceleration of the man from the time his feet first touch the patio to the > time he is brought fully to rest?_ Now, I know that the man has a velocity of $v_1=\sqrt{2gy}$, where $y_1=0.48$ m, when his feet first touch the patio. From the equation of motion for constant acceleration, $a=\frac{v_1^2}{2y_2}$, where $y_2=2.2$ cm. However, I am not sure if I can use this since the equation of motion is derived for _constant_ acceleration. What do I do in the case of _average_ acceleration? Do I need an additional assumption such as constant jerk?


title: How to determine size of a Heat Exchanger?

text: I am designing a Tube heat-exchanger, similar to this: ![Heat exchanger image](http://upload.wikimedia.org/wikipedia/commons/f/fb/Heat_exc_2-1.png) My process requires water (at room temperature, 18C ~ 22C) that is being pumped out of a small tank (300 Liters) to be heated in a heat-exchanger to upto 65C. I have to use steam from a small steam generator (which we have to purchase) to heat that water. The primary purpose of the system is to pump out water from a small tank (300 Liters) with a pump and spray it in another tank with a nozzle for cleaning the tank. Once the water is sprayed in the final tank, it will be drained. For effective cleaning, we need the water heated to around 60C ~ 65C. I am looking for advice or a way to calculate how to design a simple heat exchanger for the system. The data i have at hand is the flow rate of water out of the pump, which is around 35 Liters per minute. The pipe at the pump outlet will be Stainless Steel, 1/2" in diameter (OD). Can any one point me in the right direction or help me calculate the following : 1) Size of outer shell of heat exchanger, 2) Size/Diameter of inner tubes of heat exchanger, 3) Number of inner tubes (or passes) of heat exchanger, 4) Steam flow-rate to achieve my desired results. Thanks. Zee


title: If a puck on ice deccelarates, is its speed "v = v0 - t * a" or is it "v = v0 -k * v0"?

text: I've been wondering about a puck sliding on ice or a puck in an air hockey table game. If a puck is hit and we start watching it as soon as it has reached its maximum speed and starts becoming slower, what will this deccelaration look like? I assume we take a snapshot of the puck in intervals.               a = Deccelaration     t = time passed since last snapshot     vCurrent = the current speed to be calculated when taking the snapshot     vPrevious = the speed it had at the last snapshot        * Is the deccelaration constant, so that vCurrent = vPrevious - a * t?   * Or is vCurrent = vPrevious - k * vPrevious, where k is some factor in the range of 0.01 to 0.1? The first assumption seems to make sense to me but I wrote a simulation of it and it just does not look right. The second one looks better, but is it real?   * If the latter one is the true, what would that "k" be? Does it have a name?   * What "kind" of deccelaration is the 2nd one?   * For the first assumption I can easily calculatethe way and time (v² = 2*a*s) it takes until the puck comes to a rest, but how do I have to calculate way and time for the second case?


title: MEMS gyroscope and orientation

text: I'm trying to understand how a MEMS gyroscope can give you orientation. The question may not make any sense, I may have some misunderstandings about the different topics... From the Wikipedia page about gyroscope: > _A gyroscope is a device for measuring or maintaining orientation_. If we have a gyroscope that can measure rotation around one axis, I interpret that statement as saying the gyroscope can also tell you what your orientation is relative to some position. Is this right? And what is the orientation relative to? I used this article to try to understand how a MEMS gyro works: http://sensorwiki.org/doku.php/sensors/gyroscope I can see how such a device can measure changes in angular velocity, but once the frame of reference stops spinning, how does it know the orientation? What is the position it is using to find the orientation? If you put these gyroscopes in a phone (like the iPhone has), how does it know the orientation of the phone? Again, I understand how it could calculate rotational velocity as the phone moves, but how does it know the final orientation?


title: Point charge potential (sign problem)

text: I'm a bit embarrassed, but I'm not able to compute the electric potential at point $P$ (at a distance $R$ from the origin) generated by a positive unitary point charge in the origin with the right sign. Simply use the definition $V(P) = -\int_\infty^P \vec E\cdot d\vec l$, forgetting the constant and choosing a straight line to integrate from infinity (so in the direction of $d\vec l=-\frac{\vec r}{r})$: $$V(P) = -\int_\infty^P \frac{\vec r}{r^3}\cdot d\vec l = -\int_\infty^P \frac{\vec r}{r^3}\cdot d\left(-\frac{\vec r}{r}\right) = \int_\infty^R \frac{1}{r^2}dr = -\frac{1}{R} $$


title: What is equation to find force of magnetic attraction

text: I was wondering as a student, when I was playing with magnets I thought like Gravitational force equation of Newton's Gravitation Theory, can we also calculate force of an magnetic attraction on an para-magnetic object\material as it can help me learn more about how big an magnet needs to be to create this much pull or something along lines of Engineering or understanding how objects work. I could not find any formulas pertaining the force of attraction on an para- magnetic body when induced to an magnetic field, therefore I want to ask an equation to calculate force of an magnetic attraction on an para-magnetic object\material? Or does one even exist? It would be kind, if someone explains the equation as I want to learn as well. Thanks! _THIS IS NOT AN HOMEWORK QUESTION_


title: Cleaning Already Mounted Microspheres on an AFM

text: I am running an experiment that uses a microsphere (Diameter ~ 50um) mounted onto the end of an AFM cantilever. I run several experiments in a row, but somewhere during a sequence, the microsphere acquires some non-organic dirt that effects the outcome of the experiment. Does anyone know - or can suggest - a way to clean the ball while it is still mounted onto the AFM? Or a way to clean the ball at all? We have a UV plasma cleaner, but it is not doing the job. Thanks


title: Simple ohms law on a battery ? Paradox or conceptual error?

text: Suppose we have a regular pencil battery which supplies DC voltage $V$. Say we take copper wire and connect the ends of the battery to an $R$ ohms resistance. Then Ohm's law tells use the current in the wire is $ \frac{V}{R}$. This means as we keep decreasing the value of $R$, we will keep getting higher and higher values of current, since $V$ is fixed. Now if we simply connect the ends of the battery by a copper wire without an intermediate resistance, of course the value of the current will not be infinity, but it will be $\frac{V}{R_{copper}}$ which is still very large. The resistance of copper is so small that even for $V=1.5$ volts we will get current of larger than 1 Amp with copper. And according to this link 1 Amp can almost give you a heart attack. So why is it that we dont hear about major accidents about people connecting two ends of a pencil battery with regular copper wire? Is there some fallacy in my reasoning above?


title: Angular Displacement

text: If something is rotating about a point and it covers a complete circle, should we take its angular displacement as 360 degree or 0? Please give link to some established material on this subject which defines your answer, whether it is that it should be taken as 0 or 360 degrees. Question that led to this problem : The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 seconds. 1. What is its angular acceleration, assuming the acceleration to be uniform, 2. How many revolutions does the wheel make during this time. In the solution to above question the author(s) for solving part 2 have used equation of motion and mentioned that they have obtained angular displacement for it, it basically implied that the equations of motion used for rotation provide angular displacement which does not become zero on returning to original point which is not followed when we consider it analogous to displacement of linear motion. Addendum : Even here ( Angular displacement and the displacement vector ) the selected answer says that on completing the circle, angular displacement is 360 degrees, is there some established text to support this ? Similarly here ( http://www.ask.com/question/calculating-angular-displacement ) something else is said in the answer, is then angular displacement ambigous and hence has no correct definition, if there is please guide me to some established text.


title: The resolution limit for lithography in practice?

text: For a given wavelength of light $\lambda$, and a given numerical aperture (NA), I always see the statement in papers/etc. that we can perform lithographic patterning at the Rayleigh limit given by $\approx \frac{0.61 \lambda}{NA}$. This seems really odd to me because, in practice, I've always assumed that the upper-bound for how well one can do is a function of a particular polymer/etc. resist's threshold irradiance before exhibiting a chemical change? In practice how far apart do we need to space e.g. two Airy disks in order to have two well-defined lithographic features? Don't we also need to care about partial spatial coherence of the light (after passing through e.g. pinholes in a mask) leading to some kind of constructive interference?


title: Splitting light into colors, mathematical expression (fourier transforms)

text: I am trying to solve a problem that includes a function of the light hitting a certain area. My question is, how would I change a function $G(x)$ of photons hitting a certain area to include just photons of a certain wavelength, say red light. I feel like this could be accomplished using a Fourier transform and de Broglie's law, but I'm not sure. Can someone please help, just for a general Gaussian function $G(x)$? More information: Basically, given a function that gives the number of photons hitting a certain area, I want a mathematical way to determine how many of those photons are of a specific frequency (such as red light). G(x) is defined as the integral in a gaussian slit experiment (that is, a double slit experiment with the path integral of a gaussian probability) such as in Feynmann's Path Integrals and Quantum Mechanics or in arxiv.org/pdf/1110.2346.


title: Projectile Motion with Air Resistance and Wind

text: I am wondering how the general kinematics equations would change in the following situation. If an object were fired out of a cannon, or some sort of launcher, so that it had both an initial velocity and an initial angle, and air resistance is taken into account, what would be the equations for the x and y components of the position, velocity, and acceleration. Furthermore, I am wondering how these equations would change if there were also a wind blowing at an angle. In essence, what I would like to know is how to rewrite the kinematics equations to take into account the air resistance and moving wind and the terminal velocity. The reason I want to know this is that I am writing a program to model this behavior, but I first need to know these equations. Also, if possible, could someone provide some help on finding equations for the maximum height the projectile reaches, as well as the distance it travels before it hits the ground? I would like both of these to be values the user of the program can find if desired. Oh, and in the scenario of the wind, it can blow from any angle, which means it will affect the x and y velocities and either augment them or lessen them depending on the angle at which it blows. So I guess another request is an explanation of how to obtain the set of equations (position, velocity, acceleration) for the x direction based on whether the wind angle is helpful or hurtful, and how to obtain the set of equations for the y direction, based again on whether the wind is helpful or hurtful. I would naturally have a constraint on the wind velocity so that the object would always inevitably hit the ground, so the force of the wind in the y-direction, if it were blowing upwards, would have to be less than the force of gravity of the object, so that it still fell. Sorry, I know I'm asking a lot, it's just that I really want to understand the principles behind this. Any help at all here would be very much appreciated, but if possible, could whoever responds please try to address all of my questions, numerous though they are? Oh, one final note. As this is being written in a computer program (python 2.7.3, to be exact), I cannot perform any integration or differentiation of the functions. Instead, I will need to create a small time step, dt, and plot the points at each time step over a certain interval. The values of the radius of the object, its mass, its initial velocity and angle, the wind velocity and angle, and dt can all be entered by the user, and the values of wind angle and wind velocity are defaulted to 0, the angle is defaulted to 45 degrees, and dt is defaulted to 0.001, although these values can be changed by the user whenever they desire. Thanks in advance for any help provided!


title: What is the force of friction between two bodies given their masses and a force pulling them as a unit accross a surface?

text: Where a force of 200N pulls two blocks together(as one system) across a horizontal table top(µ=0.800) $m_A$ = 5.00kg, $m_B$ = 10.0kg   1. Find the acceleration of the system.    2. Find f$_k$ between B and A I found a to be 5.485 m/s² which agrees with the textbook's 5.5m/s². The textbook says b is 173N but I can't seem to get a number even close to that. How does one go about solving this kind of equation, please provide calculations or formulas in the order they are needed, insteed of just abstract steps.


title: Can I estimate the long-term surface heat transfer coefficient based on a temperature difference between the air surface and ground surface?

text: I want to estimate the long-term or annual heat transfer coefficient for the earth's surface in a particular area where the mean annual air surface temperature is about 13$^\circ$C, and the mean ground surface temperature is about 15$^\circ$C. How can I do this? The general expression is $h=\frac{Q}{A \cdot \Delta T}$. So I suppose the heat flux term $Q$ is some sort of sum of the earth's outward flux and the sun's inward flux (I have a good estimate of the former: ~70mW/m^2, but I don't know the latter for this latitude. The latitude is about 37 degrees south.)


title: picture and isomorphisms

text: I found a paper by A. Belopolsky : "Picture changing operators in supergeometry and superstring theory" where he says there exists a possible physical state in one picture that doesn't exist in another picture. What A.B. does is essentially defining the picture formalism on the BRST complex and the de-Rham complex saying that the main idea would be that there is an even and an odd ghost number, picture changing involving the change in the odd ghost number. What strikes me here is the splitting of the complex on the odd number. I am not sure I get the full idea about what this means? Is it a sort of split-exact complex? And then why are the isomorphisms on the cohomology such a big deal? Shouldn't that be natural?


title: Uncertainty principle with two photons

text: Imagine an experimental setup in which you have to measure the momentum and location of a particle. To measure it we know we will have to affect it, and the uncertainty principle would come into the picture, but I have a different setup. The classical setup is that you fire a photon to measure the location of the particle, but the particle will change its momentum due to the collision with the photon. I decided to take two photons. I will shoot one photon from either side of the particle, so the effects of the two photons cancel each other, giving an accurate measurement. To understand this, see the picture below.   1. **The classic experiment** > ![enter image description here](http://i.stack.imgur.com/uLGjn.jpg)   2. **My thought experiment** > ![enter image description here](http://i.stack.imgur.com/cfs3w.jpg) In the second experiment, we shoot a photon of the same energy as the first one and counteract the effect of the first photon, so the electron would continue on its original path. Please tell me where I am wrong. **EDIT** We will have to take multiple photons but equal from both sides and in opposite directions.


title: Which are the good universities for doing PHD in computational physics?

text: Currently i am doing MSC(physics) from Pune university, India. And I want to do PHD in computational physics as it interests me the most. So I want to know which universities will be a good option for me to do PHD (Specify only those which provides scholarships/fellowships). With that I would like to know what are the basic requirements I will have to fulfil for admission.   Which exams are compulsory of the following 1) GRE 2) TOEFL/IELTS 3) PHYSICS GRE to get admitted. And i want name of the few universities which majorly focus on research in computational physics


title: Computing the force generated by a sail on a boat

text: This is a follow up question to the question I asked yesterday: Problem understanding basic sail mechanics I am focusing purely on the Newtonian aspect of motion and I am computing this as follows: First I compute the relative wind ($v_r$) velocity by subtracting the ships velocity ($v_s$)from the true wind velocity ($v_t$) $v_r = v_t - v_s$ Next I take the normal of the sail (in to the wind), $n_s$, and "bounce" the wind off it, computing the out velocity of the wind, $v_{out}$ $v_{out} = v_r - (2 * v_r \cdot n_s) * n_s $ Next I compute the change in wind velocity, $\Delta v$ $\Delta v = v_{out} - v_r $ This is linearly proportional to the force the sail exerts on the air, hence $-\Delta v$ is linearly proportional to the force exerted on the boat. Next, I compute the keel force that offsets the horizontal part of the sail force, allowing the boat to move against the wind. I take $n_k$ to be the normal of the keel going in the opposite direction to the sail force and perpendicular to the boat heading. I then compute the keel force, $F_k$ to be $F_k = n_k * |-\Delta v|$ i.e. the magnitude of the sail force in the direction of the keel (perp to direction of boat facing). To compute the resultant force, I of course sum these two forces. Firstly, is all that correct. Clearly it is missing resistance from the water, but aside from that, do the calculations correctly reflect the answer given in my previous question. Secondly, what parametrises these forces and how. What I am seeing at the moment is, when sailing with the wind, the boat accelerates very quickly (up the the speed of the wind). However, when I try to sail near to the wind (is that the correct phrase? for when my boats forward and the direction of the wind are near and opposite) although I can see the apparent wind speed increasing, the force applied is still very small. Is this was you would expect to see?


title: Reducing the distortion of transmitted light through a prismatic array

text: I'm wondering if there is a way to reduce the distortion of light transmitted through a prismatic array ( _without touching the surface of the prisms_ ). ![enter image description here](http://i.stack.imgur.com/254rn.png) The obvious thing to try is a corresponding prism array: ![enter image description here](http://i.stack.imgur.com/aWDbF.jpg) Although this might reduce some of the distortion, it is far from perfect. Is there something better? An array of concave lenses?


title: Surface potential resulting from the charge transfer between insulator and conductor

text: Common non-contact electrostatic voltmeters are used to measure the surface potential. Imagine we place a charged insulator on top of the conducting plate (insulated from the surrounding) and measure the resulting potential from the bottom of the plate. How is the measured potential related to the charge transferred from the insulator? To my understanding, the charge will be transferred from the insulator to conductor only at their interface. Therefore, the potential detected by the voltmeter at conductor surface should be only due to this portion of charge transferred. Is that correct? Does the conductivity affect the surface potential detected? If yes, what is the relationship? I do not have much experience in electrostatic events, I am a chemist trying to understand the above situation.


title: Water draining from a height into the bottom of a reservoir

text: If I hang one 5 gal. Bucket directly above another, put a hole in the bottom of the upper bucket with a tube inserted just inside hanging all the way to the bottom of the lower bucket and fill the upper, will it drain completely into the bottom bucket?


title: Having a problem about entropy, thermodynamics

text: I am a high school student. So, while studying about thermodynamics, I got a little curious about entropy. As I read, entropy is the rate of change of chaos. So, if the entropy change of a system is $\delta$S and the primary and final entropy is $S_1$ and $S_2$, then, $\Delta$$S$ = $S_2$ - $S_1$ Now, come to the mathematical expression of $\Delta$$S$ I am really disgusted by the very brief answer of the mathematical expression in my book. It says that, in a reversible process, the amount of heat or $\Delta$$Qrev$ a system is emitting or producing, divided by the temperature at which the heat is emitted or produced of $T$, or $\Delta$$Qrev$$/$$T$, is equal to $\Delta$$S$. So, $\Delta$$S$ = $\Delta$$Qrev$$/$$T$ Ok, so my book doesn't tell how does this equation arise, and that is the irritating thing. Also, there is another question regarding this topic, when we are talking about the rate of change of chaos: what is the relation of temperature and heat in here? Although I know that this is a complex part of physics, I am asking for your help so that I can be able to have a clear idea about the matter. Thank you.


title: How many coupling constants if my gauge group has many factors?

text: I am reading a review article where $U(1)\times{}SU(2)\times{}SU(3)$ gauge transformations are considered. It says that when such a gauge transformation is done the gauge fields $A^{\alpha}_{\mu}$ transform like this ($\alpha$ is just a label of the different fields) $A^{\alpha}_{\mu}\to{}A'^{\alpha}_{\mu}+\partial_{\mu}\epsilon^{\alpha}(x)+C_{\alpha\beta\iota}\epsilon^{\beta}(x)A^{\iota}_{\mu}$ where we have $C_{\alpha\beta\iota}=gf_{\alpha\beta\iota}$ being $g$ the gauge coupling constant. Am I to expect there to be 3 different coupling constants, one for each factor of my gauge group, or do they somehow mix to generate one?


title: Why is electric current dangerous to humans?

text: How does a strong electric current harm our body? A strong electric current will posses a great charge. But how does that charge injure us?


title: Is speed of sound really constant?

text: Does not speed of sound actually depend on the frequency and/or amplitude of the waves? If so, why it is constant?


title: Magnetic field and Newton's third law

text: If a magnet exerts force on a iron block (opposite and **_EQUAL_** ), does a iron block also exerts force on magnet (via Newton's third law)? If yes then what magnetic property does it has to produce equal and opposite force on magnet considering that its not a ideal environment? If no then is it not the violation of newton's third law?


title: Aerodynamics drag of hollow cylinder vs solid cylinder of the same cross area?

text: I wonder how a hollow cylinder at the same cross area perform vs a solid one, i.e the hollow cylinder has larger radius? I guess they have a similar drag, is that true?


title: What is the difference between Feshbach resonance and Fano resonance?

text: What is the interpretation of "resonance" in Feshbach resonance and Fano resonance? What is the difference of Feshbach resonance and Fano resonance?


title: Placing two similarly charged particles in space

text: Now, I will make a hypothetical situation. Assume that we place two similarly charged particles (lets take electrons) in space. Imagine that there is no other force acting on the particles except the repulsive force and the gravitational force of the particles. In other words, only these two electrons are present in the universe. So they are free from any outside interference. Now by nature, these electrons will start moving away from each other due to the repulsive force. Since there is nothing to stop them (gravitational force will only slow them down and not stop them as it is of a lesser magnitude than the repulsive force) they will keep moving and never stop. Over here we exclude expansion of space also for no complications. Now since the particles will keep moving as there is a constant repulsive force acting on them, they will do infinite work because $Work = Force * displacement$ and the displacement over here will keep increasing. Please tell me what is the problem in my thought experiment because it violates conservation of energy.


title: Calculating the components of angular momentum of a rigid body

text: You have a rigid body with 1 fixed point in space (the origin). It's self-explanatory how to get the following equation for the angular momentum: > $\vec L = \sum_n m_n\vec r_n\times\vec v_n$ Where you take the sum of all "$n$" indicates all "$n$" points of mass.   This can be transformed into: > $\vec L = \sum_n m_n(\vec\omega(r_n^2)-(\vec\omega.\vec r_n)\vec r_n)$ Now, out of this, I have to get the following: > For component "$i$" of this equation, you get:   >  $L_i = \sum_n m_n(r_n^2\omega_i-x_{ni}\sum_j\omega_jx_{nj})$ I understand that for component "$i$", the scalars $m_n$ and $r_n^2$ are the same as for the other components, I also understand that for component "$i$" I need to take the $\omega_i$ component.   But what is meant with everything that follows after that? What does the "$x$" indicate for example? Does the "$j$" indicate the other components?


title: How is a qubit realized in a cavity?

text: Considering a single photon in a cavity, how is a qubit realized in this setup? How is the qubit $|0\rangle$ or $|1\rangle$ manipulated? I.e. how are the transitions $|0\rangle \to |1\rangle$ and $|1\rangle \to |0\rangle$ achieved in a controlled manner?


title: How was the universe created?

text: I do not know much beyond high school Physics. Thus, I am asking this question from almost layman's perspective: > _What, as per the best of our existing knowledge and widely accepted among > the scientific community, are the models of creation of the universe, and > what is their core argument?_


title: Doppler cooling limit vs recoil limit

text: I was discussing laser cooling in class today and I understood that the main principle of the process is to tune a laser to a frequency lower than the absorbtion frequency of the atom and so only the atoms with a certain velocity will absorb the photons. These atoms then re-emit a photon in a random direction thus on average cooling the atom. But I didn't understand the difference between the so called 'doppler cooling limit' and the recoil limit. I've read on hyperphysics.com that the doppler cooling limit has something to do with random walk motion. Isn't this, though, just the atom recoiling in random directions thus the recoil limit? Could someone explain the difference?


title: Quantum uncertainty of a singularity: A Black Hole Problem

text: A black hole in GR seems to have a sharply defined radius. Of zero, that is since all the mass has been compressed into the infinitely dense center point. However, shouldn't the fuzziness of quantum mechanics destroy this well- defined shape before the absolute point is reached? That is, how can the classical diagram of a black hole like a vortex exist when the sides of the vortex are quantum-close to each other? So here's the quantum uncertainty I'm referring to. Pink is the quantum closeness one can have I suppose.![enter image description here](http://i.stack.imgur.com/TCtA0.png) Next, in respect to Jeremy Schirmer's answer, are you saying that within the event horizon space basically doesn't exist anymore? That's quite wild of a thing to say but in no way surprising when it comes to black holes. ![enter image description here](http://i.stack.imgur.com/AsTzi.png)


title: What is $c + (-c)$?

text: If object **A** is moving at velocity $v$ (normalized so that $c=1$) relative to a ground observer emits object **B** at velocity $w$ relative to **A** , the velocity of **B** relative to the ground observer is $$ v \oplus w = \frac{v+w}{1+vw} $$ As expected, $v \oplus 1 = 1$, as "nothing can go faster than light".   Similarly, $v \oplus -1 = -1$. (same thing in the other direction) But what if object **A** is moving at the speed of light and emits object **B** at the speed of light **in the exact opposite direction**? In other words, what is the value of $$1 \oplus -1?$$ Putting the values in the formula yields the indeterminate form $\frac{0}{0}$. This invites making sense of things by taking a limit, but $$ \lim_{(v,w)\to (1,-1)} \frac{v+w}{1+vw}$$ is not well-defined, because the limit depends on the path taken. So what _would_ the ground observer see? Is this even a meaningful question? **Edit:** I understand $1 \oplus -1$ doesn't make sense _mathematically_ (thought I made it clear above!), I'm asking what would happen physically. I'm getting the sense that my fears were correct, it's physically a nonsensical situation.


title: Jahn-Teller effect is based on the Born-Oppenheimer approximation?

text: I am now reading the quantum mechanics textbook by Landau and Lifshitz. In section 102, they discuss the Jahn-Teller effect. It seems that they assume the Born-Oppenheimer approximation. There is no dynamics for the nuclei. Their positions are simply parameters for the electrons. This then means a pitfall. The finiteness of the masses of the nuclei means the nuclei have dynamics and can tunnel between Born-Oppenheimer potential minima. This then means the symmetry of the nuclei configuration is restored. Is this understanding right?


title: Will the CMB ever stop shining?

text: Will we ever reach a point where all the light that was set free by recombination finally reaches us from our point of view and the CMB stops "shining" for observers on Earth?


title: How does interaction of a system with the environment lead to the damping of interference terms?

text: A general way to describe a system $S$ that is entangled with an environment $E$ is $\rho_{S}=Tr(\rho_{SE})=\sum\limits_{m,n}c_mc^*_n |s_m\rangle \langle s_n| \langle e_n|e_m\rangle$ with $\psi_S=\sum\limits_n c_n|s_n\rangle$ the state of the system and $|e_n\rangle $ the corresponding environment states. In general the different environment states can not be considered as orthogonal, thus my question more neatly formulated is: Is there a general mechanism, such that the environment states become orthonormal, or is this actually just a _hypothesis_ essential for the emergence of decoherence (that has been supported by many model calculations and experiments).


title: Interpreting Argyres' spectrum of spontaneously broken SUSY QM

text: I can't understand the spectrum in the figure on page 19 from Argyres' lecture notes on supersymmetry: http://www.physics.uc.edu/~argyres/661/susy1996.pdf ![AryresFigure](http://i.stack.imgur.com/NzMfg.png) Argyres is considering a supersymmetric quantum mechanical system of an anharmonic oscillator, with a superpotential $W\sim x^3$. The plots of $W$ and $V$ make perfect sense. What doesn't make sense is the spectrum on the right. Why are there _both_ x's and o's over each Hamiltonian $H_1$ and $H_2$?? I thought $H_1$ is exclusively the spin-up Hamiltonian and $H_2$ is exclusively the spin-down Hamiltonian, so therefore the spectrum consist of a column of _just_ x's over $H_1$ and a column _just_ of o's over $H_2$. Additional request: Would someone please write down the form of $H_1$ and $H_2$ in their answer, so to make sure we're on the same page? A graph of the the respective potentials $V_1$ and $V_2$ would be even better. Take a look at the _much more_ sensible figure on page 7. This is something that I can comprehend. ![enter image description here](http://i.stack.imgur.com/JMqgJ.png)


title: How can I keep a smaller water reservoir's water level at half available when being fed from a larger reservoir?

text: I'm trying to create my own ultrasonic humidifier. I ordered the misting part which works great but it only functions correctly in shallow water. So I'd like to feed from a large water reservoir to a smaller one. My question is how can I fill the smaller reservoir to a desired water level? Will I have to use a closing/opening valve or is there a simpler way? (I was thinking a small balloon hooked up to a pulley that opens and closes a latch much like a toilet but I am trying to avoid complexity.) ![enter image description here](http://i.stack.imgur.com/shdiO.jpg)


title: heat of a laptop when placed on a table, when placed on a pile of books and when placed on a bed

text: I heard somewhere that it is dangerous to place a laptop on a bed. The reason given was that placing the laptop on the bed blocks (assume that the laptop does not have sideway fans - it only has air holes or air intake fans at the bottom.) the air intake fans of the laptop. However, we often place our laptops on a table or desk. So, what makes the laptop to over-heat when placed on a bed? Also, If one places a laptop on a pile of books, will the laptop over-heat?


title: Scattering Amplitudes in Centre of Mass Frame

text: I'm reviewing page 59 of the QFT notes here and am a little confused by a reference frame argument. You can compute the second order probability amplitude term for nucleon-nucleon scattering to be $$-ig^2\left[\frac{1}{(p_1-p_1')^2-m^2+i\epsilon}+\frac{1}{(p_1-p_2')^2-m^2+i\epsilon}\right](2\pi)^4\delta(p_1+p_2-p_1'-p_2')$$ in a scalar field theory approximation. Now the author argues that we may remove the $i\epsilon$ terms by moving to the centre of mass frame. Here he says that $p_1=-p_2$ in this frame and that $|\vec{p_1}|=|\vec{p_1'}|$ by conservation of momentum. He continues to claim that the four-momentum of the meson is hence $k=(0,\vec{p}-\vec{p'})$ so $k^2<0$. Quite what $p,p'$ are I don't know exactly. I don't understand this argument at all. Surely in the centre of mass frame, the sum of all momenta $p_i$ and $p_i'$ is zero (.)? Also where has the second constraint come from? I don't see how morally you could get more than my claim (.). Could someone explain this argument to me? Very many thanks in advance.


title: Thermal equilibrium and non correlations

text: I read in a book on quantum fluctuations and quantum noise that, at thermal equilibrium the classical canonical variables are uncorrelated, ie: $$\langle xp\rangle=\langle x\rangle\langle p\rangle$$ But I am not sure to understand the sense of _at thermal equilibrium_ , for me it just means $$\langle x^2\rangle=\langle p^2\rangle=\frac{T}{2}$$ in the correct units with $T$ the temperature. On the other hand what I can derive easily in the canonical ensemble is: $$\langle xp \rangle = Z^{-1}\int {\cal{DxDp}}\;\text{e}^{-\beta H(x,p)}xp$$ and $$\langle x\rangle\langle p \rangle = Z^{-2}\int {\cal{DxDpDx'Dp'}}\;\text{e}^{-\beta H(x,p)}\text{e}^{-\beta H(x',p')}xp'$$ which are equal if we have the following equality $$H(x,p) = H_1(x) + H_2(p)$$ separability of $x$ and $p$ in the Hamiltonian, which seems unrelated to the previous hypothesis of thermal equilibrium (used here by taking the mean over the canonical distribution of course).


title: How far can a voice carry through the desert at night?

text: Let's use these conditions: temp = 7C, relative humidity = 10%, air pressure = 85 kPa, elevation = 1500m, shouting at 100dB (not sure if this is a reasonable volume). Given these conditions, what distance could a human voice travel and still be mostly understandable? How far to be heard at all? I haven't done any physics for a long time, and I really don't know how to go about this. Thanks.


title: Do orbitals overlap?

text: Yes, as the title states: Do orbitals overlap ? I mean, if I take a look at this figure... ![enter image description here](http://i.stack.imgur.com/8aDOv.jpg) I see the distribution in different orbitals. So if for example I take the S orbitals, they are all just a sphere. So wont the 2S orbital overlap with the 1S overlap, making the electrons in each orbital "meet" at some point? Or have I misunderstood something?


title: Lagrange's equations: What is $\dot{q}_j$?

text: I'm looking at the solutions to a problem about a uniform thin disk. For the sake of this question, I start with $$L=\frac{1}{2}m\left( r\omega \right)^2$$ Then we plug it into Lagrange's equations: $$\begin{align*} \frac{d}{dt} \frac{\partial L}{\partial \dot{q}_j} - \frac{\partial L}{\partial q_j} &= Q\\\ \frac{d}{dt} \frac{\partial \frac{1}{2}m\left( r\omega \right)^2}{\partial \left( r\omega \right)} - \frac{\partial \frac{1}{2}m\left( r\omega \right)^2}{\partial q_j} &= Q \end{align*}$$ **How is it that $\dot{q}_j = r\omega$?**   **What is $q_j$ then, as well?** I'm thinking along the lines of $$\begin{align*} \dot{q}_j &= r\omega\\\ \dot{q}_j &= r\frac{d\theta}{dt}\\\ q_j &= r\theta \end{align*}$$


title: Tidal acceleration for a retrograde rotation?

text: Consider two nonelastic spherical bodies with uniformly distributed density, a small such body in a circular orbit around the bigger one. And consider the smaller body's rotation is matched (as if "tidally locked") to its orbit so the same hemisphere always faces the larger body. Now, here's my question: a particle on the daylight surface of the orbiting body is orbiting the "sun" with a smaller radius than a particle resting on the "night" side. If the two particles weren't attached to the body, the daylight particle would have a faster solar orbit and the nighttime particle a slower orbit. Would this not impart a retrograde rotational force on the orbiting body? If this is an already understood concept, what is it called? I read up on tidal locking and tidal acceleration on Wikipedia, and this dynamic wasn't mentioned. I think it's kind of interesting because I never thought about tidal forces doing anything with inelastic objects.


title: London penetration depth

text: Which type two s-wave superconductor has the smallest London penetration depth? What is l_lamda ?


title: AdS Space Boundary and Geodesics

text: I'm new to working with AdS space and am primarily concerned with black holes. I'm just playing round with the metric for AdS$_4$ $$ds^2=-f(r)dt^2+f^{-1}(r)dr^2+r^2d\zeta^2$$ for $f(r)=r^2+m $, $\space\space\space\zeta=d\theta^2+\sin^2\theta d\phi^2$. My problem is trying to understand the boundary; specifically when considering particle trajectories:   1. For null geodeiscs, I've read that they reach the boundary of AdS space, which seems to commonly expressed as saying they are represented as straight lines. I don't understand how these two phrases are the same and how to show that this is the case starting from the metric I've stated. Using constants of motion etc, and assuming a radial path, I find the equation $\frac{dr}{d\lambda}=k$, for $k$ constant.   2. For timelike geodesics, I know they do not reach the boundary and equivalently I read that they are represented by the boundary of slices of the hyperboloid i.e. ellipses. Again, how do I show that this really represents timeline geodesics? As above (but $ds^2=1$ in this case) I find the equation $\Delta\tau=\log(r+\sqrt{k^2+m+r^2})\space \vert^b_{r_0}$ where $b$ is the boundary and $r_0$ the initial $r$. I've been reading (as much as I can using the fairly limited coherent literature on the topic) and I can only find discussions on this matter, with some diagrams. None seem to go about this question the way I have above and consequently I'm thinking there must be something wrong with what I've done.


title: Why are the virial coefficients functions of temperature only?

text: I have read in multiple places that the virial coefficients in the virial equation of state, $Z=1+{B \over v}+{C \over v^2}...$, are functions of temperature only and are independent of pressure (or equivalently, molar volume). Is this purely an empirical observation or is there some deeper statistical mechanics reason why the virial coefficients should not depend on how close the particles are together (i.e. the molar volume)? I understand that $B$ represents pair-wise interactions, $C$ represent three- particle interactions, etc. but again shouldn't the coefficient, say $B$, depend on how close the two particles are to each other?


title: Wave function collapse

text: When we try to measure the position of a system, wavefunction collapses to form a spike. After a while, the wavefunction spreads again, and you take another measurement, the results will be different" in general. What would happen if we measure the energy instead? Again, the wavefunction collapses to one eigenstate, after a while, would the wave spread out again? _And how_ could one measure the energy without knowing its momentum and potential?


title: Orthonormality of Radial Wave Function

text: Is the radial component $R_{n\ell}$ of the hydrogen wavefunction orthonormal? Doing out one of the integrals, I find that $$\int_0^{\infty} R_{10}R_{21}~r^2dr ~\neq~0$$ However, the link below says that these wave functions should be orthonormal (go to the top of page 3): http://www.phys.spbu.ru/content/File/Library/studentlectures/schlippe/qm07-05.pdf Am I doing something wrong? Are the radial components orthogonal, or aren't they? Are there some kind of special condition on $n$ and $\ell$ that make $R_{n\ell}$ orthogonal? Any help on this problem would be appreciated.


title: How does one prove that the current of a spontaneously broken symmetry generates a particle?

text: I am having a hard time arguing that, after spontaneous breaking of a continuous symmetry of a field Lagrangian, local fluctuations around the vacuum can be interpreted as particles (without referring to analogies from condensed matter physics). I encountered a treatment which stated that, when the symmetry is unbroken, the corresponding current annihilates the vacuum $$J^{\mu} | 0 \rangle = 0$$ while after spontaneous symmetry breaking, the current creates a state out of the vacuum with some momentum $k^{\mu}$ $$J^{\mu} | 0 \rangle = k^{\mu} | k \rangle $$ My question is why this second equality holds only after spontaneous symmetry breaking.


title: Microwave absorption in tissue

text: Why do I have a big microwave absorption in tissue, when the tissue conductivity is high? I thougt the opposite would be correct. Can somebody explain the reason?


title: Alternative theories to the big bang?

text: Hey all, are there any theories out there on the origins (or infinite existence of) the universe beside the big bang that actually adhere to current scientific knowledge and fact?


title: Finite Square Well Inside an Infinite Square Well

text: Ok here's a potential I invented and am trying to solve: $$ V(x) = \begin{cases} -V_0&0<x<b \\\ 0&b<x<a \\\ \infty&x>a \\\ \end{cases}$$ and $V(-x) = V(x)$ (Even potential) I solved it twice and I got the same nonsensical transcendental equation for the allowed energies:   $$ \frac{-k}{\sqrt{z_0 - k^2}} \frac{e^{2kb} + e^{2ka}}{e^{2kb} - e^{2ka}} = \tan(b \sqrt{z_0-k^2}). $$ , where $k=\sqrt{-2mE}/\hbar$ and $z_0 = 2mV_0/\hbar^2$ The problem is that when I take the limit as $b→a$ (the ordinary infinite square well) I get a division by 0. So is there something fundamentally wrong with trying to solve this potential? Is it wrong to have an Infinite potential and bury some of it under the 0 (negative potential) ? Note: I am solving it for negative energies (bound bound states?).


title: Can clouds quench thirst?

text: Suppose you are standing on a mountain surrounded by clouds. You open your mouth and try to swallow the clouds (it's crazy, but still).   1. Can the droplets of water in the form of vapor actually be counted as 'drinking water'(or swallowing, same thing) ?    2. Will the clouds enter the body? And what happens when you breathe the clouds?    3. Or suppose you lower the temperature of the clouds(if you can), will it change to water?


title: Lorentz transformations, why $t$ and not $t'$?

text: In the derivation of the Lorentz tranformation you get the fromuls: $$x=k(x'-ut')$$ $$x'=k(x+ut)$$ where $k$ is a constant that is yet to be determied ($k= \frac{1}{\sqrt{1-\frac{u^2}{c^2}}}$) why is the formulas of the above like tis rather then the below: $$x=k(x'-ut)$$ $$x'=k(x+ut')$$ (where all values with ' after them are from the same reference frame).


What happens if we put a pinch of salt on the ice cubes which is melting in the water? How will the ice react to the salt, and what other things will happen after mixing them?


title: Is this how I find the rate of change of internal energy for filling a vessel?

text: If I am filling a tank with something (lets say air) and both its volume and pressure are changing with time (It's not rigid), it it safe for me to say: $$u=h-Pv$$ $$\frac{du}{dt}=\frac{dh}{dt}-P\frac{dv}{dt}-v\frac{dP}{dt}$$ I used the product rule when I differentiated the $Pv$ term


title: What could make the SWITL materials behave like this?

text: SWITL - what could this be? Ultra thin paper with some adhesive that binds to fat? (or as I originally thought, a hoax)? A robotic hand to scoop gel-like substances... http://japantechniche.com/2009/06/09/the-world-first-robotic-hand-scoop-switl/ Truly weird video - looks like some kind of super gluey paper http://furukawakiko.com/tech/page285.html http://www.youtube.com/watch?v=MQECrcZs6W Update: I did do a patent search. I think it might be this patent I found via Espacenet


title: Size of atoms based on atomic number

text: I'm interested in the size of atoms (extent of the outermost electron cloud), in particular its cross-sectional area and how it scales by increasing Z. (I trust that this won't be affected much by the number of neutrons?) I recognize that for a given atom/ion one can simply look up the data, but I'm interested in a more 'first-principles' kind of view. The distances of electrons in given orbitals is not constant across different atoms, since as the nucleus gains protons the orbitals tend to get crushed somewhat closer I believe. (In fact my final goal will be to determine scattering for charged particles, which is based on much more than the geometry, but I became interested in this particular subproblem apart from that ultimate question.)


title: What is the most stable nuclide of an isobar?

text: From the semi-empirical mass formula, the mass of an atomic nucleus is $$M\left(A,Z\right)=Zm_p+(A-Z)m_n-\frac{E_b(A,Z)}{c^2}$$ I've been told (at first) that for a given mass number $A$, the most stable nuclide of the isobar is the one with the smallest mass. Then it should be the one with proton number $Z$ such that $$\frac{\partial{M}\left(A,Z\right)}{\partial{Z}}=0$$ i.e. \begin{equation}m_p- m_n-\frac{1}{c^2}\frac{\partial{E_b}(A,Z)}{\partial{Z}}=0\end{equation} but then I had a test where the professor asked for the most stable isobar and he argumented that this was the one for which the binding energy was the highest, meaning only that $Z$ satisfies $$\frac{\partial{E_b}(A,Z)}{\partial{Z}}=0$$ so I got it wrong on the test. Either way the difference is just a (small) constant, so the values $Z$ they both predict are roughly the same for low values of $A$. Let me call ${Z_m}$ the one obtained through minimizing $M$ and ${Z_E}$ the one obtained through maximizing ${E_b}$, then a plot looks like this ![Most stable isobars through minimizing $M$ and through maximizing $E_b$](http://i.stack.imgur.com/3jrDr.png) The values of $Z$ begin to separate for large $A$, but the good values here _supposedly_ * are those of $Z_m$, for example, for $A=209$: \begin{align}Z_m(209)&=83.36\approx83\\\ Z_E(209)&=82.22\approx82\end{align} because the most stable isobar for $A=209$ _as given in Table A.4 in Shultis & Faw's book_* corresponds to $Z=83$ (element $\text{Bi}$). But both that the binding energy should be a maximum and that the mass should be a minimum makes sense; in the Wikipedia article, for example, the correct one is given as $Z_E$, and I'd even go with the first one, but as I've seen, the best one is the one for minimum mass, so... How come this happens? Is it a just a fault of the theory (namely the liquid drop model) or what?


title: formal framework for talking about 'minimal couplings'

text: usually on physical theories one would have Lagrangians or Hamiltonians with multiple fields; say, a vector $A_{\mu}$ and a scalar $\phi$ and one would postulate ad hoc a coupling between the fields which will be used to derive some physical states and then, retroactively support the coupling from a match with the physics Usually one reads about 'minimal couplings' and for scalars with vectors on might see a factor like $\frac{ \partial{\phi}}{ \partial{ x_{\mu}} } A_{\mu}$ But my question goes on in what general or abstract sense such factors represent a minimal coupling? minimum of what? if is the total degree of powers of the fields? do we have some variational principle for lagrangian couplings that these terms can be called a stable point in such variations?


title: Higgs boson production via positron-electron collision

text: One of the suggested diagrams for the Higgs production is the following:![enter image description here](http://i.stack.imgur.com/498wO.png) so basically an electron-positron pair annihilates and forms an (excited?) Z boson, which then decays into another (less excited?) Z boson and a Higgs boson. Why can't the electron-positron pair decay **directly** into a Higgs boson? Charge and lepton number would be conserved anyway, and if the pair has enough energy to produce the $Z^*$ boson in the first place it should have enough energy to produce the Higgs boson... ?


title: Helium and its unique behaviour

text: It is said that helium is lighter than air. What does that exactly mean ? If it is lighter than air,then there should be absolutely no trace of helium in earth's atmosphere(it should have flown into the space) Yet it is one of the most abundant element on earth ? How is this stored ?. If the balloons filled with helium rise in the air, why don't the helium storage tanks/vehicles rise ?


title: Can we treat $\psi^{c}$ as a field independent from $\psi$?

text: When we derive the Dirac equation from the Lagrangian, $$ \mathcal{L}=\overline{\psi}i\gamma^{\mu}\partial_{\mu}\psi-m\overline{\psi}\psi, $$ we assume $\psi$ and $\overline{\psi}=\psi^{*^{T}}\gamma^{0}$ are independent. So when we take the derivative of the Lagrangian with respect to $\overline{\psi}$, we get the Dirac equation $$ 0=\partial_{\mu}\frac{\partial\mathcal{L}}{\partial\left(\partial_{\mu}\overline{\psi}\right)}=\frac{\partial\mathcal{L}}{\partial\overline{\psi}}=\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi. $$ Now if we include a term with charge conjugation, $\psi^{c}=-i\gamma^{2}\psi^{*}$, into the Lagrangian (like $\Delta\mathcal{L}=\overline{\psi}\psi^{c}$), does this $\psi^c$ depend on $\overline{\psi}$ or $\psi$? Why or why not? If $\psi^{c}$ depends on $\psi$, why wouldn't the reason that $\overline{\psi}$ and $\psi$ are independent apply for $\psi^{c}$ and $\psi$? If $\psi^{c}$ depends on $\overline{\psi}$, how should we take derivative of $\Delta\mathcal{L}$ with respect to $\overline{\psi}$?


title: Application of Displacement Current

text: I'm reasonably happy with the derivation and results of displacement current, however, I'd like to be aware of a few practical applications of this idea. So far, the only one I'm aware of is when finding the magnetic field in between a capacitor using Ampere's Law. In such a case $I_c=0$ and $I_D$ has some definite non-zero value so as to account for the magnetic field we can physically measure in between the plates of the capacitor. What are other examples can you throw at me ?


title: Certain material heating water in a recipient

text: I don't know how to resolve a problem, but I don't want the answer since I'm almost going to have it resolved. What the problem says is we have 85 liters of water at 7ºC in an iron pot of 29kg. We want the water to be at 86ºC. The temperature of the iron pot is 12ºC. The water is heated by fire wood (65% of the thermal energy is wasted in combustion), and has a heating value of 12 MJ/kg. We need to determine the amount of wood needed to heat the water. I would apply the normal formula of energy transfer: m1*c1*(t2-t1)=m2*c2*(t2-t1). But since we are using fire wood there, I don't know how to resolve this problem, probably because I'm missing something there... and I don't know what should I do. Which formula or principle would I need to use when having the material and the heating value of the material used?


title: Horizontal Speed of Descending Parachute

text: I understand how to get the vertical (descent speed) of a parachute and its payload, but how could one find the horizontal speed/velocity of this parachute depending on the speed of the wind? (yeah I understand the higher the wind is, the smaller it's influence is as well) I'm having a hard time trying to figure out what the winds influence on a descending balloon is. I know it would push the parachute, but how much would that matter? I know it would push the payload, which trying to figure out a CD for would be rather hard!


title: Subgroups of the Clifford Group

text: We recall the definition of a Clifford group (over $n$ qubits) is the set of unitary transformations: $$\\{U: UPU^\dagger\in\mathcal{P}\\}$$ where $\mathcal{P}$ denotes the corresponding Pauli group (again over $n$ qubits). What progress has been made in characterizing the subgroups of the Clifford group, and in particular, what progress has been made in characterizing those subgroups isomorphic to the Pauli Group?


title: Has gravity ever been experimentally measured between two atoms?

text: Has there been any experiments, or are there any references, demonstrating gravity between atoms? If so, what are the key experiments/papers? Or if not, what is the smallest thing that has actually experimentally been shown to be affected by gravity? I don't know of specific papers demonstrating gravity between larger objects, but I can vaguely remember learning about them in my classical physics class as an undergraduate. However, I have never heard of experiments demonstrating gravity at atomic or subatomic levels. I don't have a physics background so it's not obvious to me, so just looking to see the actual research/evidence behind it, so I can start to try to imagine how gravity works at a quantum level.


title: Efficiency of a thermal reactor

text: I was told that the efficiency of any thermal reactor increases if it is operated at higher temperature- in this case, nuclear reactor was referred to. But I cannot seem to understand why...


title: What is the concept of cosmic strings?

text: What is the concept of cosmic strings? Is it related to the strings in the string theory, and if it is, then how?


title: Why doesn't De Broglie's wave equation work for photons?

text: Well, as I am learning about quantum physics, one of the first topics I came across was De Broglie's wave equation. $$\frac{h}{mc} = \lambda$$ As is obvious, it relates the wavelength to the mass of an object. However, what came to my mind is the photon. Doesn't the photon have zero mass? Therefore, won't the wavelength be infinity and the particle nature of the particle non existent? Pretty sure there is a flaw in my thinking, please point it out to me!


title: Do all event horizons emit radiation?

text: So, the event horizon around a black hole emits radiation, and Rindler space is full of thermal energy. I guess I have two questions- does the Unruh effect have anything to do with radiation from the apparent horizon in Rindler space? And what about the cosmological horizon- any radiation there?


title: What is the energy functional for $\nu=5/2$ Moore-Read state?

text: I am trying to do some Monte Carlo simulations for Pfaffian state from Fractional Quantum Hall effect. I am wondering what is the energy functional for $\nu=5/2$ Moore-Read state?


title: What makes excimer lasers so complex, rare and expensive?

text: We all can agree that UV lasers are extremely useful, but we (poor majority) are still struggling with 355nm DPSS ones, while excimer lasers being prohibitively expensive (let's say at 1-10W average power, or 100Hz @ 0.1J pulse). What is the reason for this? What is the complexity, making excimer lasers (namely, 248nm KrF / 308 XeCl ones) so complex? Mirrors & optics is simpler than for CO2 ones, gas is not expensive too... What am I missing? Just reread my laser optics book - it needs aggressive laser pumping (50kV @10-30ns pulses), forced 'gas mixing' (just like in high- power CO2 ones), also needs preionization, but nothing too scary...


title: Could one "build" elements?

text: I was wondering this: would it be possible to "construct" elements by arranging their constituent particles in high-energy environments? So apart from just fusion, could you sub-atomically manufacture elements?


title: General Relativity: Christoffel symbol identity

text: I want to show that $$\Gamma ^{\mu}_{\mu \nu}=\partial _\nu (\ln \sqrt{|g|}) .$$ (Here $|g|$ denotes the determinant of the metric.) Working out the left hand side:\begin{align} \Gamma ^{\mu}_{\mu \nu} &= \dfrac{1}{2} g^{\mu \rho}(\partial _{\mu} g_{\nu \rho } + \partial _{\nu} g_{\rho \mu} - \partial _{\rho} g_{\mu \nu})\\\ &= \dfrac{1}{2} g^{\mu \rho} \partial _{\nu} g_{\rho \mu} \end{align} where I've used the symmetry of the metric. The right hand side yields \begin{align} \partial _\nu (\ln \sqrt{|g|})&= \dfrac{1}{2|g|}\partial _\nu |g|\\\ &= \dfrac{1}{2}|g^{-1}|\partial _\nu |g| \end{align} A definition for the determinant of the metric is \begin{align} \tilde{\epsilon}^{\mu \nu \rho \sigma}|g|= \tilde{\epsilon}_{\mu' \nu' \rho' \sigma'} g^{\mu' \mu}g^{\nu' \nu}g^{\rho' \rho}g^{\sigma' \sigma} \end{align} where $\tilde{\epsilon}^{\mu \nu \rho \sigma}$ is the Levi-Cevita symbol. My questions:   * Is what I've done so far correct?   * How can I match the result $\dfrac{1}{2} g^{\mu \rho} \partial _{\nu} g_{\rho \mu}$ with $\dfrac{1}{2}|g^{-1}|\partial _\nu |g|$? I don't see how to incorporate the definition of the determinant...


title: Center of charge in quadrupol tensor

text: In theoretical classical electrodynamics we defined the quadrupol tensor of $n$ charges $q_k$ at positions (from origin or center of charge, see below) $\vec r_k$ like so: $$Q_{ij} = \sum_{k=1}^n q_k \left( 3 r_{ki} r_{kj} - r_k^2 \delta_{ij} \right)$$ I assumed that the $\vec r_k$ should be from the center of charge, so that the quadrupol tensor is translation invariant, which would seem logical to me. Out tutor said that we should just use the origin of our coordinate system. That would make the quadrupol tensor translation variant, which does not make sense to me. Is $\vec r_k$ from the center of charge or from the coordinate origin?


title: How would one calculate the amount of water contained in a cloud?

text: So I was looking out the sky one day and I wondered how I would go about calculating how much water was contained in a cloud. I figured the following simple outline 1) We need to roughly know how big it is. We'll also be figuring out how high the cloud is. Use some sort of geometric method? Triangles? 2) We need to relate its color to its density. (Darker clouds more dense) (White fluffy clouds less dense) 3) Correction factors due to lighting conditions during different parts of the day. Can some body help me figure out the relevant calculations needed? Or how much water does a cloud contain based on its category?


title: Feynman diagrams and Hartree-Fock

text: I am puzzled by some lines I read in Mattuck's book on Feynman diagrams in many-body problems ( http://www.amazon.com/Feynman-Diagrams-Many-Body-Problem- Physics/dp/0486670473 ) Page 21 (1.14) for those who have the book. Basically after representing the full propagator of an electron in an electron gas by expansion of the electron-electron interaction (not specified but QED I guess), it says: "this is the 'Hartree-Fock' approximation for the electron gas", which I still don't understand. The Hartree-Fock method for me is just an iterative tool to calculate the collective wave-function of self- interacting fermions satisfying the correct anti-symmetrized form. This statement is evasive to me, and I'd like to understand in which way it makes sense.


title: What does the wavevector $\textbf{k}$ mean?

text: In Ashcroft, Mermin Solid State Physics, Eq. 17.43 is $$ \epsilon(\textbf{k}) = \frac{\hbar^2 k^2}{2m} - e\phi(\textbf{r}) $$ where $\textbf{k}$ is the wavevector and all other symbols have their usual meaning. What does the wavevector tell me and why do we use it instead of position $\textbf{r}$?


title: Does space expansion imply light will *never* reach objects currently distant enough?

text: Let's say two objects are at about twice the Hubble Distance from each other. One of them emits light towards the other. When light emitted from one reaches the Hubble Distance from its origin (within less than Hubble Time, but more than half of it) the other will be more than another Hubble Distance farther from the first than it was - the distance from the point the light reached will be more than at the beginning of the travel. Is that correct or am I perpetuating another misunderstanding concerning Space Expansion?


title: Bekenstein bound for electron?

text: Using the Wikipedia version of the Bekenstein bound, and substituting the Wikipedia values for electron mass and radius, one obtains 0.0662 bits. Does this really mean that a system, any system, placed inside a sphere the size of an electron, and weighing no more than an electron does, is almost determinate? How about an electron itself? Wouldn't one need at least a few bits to characterise the behavior of an electron in magnetic space? (I am a professional mathematician but I know very little about physics, I'm sure I'm missing something obvious here...)


title: Creating a atmosphere bubble in space with electromagnetism

text: would it be possible to contain an atmospheric bubble in space with a magnetic field, and wouldn't doing so protect it from solar radiation also?


title: Would half of electromagnetic wave be absorbed on first sensor?

text: If I would set up electromagnetic emitter that would emit one wave, but while it would be emitting it I would spin emitter 180 degrees at such speed that one half of wave would be emitted in that time (or it could be 1 degree, but the speed of turn would have to match the half of wave's oscillation) and then would set up a lot of sensors on the path of the wave that are able to measure strength of electromagnetic field (so that it would hit multiple sensors with that partial wave, sensors can be placed as far away as it needs be to allow the small turn in angle allow to have bigger affect). Would all the sensors show the value of the field going up to the peak and back down to zero, or would first sensor absorb the wave and all other sensors would show 0 values. **Update:** Reason I am asking is that I can't wrap my head around - for sensor to register something it has to be affected by electromagnetic field - to affect sensor some energy has to be used, if wave would affect all the sensors it would imply that it has infinite energy as increasing the amount of sensors would still 'do to the work' register a value, but there has to be more 'work' done with each additional sensor, so in my understanding 1st sensor (or some other) would have to take all the energy of the wave and rest would not get anything. Please forgive me if question is unclear or silly, I am not a physicist. If you need additional information please ask I will do my best to clarify.


title: Why does solar cell will create as a Multiple cells instead of one large cell area?

text: Why is a solar module assembled from multiple cells instead of one large cell area?


title: absorption length of thermal neutrons in a medium

text: My book states that $$N(x)=N_0\cdot e^{n\cdot \sigma \cdot x}$$ for $n$ absorbing particles per volume element with a cross section $\sigma$. Can somebody explain where this comes from?


title: What is "k-Local Hamiltonian Problem" in quantum complexity theory?

text: An example of a QMA problem is the k-LOCAL HAMILTONIAN problem. What exactly is it?


title: Naive question about the S-matrix

text: In quantum field theory, the elements of the S-matrix are defined as the amplitude describing the transition from an initial $n$-particle state (the "in" state) to an final $m$-particle state: \begin{equation} S_{fi} = \langle \mathbf{q}_1,\dots,\mathbf{q}_m; \text{out} | \mathbf{p}_1,\dots,\mathbf{p}_n ; \text{in} \rangle \tag{1} \end{equation} To me it seems that this equation only makes sense if the amount of "in" particles is equal to the amount of "out" particles (i.e. $m=n$) otherwise we can not take the inner product. For instance, if $m=2$ and $n=3$, then we can write equation $(1)$ as: \begin{equation} \begin{pmatrix} \mathbf{q}_1 & \mathbf{q}_2 \end{pmatrix} \begin{pmatrix} \mathbf{p}_1 \\\ \mathbf{p}_2 \\\ \mathbf{p}_3 \end{pmatrix} =\ ? \end{equation} which is undefined. Therefore, my question is how to interpret equation $(1)$ if $m \neq n$? I must admit that I have never studied the S-matrix in quantum mechanics. Therefore, I apologize in advance if this is a naive question.


title: Velocity required for Horizontal Rain

text: Related to my previous question - Change in appearance of liquid drop due to gravity... Ok, I think we all have noticed this practical phenomena (a kind of _illusion_ though)... During rain (while we're at rest), rain drops would definitely fall in the form of somewhat _perfect_ vertical lines (assuming there's no wind). And When we're in motion, those "lines of rain" would be inclined to some $\theta$. That inclination depends on our velocity (what our eyes perceive at our speed). A friend of mine drove his car to _some_ 120 km/h. Unfortunately, I didn't observe any horizontal line. So, Is there any way we could observe "rain lines" _horizontal_..? What would be the velocity required for it? I think we don't have to break _any barriers_ for that perception :-) I googled it. But, I can't find anything regarding **lines**. Any explanation or perhaps a link would be good. _(As the climate would be rainy for atleast 2 months, I could test it in some grounds)_


title: I need help with this question on Heat Capacity

text: > A calorimeter has a Heat Capacity of $70 J/K$. There is $150g$ water with a > temperature of $20^oC$ in this calorimeter. In this, you put a metal cube of > $60g$ with a temperature of $100^oC$. The final temperature of all of this > is $24^oC$. > > _What is the specific heat of this metal?_ So, I'm having trouble understanding this problem, mainly the intuition behind this. I'm going to show you my progress (cm = calorimeter, w=water, m=metal): $Q_{cm} = 70 J/K$ $m_w = 150\times10^{-3} kg$ $\Delta T_w = 4 $ $m_m= 60\times 10^{-3} kg$ $\Delta T_m = 76 $ I know I have to use the formulae:   * $ Q = c\times m \times \Delta T $   * $ Q = C \times \Delta T $ However, I'm lacking the insight needed the solve this problem. How would I have to go about solving the problem? I think I'm missing a fundamental insight needed to solve this problem. Can anybody help me with this? **In other words, I have the data, I have the correct formulas, but I don't know what to do with it!**


title: When Hamiltonian and the total energy are the same

text: In which condition, the Hamiltonian is the same as the total energy of the system, or say $H=T+V$?


title: Widom-Larsen Theory

text: Does the Widom-Larsen theory pose a credible underpinning for Low Energy Nuclear Reactions, often incorrectly referred to as "Cold Fusion"? http://arxiv.org/abs/cond-mat/0505026


title: What are the properties and impediments of a liquid air fueled engine?

text: I recently came across a very interesting article that suggested the possibility of using liquified gases like air, nitrogen, or oxygen as a power source for cars. It appears that this company is moving forward with the idea, but surely the concept is not entirely novel. See, for example, claims from over a century ago to have invented a car using liquid air. Why has this concept not been explored more thoroughly? It seems to me that some basic questions are as follows: What is the recoverable energy content per volume of liquid air? How does this compare with gasoline or aviation fuel? What are the practical problems with the of handling liquid air? Could liquid air be used more effectively in something other than the four- stroke-cycle?


title: What happens if a black hole sucks up a massive amount of oxygen and hydrogen?

text: Suppose a black hole were to suck up a massive amount of surrounding oxygen and hydrogen. Would this ignite inside the black hole and turn it back into a star?


Many light sources like LEDs and lasers only emit a single wavelength of light. Is there a light source that emits all wavelengths of visible light at the same time?


title: Evaporation from a capillary tube

text: Consider a capillary tube (say from a liquid / capillary thermometer), that means a tube of small internal diameter which holds liquid by capillary action . The tube is fulfilled with water and closed at one end. How long it would take for water to completely evaporate out through the open end of the tube? To be specific, let the diameter of the tube be $d=1$mm, the length of the tube $L=1$m, the environmental temperature $T=300$ K and pressure $P=10^5$ Pa, the relative humidity $f=60$ %, the contact angle a) $\theta=0^{\circ}$ and b) $\theta=180^{\circ}$. Does it have any effect on the time when the tube is positioned horizontally or vertically(open end above)? ![A capillary tube with a liquid](http://i.stack.imgur.com/1akdv.gif)


title: A fan in a hot room at what point does it put in more energy that it dissipates

text: If a fan that is using 50 watts is moving 1 m³/min of air. Lets say the walls are the same temperature as the air so there’s no heat dissipation there. How do I know if the fan is putting in more energy in to the room than its dissipating? If the walls are 10 deg cooler than the air will this be sufficient for the molecules to dissipate the heat in to them. Where’s the point of balance.


title: Artificial Gravity - Spinning Station Questions II

text: In an answer to Artificial Gravity - Spinning Station Questions Vintage wrote: > A theoretical space station of radius 900 meters, doing a complete rotation > every 60 seconds (in order to generate about 1g at the outer rim) would have > an outer tube tangential velocity of about 90 m/s. The air in the tube would > have the same tangential velocity. If you were instantly instantiated in > this tube, weightless, with zero tangential velocity, you would experience > an air blast somewhat similar to standing on the hood of a Ferrari, > screaming down the Autobahn at 324 km/hr. The original question was from slight_disregard, I'm just expanding on it.   1. If I’m standing inside the station as Vintage states I’m going 324 km/hr if I jump straight up at 1 m/sec where do I land?    2. Does the air 10m up from where I’m standing going at the same speed or does the Coriolis effect make it go slower?    3. If I get in my Ferrari and go 324 km/hr opposite to the spin direction does my car become weightless?


title: electron orbits

text: Is there an upper limit to the number of orbits an electron can have around say a proton? Arent there states that are unstable(for n!=1) with corresponding mean/half lives and therefore uncertainty in energy. So how do we differentiate between 2 n values (say v1,v2) esp if the uncertainty associated with their energy levels gets larger to the order of the energy difference associated with the transition? Also is it known that we can predict the following data with only computation resources being a bottleneck? The half lives of each state(decay rate). The transition rate(from v2 to v1 given v2>v1)


title: Explanation of Cardy's "a theorem"

text: There seems to have been some discussion of Cardy's "a-theorem" recently: > “It is shown that, for d even, the one-point function of the trace of the > stress tensor on the sphere, Sd, when suitably regularized, defines a > c-function, which, at least to one loop order, is decreasing along RG > trajectories and is stationary at RG fixed points, where it is proportional > to the usual conformal anomaly.” said Cardy. “It is shown that the existence > of such a c-function, if it satisfies these properties to all orders, is > consistent with the expected behavior of QCD in four dimensions.” I would appreciate it if someone could give a reasonbly concise explanation of what the theorem states and implies, at a level for someone with a superficial understanding of quantum field theory. For example, what is the sphere in the above quote and how does the existence of the c-function lead to the main conclusion of the a-theorem which is purportedly: > "... a multitude of avenues in which quantum fields can be energetically > excited (a) is always greater at high energies than at low energies. " Edit: I think I found what I needed. Section 4.4 of David Tong's string theory notes gives a nice explanation of the trace anomaly and the "a" and "c" theorems. I assume the sphere they were talking about in the Nature article is just the $S^4$ of Euclidean compactified spacetime, in which case "a" is its Euler characteristic.


title: What is the physical meaning of a product of vectors?

text: My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B & then to C is equivalent to going from A to C directly. But what is the meaning of a product of vectors? I cannot imagine how a product of displacements would look like in reality. Also, how do we know whether we need the scalar (dot) product or a vector (cross) product? Please explain.Thanks in advance.


title: Does spacetime have momentum?

text: In what sense can it be said that spacetime possesses momentum? Can an experiment be envisaged to test this question?


title: GUT predictions for charm mass?

text: Most GUT models have some relationship between down-type quarks and leptons, that more or less agree with the observed values after running the renormalization equations. But, what about up-type quarks? How good are GUT predictions for up-type quarks? And, particularly, Is there some model explaining why the mass of charm is so near of the mass of the tau lepton?


title: particle accelerator in space

text: I'm attempting to learn special relativity and i'm having trouble calculating velocity and momentum for each part of the system after interactions. I wanted to know how fast a linear accelerator and particle would move with respect to the rest frame after a period of acceleration assuming the system is placed in free space. I had some trouble understanding how to apply acceleration to a particle at rest that would result in relativistic speeds so I took the energy approach. If we imagine the accelerator can accelerate a proton to 1TeV of kinetic energy we get the velocity for the proton given: $$ KE = \frac{m_0c^2}{\sqrt{1-\frac{v^2}{c^2}}} $$ solving for v: $$ v = \sqrt{1- (\frac{m_0c^2}{KE})^2}c $$ and the velocity for the accelerator given: $$ KE = \frac{1}{2}mv^2 $$ solving for v: $$ v = \sqrt{\frac{2KE}{m}} $$ When I plugged in the numbers and double checked the energy I found that: $$ \frac{1}{2}m_av_a^2 = (\gamma(v_p) -1)m_0c^2 $$ where the left hand represents the kinetic energy of the accelerator and the right hand represents the kinetic energy of the proton. So at this point I felt pretty confident in my calculations for the velocities, but when I looked at the momentum I discovered that something was terribly wrong. The momentum of the accelerator $m_av_a$ definitely was not equal to the momentum of the proton $\gamma m_0v$. Ultimately I wanted to look at inelastic collisions between relativistic and non-relativistic systems, but I wanted to be able to to do the calculations from rest to rest(which should be easy in a closed system) and i seem to be stumped. So what am I doing wrong? Do I need to be approaching this from another frame? How should I calculate momentum and velocity correctly.