title: transforming experimental rate constant to monte-carlo rate constants?

text: I am trying to write a kinetic monte carlo code for polymerization process, but i am confused about how to compare my monte carlo equilibrium with analytical calculations. as an e.g. $X + X <=> X_2$ with a forward rate $k_a^+$ and backward rate $k_a^-$. $X_2 + X <=> X_3$ with a forward rate $k_e^+$ and backward rate $k_e^-$. $X_3 + X <=> X_4$ with a forward rate $k_e^+$ and backward rate $k_e^-$. ............ etc. Now i want to specify concentration of monomer X. volume of the container V and avogadro's number. But what i am confused in is that how to transform experimental rate constants to monte carlo rate constants. real or experimental units for $k_a^+$ are $mol^{-1}s^{-1}$ and $k_a^-$ are $s^{-1}$ and same for $k_e^+, k_e^-$ the equilibrium constant $K_e = \frac{k_e^+}{k_e^-}$ and $K_a = \frac{k_a^+}{k_a^-}$ is usually given in (/mol) units in literature. Nitin


title: Radiation pressure on a Dyson sphere

text: To find the outward pressure from the sun's light on an enveloping spherical shell (Dyson sphere), one can simply divide the insolation by $c^2$. Using the entire system, we can specify the power of the sun in watts, $W$, leading to a pressure of $P=W/(4 \pi R^2 c^2)$. The problem is that a Dyson sphere structure emits its own thermal radiation. So then one would think that the pressure from the thermal radiation on the outside surface of the Dyson sphere could just cancel with the inside radiation pressure from the sun since the power rates are the same. There's one more problem, the outer surface's thermal radiation has a different directionality. There _would_ be a net pressure pushing outward since the sun's light is preferentially directed outward. What would that be?


title: Total Electrical potential energy of two particle system

text: I recently have been studying Electro-statics and I couldn't understand properly how the potential energy of two particle system is found. > Suppose you have two particles with charges $Q_1$ and $Q_2$ respectively. > The distance between them is $r$. What is the total electrical potential > energy of the system comprising of the two particles? Well, I know the > answer. I want to know the reasons behind the answer. My book says "Fix one of the charges and then bring the other from infinity. Hence we get the answer. I am not satisfied with the answer, as I saw in Wikipedia they find the potential of each other with respect to the other and then add and divide by $2$. Why is this taking potential with respect to each other valid? Why do they divide by two? What does taking potential with respect to other mean? Do they fix one charge and bring another one? what about three charges $Q_1, Q_2$ and $Q_3$ which are situated in the vertices of an equilateral triangle with side length $r$?


title: Alpha scattering, observations and conclusions

text: For Rutherford's alpha scattering experiment where he fired alpha particles at a thin sheet of metal to determine the size of the nucleus, please can someone give me the direct link between his observations and his conclusions e.g. this observation lead to this conclusions.


title: Which coordinate system confirms quantum-level experimental data?

text: We often use the Cartesian coordinate system, since it is the naive approach at macro level (placing a box just "next to" or "above" the other box). There are, however, many more such systems, incl. these here: http://en.wikipedia.org/wiki/Coordinate_system. Which of the systems allow modeling experimental data in the most effective way (exploiting the most explicit characteristics of quantum-level interactions)?


title: What do ants see?

text: After watching some ants in my garden today, and then looking at this very illuminating demonstration, I got to wondering, about what they would see. Not specifically ants (I understand their eyesight is quite poor), but similarly small, or even smaller creatures. I guess I'm asking more about the nature of light and how photons are reflected off very small surfaces. Would a very small creature, like say, an ant, with vision, be able to see something as small as a single e. coli bacterium? or a virus? Would their world 'look' the same as ours or does the viewers relative size have a bearing on the quality of their perception? And additionally beyond the realm of reality, if I could shrink myself down to the size of a bacterium, could I see atoms?


title: Calculating displacement amplitude of ultrasonic power transducer

text: I am not a physicist, but my current project drives me to some physics-related computations, hence seeking help. I have some ultrasonic transducers, 5938D-25LBPZT, for which very limited information is available. ![Transducer Diagram](http://i.stack.imgur.com/PCWcM.jpg) ![Transducer Photo](http://i.stack.imgur.com/j5dKc.jpg) In order to define the parameters for an ultrasonic booster and amplification horn for this device, I need to compute the displacement amplitude of its radiating surface. The procedure I am following, and the **base data** ( _or where data is unavailable, my assumptions_ ) are thus:   * Operating power: **50 Watts** RMS (the transducer is rated for 60 Watts)   * Emitting horn material: Stainless Steel **SS316** (best-guess, unfortunately, as SS316 is typical in other such transducers)   * Emitting face diameter: **5.865 cm** (measured)   * Frequency at resonance: **_f_** = **24989 Hz** (measured)   * Best-case power transmission: **90%** (in forward direction, according to various sources) **Constants** :   * Density of SS316: **ρ** = **7.8 gm/cm^3**   * Velocity of longitudinal sound propagation: **C** = **5.8 mm/μSec** (from this reference, approx)   **_Should the axial velocity of sound be considered instead for this calculation?_** **Calculations so far** :   * Face area: **27.016 sq cm** (ignoring area lost to bolt-hole)   * Sound intensity at face: **I** = 90% x Power / Area = **1.666 Watts / sq cm**   * Displacement Amplitude: **A**   ![Amplitude Formula](http://i.stack.imgur.com/dfeib.jpg)   * ... where **ω** = 2 x π x _f_   * Thus, **A = 172.8296514 nanometers** * * * **My questions are:**   1. I am not sure I have managed to convert everything to consistent SI units, so I need help confirming that I've got that part right   2. If anyone has experience in such power ultrasonic piezo transducers, a confirmation that my results are more or less within the realms of plausibility would really help.   3. Is there some significantly incorrect assumption or constant value in the foregoing?   4. Should I be using some online resource that trivially calculates all this from the rated power and other inputs, instead of struggling with it manually? * * * **Update** : _Adding diagrams to show the excitation direction and materials involved._ ![Ultrasonic Stack](http://i.stack.imgur.com/wknTr.gif)   (please ignore _Diamond insert_ ) This is the final arrangement of the Ultrasonic Stack. The _booster_ and _horn_ in the diagram above will both be SS316. In order to compute dimensions for these two parts for resonance, I need the displacement amplitude of the front face of the steel "radiation head" in the transducer ( _first diagram here_ ), which is to be bolted to the booster. The bolt-hole in the radiation head can be seen in the photograph above. Another diagram, for a similar "Ultrasonic Stack", with the Langevin transducer itself split up. This diagram has a cylindrical radiation head, as opposed to the cone section shape in the transducers I need to compute for. ![Ultrasonic Stack](http://i.stack.imgur.com/5zuUG.jpg)   (please ignore _Wedge_ ) (Last two diagrams are from articles on ScienceDirect.com)


title: Why do power lines sag when they are heated up?

text: I was reading some information about the 2003 power blackout in the Northeastern US. > Beginning early in the afternoon of August 14, 2003 big transmission lines > began to fail in First Energy's operating area, several because the utility > had not kept up with tree-trimming, so that **as heavily loaded lines heated > up, they sagged into brush and shorted out**. As one went down, the next > would become too loaded, sag still more, and short, and so on. All that, the > result of a serious infringement of operating standards and no small matter > in its own right, would have remained a local problem if First Energy and > the midwestern power regulator had quickly recognized what was going on and > had promptly cut service to enough customers to keep the whole system from > getting overloaded. From "A Coal Power Ban Is a Necessity." Coal. Ed. Michael Logan. 5 Aug. 2010 What about overheating causes power lines to sag? I understand that increasing the load on the line will increase the line's temperature due to the resistance in the cables. Why does this increased heat cause the lines to sag though?


title: Is this a weather phenomenon or an instrumental artifact?

text: The radar image of the midwest provided by Weatherunderground at 10:30 PM Central time, May 8 2011 has odd patterns. Are these patterns real? Perhaps caused by large scale convection over cities? Or are they artifacts of radar placement? Here is the image that I am referring to, where green indicates light and yellow moderate rain: ![enter image description here](http://i.stack.imgur.com/xlvW8.png)


title: Solving the time independent Schrodinger equation: Does a complex solution make sense?

text: In my notes, I have the Time Independent Schrodinger equation for a free particle $$\frac{\partial^2 \psi}{\partial x^2}+\frac{p^2}{\hbar^2}\psi=0\tag1$$ The solution to this is given, in my notes, as $$\Large \psi(x)=C e^\left(\frac{ipx}{\hbar}\right)\tag2$$ Now, since (1) is a second order homogeneous equation with constant coefficients, given the coefficients we have, we get a pair of complex roots:$$r_{1,2}=\pm \frac{ip}{\hbar}\tag3$$ Thus, the most general solution looks something like:$$\psi(x)=c_1 \cos \left(\frac{px}{\hbar}\right)+c_2 \sin \left(\frac{px}{\hbar}\right)\tag4$$ However, instead of writing the solution as a cosine plus a sin, the professor seems to have taken a special case of the general solution (with $c_1=1$ and $c_2=i$) and converted the resulting $$\psi(x)=\cos \left(\frac{px}{\hbar}\right)+ i\sin \left(\frac{px}{\hbar}\right)\tag5$$ into exponential form, using $$e^{i\theta}=\cos \theta + i\sin \theta \tag6$$ to get (2). The main question I have concerning this is: shouldn't we be going after real solutions, and ignoring the complex ones for this particular situation? According to my understanding $\Psi(x,t)$ is complex but $\psi(x)$ should be real. Thanks in advance.


title: Quick-and-dirty way to integrate out heavy fields

text: I understand the roughly understand the process of integrating out heavy degrees of freedom of a Lagrangian, namely, taking the action and performing the path integral over the high momentum modes. However, in the case of the W boson this approach isn't really needed. You can just compare the four-Fermi interaction to the full theory result and you can find the coupling of the four-Fermi interaction. Is there always an "easy way" to accomplish this? * * * In my particular case, I am trying to understand this paper. We have two Higgs bosons and the interaction of the heavy triplet Higgs, $\xi = (\xi ^{++}, \xi^+ , \xi ^0) ^T$ with the leptons is \begin{equation} f _{ ij} \left[ \xi ^0 \nu _i \nu _j + \xi ^+ \left( \nu _i l _j + l _i \nu _j \right) / \sqrt{2} + \xi ^{ + + } l _i l _j \right] + h.c. \end{equation} The heavy Higgs also interacts with the SM Higgs, $\Phi=(\phi^+,\phi^0)$ through: \begin{align} V_{\xi \phi} & = \lambda _3 (\Phi^\dagger \Phi )(\xi^\dagger \xi) +\mu \left( \xi ^0 \phi ^0 \phi ^0 + \sqrt{2} \xi ^- \phi ^+ \phi ^0 + \xi ^{ - - } \phi ^+ \phi ^+ \right) + h.c. \end{align} After integrating out the heavy Higgs the Yukawa interactions take the form, \begin{equation} \frac{f_{ij} \mu }{M ^2} \left[ \phi^0\phi^0 \nu_i\nu_j - \phi^+\phi^0 (\nu_i l _j +l_i \nu_j ) + \phi^+ \phi^+ l _i l _j \right] +h.c. \end{equation} Is the replacement $\xi \rightarrow \frac{\mu}{M^2} \phi \phi$ (with an obscure sign change) obvious?


title: P-type MOSFET performance

text: I was reading somewhere that the (110) plane has the highest atomic density and is best for p-channel MOSFET performance. How high atomic density influence the performance of P-channel crystal?


title: Is there a connection between exclusion principle and the speed of light?

text: As far as I know exotic stars are composed of degenerate matter created by the balance between gravity and pressure of exclusion principle and as the mass of the star grows it goes into more compressed stages. At the same time with growing density of the star gravitational pull rises and so does its escape velocity. The thing I don't understand is why the point at which escape velocity reaches the speed of light is the same point as the one at which star becomes a black hole? Why there are no "black stars" which hadn't collapsed? Is there some connection between exclusion principle and the speed of light?


title: Sign of Work and potential energy in electrostatics

text: Conceptual question: Suppose we have a configuration of point charges. If the potential of the energy of the system is negative, this means work is positive. I'm kind of rusty with my mechanics, does the fact that the work is positive mean that to arrange the configuration you have to do work against the electric field? I.e. supply energy via some external force? In terms of electrostatics, is there a general way of interpreting the sign of potential energy and work?


What conditions must be met for a ball to roll perfectly down an incline without slipping? A mathematically rigorous definition, please. I honestly don't know where to begin with answering this problem.


title: How do we see different colours?

text: * Why do different wave lengths cause electrons to behave(?) differently, causing us to see different colors?   * What is happening at the quantum level which causes the colour black to absorb all of the wavelengths of white light?   * Why is it that a black can of soft drink will heat up more than a white one?    * How does the energy, while passing through different colours, increase the temperature differently?


title: What is the exact relationship between on-shell amplitudes and off-shell correlators in AdS/CFT?

text: In this answer to a question, it is mentioned that in the AdS/CFT correspondence, on-shell amplitudes on the AdS side are related to off-shell correlators on the CFT side. Can somebody explain this to me in some more (technical) details, maybe by an explanatory example?


title: Wavefunction in first Brillouin zone

text: We know that with symmetry, Brillouin zone is nothing but copies of its irreducible zone, so can we conclude that we can find all possible wavefunctions in its irreducible zone? What about wavefunctions in high- symmetric points?


title: Lower state of energy for 'connected' molecules

text: Quote from Wikipedia: > Another way to view surface tension is in terms of energy. A molecule in > contact with a neighbor is in a **lower state of energy** than if it were > alone (not in contact with a neighbor). As I understand the above statement, is that if two molecules (of the same liquid) are separated, then they have a larger energy as when they are together. Can you please explain a bit why this happens? Is there a physical/chemical reason? Thank you.


title: Orbital mechanics of Dragon's Egg

text: In the novel Dragon's Egg, the human crew use one asteroid to swing other asteroids in place to counter the gravity of the neutron star. I understood that it was similar to a gravity sling shot, but I wasn't able to fully get how the crew were able to move the smaller asteroids in place using the big one. Can anyone explain that further?


title: Couch shocks everything!

text: How do I get rid of the static charge I get from my microfiber couches? Every time I get up and touch something it zaps me...   I'm mostly worried about my laptop getting fried.


title: Forced harmonic oscillator with two springs

text: Consider a vertical system of two springs in series, with a mass(50 g) between them. From below the system is driven by a vibration generator. The setup is shown here, but the picture is taken while the mass was moving, and therefore the mass is not in the equilibrium position: ![enter image description here](http://i.stack.imgur.com/AtK14.png) I expected the system to act close to a system of springs coupled in series, but it does not. For instance, there is a big difference in resonance frequency between a setup with the spring with elastic constant $K_1=15\:\mathrm{N}/\mathrm{m}$(m=3.876 g) on top and the one with $K_2=5\:\mathrm{N}/\mathrm{m}$(m=3.070 g) below, and the setup where these two springs change place. EDIT: The results are shown under: ![enter image description here](http://i.stack.imgur.com/0iy5X.gif) Why is this? In the equilibrium position the two springs are not streched equally. Is that the reason?


title: How quickly was the Earth rotating 250 million years ago?

text: The Earth is slowing at a rate of $4.7\times10^{-4}$ miles per second every 100 years due to tidal forces of the moon. See:   * http://en.wikipedia.org/wiki/Earth%27s_rotation   * http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970401c.html 250 million years ago, it would have been spinning at 4.2 million miles per hour! The dinosaurs would have flown off the earth. If the deceleration rate is inaccurate by 95% (assume it is slowing more slowly), then 250 million years ago, it would be spinning at 213,000 miles per hour. Also, given the fact that the moon is receding from the Earth, the effect the moon has on the Earth would have been greater in the past. I don't understand; can someone explain?


title: How to make a base tranformation for a linear operator in QM?

text: I have 2 bases A and B with the following kets: Base A: $|a_1\rangle$ and $|a_2\rangle$ Base B: $|b_1\rangle = \frac{1}{\sqrt2} \cdot(|a_1\rangle + i\cdot|a_2\rangle)$ $|b_2\rangle = \frac{1}{\sqrt2} \cdot(|a_1\rangle - i\cdot|a_2\rangle)$ Both bases are orthonormal in the 2D Hilbert-space. The linear operator $\hat{T}$ is given in base A: $\hat{T}= \begin{pmatrix} 1& 0\\\ 0& -1 \end{pmatrix}$ Now I should find out how the linear operator $\hat{T}$ looks in the base B image? Should be easy, but I cant wrap my head around it.


What does an atom radiate: a wave packet or a single photon?


title: Lattice with snowflakes

text: Trying to understand these better. I'm trying to find a conventional primitive unit mesh and find the planes of symmetry. ![enter image description here](http://i.stack.imgur.com/bbSuq.png) Now my attempt was simply finding the next points where it repeated itself. ![enter image description here](http://i.stack.imgur.com/xJoHl.png) It seems like a p4m to me, any opinions?


title: Office Air Conditioning and Open Windows

text: Today is nice and sunny and the air con is on in the office. It's a fairly large office seating 20 people, 30x30x15ft with 20 small windows and a single large AC unit on the back wall where there are no windows about 12ft up. It blows air diagonally downwards and in front of it. It's about 25 degrees Celsius in here and the AC is set to 19, outdoors it is about 15 degrees. My question is: If I open the windows do I contribute towards cooling the room or am I making it harder for the AC to reach optimal temperature? My instinct tells me that because it's cooler outside than inside, by opening the windows It helps in cooling the room. Others think that opening the windows lets all the cooled air out. Which way does it work?


title: Vector plus vector equals scalar ? (Nabla operator)

text: A quick question that is currently bothering me. I have the following equation: $\mathbf{E}+\frac{\partial \mathbf{A}}{\partial t} = -\nabla V$ My question is, how can the right side, being a vector, ever become a scalar ? Or am I missing something fundamental here ? (The equation is from my Electrodynamics book) Thanks in advance.


title: Where is the energy lost in a spring?

text: Thinking about springs, and their extensions, I recently came to a confusion which I hope this wonderful community can help me solve. ![the figures](http://i.imgur.com/PhHUx82.png) The question is this. When the block is initially attached to the spring, the spring has some extension $x_0$. Now the spring gets extended to some extension $x=\frac{mg}k$ by an external force maintaining equilibrium at all the points such that $KE=0$ at the bottom. As my reference is the line shown in the figure, the initial potential energy $U$ is 0 due to both gravity and spring potential energy($x=0$). Now as the block comes down, the spring potential energy is: $U_(spring)=\frac12kx^2$. Final extension is $\frac{mg}k$. So spring potential energy is $\frac{m^2g^2}{2k}$ But the decrease in gravitational potential energy is $mgx$ which equals $\frac{m^2g^2}k$. This means that potential energy has decreased. Intitially, $U_{net}=0$ but finally $U_{net}=-\frac{m^2g^2}{2k}$. Where if any, did this energy get compensated(to ensure COE is still true)?


title: N=1 v N=2 supermultiplets

text: I read that the chiral nature of SM fields is an indication that they must be realized in a N=1 supermultiplet (and not N=2). I don't quite understand how so. Please enlighten.


Why two connected 1.5 volt battery become 3 volt? If one battery plus side is connect to minus side of another battery, there should be a current flow between them until no free charge move anymore, then the final state of these two side is 0 volt. So the total two connected battery should be still 1.5 volt. This is wrong actually, but I can't think out why.


title: Motion in insulating fluid under high voltage

text: I observed the following phenomenon in an experiment (I'm not a student of physics, just an amateur) and was hoping for an explanation. A metal pan is electrically grounded and a layer of insulating fluid (vegetable oil) is placed in the pan. If you like, assume the pan is infinite in diameter. An electrode (a needle) is placed above the pan, pointing downward at the oil. A high voltage (-12kV) is applied to the electrode. The electrode is close enough to the pan to generate an ion wind, but not close enough to overcome the breakdown voltage of the air and oil, so there is no arc. The oil is repelled from the electrode (perhaps because it acquires a negative charge from the ion wind) and also, more remarkably, the surface of the oil begins to undulate. My theory to explain the undulation is that the negatively charged oil on the surface is repelled from the electrode until it touches the pan, where it loses its charge and therefore is permitted to rise to the surface again, and the process repeats. So the undulations are something like convection cells, only with electric charge instead of heat. Is this explanation correct? Is there a name for this phenomenon? Would a similar phenomenon create leakage current in capacitors with liquid dielectrics?


title: What Elements Is Mono-atomic Hydrogen Capable Of Penetrating?

text: I recently learned that monoatomic hydrogen passes directly through solid aluminum and even combines inside aluminum to form $H_2$ which cannot pass through solid aluminum and therefore causes deterioration, blackening, and flaking. Source I am curious if mono-atomic hydrogen is capable of passing through any other solds?


title: Why Don't Birds Stall?

text: I often hear about planes stalling when they lose lift due to low airspeed/too high angle of attack. Why don't birds stall? Does it have to do with the structure of their wings and their flexibility, or their higher power/weight ratios relative to aircraft?


title: When sun is exactly overhead in my place in the tropics

text: What formula to use to find dates and times when the sun is exactly overhead in my place in the tropics?


title: Need a more efficient way to find where the $E$ field is zero

text: So this is a problem I already know how to solve, but I feel like my method is really inefficient and I'm wondering if there's a more intuitive, less tedious way to arrive at this conclusion. If we have two charges separated by the distance $a$. One charge has charge $+4Q$, the other has charge $-Q$. The right charge $-Q$ is sitting on the origin.                                     (y)                            ^                            |                            |                            |     ----(4Q)<_____a_____>(-Q)-------------------> (x)                            |                            |                            |      The problem is to find where the electric field is zero. My solution: I know that the electric field from a point charge is $kq/r^2$, so I tried setting them equal to zero: $$\frac{k4q}{(a+x)^2} - \frac{kq}{x^2} = 0$$ Solving this for $x$ with `Solve[4/(a+x)^2 - 1/x^2 == 0, x]`, I get the solutions $$x = -\frac{a}{3}$$ $$x = a$$ $$(a\neq0)$$ We can disregard the negative solution since the equation we solved only gives valid solutions from the right of the x axis. But this means that I need to solve two more equations to be sure that I didn't miss any solutions. For the space between the two charges (clearly no solution, as they have different charges): $$\frac{k4q}{(a+x)^2} + \frac{kq}{x^2} = 0$$ For the space on the left of the two charges: $$-\frac{k4q}{(a+x)^2} + \frac{kq}{x^2} = 0.$$ The final answer is that the electric field is zero at $$x=a,$$ but it took three equations to get there. Is there a simpler way to do this that I'm missing? Thank you!


title: How far can diffused undersea light travel and still be perceived by the human eye?

text: Example: If one SCUBA diver looks past another SCUBA diver horizontally into negative space, how far away is the most distant emission of 'blue' light waves? Consider the sight angle in question to be that which offers the maximum perceived distance, which I speculate is horizontal or along the Mariana Trench to nullify the Earth's curvature or something else beyond my assumption. Please disregard local water visibility conditions as in how far away an object can be discerned due to suspended matter. I am curious about the actual 'blue' region you see in an undersea photo. I assume this is scattered light from distant water molecules. I suppose that, unlike the black of outer space between star light emission, the 'blue' of water is not the absence of emitted light from a source but a non-point diffusion of light.


title: Energy Conservation

text: Supose that I throw a ball on the surface of the Earth at a given instant t. Chosing the referencial as the surface of the Earth, the PE is zero (and the KE is different from zero). Imagine that when all the KE is converted to PE (when the ball stops in the higher point of the trajectory) the Earth instantly disapears. Let's assume the Earth can disappear in two ways: _Case 1_ : The Earth is removed from the universe; _Case 2_ : The Earth is removed from the Solar System and instantly appears in other place in the universe, far away from the Solar System; Well, in Case 1 the the universe itself wouldn't be a isolated system, so the laws won't work (is that right?) So let's think in _Case 2_ : The ball wouldn't be afected from the gravitational pull of the Earth anymore so the PE that depends on earth's gravity would be lost, and I really mean lost, and that doesn't make sense. Then I remembered the special relativity theory that tells us when the earth disappears, a wave from the space-time fabric is generated and travels at the speed of light as a signal, because the Earth was creating a high depression on the space-time fabric before was removed. Can we interpret the wave as a form of energy converted from the delocalization of the Earth's mass? So it's correct to imagine that the wave "hits" the static ball and that ball would adquire again velocity, that we can translate to a KE? But wouldn't that KE be way bigger than the PE that the ball had on Earth? How conservation of energy works in this case? Thank you for your time **Note:** For _case2_ instead of the Earth disappearing instantly imagine a perfectly elastic collision between Earth (suposing Earth is like a giant billiard ball) and another planet (as a giant billiard ball too) at the instant the little ball thrown in the air stops. That collision is so fast that the Earth and the other planet instantly move at oposite directions before our little ball starts to "fall". Would the ball "fall" without any of the planets being around? –


title: Is Time Significant in the Double Slit Experiment

text: When doing the classic double slit experiment is the time between emitting photons significant at all? Say, a single photon is emitted, the scientist waits T seconds, then emits another photon. Are there any values for T which do not cause interference patterns on the detector? How about if the slits are closed during the time between photons?


title: How does one produce entanglement?

text: In practice, when entangling two particles (say two electrons), is creating an entangled state purely a matter of bringing them close enough together? What I mean is, to make their wave functions correlated, is it just a matter of bringing them close enough together (regardless of what is required to accomplish this), or are there other processes necessary to cause the entanglement?


title: If most satellites in orbit were destroyed from debris, would we ever be able to recover?

text: Suppose enough satellites were destroyed in orbit to cause so much debris from the explosions that a chain reaction destroying other satellites took over to generating more and more debris (even destroying the ISS). If this were to occur, would we be able to recover? Would our geostationary orbit be rendered useless? Would the debris eventually fall back into atmosphere and burn? If so, how long would that take? Is that too much time for mankind to live without its telecommunications?


title: Energy in a Solenoid?

text: > Consider a circuit consisting of a battery, a resistor and a solenoid > inductor. Then, the emf $\mathcal{E}$, is defined as: > > $$\mathcal{E} = L\frac{di}{dt} + iR$$ > > Multiplying both sides by $i$ gives: > > $$\mathcal{E}i = Li\frac{di}{dt} + i^2R$$ > > The term on the left side gives the rate at which the battery does work. > Since the second term on the right side gives the rate at which energy > appears as thermal energy in the resistor, the second term gives the rate at > which magnetic potential energy is stored in the magnetic field. > > Therefore $$\frac{dU_B}{dt} = Li\frac{di}{dt}$$ $$\int^{U_B}_{0} dU_B = > \int^i_0 Li\text{ }di$$ $$U_B = \frac{1}{2}Li^2$$ **Q1)** I'm assuming there finding the energy in the steady state. I thought the current was constant in the steady state so shouldn't $\frac{di}{dt}$ be zero? **Q2)** Why isn't the emf: $$\mathcal{E} = -L\frac{di}{dt} + iR$$ Since the self-induced emf generated by an inductor tries to _oppose_ the flow of current, shouldn't the emf be the opposite way? **Q3** )The bounds of the integral: $U_B$ and $i$. How are they related? Are they the energy and current at the same point in time $t$? Or is $U_B$ the energy at any point in time and $i$ the current at some other point in time (not necessarily the same times)?


title: Focused beam of light

text: I'm trying to understand what happens to photons when a beam of light is focused down to its waist. In the image attached, do photons take the path 1 or 2. That is, do the photons cross or just get 'deflected'. ![Beam of light focused](http://i.stack.imgur.com/xEnCv.jpg)


title: Tension on a string between two objects on a friction less surface

text: I just need my work checked here. Please let me know if I am correct. I had this problem in one of my test in which I did not get full credits. I am re- doing this(hopefully correctly this time) just for my own peace of mind and understanding. Problem statement: The force shown of 6.4N pulls horizontally on the 1.5kg block that is connected by a string to the second block of mass 0.93 kg. Assuming a smooth friction less surface find acceleration of the blocks and tension in the string. If there is friction, what happens to the tension in the string? (increase, decrease, stay the same? show your logic) The system and my free body diagram: ## ![enter image description here](http://i.stack.imgur.com/x95vx.gif) * * * Given: m1 = 1.5 kg m2 = .93 kg F = 6.4 N * * * Total Mass = m1+m2 = 2.43 kg Finding acceleration: F = ma F = (m1 \+ m2)a 6.4N = (2.43kg)a ## a = 2.63 m/s2 * * * Finding Tension: m1 = (1.5 kg)(9.81m/s2)= 14.7 N m2 = (0.93 kg)(9.81m/s2)= 9.11 N ## T = (m1+m2) + 6.4 N = 14.7 N + 9.11 N + 6.4 N = 30.4 N * * * If there is friction, the tension would increase. As the friction increases the force that pulls the two objects would have to be greater therefore increasing the tension.(The way I thought about is if there was friction, the blocks would require more force to move, since we already established that the net force is 6.4, the tension would have to increase to balance the frictional force.) I just wanted to make sure that I at least had the correct concept down. Any, criticism and suggestions are welcome.


title: Aerosol size distribution

text: When the size distribution of particles in an aerosol is obtained, there is always a bimodal distribution. The small peak accounts for the particles that are in sub-nanometer size range and the larger peak accounts for the particles that are in nanometer to micrometer size range. Why does it show a bimodal distribution? What is the physical reason for this occurrence?


title: What are the practical applications of quantum foundations?

text: Many quantum foundation researchers keep emphasizing that For All Practical Purposes (FAPP), quantum foundations are irrelevant. They even invented an acronym for it! Does that mean that quantum foundations have no practical applications? If so, why bother working on quantum foundations?


title: What happens to the electrons that escape an atom when matter is converted to a plasma state?

text: Lets say we have a device that generates plasma fields; if this device creates plasma by heating a gas, where do the electrons that escaped the "orbits" of the atom go? Would the electron physically shoot out of the atom at high speed and maybe be absorbed by another (plasma-less) atom? Is this a naïve intuition?


title: Is it possible that there is no theory of quantum gravity?

text: {{Under Construction}} Short question: What published works and what research groups are investigating the possibility of inexistance of gravity at quantum level? Long question: I am no phisicist, but of what I read and understand of the subject, no one has been able to fit graviton into the standard model, it seems that the equations won't renormalize, thus it would be useless for predictions. Gravity also is undetectable at quantum level, it seems because the force is too small. Also, about every book about the subject traces a strong distinction between "quantum level" and "classical level", almost if they were different worlds that obeys different laws of nature, and how they relate to each x other is an open question. Finally, at least two sources I have seen states that Einstein's General Relativity is the most well veryfied thoery of all physics, because of something related to pulsars. Thus there are two distinct "worlds": in one gravity is pretty much settled, while in the other, it is neither detectable nor mathematically explainable in the most succesful model. From that, the most logical and simple explanation I can have is that simply there are no such thing as quantum gravity, and that it is a purely classical phoenomenon that arises from whatever may be the relation of the both "worlds". I like to imagine that space coordinates of both worlds are quite not the same, although very similar locally, thus, if classical world emerges from a projection of the quantum world, like a shadow, gravity are bumps in the surface where that shadow is projected (holographic principle comes in my mind now). It does't seems to be the mainstream view of the problem, with millions of dollars spent in trying to find the mythical graviton (that is what a physicist of INPE, Brazilian's spacial research institute, told me yesterday). Thus, I whant to know, what are the works, and what people shares with me this view of the problem?


title: Fabry-Perot cavities and phase difference

text: I'm reading a paper which says > The beam that reflects from a Fabry–Perot cavity is actually the coherent > sum of two different beams: the 'promptly reflected beam', which bounces off > the first mirror and never enters the cavity; and a 'leakage beam', which is > the small part of the standing wave inside the cavity that leaks back > through the first mirror. I understand this. However, the author then writes > If the cavity is resonating perfectly, then the promptly reflected beam and > the leakage beam are exactly 180° out of phase. In this case the two beams > interfere destructively, and the total reflected beam vanishes. I don't understand why these two beams would be 180° out of phase. This is my (flawed?) understanding: ![enter image description here](http://i.stack.imgur.com/nH8EM.png) The light beam comes in as beam 1. Beam 2, the part that is reflected, get a 180° phase shift w.r.t. beam 1. Beam 3 continues without any phase shift w.r.t. beam 1. Part of beam 3 is reflected as beam 5. So, beam 5 has a 180° phase shift w.r.t. beam 3. The part of beam 5 that goes back through the first mirror is called beam 6, and this has the same phase as beam 5. So, both 2 and 6 are both shifted by 180°, each. So, they are in phase, and would *con*structively interfere... right?


title: Workaround to fermion sign problem?

text: My (rather incomplete) understanding of the NP-hard fermion/numerical sign problem is that it occurs when attempting to converge on a wavefunction for many-body fermion systems (for example, a small system of carbon atoms). And the problem is the noise introduced by the near-cancellation of large positive and negative amplitudes. It sounds to me like most of the difficulty comes in trying to solve a large collection of differential equations for a system that already exists; the computational cost goes with $2^N$, where $N$ is the number of particles. Now this may be naive, but why couldn't you simply start with a system of electrons and a positive "nucleus" charge that are far apart (so you've got a bunch of uncorrelated/unentangled single-particle wavefunctions), combine these into one multi-body wavefunction fairly easily at this point, and then evolve that overall wavefunction according to the time-dependent Schrödinger equation? I mean, since that wavefunction would numerically evolve the same way a similar one in reality would, I assume such a "separated" system would in real-life coalesce into an atom at some point in time. And it's much easier to evolve a function over time than solve a differential equation. Thus, electron-electron correlations would naturally develop in the many-body wavefunction without any additional computational effort. I imagine if it was this easy though, someone would have already done it. Thoughts?


title: Is it possible that galaxies' redshift is caused by something else than the expansion of space?

text: I was thinking that maybe photons loss energy naturally when they travel great distances. Or maybe the mass of all matter is increasing over time and therefore photons emitted in the past are necessarily less energetic. Or is the expansion of space backed up by so much other evidences that trying to find another explanation is completely foolish?


title: Given stereo sound record, is there an algorithm extract the sound coming from a direction?

text: Given a stereo record of music with singing (2 channels), subtract the left- channel waveform by the right-channel's, you might get the music only without the human singing. The question is: can I, on the contrary, get the singing part only?


title: How is relativity equation approximated

text: What is the technique with which I can approximate the equation $$\frac{mc^2}{\sqrt{1-(\frac{v}{c})^2}}-mc^2$$ when $v\ll c$? Any hint would be much appreciated


title: The degeneracy of the ground state

text: I wonder how can i know the degeneracy of the ground state of certain elements? I'm doing Boltzmann distribution problems, and I'm not sure what to do. I have to calculate ratio of ions in 3p excited state, regarding ground state for Na$^+$ and Mg$^{+2}$ ions. I think that 3p degeneration is 6, but I don't know what else to put in this fraction. Also, I've noticed that sometimes we just ignore that part of equation (count it as one) but I'm not sure when I'm allowed to do that.


title: Where should a physicist go to learn chemistry?

text: I took an introductory chemistry course long ago, but the rules seemed arbitrary, and I've forgotten most of what I learned. Now that I have an undergraduate education in physics, I should be able to use physics to learn general chemistry more effectively. What resources, either books or on-line, are useful for physicists to learn the fundamentals of chemistry? I'm not enrolled at a university, so official courses and labs aren't realistic. Please note that I am not looking for books on specialized advanced topics, but a general introduction to chemistry that takes advantage of thermodynamics, statistical mechanics, and quantum mechanics while requiring little or no prior knowledge of chemistry.


title: Why does the second Weyl scalar describe electromagnetic radiation?

text: I've been reading about the null tetrad, the Weyl tensor, and the Newman- Penrose identities, and so I found out about the Weyl scalars. While the zeroth, first, third, and fourth scalars describe ingoing and outgoing transverse or longitudinal waves, the second ($ \Psi_2$) describe electromagnetic radiation? Why not something completely different?


title: Is "microbunching" in a free electron laser limited by the Pauli exclusion principle?

text: As I understand it, a free electron laser can basically be pictured as a synchrotron light source with an undulator which by the particular setup causes the electrons to self-attune so that they produce light which is both coherent and monochromatic (as opposed to the usual synchrotron which produces monochromatic but incoherent light). The process of self-attuning can be also replaced by attuning the electrons by an external laser. Skipping the details, the resonance caused by the right set of parameters causes something which is called "microbunching" in the electron beam, i.e., an effect which can be classically pictured as all the electrons clumping around points in the beam with a distance of one optical wavelength in between. Same spatial points means same undulation, so they oscillate throughout the beam with the same phase causing coherence of emitted light. (I have just read about it, this might be a slightly naive description.) All the electrons at one place and with one velocity? Pauli exclusion principle comes quickly to mind. It seems to me that at least for small wavelengths (say ångströms $\to$ X-rays) the bunching has to be done at the cost of a noticeable velocity dispersion of the electrons due to the Pauli exclusion principle. This would mean a dispersion of the produced wavelengths and possibly a tendency to further dilute the bunched electron packets. Also, a larger required brightness of the output means more electrons and once again a wider peak in the phase space to fit the electrons into. This would in a very hand-waivish manner suggest that there is a certain constraining relation between the wavelength/monochromaticity/coherence/brightness of the outcome. So the question is: **_Does such a fundamental constraint of a free electron laser exist? And is it relevant for the current state of art or the near future?_**


title: Problem regarding heat engines

text: We have two different set ups:   1. A 200K brick in a 300K environment   2. A 300K brick in a 200K environment From which one of these can you extract more work? Assume equal mass and heat capacity. Using these equations: Efficiency - $$\eta=\frac{T_H−T_L}{T_H}$$ and: $$W = ΔQ => W≤Q_H\times\eta_C$$ I regard both as cases as infinitesimal Carnot engines. a) $T_L$ is varying, and after integration I get m*c*16.67 (m and c are the mass and heat capacity) $$ \int_{200}^{300} {\frac{300 - T}{300}}{dT} = 100 - 250/3 = 16.67 $$ b) $T_H$ is varying, after integration the result is m*c*19. $$ \int_{300}^{200} {\frac{T - 200}{T}}{dT} = -100 + 200 * \log(3/2) = 18.9$$ Therefore, I conclude that I can get more work from b; the problem is that the correct answer is marked a. Does anyone have any idea what I am doing wrong? (Or perhaps can you assure me I'm correct?)


title: What is the lowest possible theoretical temperature that nuclear fusion can occur at?

text: I am not talking about the pseudo-science of so called cold fusion I am interested in what temperature you can get away with to produce fusion reaction. I was thinking in terms of micro-fusion or at least at levels below the huge tokamaks being produced because obviously small scale devices couldn't handle millions of degrees of temperature. Or correct me if I am wrong please as I am no expert just a curious student!!


title: Meaning of the first and second laws of the photoelectric effect

text: I was reading the introduction to quantum mechanics in my physics book and it begins with a discussion of the photoelectric effect and energy quantas. The first law, the one that says that the intensity of the photoelectric saturation current is directly proportional to the flux of incident EM radiation, means that the more radiation will hit the plate the higher the intensity of the current produced (via displacement of electrons), right? And the second one, the one that says the kinetic energy of the emitted photoelectrons varies linearly with the frequency of incident EM radiation, and does not depend on the flux, means that the further up the EM spectrum the radiation is, the higher the voltage (electric potential) produced?


title: Why is there no interference pattern at D0 in the delayed erasure experiment?

text: The apparatus below represents an apparatus for the typical delayed erasure experiment. My question is, why is there no interference pattern observed at D0 in this experiment (interference is only observed in hindsight looking at photons that coincided with photons striking D2 and D3)? I would have thought the top part of the apparatus, looking like the typical double slit experiment, should show an interference pattern. I would like an answer that does not make reference to the rest of the apparatus, since according to Lubos Motl, the results at D0 should not depend on the set up or measurements in rest of the apparatus, although results may be correlated with the rest of the apparatus. Below is the quote from Lubos Motl in his answer to this question, > If you're only observing what's measured in the upper part of the picture, > e.g. the photographic plate D0, then everything that happens in the lower > part of the picture is completely inconsequential for the measurements done > in the upper part of the picture. So whether you replace the system of > mirrors and detectors by another photographic plate E0 is totally irrelevant > for the results in D0 only. I have read the entirety of Lubos' post yet this fundumental question remains unanswered. ![enter image description here](http://i.stack.imgur.com/N9ofU.png)


title: Absolute isotope activity in a nuclear fallout

text: I've seen nice graph showing _relative_ activity of each isotope in Chernobyl fallout: ![enter image description here](http://i.stack.imgur.com/mbFOK.png) Could anyone suggest similar graph or raw data but for _absolute_ isotope activity for the case of nuclear explosion fallout? (for some boosted fission bomb) So that one could see how much gamma, beta and alpha-active particles one should expect over time, and particle energy. PS. This graph is for damaged nuclear plant fallout, but I want absolute graph for nuclear explosion fallout. Explosions have different isotope content due to much shorter duration. **Update:** I see that graph might be hard to find. Maybe someone have isotope content i.e. how much % of each isotope? Or at least how it is supposed to be different from Chernobyl fallout. Then I might be able to simulate decay by myself.


title: Physical question on an RLC circuit

text: I do not know if this is an appropriate place to ask this question here but this is the only website that I am a member of so I hope that it is okay. If not, I can delete it. This circuit question was brought to me while tutoring yesterday that I was not able to answer physically. Initially the capacitor had been charged to 2V so $v_C(0^−) = 2V$. Before the switch is thrown there is no current through either the resistor or inductor, so $i_L(0^−) = 0A$. ![enter image description here](http://i.stack.imgur.com/jlIuR.jpg) Since the inductor and capacitor cannot have an instantaneous change in their values just before and after the switch is thrown, these values must remain the same: $i_L(0^−) = i_L(0^+−) = 0A$, $v_C(0^−) = v_C(0^+) = 2V$ This implies that at the moment the switch is closed, the inductor shorts out the capacitor and resistor, and no current occurs along any branches of the circuit. That is, the voltage drop across all three elements is zero. What is happening to the capacitor’s and inductor’s current and voltage in the circuit? How can the capacitor have a voltage drop of 2V and yet the inductor appears to short it out simultaneously?


title: Is it wrong to talk about wave functions of macroscopic bodies?

text: Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not? For example in the "Statistical Physics, Part I" by Landau & Lifshitz it is argued that such systems must be described via the density matrix (chapter I, about statistical matrix). As far as I got it, roughly speaking, macroscopic bodies are so sensible to external interaction that they never can be counted as systems, one have to include everything else to form a system. Is my interpretation right? When is it wrong to talk about wave functions of bodies that surround us?


title: Relation between Electric and magnetic fields

text: I've read that both the electric and magnetic field vectors are perpendicular to each other in an electromagnetic wave. Passing steady current through a straight conductor shows some magnetic flux (because most of the energy is wasted into outer space as magnetic lines). But, when it is passed through a helical coil such as the solenoid or even an inductor, a steady magnetic field is produced along the axis of the coil. Hence, both magnetic and electric fields are related to each other. How is this actually happening? Can one field be always produced by the other? An explanation focusing on Electric and magnetic fields would be appreciated.


title: When polarized light hits a polarizer, what happens to the polarization which is not transmitted?

text: It is typically said that in polarization of light only those waves can pass through a polaroid which has a plane of vibration parallel to the axis of polaroid. My question is: what happens to the other waves (the other polarization)?


title: Adiabatic expansion in the atmosphere

text: When an air parcel rises and cools adiabatically, it is said that there is no heat transfer as work is done on the surrounding atmosphere as the parcel expands. The parcel loses internal energy and condensation occurs. I do understand this concept, but why is it that work is done on the surrounding lower temperature particles by the higher temperature particles and not simply conduction, which would be a heat transfer? Wouldn't the faster moving particles in the air parcel not conduct heat on collision?


Determining of Fracture Toughness without fatigue pre cracking, is it possible? I want to find the consistent method for determining fracture toughness values without fatigue test for creating starting micro cracks


title: Why does the windshield of my car freeze even if the outside temperature is above freezing?

text: Under what conditions does the windshield of a car freeze even if the outside temperature is above freezing? It is not clear whether this is related to the question why bridges freeze with non-freezing outside temperatures (see related topic), as I did not see an explanation in terms of radiation there. It indeed seems that electromagnetic radiation is the culprit for windshields, which would predict that this phenomenon can only occur with an open sky. Does anybody know whether this is true? And why does ice only form on top of the windshield and not on the metal surface of the car? Is this because heat is conducted much faster on the metal surface?


title: Microscope Objective / NA, F/#, Exit aperture - when are they non-intuitive?

text: Numerical aperture (NA) $= sin(\theta)$ where $\theta$ is the half-angle (see: http://en.wikipedia.org/wiki/Numerical_aperture) F/# $= \frac{f}{D}$ (same reference as above) where F/# is the f-number, $f$ is the focal length, and $D$ is the lens diameter. An infinity corrected microscope objective is essentially an infinite conjugate. Therefore: $\frac{D}{f} = 2 \times tan(\theta)$ Olympus objectives are typically designed such that the power is related to the focal length using the following: $f = \frac{180mm}{P}$ where $P$ is power. Taking this to the logical conclusion reaches a paradox. Use a 60X objective with a $NA = 0.95$. $f = \frac{180mm}{60x}$ = 3.0 mm $\theta = a sin(0.95)$ = 71.8 deg $D = 2\times tan(\theta) \times f$ = 18.2 mm! The lens diameter appears too large. There are no microscope objectives this large. Although I can accept that the optical prescription can increase (decrease) the marginal ray, the exiting beam from a point source at the object plane is collimated. Under what conditions can this beam be smaller than the "lens diameter"? _By the way, I've modeled some microscope objectives in Zemax using US Patents. Some obey these equations above, some do not._


title: What happens to light at sharp points?

text: ![enter image description here](http://i.stack.imgur.com/KHnJN.png) At the tip of the sharp point shown, what will happen to light incident on it. This curiosity was invoked by a friend and also my childhood of watching shiny pointed swords in cartoons. Original Question asked to me: http://chat.stackexchange.com/transcript/message/17375026#17375026


title: Why does frequency increase as the length of an open air column shortens?

text: I am curious as to why the frequency of a wavelength increases as an open air column becomes smaller in length. Is it because an open air column will always contain half a wavelength, therefore if the tube is smaller, it means a shorter wavelength, which in itself means a higher frequency?


title: How fast can time flow? A question of time dilation

text: (I would describe myself as an illiterate physics enthusiast, so I hope you'll forgive me if my ignorance is borderline _offensive_.) If I've understood anything of the concept of time dilation, your perception of time slows down as you're approaching the speed of light. And I was wondering if you could revert the process and experience time actually going faster if you went out of your way to not move. Suppose you're standing atop of the Sun, observing the Earth revolving, –and for the purpose of this thought experiment, you have no mass because I've come to understand gravity also bends time– am I right to think you'll find earthlings living ever so slightly slower? Then, repeat the process and place yourself atop of the center of the galaxy, looking again at Earth revolving around a revolving star. Even slower? And then... I realized at this point there lacks an higher traditional referential we could use to "not move" even more as to see Earth's years pass as seconds. Considering time (rather your perception of it) stops when moving at lightspeed, is there an exact opposite phenomenon occurring when at "absolute zero speed" that would make time seem to go infinitely fast? And how would that exist considering any speed is measured relative to something else?


title: Lens parameters / Principal Planes vs. Entrance and Exit Pupil

text: Under what conditions are the **Principal Planes** _not_ the **entrance** and **exit pupil**? For the definition of Principal Planes see:   1. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/priplan.html   2. http://www.optique-ingenieur.org/en/courses/OPI_ang_M03_C01/co/Contenu_26.html For the definition of entrance and exit pupil see:   1. http://ocw.mit.edu/courses/mechanical-engineering/2-71-optics-spring-2009/video-lectures/lecture-6-terms-apertures-stops-pupils-and-windows-single-lens-camera/MIT2_71S09_lec06.pdf   2. http://en.wikipedia.org/wiki/Entrance_pupil Are the principal planes defined for any **particular imaging condition**? (e.g. magnification of 1:1) Can you supply a good reference for their definition? Smith's Modern Optical Engineering falls short of a good definition.


title: Summing moments, where have I gone wrong?

text: Because I don't have enough rep to post images, the question is question 3 part iii) from here: http://www.mei.org.uk/files/papers/m209ju_jk32.pdf The surface at the contact point B is rough. The reaction at B is: $R_{b}$ and the friction at B is: $F$ acting left, also $\tan(\alpha)=\frac{15}{8}$. I am trying to find the friction, $F$ Therefore if I resolve for the system vertically taking upwards as the positive direction I get: $$R_{b}-34\cos(\alpha)-85=0$$ Therefore $R_{b}=115$ therefore the reaction at B is $115N$ Taking clockwise moments about A gives: $$(34\times2.5)+(85\cos(\alpha)\times3)+(F\sin(\alpha)\times5)-(115\cos(\alpha)\times5)=0 $$ Where $\cos(\alpha)=\frac{15}{17}$ and $\sin(\alpha)=\frac{8}{17}$ Solving the equation for $F$, I get $F=\frac{671}{8} \approx 83.9$ But the answer says that $F = 7.4$, help on where I went wrong would be appreciated, thanks


title: Saturn's polar versus equatorial gravity

text: Wikipedia's reference for Saturn's gravity gives $10.44 m/s^2$ at the equator, but this conflicts with Britannica, which gives $8.96 m/s^2$ at the equator and $12.14 m/s^2$ at the poles. All values are at whatever elevation has a pressure of $1 bar$. I've noticed this has led to the funny situation of people Goggling the subject and erroneously citing that one would weigh more on the surface of Saturn... which is wrong. It's certainly an understandable error, because the Wikipedia number could mean one of several things:   * "the literal gravity vector on the surface in an inertial reference frame"    * the apparent surface acceleration in the reference frame of a point on the surface   * EDIT: A false metric of gravity by just using the mass and equatorial radius Not so clear is who lies at fault here. Both Wikipedia and Britannica call their numbers "gravity". Here's Britannica's very intentional wording: > The equatorial gravity of the planet, 896 cm (29.4 feet) per second per > second, is only 74 percent of its polar gravity. How correct is this wording? What is the best way to handle the subject?


title: Newton's third law does not apply to the kinetic energy formula?

text: Here is a classic problem: > _A 60kg boy and a 40kg girl are sitting in front of each other on > skateboards on a frictionless horizontal surface. The boy pushes the girl > and the girl gains a velocity of 0.3m/s during the 0.5s the boys hand was in > contact with her. What is the boy's resulting velocity?_ Considering Newton's Third Law, the best way is to find the total force applied and rearrange the formula to find the boy's speed. **Newton's Law Method:** $F = m*a$ $a=\frac{0.3m/s}{0.5s}$ $F = 40kg * 0.6m/s^2$ $F = 24N$ Therefore the boy's speed will be: $\frac{24N}{60kg} = a$ $a = 0.4m/s^2$ $v = 0.4m/s^2 * 0.5s$ $v = 0.2m/s$ **Kinetic Energy Method:** $E_{k}=\frac{1}{2}*m*v^2$ the girl's kinetic energy $E_{k}=\frac{1}{2}*40kg*(0.3m/s)^2$ $E_{k}=1.8J$ Since every action has an equal and opposite reaction the boy _should_ have the same amount of kinetic energy. $E_{k}=\frac{1}{2}*60kg*(0.2m/s)^2$ $E_{k}=1.2J$ As you can see, using Newton's Third Law, the kinetic energy was not the same. So what's going on here? I thought that in this case they should both have the same amount of kinetic energy due to Newton's Law. I must be missing something since there is more energy going in one direction than the other after meeting. My book used the first method as the answer and, well, it feels wrong.


title: Why does a flat clover-like shape fall slower when it is rotating?

text: The plastic flat clover-like shape pictured below falls noticeably slower when it is rotating fast. I wonder why. Its three edges are flat, so I don't think that the rotation makes it act like a propeller. An ideal explanation would include an analogy that a young child can understand (e.g. rain bouncing on a car's wind-shield). Here is a photo of the object. ![object that falls slower when rotating](http://i.stack.imgur.com/i9pNt.jpg)


title: Use of advanced mathematics in astronomy, like topology, abstract algebra, or others

text: I know that topology, abstract algebra, K-theory, Riemannian geometry and others, can be used in physics. Are some of these areas used in astronomy, and are some astronomical theories based on them? I'm not considering calculus, linear algebra, or other common courses in the first years of college, for many, like engineering, etc.


title: What is lighting up Space Shuttle Endeavour's main engines?

text: Al Jazeera has a terrific collection of Space Shuttle photos. In photo #11 we can see something bright in each Space Shuttle Main Engine (SSME) as Endeavour lands. What might that be? A reflection off the back of the combustion chamber? Something related to the auxiliary power units (APUs) venting through the SSMEs? Here's a smaller cropped version; see the "photo #11" link for the original. ![Endeavour landing](http://i.stack.imgur.com/9B6WZ.jpg)


title: Why do we see laser beams?

text: A laser produces a coherent beam of photons with particular $\mathbf{k}$ and $\mathbf{\omega}$. So, if there is no particular $\mathbf{k}_0$ directed toward our eyes, why do we see laser beams? I think this is related to the Huygens–Fresnel principle, but I wasn't sure.


title: Given a photo of the Moon, taken from Earth, is it possible to calculate the position of the photographer's site?

text: Given a photo of the Moon, taken from Earth, is it possible to calculate the position (Earth longitude and latitude) of the photographer's site? I am thinking about photos taken with a normal camera lens and not with a telescope, for example photos taken with a 300 mm lens like these one: http://www.flickr.com/search/?q=100+300+moon&l=cc&ct=0&mt=all&adv=1 I assume the photo shows enough detailed features like recognizable craters and maria. Is there any software capable of solving the problem? Thank you. Alessandro Addendum: A diagram of a simplified model of the problem: ![A triangle with vertexes in the center of the Moon, in the center of the Earth and in the photographer site on Earth](http://i.stack.imgur.com/BVide.png) R is the radius of the Earth. D is the (average) distance from the center of the Moon to the center of the Earth. P is the photographer site on the surface of the Earth.


title: Physical interpretation: weighted eigenvalues of the Laplacian with a potential

text: I'm a mathematician with only the basic knowledge of Physics, so my question may be trivial: in this case, mercy me. :-) Let $\Omega \subseteq \mathbb{R}^N$ be a domain and let $V,m:\Omega \to \mathbb{R}$ be two measurable and sufficiently summable functions. When one considers the eigenvalue problem for the operator $\mathcal{L}:=-\Delta +V$ w.r.t. the weight $m$, i.e.: $$\tag{P} \begin{cases} -\Delta u(x) + V(x)\ u(x) = \lambda\ m(x)\ u(x) &\text{, in } \Omega\\\ u(x)=0 &\text{, on } \partial \Omega , \end{cases}$$ the function $V$ is usually called _potential_ and the function $m$ is called _weight_. Then, _a weighted eigenvalue of $-\Delta +V$ w.r.t. $m$_ is any number $\lambda \in \mathbb{R}$ s.t. ( **P** ) has at least one nontrivial weak solution $u\in H_0^1(\Omega)$, i.e.: $$\forall \phi \in C_c^\infty(\Omega),\quad \int_\Omega \nabla u\cdot \nabla \phi\ \text{d} x + \int_\Omega V\ u\ \phi\ \text{d} x = \lambda\ \int_\Omega m\ u\ \phi\ \text{d} x\; .$$ My questions are: >   1. Is there any reasonable physical interpretation of those eigenvalues? > And what is it? > >   2. Why have the functions $V$ and $m$ those names? > > Moreover: > What about any possible physical meaning of the nonlinear weighted > eigenvalues coming from the problem: $$\tag{Q} \begin{cases} -\Delta_p u(x) > + V(x)\ |u(x)|^{p-2}\ u(x) = \lambda\ m(x)\ |u(x)|^{p-2}\ u(x) &\text{, in } > \Omega\\\ u(x)=0 &\text{, on } \partial \Omega , \end{cases}$$ where $1 < p > < \infty$ and $\Delta_p$ is the $p$-laplacian (i.e., $\Delta_p u := \nabla > \cdot (|\nabla u|^{p-2}\ \nabla u)$, which reduces to the usual laplacian > when $p=2$)? Many thanks in advance.


title: Magnetic moment precession around magnetic field

text: I have a question regarding the magnetic moment of an atom. If you just have one atom, and you apply an external magnetic field in lets say the z-direction. Then the magnetic moment will precess around the direction of the magnetic field applied, and depending on the quantum numbers it can precess in different quantized directions. The question is rather simple: WHY does it precess around the magnetic field ? My book only states that it do indeed precess if a magnetic field is applied, but as I'm asking, I'm not sure WHY it does ? Why can't it just point in one direction all the time ?


title: Do we need infinite energy to make 2 similar charges touch only in theory?

text: By Coulomb's law, say if we have 2 point particles each having a charge of +1C then by the formula, F = k/(d)^2 if we need to make the distance between them zero, clearly y the formula, we need to have an infinite amount of force. However, in a real life scenario, we see that if we rub two balloons with our head, they acquire the same charge. However, it is still possible to make them touch. Is this because the two balloons are not point objects? OR is the definition d=0 actually mean "to occupy the same space". for d to be 0, do the objects only need to touch or do their centers need to be together?


title: Examples of circuitry using proton currents

text: Proton cuircuits and proton motive force are part of standard discussion in biology and processes involving photosynthesis. The sort of proton currents discussed in biology are obviously slightly different than the magnetically confined proton currents in an acclerator like LHC, however, although we are very familar with electronic circuitry, I was wondering if there are example of protonic circuitry outside of biological processess.


title: Age of universe estimates

text: I was recently involved in a discussion on a sister site regarding how tightly coupled Physics is with the age of the Universe (and Earth). I believe that the Earth and the Universe are both billions of years old, but don't know enough on why exactly other than having confidence in peer reviewed science. Moreover, it would be helpful if I knew which parts of physics are tightly coupled with the current age estimate. So,   1. Are there any notable hypotheses or entire fields of modern physics that both:     * do not rely on the age of the Earth for their predictive and explanatory power and     * do not predict an old Earth   2. If so, which fields depend (directly or indirectly) on the age of the Earth, and which do not? Put differently,   * _consistent with old Earth_ = hypotheses that either rely on the age of the Earth for their predictive power or predict an old Earth   * M = Modern physics.   * Mo = Modern physics consistent with old Earth.   * Mn = Hypotheses that both do not rely on the age of the Earth for their predictive power and do not predict an old Earth. Then M = Mo∪Mn. **My question is if there are any hypotheses in M n, or Mn is an empty set?**


title: Is it possible to be changed Energy Unit in future or it is strict reality in nature?

text: Could you pease tell me why energy unit must be $Energy=Mass . \frac{Distance^2} {Time^2}$? (I tried to write general form of Energy unit) What is the strong proof of that unit? Does it just depend on Newton's second law ($F=ma$) and Work formula. Or something else? Newton's second law: ($F=ma$=Mass x Acceleration of the center of mass=$Mass.\frac{Distance} {Time^2}$) $Work = Force . Displacement =Mass . Acceleration .Distance =Mass . \frac{Distance^2} {Time^2}$ Is it possible to change the Energy unit after realizing that Newton's second law and work formula are approximation? Or is it strict true in nature? Note: Einstein showed that the relativity can change our approach to the nature but he did not touch Energy unit. ($E=m.c^2$)


title: Solar heating of an object in air

text: I need a solution to the heat equation that shows temp increase in an object, e.g. a cube or sphere, in sunlight. The object is assumed to be exposed on all sides except one. It is a solid object with a certain surface emissivity and heat capacity. In other words, I don't care what is inside the object. It absorbs some light from the sun and heats up, and heat is radiated and convected in air so that it reaches an equilibrium temperature. The solution presumably uses the parabolic PDE and the Neumann boundary condition. A Matlab formulation would be great!


title: Derivation of the equation of motion of a viscous fluid by Landau & Lifshitz

text: I am trying to follow Landau and Lifshitz, from the Volume 6 (Fluid Mechanics) of the Course of Theoretical Physics, on their derivation of the momentum equation for a newtonian viscous fluid, but I do not understand how the viscous stress tensor is found. * * * # Background The derivation starts from Euler equation: $$\frac{\partial}{\partial t}\left(\rho v_i\right) = - \frac{\partial \Pi_{ik}}{\partial x_k}, $$ where $$ \Pi_{ik} = p\delta_{ik} + \rho v_iv_k $$ is the momentum flux density tensor for an ideal fluid. According to Landau & Lifshitz : > [this momentum flux density tensor] represents a completely reversible > transfer of momentum, due simply to the mechanical transport of the > different particles of fluid from place to place and to the pressure forces > acting in the fluid. The viscosity (internal friction) causes another, > irreversible, transfer of momentum from points where the velocity is large > to those where it is small. > > The equation of motion of a viscous fluid fluid may therefore be obtained by > adding to the "ideal" momentum flux a term $-\sigma^\prime_{ik}$ which gives > the irreversible "viscous" transfer of momentum in fluid. Thus we write the > momentum flux density tensor in a viscous fluid in the form $$ \Pi_{ik} = > p\delta_{ik} + \rho v_iv_k - \sigma^\prime_{ik} $$ where $ \sigma^\prime_{ik} $ is called the viscous stress tensor. * * * # Expression of $\sigma'_{ik}$ Firstly, it is explained why it can be considered that this tensor will contain only linear combination of partial derivatives of the velocities regarding the positions. I understand that. > Processes of internal friction occur in a fluid only when different fluid > particles move with different velocities, so that there is a relative motion > between various part of the fluid. Hence $\sigma^\prime_{ik}$ must depend on > the space derivatives of the velocity. If the velocity gradients are small, > we may suppose that the momentum transfer due to viscosity depends only on > the first derivatives of the velocity. To the same approximation, > $\sigma^\prime_{ik}$ may be supposed a linear function of the derivatives > $\frac{\partial v_i}{\partial x_k}$. There can be no terms in > $\sigma^\prime_{ik}$ independent of $\frac{\partial v_i}{\partial x_k}$, > since $\sigma^\prime_{ik}$ must vanish for $\mathbf{v}$ = constant. Then: > Next, we notice that $\sigma^\prime_{ik}$ must also vanish **when the whole > fluid is in uniform rotation, since it is clear that in such a motion no > internal friction occurs in the fluid.** In uniform rotation with angular > velocity $\mathbf{\Omega}$, the velocity $\mathbf{v}$ is equal to the vector > product $\mathbf{\Omega} \times \mathbf{r}$. The sums $$ \frac{\partial > v_i}{\partial x_k} + \frac{\partial v_k}{\partial x_i} $$ are linear > combination of the derivatives $\frac{\partial v_i}{\partial x_k}$, and > vanish when $\mathbf{\Omega} \times \mathbf{r}$. Hence $\sigma^\prime_{ik}$ > must contain just these symmetrical combinations of the derivatives > $\frac{\partial v_i}{\partial x_k}$ I can understand that we do not want any internal friction when the fluid is in uniform rotation, but why is it clear that it is true ? Is it impossible for a "special" (non-newtonian) fluid to have this kind of friction ? But even if I accept this point, where I am completely lost is hereafter: > The most general tensor of rank two satisfying the above conditions is $$ > \sigma^\prime_{ik} = \eta\left(\frac{\partial v_i}{\partial x_k} + > \frac{\partial v_k}{\partial x_i} - \frac{2}{3}\delta_{ik}\frac{\partial > v_l}{\partial x_l}\right) + \zeta \delta_{ik}\frac{\partial v_l}{\partial > x_l},$$ with coefficients $\eta$ and $\zeta$ independent of the velocity. In > making this statement we use the fact that the fluid is isotropic, as a > result of which its properties must be described by scalar quantities only > (in this case, $\eta$ and $\zeta$). The terms in [expression of the tensor > above] are arranged so that the expression in parentheses has the property > of vanishing on contraction with respect to $i$ and $k$. (footnote: That is, > on taking the sum of the components with $i=k$) I do not understand how this general form is found. I understand from the paragraph on rotation that if on a non-diagonal term $\frac{\partial v_i}{\partial x_k}$ is found then $\frac{\partial v_k}{\partial x_i}$ must be added. But in uniform rotation it is also found that $$ \frac{\partial v_x}{\partial x} = \frac{\partial v_y}{\partial y} = \frac{\partial v_z}{\partial z} = \mathbf{\nabla \cdot v} = 0. $$ Then it should be authorized to add any of these terms anywhere in the tensor, but in the "general form" described only one appears, the divergence, and only on the diagonal. Why is that ? I believe that it has to do with the assumption of isotropy, but I cannot make that clear.


title: Stopping Distance (frictionless)

text: Assuming I have a body travelling in space at a rate of 1000m/sec. Let's also assume my maximum deceleration speed is 10m/sec*sec. How can I calculate the minimum stopping distance of the body? All the formulas I can find seem to require either time or distance, but not one or the other.


title: Why did the microwave oven only heat my coffe half as much as expected?

text: A sticker on my microwave oven states its output effect to be 750W, which is 180 calories per second. This means that heating 250g of water by one degree celsius would take 250/180 = 1.4s. Now, my cup of 250 cl coffee had cooled to 35 degrees, so I figured heating it to 45 degrees would take 14 seconds. But the actual temperature after that time was only 40 degrees. I did not measure the coffee volume exactly, and the thermometer probably has an error margin, but still the 50% deviation makes me think that I've failed to take something into account. The porcelain cup should not have been heated much, and 14s is probably too short for much heat to transfer from the coffee to the cup.


title: Understanding particle's space travel

text: Before the discovery of dark matter, the prevailing popular understanding of Space content is that of celestial bodies (planets, stars..etc) floating in 'void' and emitting particles and waves (light-photons, electro-magnetic..etc) Now, if we still assume Space is void, logically why wouldn't particles travel endlessly? That is, a 'solar' flair from Betelgeuse would eventually reach Earth, since there would be nothing that would stop/slow it.


title: Is it Possible to have Adiabatic Processes other than $PV^\gamma$ for the ideal Gas?

text: Is it possible to represent an adiabatic process for an ideal gas by a formula other than $PV^\gamma=Const$?: _Relevant Considerations_ : We always need to connect a pair of _arbitrary_ points/states $A:(P_1,V_1)$ and$B:(P_2,V_2)$ on the P-V indicator diagram to define the Internal Energy function(U) If the two points do not lie on some $PV^\gamma=Const$, we may think of some abrupt process connecting the two states. Such a process cannot be represented by a continuous curve on the diagram since the intermediate states are non- equilibrium states. Pressure will not have a unique value wrt the system for such processes.It will be different from point to point.We have a pair of points A and B without any curve connecting them Now we connect the points A and B by an arbitrary "continuous" path on our diagram(on paper) and select close discrete points on it. The consecutive "close" discrete points may be connected by abrupt adiabatic "processes" as described previously. Therefore in the pragmatic sense we can have an arbitrary quasi-static "adiabatic" path connecting the points A and B : The "close" points ie physical; states,will lie on a curve different from $PV^\gamma=Const$ [In the physical/practical implementation of the $PV^\gamma=Const$ curve we do consider/implement a chain of discrete equilibrium states]


title: Forces, symmetry, and asymmetry

text: The concept of symmetry is one of the most promising and misunderstood concepts in physics. If one consider Hermann Weyl ("Symmetry"; ISBN-13: 978-0691023748), "As far as I see, all a priori statements in physics have their origin in symmetry", the symmetry concept should provide the basis for all physical theories. Nevertheless, both in high school and in College, he is shown qualitatively but used extremely rarely into math form. The concept of asymmetry is also important, at least in the sense in which the structural gradients (asymmetries) in a system, generates restorative forces (to a state without this asymmetries). My question is if there is a theory to infer forces and/or force fields starting directly from the concept of symmetry/asymmetry.


title: Has Bell really demonstrated that no local hidden variable theory can exist in his original paper of 1964? Why then verify the CHSH violation?

text: The more I read about it and the more I'm convinced I haven't understood what I thought I had. In the original paper `J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1, 195, 1964.` (link), there is a section (the section **IV** ) where   * The Bell inequality $1 + P(\vec{b},\vec{c}) \geq \left |P(\vec{a},\vec{b}) - P(\vec{a},\vec{c}) \right |$ takes form   * The fact that $\epsilon$ cannot be made arbitrarily small for all $\vec{a}$ and $\vec{b}$ in the expression $\left |\overline{P}(\vec{a},\vec{b}) + \vec{a}.\vec{b} \right |\leq \epsilon$, which implies that no local hidden variable theory can exist to arbitrarily closely approach the quantum mechanical predictions. My question is this : If my interpretation of the second bullet point is right, what's the point of verifying the CHSH inequality by experiments since it has been proved by Bell in this article that it's impossible ? Does the fact that we have $\overline{P}$ and not simply $P$ change anything ?


title: Polchinsky's Evaluation of the One Loop String Path integral

text: I try to evaluet the matrix M in the Polchinsky's article(Communications in Mathematical Physics,1986, Volume 104, Issue 1, pp 37-47,"Evaluation of the one loop string path integral",Joseph Polchinski) (1)$$\det\begin{bmatrix}1 & 0 & 0\\\ -D_{a} & \delta_{a}^{c} & 0\\\ \frac{1}{2} g^{ef}g_{ef,i} &0 & \delta_{ik}\end{bmatrix} \cdot \det\begin{bmatrix}2+4C & 0 & 0\\\ 0 & 2 \Delta_{c}^{d} & -2D_{e} {\chi_{l}^{e}}_{c}\\\ 0 &2 \chi_{k}^{ed} D_e & \chi_{kef} \chi_{l}^{ef}\end{bmatrix} \cdot\det\begin{bmatrix}1 & D^{b} & \frac{1}{2} g^{ef}g_{ef,i}\\\ 0 & \delta_{d}^{b} & 0\\\ 0 & 0 & \delta_{ij}\end{bmatrix}=J N J^{T}$$ where $\Delta_{c}^{d}= -\delta_{c}^{d} D^2-D^{d}D_{c}+D_{c}D^{d} and \chi_{iab}=g_{ab,i}-\frac{1}{2} g_{ab}g^{cd}g_{cd,i}$. I'm considering a torus, so the covariant derivatives become $\partial$. Also the determinant of $J$ and $J^T$ are $1$. So the determinant of the matrix N become $$\det(N)=\det(2+4C)\det(-2\delta_{c}^{d}\partial^2) \det(\chi_{kef} \chi_{l}^{ef}).$$ This is right? (2) $\det(\chi_{kef} \chi_{l}^{ef})=\chi_{kef}(g^{e \alpha}g^{f \beta} \chi_{l\alpha \beta})=\partial_k g^{\alpha\beta}\partial_l g_{\alpha \beta}-\frac{1}{2} (g_{\alpha \beta}D_kg^{\alpha \beta})g^{\gamma \delta} \partial_l g_{\gamma \delta}-\frac{1}{2} g^{\alpha \beta} \partial_l g_{\alpha \beta} g^{cd} \partial_k g_{cd}+\frac{1}{2}(g^{cd}\partial_k g^{cd})(g^{\gamma \delta} \partial_k g_{\gamma \delta})$ this is also right? (3) If steps 1 and 2 are correct, how can I get to the form (given by Polchinski in the article)? $$\det'(N)=\det(2+4C)\det'(-2\delta_{c}^{d} g^{ab} \partial_a \partial_b) \frac{4}{{\tau_2}^4}$$ where the prime denotes the restriction to the zero mode.


title: Is the traditional free-body diagram invalid in situations in which equal forces produce unequal powers?

text: This question is in response to question B1 in the problems/solutions located at http://aapt.org/physicsteam/2013/upload/E3-1-7-solutions.pdf. In question B1, there is a wind-powered vehicle that can travel both against the wind and with the wind, and in both cases potentially may go faster than the wind itself. The force generated by the wind on the propeller is opposite but equal in magnitude to the force the wheel exerts on the ground. In a traditional free- body diagram, one would say the forces balance, therefore the velocity is constant. Moreover, there is loss due to friction and so presumably the vehicle would come to rest. This, however, is not the case. In the against-wind case, the propellers move through more air than the wheels do ground. The propeller then produces more power than the wheels consume. As a result, the craft speeds up until the frictional loss and the wheels consume as much power as the propeller generates. It would seem that there must be a restriction on free body diagrams that all forces act through the same distance - or something else of that nature. Is this correct? What restrictions must a free-body diagram have to be guaranteed to be accurate?


title: Classical theories and AdS/CFT

text: When I was editing the Physics.SE tag wiki for ads-cft, I initially wrote something on the lines of : > The AdS/CFT correspondence is a special case of the holographic principle. > It states that a gravitating theory in Anti-de-Sitter (AdS) space is exactly > equivalent to the gauge theory/Conformal Field Theory (CFT) on its boundary. Then I thought, "Wait, it can't be ANY gravitating theory, right? It must be a theory of Quantum Gravity, right?". So I changed it to: > The AdS/CFT correspondence is a special case of the holographic principle. > It states that a quantum gravitating theory in Anti-de-Sitter (AdS) space is > exactly equivalent to the gauge theory/Conformal Field Theory (CFT) on its > boundary. Now, I'm a bit unsure. Can AdS/CFT work for classical gravity theories? . I have seen the questions Which CFTs have AdS/CFT duals? and What is on the AdS side in AdS/CFT supergravity or string theory?, but my question is a bit different.. It is a special case of the opposite of the first question, and is more general than the second. From Lubos Motl's answer to the second question, I see that supergravity theories don't form AdS theories with CFT duals, but is that true for all classical theories?. And a bit more general question: If the answer to the above question^ is yes, then do all gravitational theories in AdS's have CFT duals? . This is pretty much the opposite of Which CFTs have AdS/CFT duals?. For example, is General Relativity such a theory; with a CFT dual? If so, what would be it's CFT dual? What about... Nope I'm not going to ask about Newtonian Gravity, or Aristotilean Gravity, for obvious reasons. And certainly not LQG (something that doesn't respect holography in the most trivial situations, couldn't here.).


title: Is the Copenhagen interpretation still valid?

text: "The secret lives of photons revealed" - physicsworld.com. It seems that this experiment violates the Copenhagen interpretation. Is it still valid? Can you please give me more insight on this experiment?


title: What is the net radiative balance between two blackbodies with different temperature?

text: **Context** In trying to understand a crop productivity model, I want to figure out how to derive the equation for the net exchange of longwave radiation between two adjacent blackbodies (soil and atmosphere) over some discrete time step. In order to calculate the net energy balance, longwave radiation ($L$) is calculated first (and can easily be calculated from first principles), so we can go from: $$S_\downarrow + L_\downarrow = L_\uparrow+H+\lambda E+G$$ To here: $$S_\downarrow + (L_\downarrow - L_\uparrow) = H+\lambda E+G$$ where $S$ is solar flux, $L$ is longwave radiation, $\lambda E$ is latent heat and $G$ is conduction. **Problem** This is the equation I am trying to derive: $$L_{\text{soil}\rightarrow\text{air}}=4\sigma T^3\Delta T$$ Where   * $\sigma$ is the Stefan-Boltzman constant   * $L_{\text{soil}\rightarrow\text{air}}=L_\uparrow - L_\downarrow$ is the net heat flux over time step $\Delta t$   * $\Delta T=T_\text{air}-T_\text{soil}$  I am starting with the Stefan-Boltzman law: $$L_\downarrow=4\sigma T^4$$ And I recognize the following:   * I am trying to calculate $L_\downarrow-L_\uparrow$ over some $\Delta t$ and   * $dL/dt = 4\sigma T^3$ However, I can't get back to the SB law. I have gotten as far as $$L_\uparrow-L_\downarrow =\sigma T_\text{soil}^4-\sigma T_\text{air}^4$$


title: Is it possible to have a negative attraction to gravity just like how magnets with same pole does?

text: Layman question here, is it possible for an object to be negatively attracted to a gravitational pull of another object? Like how same pole magnets repels each other, can it happen on gravity too?


title: How can one explain gravitational time dilation in non-rotating bodies?

text: A clock on the surface of the Earth (assuming it does not rotate) will accumulate around 0.0219 seconds less than a distant observer over a period of one year (assuming the observer is using Schwarzschild coordinates). In comparison, a clock on the surface of the sun will accumulate around 66.4 seconds less in a year. How is this possible and what causes this phenomenon. Reference: Wikipedia The formula for calculating the time dilation caused by a non-rotating mass is $$ t_o = t_f \sqrt{1 - \frac{2GM}{c^2r}} = t_f \sqrt{1 - \frac{r_s}{r}} $$ where: $t_0$ is the proper time between events A and B for a slow-ticking observer within the gravitational field $t_f$ is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object $G$ is the gravitational constant $M$ is the mass of the object creating the gravitational field $r$ is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), $c$ is the speed of light


title: How exactly and WHY does matter affect space-time?

text: According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) are physically equivalent to a gravitational field of the same strength. Refer: Einstein's thought experiment of a Physicist in an Accelerated Box. I find that the 'How' part of this question is somewhat easy to understand Mathematically but hard to visualize physically and on the 'Why' part I am totally blank.


title: Question about supercooling

text: During the cooling of a liquid, if no impurity of site of nuclearation, an appreciable solidification will begin only after the temperature has been lowered to below the equilibrium solidification (or melting) temperature. This phenomenon is termed supercooling. My question is, if supercooling is necessary, what is the meaning of "equilibrium" solidification (or melting) temperature (e.g. 0oC for water)?


title: Pushing a crate on a friction floor

text: A man is pushing a crate at a constant velocity. there is a friction between the floor and the crate of $$\mu =0.41.$$ The pushing force is directed downward at an angle $\theta $ _below_ the horizontal. When $\theta $ is greater then a certain value it is not possible to move the crate now matter how large the pushing force is. Find that $\theta$. Sketching a free-body diagram of the crate I ended up with this eq: $$\mu m g=F(\cos \theta-\mu \sin \theta)$$ And at this point I looked at the answer to see that the answer is $$\theta \approx 68 \deg$$ i.e the solution to the term $\cos \theta-\mu \sin \theta=0$. Why is it so?


title: How can I read density fluctuation from microwaves?

text: The Cosmic Microwave Background Radiation shows temperature differences. The red and yellow areas are warmer. The green and blue areas are cooler. For example consider this picture of CMBR fluctuations: ![CMBR fluctuations](http://i.stack.imgur.com/58hOQ.jpg) I've read it also shows density fluctuations, but how I can identify them? Where does it have more matter and will form stars and galaxies? And where will it be empty space?


title: Is the classical world an illusion?

text: In the paper > Zeh, H. D. The Wave Function: It or Bit? In _Science and Ultimate Reality_ , > eds. J.D. Barrow, P.C.W. Davies, and C.L. Harper Jr. (Cambridge University > Press, 2004), pp. 103-120.  arXiv:quant-ph/0204088 does Zeh state the classical world is an illusion or that our sense of locality in the classical world is an illusion? Is he correct?


title: Atoms and electrons?

text: Consider a copper atom. If you place an electron near it, the protons in the nucleus would attract it like they attract the existing electron in the valence shell. However the electron you placed beside it won't join the copper atom because adding an electron to its shell wouldn't make the atom any more stable. But why doesn't the electron join the atom? I understand that it would make the atom less stable, but isn't the nucleus still attracting it? If the reason is that some other force repels the other electron since it makes the atom less stable, why doesn't this same force repel the current electron in the valence shell out of the atom since this would make the atom more stable?


title: Twins paradox "corrected"

text: If you know a bit of special relativity, probably you've heard of the twin paradox. I would like to know: what happens if we take acceleration into account in the paradox. Usually we consider an instantaneous change of velocity for the moving twin (before he was moving at, say, $\frac{c}{2}$, when coming back, he's suddenly moving at $-\frac{c}{2}$...) My work on the problem: Let Alice (the first twin) be still in an IS (coordinates $t,x,y,z$), and Bob (they're heterozygotes, obviously!) be moving. The coordinates system KS' of Bob ($t',x',y',z'$) is **not** inertial and satisfies: $$\left\\{\begin{array}{l}t=t'\\\x=x'+\sin(t')\\\y=y'\\\z=z'\end{array}\right.$$ so that Bob (located at the origin of KS') moves away from Alice for $0\le t\le\frac{\pi}{2}$, and comes back for $\frac{\pi}{2}\le t\le\pi$. We have: $$\begin{array}{l}dt = dt'\\\dx = \cos(t')dt'+dx'\\\dy=dy'\\\dz=dz'\end{array}$$ and thus: $$\begin{array}{ll}ds^2 & = dt^2-dx^2-dy^2-dz^2 =\\\ & =(1-\cos^2(t'))dt'^2-2\cos(t')dt'dx'-dx'^2-dy'^2-dz'^2\end{array}$$ By fixing a clock at constant $x',y',z'$ in KS' and looking at the proper time, we get: $$d\tau = \sqrt{1-\cos^2(t')}dt' = \sqrt{1-\cos^2(t)}dt = \sin(t)dt$$ (where we used $t=t'$ and $dt=dt'$). Integrating from $t=0$ to $t=\pi$ (the time Bob takes to go away and come back) we get the time a clock in KS' will mark when Bob is back home (where the clock marked $0$ when he went away): $$\int_0^\pi\sin(t)dt = 2$$ which looks _weird_... (Note: I expected this to give $\pi$, so that there would have been no paradox at all.) Can someone spot eventual mistakes I made? **Note:** I followed the same procedure I found in these lecture notes at pages 18-19.


title: Elementary particles

text: That's what Wikipedia says about Elementary Particle: > _In particle physics, an elementary particle or fundamental particle is a > particle whose substructure is unknown, thus it is not known to be composed > of other particles._ Assumed the above sentence: Can we ever know the structure of an elementary particle "Z" if it is an agglomeration of other n sub-particles "T" that, toghether, cancel their actractive forces creating our singular Z particle? An answer could be to collide 2 "Z" particles until they break and show us the "T" particles, but again, the same question can be formulated for the "T" particle. We can demonstrate that a particle is not elementary, but we can't say that it is NOT composed of other particles. This leads to another concept: suppose we make and demonstrate an M-Theory called "X" which affirm that "n" different particles can stick making all other known particles with the same known properties , we're not able to demonstrate that there's no other M-Theory "Y" that generalize the "X" one. Furthermore can even make sense to formulate tens of different "Y" M-Theories which logically generalize the "X" one and that, simulated on a utopian machine, generate the "X" environment. The core question is, will we ever know when we are done?


title: Can a bracelet fitted to hand, slip off and stay connected?

text: Hello I have a bracelet in my hand with a clip that holds it connected. The bracelete can not slip off my wrist, it is not loose. However while I was standing, it felt from my hand and I found it still connected on the floor. I don't believe in magic and I am not making any fun out of this. I am a physics/mechanics enthusiast and I am trying to think of a possible logical reason, how this can happen. Thank you. this is how the connector is ![this is how the connector is](http://i.stack.imgur.com/RQdFm.png)


title: Is it possible to Vectorialize Quantum Field Theories?

text: If I take the rules for classical electrodynamics in the covariant formulation (the closest to QFT), I have a tensor that describes the field, $F_{\mu\nu}$. Now we know that we can take some of the components of that tensor and find two vectors, $\mathbf{E}$ and $\mathbf{B}$, that obey Maxwell equations and have an identity on their own. In my understanding the "photon field" has been reduced to something much more material, that I can visualize. I can see easily, for example, a wave propagating in a particular direction. I am aware that I tacitly assumed that the "photon field" is described by the classical theory, but I think that the concept is clear nonetheless. Now, is it possible to do something like that to the "electron field", the "positron field", the "gluon field" and so on? If you take all the forces together and you have a giant field with many components (as in my understanding is the Standard Model), is it possible to find some combinations of those components that behave like vectors?


title: How do I show that the eigenstates of a Hamiltonian can be made orthonormal?

text: I've been tearing my hair out over this all evening. It should be simple but I must be missing something somewhere. Can someone show me how to prove that the eigenstates of a Hamiltonian can be made orthonormal, please?


title: Finding maximum speed in a work-energy problem

text: I have the following problem: > _The Royal Gorge bridge over the Arkansas River is $310\text{ m}$ above the > river. A $57\text{ kg}$ bungee jumper has an elastic cord with an unstressed > length of $64\text{ m}$ attached to her feet. Assume that, like an ideal > spring, the cord is massless and provides a linear restoring force when > stretched. The jumper leaps, and at at her lowest point she barely touches > the water. After numerous ascents and descents, she comes to rest at a > height h above the water. Model the jumper as a point particle and assume > that any effects of air resistance are negligible._ > > _(a) Find $h$._ > > _(b) Find the maximum speed of the jumper._ I was able to solve part (a) (the answer is $148.3\text{ m}$), but I can't figure out how to do part (b). How do I go about solving it? (As an aside, I calculated that the spring constant for the bungee cord is $k=5.72$.) One thing I tried was setting the gravitational potential energy at the top of the jump equal to total energy when the jump was `h` meters above the water: $U_{grav} = K_{grav} + U_{spring} + U_{grav}$ $mg(310) = \frac12mv^2 + \frac12kh^2 + mgh$ $(57*9.8*310 = \frac12(57)v^2 + \frac12(5.72)(148.3)^2 + 57*9.8*148.3$ This gives me $v=31.02\text{ m/s}^2$, which is incorrect.


title: If photons move linearly, what's actually stopping them from passing through a microwave oven mesh?

text: So, my understanding is that the wavelength of a photon is the distance traveled in the time it takes it's magnetic field to oscillate. And it's inversely proportional to it's energy and it's frequency. In other places I've read that the wavelength is actually volumetric, but then, how can the radio wavelength be the size of a building, or other wavelenghts (citing Wikipedia) "the size of the Universe"? Is the photon actually affecting things millions of kilometers away?? How is that even possible? I just can't understand this explanation. Then in the other hand I have this other explanation that the wavelength is actually not a property of each single photon but of a pack of photons. But then I can't understand how can the wavelength be indirectly proportional to a particular photon energy, when it's not a property of a particular photon! Also, if the wavelength changes with a change in speed (for example entering water), then it means that it has to be actually a proportional to the distance traveled, so I came to accept that explanation. So, when I have a microwave oven it has a mesh that allows visible light to pass through, but not microwaves. **The usual explanation given to everyone is that the mesh holes are smaller than the microwave wavelength, but larger than the visible light wavelength.** But I can't make sense of this. If the wavelength is the distance traveled by a photon, what does it have to do with the size of a hole the photon can fit through? I mean, photons move linearly and are all equal in size, so what's stopping them from actually passing through the empty space?