title: What is light and how does it travel?

text: My question is: **What is light, and, more specifically, how does it travel?** I've been contemplating a theory that I watched on Youtube _(which has no real credibility to my knowledge)_ , the Cosmic Matrix Displacement Model. I was intrigued by one certain aspect, discussed starting at 5:53 (the video is linked to that time), which talks about strings in String Theory being 4 dimensional Vortispheres, which are explained in the video. Basically, my interest in this is that it brought me to question my acceptance of the idea of light just being waves capable of traveling through **empty** space. I had never thought the phenomenon through any further than that. So the specific piece of my question, "How does light travel?" is inspired by the contemplation of the fact that light (and all energy) must need _some_ sort of structure to travel through. The concept explained in the video is that Vortispheres statically fill the universe and transfer 100% of their motion energy as they rebound off of each other. ![enter image description here](http://i.stack.imgur.com/69EdG.jpg) The model asserts that the pre-universe matrix was: ![enter image description here](http://i.stack.imgur.com/jFHIk.png) (according to the model) When motion did occur in the space-time quantum vacuum, Vortispheres formed from the matrix substance with the sheer sphere boundary layer between the still matrix and the moving Vortispheres. ![enter image description here](http://i.stack.imgur.com/szA9Q.jpg) The Vortispheres continued to form and expand exponentially out through the new universe and were rebounding off of each other, transferring 100% of their motion energy to the next Vortisphere upon impact with zero friction loss. **According to the model, the minute length of time it takes for a Vortisphere to move across the matrix gap and impact the next Vortisphere establishes the average speed of light at 299,793,458 meters per second.** **So anyway** the video goes on to explain its explanation of the creation of matter and the workings of gravity, with gravity working in precisely the same way as molecular diffusion. Be that correct or incorrect as it may be, it sparked my curiosity on the subject of how light moves through empty space. * * * **A Programmers's Metaphor** As a programmer, I'd sum up my question as being similar to me just accepting that JavaScript works, without caring about all the complex layers infrastructure programmed at lower levels to make it seem simple. Waves of light being like simple JavaScript and Vortispheres in the video being like complex Assembly code at a lower level. Hopefully this helps clarify what I'm asking somewhat. I'm curious about the infrastructure that acts as a medium for the light waves to work. Of course, asking these questions may just be a silly task, since when you explain the "Assembly" infrastructure to me, I'll want to about what makes the Assembly work, and so on and so forth forever and ever in an endless chain of curiosity that will go on as long as we continue to ask questions... bleh. Physics...


title: Work done or not in this case?

text: I have a very simple question. A motorboat directed upstream is seen to be at rest from the bank of a river. Is the engine doing any work? Is it right to say that since it is not causing any displacement, so it is not doing any work.


title: What are the means to consider that a specific function is phase of an oscillator?

text: I hope the experts of the field forgive me for this n00b questions, but I am just trying to understand physics. Assume the following function: $$\phi(t)=\omega t+\cos(\omega t)$$ The above function has the property that: $$\phi(t+T)-\phi(t)=\omega T=const.$$ Where $T=\frac{2\pi}{\omega}$. Now the question is based on these facts, may I consider that $\phi$ actually represents the phase of an oscillator?? NOTE: I know my question is a bit silly because I am not modelling any kind of real physical phenomenon but only introducing a function, but I imagine the function I have written is simple case of an oscillator perturbed by means of a second oscillator.


title: What causes the vacuum in my bento box?

text: I can't think of a good title for my post, sorry about that. I've got a lunch box (called a bento box) Basically it's a plastic box with a plastic lid with a rubber rim around the lid to create an air tight seal with the top is on. Now when I microwave my lunch (take the top off, stick it in the microwave to heat the contents, then take it back out and put the top on) it creates a vacuum such that sometimes I really need to pry the lid off with a fork. How does this work? Does it have to do with the lid and base being different temperatures? My very rudimentary understanding of physics is that the hot gases should be expanding and pushing outwards. I would think that would make it easier to open when the contents were hot.


title: Is omniscience impossible?

text: I remember reading a brief note in Scientific American years ago about a mathematician/physicist who had published a paper that formally stated that no entity could both participate in a given system and simultaneously know all information about that system. His conclusions were not particularly ground breaking for the physics/math community since he did little more than apply Godel's Theorem to physical systems but he did generalize his results for any conceivable entity in any conceivable system irrespective of number of dimensions etc. After I realized that the article formally proved the impossibility of omniscience, I wanted to be able to refer to it. Sadly, I did not think to clip this little article from the magazine when I read it and I have never since been able to find anything on the subject. Does anyone know of such a formalism or paper drawing this conclusion?


title: The Ultimate Hand Dryer

text: I have come across many hand dryers that attempt to dry your hands really fast after you wash them. Here are two of them: XLERATOR http://www.exceldryer.com/ Dyson Airblade http://www.dysonairblade.com/homepage.asp So I guess I have a ridiculously high standard cause I think even these are too slow. Would it be possible to create a large static electric field to attract the water molecules off of your hand? Can someone offer some ideas that would remove the water off of your hand using some type of electric field generated by charged plates or something?


title: Why is the receiver of this solar tower cream-colored?

text: I wonder, why the receiver of this solar tower is not black? Wouldn't a black receiver be more efficient? If not, why is it not white then, but is an intermediate color? ![enter image description here](http://i.stack.imgur.com/qrWIF.jpg) It seems that the receiver of other solar towers, such as Solar One is indeed black: ![enter image description here](http://i.stack.imgur.com/7sgPV.jpg) Does it mean that the color is not important at all?


title: Principle of locality

text: Why does the principle of locality have so such great importance in physics that theory should be consistent with it?


title: Why do reversible processes not increase the entropy of the universe infinitesimally?

text: The book _Commonly Asked Questions in Thermodynamics_ states: > When we refer to the passage of the system through a sequence of internal > equilibrium states without the establishment of equilibrium with the > surroundings this is referred to as a reversible change. An example that > combines the concept of reversible change and reversible process will now be > considered. > > For this example, we define a system as a liquid and a vapor of a substance > in equilibrium contained within a cylinder that on one circular end has a > rigid immovable wall and on the other end has a piston exerting a pressure > equal to the vapor pressure of the fluid at the system temperature. Energy > in the form of heat is now applied to the outer surface of the metallic > cylinder and the heat flows through the cylinder (owing to the relatively > high thermal conductivity), increasing the liquid temperature. This results > in further evaporation of the liquid and an increase in the vapor pressure. > Work must be done on the piston at constant temperature to maintain the > pressure. This change in the system is termed a reversible change. It can > only be called a reversible process if the temperature of the substance > surrounding the cylinder is at the same temperature as that of the liquid > and vapor within the cylinder. This requirement arises because if the > temperatures were not equal the heat flow through the walls would not be > reversible, and thus, the whole process would not be reversible. But if the system and surroundings are in fact at the same temperature then why would this process occur at all? My understanding is that in fact that they are _infinitesimally_ different in temperature so I guess my question is why infinitesimality gets these processes "off the hook" for being irreversible. In other words, why do these infinitesimal changes not correspond to an infinitesimal increase in the entropy of the universe, rather than none at all?


title: Dropping an anchor from a boat

text: > A yacht on a lake drops its anchor overboard. What happens to the water > level in the lake? > >   1. It rises very slightly. >   2. It falls very slightly. >   3. It stays exactly the same. >   4. It's impossible to say. > My understanding is that due to Archimedes principle, when the anchor is in the boat, it contributes to the mass of the boat, and thus the mass of water displaced. When it is thrown overboard, it is now the volume of the anchor which contributes to the amount of water displaced. Therefore, without knowing the density, mass and volume of the anchor, it is impossible to determine the effect on the water level, therefore the correct answer is option 4. Can anyone tell me if my reasoning is correct as there is no mark scheme for the test where this question came from. Thanks in advance!


title: Waterflow of coolant in nuclear reactor

text: > The generator in a nuclear reactor delivers 580 MW electric power. > > **a)** How much TWh electrical energy is delivered yearly if the reactor > runs only 70 % of the time? > > **b)** What flow of coolant (water) is required if the efficiency of the > steam turbines is 35 % and the temperature increase of the water is 8 °C? a) was easily solved but I am still posting it for contextual purposes; fact is that I am struggling with b). Since the reactor is only running $70\,\%$ of the time, the energy-output (per second) is $406 \cdot 10^6 \text{ J}$. The steam turbines are only able to harness $35\,\%$ of that energy i.e. $1.421\cdot 10^8 \text{ J}$. Now, using $mc\cdot\Delta \text{T}$, we arrive $1.421 \cdot 10^8 = m \cdot 4180 \cdot 8 \iff m \approx 4249 \text{ kg}$ A mass of $4249\,\text{ kg}$ (of water) entails approximately $4000$ litres but the key in my book says $32 \text{ m$^3$/s}$. What went wrong?


title: Why does this integral come out imaginary?

text: Im working through Zee and I'm having a little trouble with some integrals. I'm trying to reproduce the analogue of the inverse square law for a 2+1 D universe and I figured I could start with the statement for the energy $$E=-\int \frac{d^2 k}{(2 \pi)^2}\frac{e^{i \vec{k}\cdot (\vec{x}-\vec{y})}}{k^2 + m^2}=-\int_{0}^{\infty}\frac{k\,dk}{(2\pi)^2(k^2+m^2)}\int_{0}^{2\pi}e^{ik|x-y|\cos\phi}d\phi$$ which turns into $$=-\int_{0}^{\infty}\frac{k\,J_{0}(k|x-y|)\, dk}{2\pi (k^2+m^2)}$$ Then contour integrated after seeing $k$ and $J_0$ were both odd to get $$-\frac{(2\pi i)(im)J_{0}(im|x-y|)}{4\pi (2im)}=-\frac{i\, J_{0}(im|x-y|)}{4}$$ but this is imaginary, where did I go wrong?


title: What really is the smallest "mass" or "object" in the universe?

text: Look at this here. With respect to the sciences, the atom is obviously not the smallest piece of mass. Apparently, if people have already broken down the atom in to particles smaller than so, why haven't particles been understood yet? Old scholars reasoned that everything has smaller parts, so what's smaller than subatomic particles? Or is there a limit in the size of mass, only being able to be small to an extent? Because mass always seems to keep growing, but when scaling opposite in size we reach a limit. Therefore, big always gets bigger, but why does small have limits?


title: Glass - paper: Stevin's Law

text: In my understanding the well-known experiment of the glass full of water in equilibrium with a piece of paper, the atmospheric pressure acts on a small layer inside the glass (on the top) and under the paper (outside the glass), the hydrostatic pressure (basically the weight of the water) acts downward, so in term of forces I initially have a net force $$ \boldsymbol F = (p_A -p_A+\rho g h)A\hat z$$ where $A$ is the section of the glass, $\hat z$ is the vertical direction, and $h$ the height of the layer of water. ![enter image description here](http://i.stack.imgur.com/XmiCy.jpg) ![enter image description here](http://i.stack.imgur.com/KOjYP.jpg) Now, when the paper bends under the weight of the water, and the air layer on the top increases in volume, so I can apply (with good approximation) $$pV=nRT,\ V\ \uparrow\ \Rightarrow\ p\downarrow\ \Rightarrow\ p'<p_A $$ So we have: $$\boldsymbol F = A(p'-p_A+\rho g h)\hat z$$ and since $p'-p_A<0$, it is possible to have $\boldsymbol F$ upward (clearly, depending on $h$ and $\rho$) Now, I made the experiment with water, and the bending of the paper was upward. Can I say that the only reason is the presence of the surface tension of water? Or my reasoning is lacking somewhere else too? Moreover, if instead of the paper I put a strongly stiff material, I can't have the same effect, no matter the weight, the geometry, etc? Thanks


title: quadripolar moment in curved space

text: So, i'm going over the Thorne's derivation of the quadrupolar radiation term, and they write the core term as: $$ \frac{3 r_i r_j - 2 r^2 \delta_{ij}}{4 r^5} $$ But if i try to obtain this term by _Covariant_ deriving the dipole term; $$ \nabla_{ij}{ \frac{1}{r}} = - \nabla_{j}{ \frac{r_i}{2 r^3}} $$ i am left with: $$ \frac{3 r_i r_j - 2 r^2 \delta_{ij}}{4 r^5} - \frac{\Gamma^i_{kj}r_k}{2r^3} $$ Where the last term seems to be dismissed in the text with no good reason. Is there a reason why this term is being ignored?


title: Temperature and latent heat

text: Building a bronze stature we make a mold and pour in the liquid bronze when the bronze hardens we remove the mold. The mold is made of 3 Kg of steel and the statue has a mas of 1 Kg. The specific heat of bronze is 360 and the specific heat of steel is 165 If we cool the statue and the mold from 500 degrees C by dropping it into a bucket with 10 Kg of water at 20 degrees C what will the final temperature of the water be? (ignore any steam). Specific heat of water is 4186. So far I have: (165)(3 kg)(change in temp) + (360)(1 kg)(change in temp) = (4186)(10 kg)(change in temp) Am I on the right track? Any tips for further help?


title: Higgs field existence and zero energy

text: If the Higgs field permeates all space, why some claim, that total universe energy equals (or is very close to) zero?


title: Why does a semiconductor hole have a mass?

text: I have read that holes in semiconductor are nothing but vacancies created by electrons. But how can this vacancy i.e. hole has a mass?


title: The transit of Venus and solar neutrino rates

text: The following question was posed at the end of Maury Goodman's June 2012 long- baseline neutrino newsletter. > During the Venus transit of the sun, were more solar neutrinos absorbed in > Venus, or focused toward us by gravity? As I don't know off the top of my head I thought I'd pass it along. Maybe latter I'll have time to look up the relevant figures for order of magnitude estimates.


title: Is it dangerous if one elementary particle with high energy penetrates our brain?

text: We might be killed if a bullet penetrates our brain. How about an elementary particle moving with high energy penetrates our brain? Assume that we can have exactly a single elementary particle for this imaginative experiment.


title: Blackbody radiation force (link), what are the fundamental forces behind it?

text: Here is a link to an article from phys.org describing what the scientists (M. Sonnleitner at the University of Innsbruck and Innsbruck Medical University in Austria, M. Ritsch-Marte at Innsbruck Medical University, and H. Ritsch at the University of Innsbruck) in the article call the blackbody force. http://phys.org/news/2013-07-blackbody-stronger-gravity.html My question is, are they suggesting that this blackbody force is a fundamental force i.e. it belongs to group of gravity, weak/electromagnetic, and strong forces. And if not, what of the fundamental forces might or do make up this blackbody force?


title: Hooke's law doesn't work well with my spring?

text: I'm trying to make an application for Hooke's law using a spring, but the law doesn't give any correct result with my spring, because when I hang a $100\,\mathrm{g}$ object on the spring it's elongates about $0.3\,\mathrm{cm}$ and when I hang a $200\,\mathrm{g}$ object the spring elongates about $1\,\mathrm{cm}$ while it should elongates only $0.6\,\mathrm{cm}$ . I'm sure that the problem is with the spring design. The spring I'm using is just like in picture below: ![image of a tight-coiled spring](http://i.stack.imgur.com/VKmVt.jpg)


title: Reference request: finding a biophysics paper about super time resolution imaging of a neuron firing

text: About a year ago I attended a talk at the University of Ottawa. The author described a method for achieving super time resolution images of a neuron firing. From what I can recall, the group found a small protein that acted as a photovoltaic cell (produced a voltage pulse in response to a photon) and engineered it to run in reverse, emitting a photon when it was subjected to a voltage pulse. They then cause this to be expressed in neurons, and were able to image action potentials moving through the network, heralded by emitted light from these proteins. Super resolution was achieved by careful timing and a lot of averaging. I have looked high and low for this paper for about a week now, with no luck. I don't remember the speaker's name (though he was a pretty young guy, a new prof at the time if I recall). If anyone is familiar with the research and can link me to the paper I would be very grateful.


title: The Integral Trick and An Equality in Nakajima's Lecture

text: In Nekrasov et al's series papers MNS, they calculate such kinds of integral $$ \frac{E_1 E_2}{N(2\pi i)^N(E_1+E_2) }\oint d\phi_1 \wedge d\phi_2\wedge \ldots\wedge d\phi_N \prod_{i<N} (-\phi_i) \prod_{i}(\phi_i+E_1+E_2) $$ $$\times \frac{\prod_{i\neq j}\phi_{ij} }{\prod_{i}(-\phi_i)(\phi_i+E_1+E_2) }\ {\prod}_{i,j} {{(\phi_{ij} +E_1+E_2)}\over{({\phi}_{ij}+ E_1)(\phi_{ij}+ E_2)}}.\tag{6.4} $$   1. The residues are given by $$\phi_i \rightarrow \phi_{(\alpha,\beta)}=(\alpha-1)E_1+(\beta-1)E_2.\tag{6.9}$$ MNS claims that the evalution of the above integral is equivalent to use of fixed point techniques. They also give some references. I can not understand their trick here after skimming over the references. Can this integral be solved by residue theorem?   2. In order to calculate the sum of critical points, they use an equality from Nakajima's Lecture (Ref. 18): $$ \Sigma_{i,j \in D}[ e^{\phi_{ij}} +e^{\phi_{ij} +E_1+E_2}-e^{\phi_{ij}-E_1}-e^{\phi_{ij}-E_2}] - \Sigma_{i\in D} [ e^{-\phi_{i}} + e^{\phi_{i}+E_1+E_2}] \tag{6.10}$$ $$~=~-\Sigma_{(\alpha,\beta \in D)}e^{(\nu_\beta-\alpha+1 )E_1+(\beta-\nu_\alpha^{'})E_2 }+e^{(-\nu_\beta+\alpha )E_1+(-\beta+\nu_\alpha^{'}+1)E_2 }. \tag{6.11} $$ Since I am not familiar with Nakajima's topic, I did not find the equality in Nakajima's lecture. Which chapter does the equality (6.10+11) come from? Thanks for pointing me out.


title: Voltage and current in parallel circuit

text: I am having a bit of a tough time understanding the following:               |____O____| <-  0A     |____O____| <- 12A     |____O____| <- 24A     |         | <- 36A     |_[|||||]_| <- 36A               Legend:          O       - A small lamp with 1Ω resistance.     [|||||] - A 12V battery.      There is 12V flowing across each of the lamps and with resistance of 1Ω, and, therefore, there is 12 Amps of current flowing across each one. So, if the current is flowing from right side, up, over and down the left side, there is a total of 36 Amps flowing through the battery itself to supply the three connected lamps. At the top portion of either side of the top lamp (above the points where middle lamp connects) there is only 12 Amps of current; to either side of the middle lamp (above the points where the bottom lamp connects) there is 24 Amps; and to either side of the bottom lamp (below the points where the bottom lamp connects) there is 36 Amps. Does it mean that a battery that could not shock us, could in fact if we connected several lamps in parallel circuit to raise the amount of current flowing through the circuit at the bottom portion? I'm just trying to wrap my head around circuits and electricity and this popped into my head. I've looked around, but couldn't find a clear answer to help me understand.


title: explicit matrix elements for a representation decomposed into subgroup by branching rules

text: I'm looking for a way to construct a representation for a simple Lie group such that one particular subgroup is manifest. I learned the branching rules from Cahn, Georgi and Slansky, but I'm still not sure how to derive the explicit representation from the weight system deformed by extended Dynkin diagram? To decompose a irreducible representation under a maximal regular subalgebra, we look at the extended Dynkin diagram, which has one more node from the minus highest root added on the original Dynkin diagram, and we then eliminate another node to deform the extended Dynkin diagram into the Dynkin diagram for the maximal regular subalgebra. The key point is to replace the Dynkin coefficient corresponding to the eliminated node by the one corresponding to the extra node of the minus highest root. Thus, deforming the weight system of the given irrep with above replacement gives us the branching rules and the Cartan matrices for the subalgebra in the given irrep. For example, under the subgroup $SU(2)\times SU(2)\times SU(2) \Subset SO(7)$, we have the 8 dimensional irrep of SO(7) deformed as $8 \rightarrow (1,2,2) + (2,1,2)$, see P33-34 LieART. To construct the explicit matrix representation, we define the coordinates for each simple roots in an orthonormal basis (Cartan-Weyl basis) and therefore the coordinates for the fundamental weights as well. Thus, the generators corresponding to Cartan matrices have its matrix entries as the coordinate of every weights. Now, my question is what are the fundamental weights for the deformed Dynkin diagram? Should I keep the old fundamental weights except the replaced one or the new fundamental weights are resolved from the deformed Dynkin diagram? Most importantly, what's the new fundamental weight corresponding to the extended root? I would also need help to reveal how generators of the subalgebra are in the subset of generators of the mother algebra. When I replace the Dynkin coefficient with the extended root, how could the corresponding Cartan matrix belong to linear combination of Cartan matrices of the mother algebra? I'm a Physics student with poor knowledge in Lie algebra. Please reinterpret my description with proper language whenever you needed to.


title: How we can manipulate the momentum of a particle?

text: Is there any way to affect a particle's momentum value?


title: Questions on degenerate ground states and the thermodynamic limit?

text: For example, let's consider a $N$ spin-1/2 system on a lattice described by the Hamiltonian $H$. My questions are: (1) If $H$ has _either_ global $SU(2)$ spin-rotation symmetry _or_ time- reversal symmetry, then $\forall $ **finite** $N=$odd, there must be **exact degenerate** ground states (GS). From this point of view, can we infer that in the thermodynamic limit ($N\rightarrow \infty $), the GSs of the above $H$ must be _degenerate_ ?? (2) This is a question about the definition of GS degeneracy. Assuming $H$ is gapped, such that the GS degeneracy can be well defined. My question is: No matter how the sites number $N$ approaches $\infty $, for instance, either $N(=\text{odd})\rightarrow \infty $ or $N(=\text{even})\rightarrow \infty $, they should both give **the same** (exact or approximate) GS degeneracy in the thermodynamic limit, right ?? Since, at least from the math side, otherwise the GS degeneracy would depend on the _way_ that $N\rightarrow \infty $ and it is thus _not_ well defined. Referring to Q.(2), let's consider the spin-1/2 Kitaev honeycomb model in a gapped phase (i.e., $\left | J_z \right |>\left | J_x \right |+\left | J_y \right |$ and $J_xJ_yJ_z\neq0$). If we take a sequence of sizes of the system $N$=odd (odd number of total spins or total lattice sites) in the thermodynamic limit, such that there always exist exact **Kramer's degeneracy** (due to time-reversal symmetry) as $N$ approaches $\infty $. Therefore, this kind of sequence would give rise to a **ground state degeneracy (Kramer's degeneracy)** in the thermodynamic limit, right? On the other hand, as pointed out by the author, both Lieb's theorem and the author's numerical study suggest that the zero-flux conﬁguration is the **unique** sector minimizing the ground state (GS) energy, indicating that the GS of Kitaev model is **nondegenerate** or **unique**. This is _in contrary to_ the above **Kramer's degeneracy**. While it seems that the original paper didn't mention that what kind of sequence of sizes of the system is chosen as taking the thermodynamic limit. So I guess that a 'reasonable' sequence should be at least ensuring the number of total lattice sites $N=$even (e.g., we may take the number of unit cells $\rightarrow \infty $ for the thermodynamic limit), which make the GS **uniqueness** possible. Is my understanding correct? Thank you very much.


title: Is an electron/proton gun possible?

text: In the 1944 SF story “Off the Beam” by George O. Smith, an electron gun is constructed along the length of a spaceship. In order to avoid being constrained by a net charge imbalance, it is built to also fire the same number of protons in the other direction, dissipating the mass of the “cathode”. With current knowledge, is this plausible? That is,   * Can a practical (i.e., not built with unobtanium insulators) electrostatic device like an electron gun separate and accelerate electrons and protons in this manner?   * Can it actually disassemble solid matter? If so, how does the composition of the cathode affect the difficulty?


title: Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

text: I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think I have created the initial Hamiltonian, $H_B$ correctly. $$H_B = \left(\frac{1}{2}\left(I_2 - \sigma_x \right)\right)\otimes I_2\otimes I_2+I_2\otimes \left(\frac{1}{2}\left(I_2 - \sigma_x \right)\right)\otimes I_2+\left(\frac{1}{2}\left(I_2 - \sigma_x \right)\right)\otimes I_2\otimes I_2+I_2\otimes I_2\otimes \left(\frac{1}{2}\left(I_2 - \sigma_x \right)\right)+I_2\otimes \left(\frac{1}{2}\left(I_2 - \sigma_x \right)\right)\otimes I_2+I_2\otimes I_2\otimes \left(\frac{1}{2}\left(I_2 - \sigma_x \right)\right)$$ When I evaluate it, the matrx is: $$H_B=\left( \begin{array}{cccccccc} 3 & -1 & -1 & 0 & -1 & 0 & 0 & 0 \\\ -1 & 3 & 0 & -1 & 0 & -1 & 0 & 0 \\\ -1 & 0 & 3 & -1 & 0 & 0 & -1 & 0 \\\ 0 & -1 & -1 & 3 & 0 & 0 & 0 & -1 \\\ -1 & 0 & 0 & 0 & 3 & -1 & -1 & 0 \\\ 0 & -1 & 0 & 0 & -1 & 3 & 0 & -1 \\\ 0 & 0 & -1 & 0 & -1 & 0 & 3 & -1 \\\ 0 & 0 & 0 & -1 & 0 & -1 & -1 & 3 \\\ \end{array} \right)$$ According to the example, the unique satisfying assignment is $011$. The problem Hamiltonian is a sum of three sub-Hamiltonians each correspond to a clause. $$H_P = H^{12}_{imply} + H^{13}_{disagree}+H^{23}_{agree}$$ Here are my results for sub-Hamiltonians. $H^{12}_{imply}$ clause can be satisfied with any of $00$, $01$ or $11$. So, $$H^{12}_{imply} = I_8 - \left(\left(\frac{1}{\sqrt{6}}\right)\left(|000\rangle+|001\rangle+|010\rangle+|011\rangle+|110\rangle+|111\rangle\right)\right) \left(\left(\left(\frac{1}{\sqrt{6}}\right)\left(|000\rangle+|001\rangle+|010\rangle+|011\rangle+|110\rangle+|111\rangle\right)\right)\right)^{\dagger} $$ The ground state of this Hamiltonian satisfies the assignment constraint. $H^{13}_{disagree}$ clause can be satisfied with any of $01$ or $10$. So, $$H^{13}_{disagree} = I_8 -\left(\left(\frac{1}{2}\right)\left(|001\rangle+|011\rangle+|100\rangle+|110\rangle\right)\right) \left(\left(\left(\frac{1}{2}\right)\left(|001\rangle+|011\rangle+|100\rangle+|110\rangle\right)\right)\right)^{\dagger}$$ The ground state of this Hamiltonian satisfies the assignment constraint. $H^{23}_{agree}$ clause can be satisfied with any of $00$ or $11$. So, $$H^{23}_{agree} = I_8 - \left(\left(\frac{1}{2}\right)\left(|001\rangle+|011\rangle+|100\rangle+|110\rangle\right)\right) \left(\left(\left(\frac{1}{2}\right)\left(|001\rangle+|011\rangle+|100\rangle+|110\rangle\right)\right)\right)^{\dagger}$$ The ground state of this Hamiltonian satisfies the assignment constraint. So, $$H_P = \left( \begin{array}{cccccccc} \frac{17}{6} & -\frac{1}{6} & -\frac{1}{6} & -\frac{1}{6} & 0 & 0 & -\frac{1}{6} & -\frac{1}{6} \\\ -\frac{1}{6} & \frac{7}{3} & -\frac{1}{6} & -\frac{2}{3} & -\frac{1}{2} & 0 & -\frac{2}{3} & -\frac{1}{6} \\\ -\frac{1}{6} & -\frac{1}{6} & \frac{17}{6} & -\frac{1}{6} & 0 & 0 & -\frac{1}{6} & -\frac{1}{6} \\\ -\frac{1}{6} & -\frac{2}{3} & -\frac{1}{6} & \frac{7}{3} & -\frac{1}{2} & 0 & -\frac{2}{3} & -\frac{1}{6} \\\ 0 & -\frac{1}{2} & 0 & -\frac{1}{2} & \frac{5}{2} & 0 & -\frac{1}{2} & 0 \\\ 0 & 0 & 0 & 0 & 0 & 3 & 0 & 0 \\\ -\frac{1}{6} & -\frac{2}{3} & -\frac{1}{6} & -\frac{2}{3} & -\frac{1}{2} & 0 & \frac{7}{3} & -\frac{1}{6} \\\ -\frac{1}{6} & -\frac{1}{6} & -\frac{1}{6} & -\frac{1}{6} & 0 & 0 & -\frac{1}{6} & \frac{17}{6} \\\ \end{array} \right)$$ This Hamiltonian, which represents the instance of the problem is expected to be satisfied only with the assignment 011. So, the ground state should be $|011\rangle$. But in reality, the ground eigenvalue is greater than $0$ and the ground state is $\left(1,4,1,4,3,0,4,1\right)^{\dagger}$. Here, $I_n$ is the $n \times n$ identity matrix. **What was I doing wrong?** My Mathematica code is available here.


title: Energy in an electromagnetic wave

text: A radio antenna creates EM waves through switching the polarization in the antenna at a certain frequency. I assume the the energy of the photons produced in this process amount to E=hf for each photon. So good so far, but classically, i read that the EM field is an oscillation of the electric field between positive and negative values, as would seem reasonable from what the antenna is doing. If individual photons simply have a single positive energy relating to the frequency of the wave, how is this positive-negative oscillation represented in that stream of photons? I guess to put it simply, how is a changing electric field represented in a stream of photons in general, and from a radio antenna specifically?


title: Why don't electromagnetic waves require a medium?

text: As I understand it, electromagnetic waves have two components which are the result of each other, i.e., when a moving electric charge creates a changing magnetic field at point X then a changing electric field is created at point Y and this repeating process is what creates EM waves, so therefore, it requires no medium. Is my understanding correct? One thing that I'm surprised to know is that light is also called an electromagnetic wave. Does this include light of any kind, for example: light from a bulb, a tube, and also from the Sun? How do they contain electric and magnetic fields?


title: doppler shift through two mediums

text: When considering the Doppler shift, the 'canonical equation' is $$f=\frac{c+vr}{c+vs}f_0$$ However, this equation seems to run into trouble in the following situation: A light source inside water is moving at a speed $v$ towards a receiver outside the water. Can we modify the above equation to deal with a transition between two media? Or is there a completely different formula that applies here?


title: A Different Lasing Medium

text: Powerful lasers are highly intense, diverge negligibly and are also coherent. These radiations are emitted through partially reflecting mirrors after simultaneous reflections within the lasing medium. Don't these EM radiations affect the lasing medium or reflecting mirrors? Also, How is plasma used as a lasing medium in certain lasers?


title: Invariance of states under local unitary transformations

text: How can I show explicitly that the bell state $$|\psi^{-}>=\frac{1}{\sqrt{2}}(|0>|1>-|1>|0>)$$ is invariant under local unitary transformations $U_{1}\otimes U_{2}$ ?


title: How can an action be dependent on both its past and future?

text: Is it true that whenever an action takes place it is dependent on both its past and future? I mean if we already know that whatever we are doing is dependent on future as much as it is dependent on the past. If that is the case how can you not tell what I will be typing next?


title: Maximum Possible Information in the universe?

text: I remember hearing about this in one of the programs in discovery science. The physicist claimed that the maximum possible information in the universe is (10)^(10^123) whereas the maximum possible information that can be known by man is (10)^(10^90). Can anyone explain to me how can we arrive at such a specific number, and also how can information be represented by only numbers?


title: Could we make a trebuchet that could launch objects to a stable orbit?

text: Inspired by this xkcd, which calculated the energy requirements for accelerating individual humans to escape velocity (regardless of consideration for what that would do to your organs), I am interested to know if a trebuchet (or catapult) could be built that could launch things out off the Earth. Escape velocity isn't necessary, as I'd consider a stable orbit 'off earth'.   1. What would be some design considerations / challenges? Do we have materials that could withstand this type of force?   2. What would be maximum weight limits, ignoring air resistance (a tennis ball? a human? a satellite? a human in a metal survival pod?)   3. What would be the speed at which these objects would need to reach at the earth's surface to be into a stable orbital velocity by the time they exit the atmosphere? (factoring gravitational slowdown and air resistance)   4. Is it ever conceivable that we could 'launch' supplies to the ISS or orbit this way? What about launching satellites like this? # Edit I misspoke when I said catapult, a string tension driven device. I meant a trebuchet, a gravity-powered heavy-object thrower. QuickLaunch, Inc. has plans to do just this launching a SSTO rocket at 6 km/s, which then fires after launch and provides the necessary correction for orbital insertion. Basically, I just need a trebuchet that will accelerate a mass (they're trying 1kg, 10kg, 50kg and 500kg masses) to 6 km/s at launch. ![Trebuchet](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Trebuchet_Castelnaud.jpg/762px- Trebuchet_Castelnaud.jpg)


title: Lab observation correct? As distance decreases, velocity increases, stderr decreases

text: The experiment goes like this: ![](http://i.imgur.com/p4EtV.png) Allow a moving cart to move from the top of an incline plane ($x_0$) downwards. The time taken will be recorded by the picket fence (those things you see wired up). Distance ($D$) is reduced by 10cm each time. And a set of recordings are recored as follows: ![](http://i.imgur.com/35Sai.png) Does the recording seem logical?   * As $D$ decreases, $v$ increases? Why, I thought $v$ should reduce as there will be less effect from gravity?    * As $D$ decreases the standard error decreases. It kind of makes sense as the time interval will be smaller and thus less chance of error. However, I would think if the $D$ is too small, the cart may not have stabalized or something? But that doesn't sound scientific.    * Is my calculation of standard error right? Or should it be standard deviation here? When do I use which?


title: Is static friction an impulsive force?

text: For example: let's consider a static sphere on an horizontal rough surface. I apply an impulse $J$ parallel to the ground and in the middle of the sphere. If, like my book says, the friction is not an impulsive force, then I can use $J=\Delta p=mv_{CM}-0$, so $v_{cm}(0)=J/m$. But this is counterintuitive, because if I apply a small impulse ,for instance $J=1 Ns$, to a sphere of $m=10^{10} Kg$, the static friction force ($F=\mu_{s}mg$) is surely enough to keep the sphere static. ![sphere](http://i.stack.imgur.com/iXkCV.png) You can repeat the reasoning without a sphere: an impulse $J_{x}=1 Ns $ on a point mass of $m=10^{10} Kg$ on a rough surface. If friction is not impulsive, then you move the object (of course, only for a very short time, because you have a dynamic friction that slow the motion) no matter what the mass is. EDIT: The definition given in my book is: "very intense forces that act on a short time, compared to the observation time".


title: Do randomness and indeterminacy in Quantum Physics mean the same?

text: I have been trying to learn about the randomness in Quantum Physics. But of the many sources I referred to, some say about "Randomness in Quantum physics" and some others say about "Quantum indeterminacy". So my question is do these two mean the same or are they completely different? Is randomness because of that indeterminacy or that randomness is actually "there" and that causes the indeterminacy in Quantum Physics? Or are they just two ways of referring to the same thing and if yes then what are they actually referring to?


title: What is the advantage of segmented particle traps?

text: I'm currently trying to familiarize myself with the physics of ion and particle traps, especially with linear Paul traps. Many scientific experiments I've come across use segmented electrodes (like in this image from a Nature article). My question is _what do you gain by segmenting the electrodes?_ I could imagine that you can move the trapped particles along the axis to some extent, or determine their position in the trap. But in both cases I believe there are more precise methods.


title: Compactification and off-diagonal terms of the metric tensor

text: In standard 3+1 dimensional spacetime, the metric tensor is of order 4 and had ten independent coefficients, hence there are 6 terms off the diagonal in the corresponding $4\times 4$ real symmetric matrix. On the other hand, superstring theory postulates that there are 6 additional spatial dimensions that have to be compactified in a Calabi-yau manifold. My question is thus: are these two facts somehow related or is it just mere coincidence? For example, would the observable dimensions correspond to eigenvalues of the metric tensor?


title: Why is force dependent on acceleration, not velocity?

text: According to $F = ma$, force is a result of acceleration and mass, right? However, I don't understand why velocity is not used instead of acceleration. A train moving at 100 miles/hour will still impart a great force on you even though it has no acceleration. Further, dropping a book at 10ft will impart a greater force on the gorund than dropping it at 1ft. So it seems that velocity would influence the force more than the acceleration would. Why is this not the case?


title: Picture of supports

text: This questions stems from Axiomatic Quantum Field Theory and is mathematical in nature. However, I feel that an answer from physicists is more in line with what I will be asking. Let $\phi$ be a real quantum field, namely $\phi$ is an operator-valued distribution. One of the requirements of $\phi$ is that it is _local_. In case $f\in C{^\infty _0 }_{real}$, then the assumption of locality requires that $$\phi(f)\phi(g)=\phi(g)\phi(f)$$ when the supports of f and g cannot be connected by a light ray. One says that such supports are _space-like separated_. **Reference** : Page 7 http://www.arthurjaffe.com/Assets/pdf/Quantum- Theory_Relativity.pdf I'd like to gather further insight into this statement. Namely, how does one picture the supports? Should I have light cones in mind?


title: Positive charges "move" from higher to lower potential

text: It's my understanding that whenever an object gains or loses electric charge this actually corresponds to losing/gaining electrons (protons do not move). So how can a positive charge always move from higher to lower potential?


title: Computing the Einstein tensor for a spherically symmetrical metric using the tetrad formalism

text: I am having some trouble understanding how to use the tetrad formalism. I will start with what I have so far, my question will be after that. I begin with the metric $$ \text{d}s^2 = e^{2a} \text{ d}t^2 - e^{2b} \text{ d}r^2 - r^2 \text{ d} \theta^2 - r^2 \sin^2 \theta \text{ d} \phi^2 $$ Where $a$ and $b$ are functions of the coordinate $r$ only. Now I want to find the basis one-forms $\theta^{a}$ such that $$ \text{d}s^2 = \eta_{ab} \theta^{a} \otimes \theta^{b} $$ where $\eta_{ab} = \operatorname{diag} (+1, -1, -1, -1)$. So $$ \theta^{t} = e^{a} \text{ d} t\\\ \theta^{r} = e^{b} \text{ d} r\\\ \theta^{\theta} = r \text{ d} \theta \\\ \theta^{\phi} = r \sin \theta \text{ d} \phi $$ Now I take the exterior derivatives of each basis one-form $$ \begin{align} \text{d} \theta^{t} &= a' e^{a} \text{ d} r \wedge \text{ d} t \\\ \text{d} \theta^{r} &= b' e^{b} \text{ d} r \wedge \text{ d} r = 0 \\\ \text{d} \theta^{\theta} &= \text{ d} r \wedge \text{ d} \theta \\\ \text{d} \theta^{\phi} &= \sin \theta \text{ d} r \wedge \text{ d} \phi + r \cos \theta \text{ d} \theta \wedge \text{ d} \phi \end{align} $$ Up to here, I am pretty sure my results are correct. Where I am confused is when it comes to computing the spin connection one-forms from the no-torsion condition $$ \omega^{a}_{\phantom{a} b} \wedge \theta^{b} = - \text{d} \theta^{a} $$ How can I use this to find the connection one-forms? My naive guess is that, for example, $$ \omega^{t}_{\phantom{a} b} \wedge \theta^{b} = - \text{d} \theta^{t} = - a' e^{a} \text{ d} r \wedge \text{ d} t $$ so that this picks out the term on the left side of the form $\text{ d} r \wedge \text{ d} t$ so that $$ e^{a} \omega^{t}_{\phantom{a} t} = - a' e^{a} \text{ d} r \implies \omega^{t}_{\phantom{a} t} = - a' \text{ d} r $$ But the wedge product is anticommutative, so this should also say that $$ \omega^{t}_{\phantom{a} b} \wedge \theta^{b} = a' e^{a} \text{ d} t \wedge \text{ d} r $$ Am I reading this incorrectly? Is there some symmetry property that I'm missing?


title: BICEP2 experiments

text: How was the polarization experimentally measured in the BICEP2 experiments and why did they look specifically at B-modes? Why is it implying the existence of gravitational waves and the need to quantize gravity? Moreover, why is it implying inflation as a unique option?


title: Determine the particle velocity of a pressure wave

text: I am using constant density wave propagators to model seismic waves in the subsurface. What I want with these acoustic waves is to estimate the energy of them at a certain grid point at a given time. One approach is using Poynting vectors based on the pressure distribution of the wave $$ \vec{S} = \dot{p} \nabla p. $$ The absolute value $|\vec{S}|$ resembles the energy of the wave. Another way (and that's the problem) is based on the accoustic energy flux $$ \vec{I} = p \vec{v},$$ where $\vec{v} = \frac{\vec{k}}{\rho \omega} = \frac{p}{\rho c} $ and $\rho$ is the density of the medium and $c$ is the medium velocity. I want to compare $|\vec{I}|$ and $|\vec{S}|$ but stumble over the problem, that I do not specify $\rho$ in the wave modelling. As I want to compare both energies and use one of them as a threshold for the other, I can not simply assume $\rho$ to be a certain constant. Is there another way to determine $\vec{v}$ without using the density?


title: Eddy Currents: Relationships between thickness and deceleration

text: This is probably a question with a very simple answer, but I want to make sure before I write too much. I'm doing an investigation on Electromagnetic fields, in particular eddy currents and how they decelerate magnets, by sliding a magnet down an incline, recording the time taken and changing the thickness of the aluminium foil that the magnet is running over the top of. My results clearly show that the thicker the foil is the longer the magnet takes to travel down the incline, but I am having a hard time finding theory to back the results up with. So far all I've been able to find so far is the equation below on Wikipedia, despite my best efforts not to rely on it: ![Power dissipation](http://i.stack.imgur.com/S4DUb.png) which finds power dissipation, where P is the power lost per unit mass (W/kg), Bp is the peak magnetic field (T), d is the thickness of the sheet or diameter of the wire (m), f is the frequency (Hz), k is a constant equal to 1 for a thin sheet and 2 for a thin wire, ρ is the resistivity of the material (Ω m), and D is the density of the material (kg/m3). My question is whether this is the function I'm looking for, as thickness is the only one of these variables I'm changing and the rest I can measure, and P=F x V when force is constant, in which case higher thickness=more power lost=decreased velocity - theoretically supporting my results. I'm just not sure though, as I haven't been able to find anywhere saying that this power lost has any relation to what I'm measuring and I don't want to write a few thousand words to be told I had the wrong equation. Thanks, sorry for the wordy post, and if you know any sites that will help me with this other than Wikipedia I'd appreciate it.


title: 2-slit experiment

text: In the 2-slit experiment, is it possible to "account" for all of the energy in the incoming beam - i.e. does all of the incoming energy show up in the bright spots or is some of it "destroyed" when destructive interference takes place? If it is destroyed, what form is it converted into? If it's NOT destroyed, what would happen if you allowed the light to pass through a hole where the dark spot had been, then, exploiting the different angle that each path arrived from, organised things such that these waves now reinforced each other? We would then have a situation where more energy comes out than goes in. Which is impossible. Or does "spooky action at a distance" come into play and the overall brightness of the previous spots slightly dim to account for the new path?


title: Current Through a Circuit with an 8 Resistor Setup

text: The following is a question from a practice Physics GRE exam (found online at ETS's website). > The circuit shown in the figure consists of eight resistors, each with > resistance _R_ , and a battery with terminal voltage _V_ and negligible > internal resistance. What is the current flowing through the battery? Here is the figure in question: ![Resistors](http://i.stack.imgur.com/I4bR2.png) In case the figure doesn't load, here's the problem from ETS: https://www.ets.org/s/gre/pdf/practice_book_physics.pdf, page 54, problem 68. Since this is a GRE question I figured there was a shorter approach than a brute-force, Kirchoff's Voltage Law around every loop. I've been trying to figure out what a simpler solution would be by reducing parallel/series resistors, which currently there aren't any that can be reduced that way. Then I tried a triangle-star conversion, where I basically reduced each closed square in the diagram (each square was essentially a triangle because each had a resistor-less wire on one of the sides) but that also didn't lend itself to parallel/series reduction. I couldn't figure out another approach after that. The correct answer is 3/2* _V/R_ , and an abbreviated solution I saw someone else put online (http://physicsworks.files.wordpress.com/2012/09/gr0877_solutions.pdf, problem 68, if you're interested) said to treat the problem as 3 separate 2 _R_ resistors in parallel, but I am not sure how that works, because there are still the two horizontal resistors. Could someone explain to me either why this approach to the problem is correct or an alternative approach to the problem? Thank you!


title: How is the mass of black hole at the center of our galaxy measured?

text: I've been watching a video about dark mater and a lot of the mass is missing in our universe. Astronomers got to this by measuring the speed that stars orbit the center of the galaxy and when they did this it didn't match the amount of gravity/mass in the galaxy. However I thought that the mass of the black hole in the Center of the galaxy was measured by the stars orbiting it? To me it sounds like a catch 22? But I don't understand it very well. So could someone explain it further?


title: A tutorial explanation of decoherence?

text: Is there a tutorial explanation as to how decoherence transforms a wavefunction (with a superposition of possible observable values) into a set of well-defined specific "classical" observable values _without_ the concept of the wavefunction undergoing "collapse"? I mean an explanation which is less technical than that decoherence is > _the decay or rapid vanishing of the off-diagonal elements of the partial > trace of the joint system's density matrix, i.e. the trace, with respect to > any environmental basis, of the density matrix of the combined system and > its environment [...]_ (Wikipedia).


title: Does a magnet contain (and potentially produce) energy?

text: Very quick question, does a magnet contain energy? The general consensus seems to be, it does not. And this is generally confirmed by the fact that it would break the first law of thermodynamics. Whatever the hell that is (joke:) The reason I ask is because a) I'm no genius and b) because I'm perplexed. So maybe some of you smart people could help me out please. Here's the scenario; Now, if I took, oh I dunno, say a metal ball and lifted it say six inches. I have converted some of my man boob calories into energy that is now stored in the ball. When I release it and it drops to original level, the energy is released. Makes sense. Now if I took the same metal ball and rolled it along the ground, it would continue to roll until the kinetic energy was depleted, through friction and stuff like that. Now if I take the same ball and roll it along the ground, but this time with a magnet suspended 6 inches from the ground and directly in the line of movement. The magnet is strong enough to attract the ball and is therefore lifted 6 inches and sticks to the magnet. Where has that energy come from? It can't have come from me putting the magnet there, as once I put the magnet back on the ground, I have released that energy. As I said, I'm not smart, nor educated, just been pondering this question for a couple of days. Would be great if you could allow my brain to get back to menial tasks. Thanks


title: Can the entangelement of basis vectors increase under local operations?

text: Say I have a bipartite state $\rho = \sum_ip_i|\psi_{i}\rangle \langle \psi_{i}|_{AB}$ Where $\\{|\psi_{i}\rangle_{AB}\\}$ forms an orthonormal basis. I now perform some local quantum operation on subsystem B, bringing my system to a new state: $\rho' = \sum_iq_i|\phi_{i}\rangle \langle \phi_{i}|_{AB}$ Where, again, $\\{|\phi_{i}\rangle_{AB}\\}$ forms an orthonormal basis. Of course, for any entanglement measure $E$ we must have $E(\rho') \leq E(\rho)$. But is it possible to have: $\max\limits_i E(|\phi_{i}\rangle\langle \phi_{i}|_{AB}) > \max\limits_i E(|\psi_{i}\rangle\langle \psi_{i}|_{AB})$ ?


title: If gravity doesn't exist,what are the implications?

text: I just heard about new theories proposed by Erik Verlinde about the fact that Gravity doesn't exist..or at least it's not a foundamental force. My question is : if this is true what are the implications on current models like string theory , eternal inflation ecc ecc ? what can change in the understanding of our universe ?


title: Help with the understanding of boundary conditions on $AdS_3$

text: So I am trying to reproduce results in this article, precisely the 3rd chapter 'Virasoro algebra for AdS$_3$'. I have the metric in this form: $$ds^2=-\left(1+\frac{r^2}{l^2}\right)dt^2+\left(1+\frac{r^2}{l^2}\right)^{-1}dr^2+r^2d\phi^2$$ And I have the boundary conditions. So if I'm correct, I should find the most general diffeomorphism, by solving $\mathcal{L}_\xi g_{\mu\nu}=\mathcal{O}(h_{\mu\nu})$, where $h_{\mu\nu}$ are the boundary conditions (subleading terms). So, if I'm doing things right, I get 5 equations. Because the $t\phi$ term of Lie derivative vanishes. Now, I should use the power expansion of $\xi$, as given in the paper, and solve these 5 differential equations or? I'm not certain if I'm on a right path, so any advice is welcome...


title: How to calculate the correct coordinates from a distorted video of a projectile?

text: I am working on a high school project that is related to projectile motion. I am exploring how exactly the position of the center of mass affects the trajectory of a long but thin, javelin-like projectile. I have created a special launching machine that gives each projectile an identical impulse, filmed all flights on a high-fps camera and extracted the position of both tips over time, frame-by-frame using Tracker. The flight distance is ~12m, and the camera's distance is ~10m from the flight path. Consequently, the image is sligtly distorted. It is not too significant but still it would be nice to be able to obtain precise data. I could fix it in Photoshop if it were just one frame but I really cannot proccess **all** my data this way. I have not found any free software that could fix videos but that would probably not be too useful anyway since I do not have sufficient computing power at my disposal to be able to complete the task in reasonable time. Also, I am only interested in the projectile and don't need the whole background to be fixed... Therefore I probably need to find a way to find the correct coordinates using the coordinates I have already obtained. I know exactly what camera I used and so I could look up any specifications if necessary. Also, I know the dimensions of the place the videos were taken. Could you please help me find the way to find (or compute, preferably) the correct coordinates or at least provide me with a link to a source where this is described? I am not sure I can _diagnose_ what type of distortion I am dealing with which made googling even harder. Thank you very much.


title: Two body particle problem with reduced mass

text: When we have two bodies and a central force acting towards the center of each other, we could treat the whole problem as a one body problem by introducing the relative coordinate. My question is, when you were to calculate the relative coordinate, you are working out the acceleration of a fictitious particle, which does not exist. However, if you work out the coupled differential equations, you would get exact acceleration of both particles. Therefore I think reduced mass is not a reliable method , but I was told that the reduced mass method can get the exact solution as the coupled differential equation. Therefore I think I am wrong, could anyone shed the light on this please?


title: Entropy inequality

text: Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following: $$S(\frac{1}{2}( \rho_1^{AB}+I^A\otimes\rho_2^B))+S(\frac{1}{2}(\rho_2^{AB}+I^A\otimes\rho_1^B)) \geq S(\frac{1}{2}(\rho_1^{AB}+I^A\otimes\rho_1^B))+S(\frac{1}{2}(\rho_2^{AB}+I^A\otimes\rho_2^B))$$ where $S$ is the von Neumann entropy, $\rho_1^B=tr_A(\rho_1^{AB}),\rho_2^B=tr_A(\rho_2^{AB})$ and $I^A$ is the maximally mixed state on $A$. It looks like it should pass with some monotony property, any hints or counterexample are welcome.


title: Why do lasers require mirror at the ends?

text: Laser uses mirrors to reflect photons in order to stimulate atoms to emit photons, but why this is so?. I mean, why does a photon stimulate atoms to produce more photons? If a photon made an atom to produce a photon, is not the first photon absorbed by the atom and therefore there is not total gain in the process?


title: Spaans, "On Quantum Contributions to Black Hole Growth"

text: This paper was posted to arxiv a couple of weeks ago: http://arxiv.org/abs/1309.1067 From the abstract: > The effects of Wheeler's quantum foam on black hole growth are explored from > an astrophysical perspective. Quantum fluctuations in the form of mini > (10^-5 g) black holes can couple to macroscopic black holes and allow the > latter to grow exponentially in mass on a time scale of ~10^9 years. > Consequently, supermassive black holes can acquire a lot of their mass > through these quantum contributions over the life time of the universe. Is this paper at all believable? The thing that immediately bothers me about it is energy conservation. He doesn't have a real theory of quantum gravity, so this is some kind of semiclassical argument based on two theories: GR and quantum mechanics. GR has conservation of (mass-)energy in an asymptotically flat spacetime. Quantum mechanics has conservation of energy. So how can he put these ingredients together to get a prediction that seems to violate conservation of energy? He says, > These mini BHs acquire their mass from the huge Planckian vacuum energy and > not the BH itself. I don't see how this gives him a free pass on conservation of energy. The vacuum's energy should be a function of its state, and its state isn't undergoing some monotonic change over time.


title: Doubts regarding dimension of a system:Definitions and algorithms

text: I need to do phase reconstruction from time series data. In doing so, I encountered Takens' embedding theorem and Cao's minimum embedding dimension $d$ by nearest neighbor method. In paper "Optimal Embeddings of Chaotic Attractors from Topological Considerations" by Liebert et al., 1991, says that minimum embedding dimension for reconstruction should be less than $2m+1$. This confused me since I am aware of Whitney's embedding dimension which stated $d=2*m$ where $m$ is the fractal dimension. Then there is Kennel's method of false nearest neighbor. Can somebody please explain to me:   1. What are the techniques for calculating embedding dimension?   2. Difference between embedding dimension and correlation dimension?   3. What is the technique of proving that a system has finite dimensionality after the signal passes through a filter?   4. Can somebody tell me what is the formula for embedding dimension      * should it be Cao's method or Kennel's false nearest neighbor method.


title: What physical significance has the Heisenberg Group?

text: I read that the canonical commutation relation between momentum and position can be seen as the Lie Algebra of the Heisenberg group. While I get why the commutation relations of momentum and momentum, momentum and angular momentum and so on arise from the Lorentz group, I don't quite get where the physical symmetry of the Heisenberg group stems from. Any suggestions?


title: Dopant Charge Transfer and Fermi Level shift

text: When a system has a dopant, how much does the Fermi level shift? For example, say a finite concentration of substitutional dopants replace some bulk atoms, and each has one extra electron. Ignore any changes in geometry. Say we do some DFT calculations that show the charge transfer to be 0.1 between the impurity and the bulk. Will the Fermi energy shift according to the new total number of electrons in the system, or as 0.1*number of electrons? I am thinking the first one, as EF should be related to the total number of electrons in the system. However, with a small charge transfer could we not regard the remaining 0.9 of charge "bound" to the dopant?


title: What is Quantization?

text: In classical mechanics you construct an action (involving a Lagrangian in arbitrary generalized coordinates, a Hamiltonian in canonical coordinates [to make your EOM more "convenient & symmetric"]), then extremizing it gives the equations of motion. Alternatively one can find a first order PDE for the action as a function of it's endpoints to obtain the Hamilton-Jacobi equation, & the Poisson bracket formulation is merely a means of changing variables in your PDE so as to ensure your new variables are still characteristics of the H-J PDE (i.e. solutions of the EOM - see No. 37). All that makes sense to me, we're extremizing a functional to get the EOM or solving a PDE which implicitly assumes we've already got the solution (path of the particle) inside of the action that leads to the PDE. However in quantum mechanics, at least in the canonical quantization I think, you apparently just take the Hamiltonian (the Lagrangian in canonical coordinates) & mish-mash this with ideas from changing variables in the Hamilton-Jacobi equation representation of your problem so that you ensure the coordinates are characteristics of your Hamilton-Jacobi equation (i.e. the solutions of the EOM), then you put these ideas in some new space for some reason (Hilbert space) & have a theory of QM. Based on what I've written you are literally doing the exact same thing you do in classical mechanics in the beginning, you're sneaking in classical ideas & for some reason you make things into an algebra - I don't see why this is necessary, or why you can't do exactly what you do in classical mechanics??? Furthermore I think my questions have some merit when you note that Schrodinger's original derivation involved an action functional using the Hamilton-Jacobi equation. Again we see Schrodinger doing a similar thing to the modern idea's, here he's mish-mashing the Hamilton-Jacobi equation with extremizing an action functional instead of just extremizing the original Lagrangian or Hamiltonian, analogous to modern QM mish-mashing the Hamiltonian with changes of variables in the H-J PDE (via Poisson brackets). What's going on in this big Jigsaw? Why do we need to start mixing up all our pieces, why can't we just copy classical mechanics exactly - we are on some level anyway, as far as I can see... I can understand doing these things if they are just convenient tricks, the way you could say that invoking the H-J PDE is just a trick for dealing with Lagrangians & Hamiltonians, but I'm pretty sure the claim is that the process of quantization simply must be done, one step is just absolutely necessary, you simply cannot follow the classical ideas, even though from what I've said we basically are just doing the classical thing - in a roundabout way. It probably has something to do with complex numbers, at least partially, as mentioned in the note on page 276 here, but I have no idea as to how to see that & Schrodinger's original derivation didn't assume them so I'm confused about this. To make my questions about quantization explicit if they aren't apparent from what I've written above: **a)** Why does one need to make an algebra out of mixing the Hamiltonian with Poisson brackets? (Where this question stresses the interpretation of Hamiltonian's as Lagrangian's just with different coordinates, & Poisson brackets as conditions on changing variables in the Hamilton-Jacobi equation, so that we make the relationship to CM explicit) **b)** Why can't quantum mechanics just be modelled by extremizing a Lagrangian, or solving a H-J PDE? (From my explanation above it seems quantization smuggles these idea's into it's formalism anyway, just mish-mashing them together in some vector space) **c)** How do complex numbers relate to this process? (Are they the reason quantum mechanics radically differs from classical mechanics. If so, how does this fall out of the procedure as inevitable?) Apologies if these weren't clear from what I've written, but I feel what I've written is absolutely essential to my question. **Edit:** Parts **b)** & **c)** have been nicely answered, thus part **a)** is all that remains, & it's solution seems to lie in this article, which derives the time dependent Schrodinger equation (TDSE) from the TISE. In other words, the TISE is apparently derived from classical mechanical principles, as Schrodinger did it, then at some point in the complicated derivation from page 12 on the authors reach a point at which quantum mechanical assumptions become absolutely necessary, & apparently this is the reason one assumes tons of axioms & feels comfortable constructing Hilbert spaces etc... Thus elucidating how this derivation incontravertibly results in quantum mechanical assumptions should justify why quantization is necessary, but I cannot figure this out from my poorly-understood reading of the derivation. Understanding this is the key to QM apparently, unless I'm mistaken (highly probable) thus if anyone can provide an answer in light of this articles contents that would be fantastic, thank you!


title: Under which representation of U(1) transform electron and photon gauge field?

text: I know that under $SU(2) \times SU(2)$, the left-handed electron transforms under $ ( \frac{1}{2},0 ) $ representation and the vector gauge field $A_\mu$ under $ ( \frac{1}{2},\frac{1}{2}) $. Since the electron transforms under $U(1)$, there must be a represenation under which it transforms. What is this representation? Does it have a name? Apparenly $A_\mu$ does not transform under the same representation, which would mean $e^{\alpha(x) Q} A_\mu$, but instead as $A_\mu + i \partial_\mu \alpha(x)$ ? What representation is this? Of course I realize that the transformation of $A_\mu$ can't be different for the Lagrangian to be invariant, but that shouldn't be used to define the it.


title: Derivation of the Polyakov Action

text: As is usually done when first presenting string theory, the Nambu-Goto Action, $$ S_{\text{NG}}:=-T\int d\tau d\sigma \sqrt{-g} $$ ($g:=\det (g_{\alpha \beta})$ is the induced metric on the world-sheet and $T$ is a positive real number interpreted as the string tension), is introduced as the natural generalization of action for a relativistic point particle, which in turn is obviously a correct action as it produces the proper equations of motion (and has a nice geometric interpretation). Not long after the introduction of the Nambu-Goto action, authors tend to introduce the Polyakov action, \begin{align*} S_{\text{P}} & :=-\frac{T}{2}\int d\tau d\sigma \, \sqrt{-h}h^{\alpha \beta}g_{\alpha \beta}=-\frac{T}{2}\int d\tau d\sigma \, \sqrt{-h}h^{\alpha \beta}\partial _\alpha X\cdot \partial _\beta X \\\ & =-\frac{T}{2}\int d\tau d\sigma \, \sqrt{-h}h^{\alpha \beta}\partial _\alpha X^\kappa \partial _\beta X^\lambda G_{\kappa \lambda}(X), \end{align*} where $G_{\kappa \lambda}$ is the space- time metric, $g_{\alpha \beta}$ is the induced metric on the world-sheet, and $h_{\alpha \beta}$ is the auxiliary metric on the world-sheet ($h:=\det (h_{\alpha \beta})$). They then usually proceed to show that these two actions are equivalent, in the sense that you can deduce the equations of motion for $S_{\text{NG}}$ given the equations of motion for $S_{\text{P}}$. Now, that's all well and dandy, but that doesn't exactly show how one would actually arrive at the Polyakov action. You can't make it as a theoretical physicist by mindlessly computing things to show you get the right answer; you have to be able to actually, you know, come up with things. Hence, instead of just pulling the Polyakov action out of a hat, it would be nice to know a way of deriving or motivating the action. So then, imagine you are handed $S_{\text{NG}}$ and you set out to come up with an equivalent action that, at the very least, doesn't involve a square- root. How do you come up with the Polyakov action?


title: Working of a vertical axis wind turbine

text: Conventional horizontal axis wind turbines use lift force generated in the blades to turn a turbine. But what is the mechanics of vertical axis wind turbine? What would be the free body diagram of the blades of a VAWT? Is Vertical axis wind turbine more efficient that a horizontal axis wind turbine?


title: How important is the cosmic censorship conjecture?

text: I would like to know how important the cosmic censorship conjecture is? Should a quantum theory of gravity must obey this? It was never rigorously proved in classical GR too. What would be the consequences if it turns out that CCC (weak) does not hold?


title: Any suggestions for units conversion?

text: > **Possible Duplicate:**   >  Photometer: measured Irradiance L converted to photon rate I am conducting a experiment where stimulus output of $470\ nm$ is measured by a radiometer at $30\ \mu W\ cm^{-2}$. The stimulus is $1$ inch from the detector. Any suggestion on how I might go about converting $\mu W\ cm^{-2}$ to log photon $cm^{-2} s^{-1}$?


title: What does the * mean in spherical harmonics?

text: In Jackson's book about classical electrodynamics, this formula comes up: $$q_{lm} = \int \mathrm d^3 x' \, Y^*_{lm}\left(\theta', \phi'\right) r'^l \rho\left(\vec x'\right)$$ What does that $^*$ mean?


title: Deducing latitude from Foucault Pendulum

text: Suppose I set up a Foucault pendulum and observe that it precesses at a rate of 216.528 degrees per day. While I am observing this, a total solar eclipse occurs. Where am I, and what is the date? My professor NEVER went over anything like this, so a shove in the right direction would be awesome.


title: Force exerted on potential wall

text: A particle bound in an infinite potential wall at $x=0$ will apply a force on the wall. For a plane wave and imagining it as a fluid bouncing off the reflection wall at $x=0$, find the force in terms of $\phi'(0)$, the derivative of wave function at $x=0$. We know, for a reflecting fluid, $\textrm{force }= \frac{dp}{dt}$, where $p$ is momentum. Classically, $p=mv$. In our case, $v$ is $\hbar k/m$, the velocity of the plane wave. Instead of mass, we have $|\phi|^2dx$, the probability of finding the massive particle in an interval $dx$. So $p= \frac{\hbar k}{m}|\phi|^2 dx$. Then, force $f=\frac{dp}{dt} =\frac{d(|\phi|^2 dx \hbar k/m)}{dt}$ By the continuity equation, $\frac{d(|\phi|^2)}{dt}=-\frac{dj}{dx}$, where $j$ is probability current = $\hbar k/m |\phi|^2$. So $f=\frac{dp}{dt}=\left(\frac{\hbar k}{m}\right)^2 \frac{d(|\phi|^2)}{dx} = \frac{\hbar k}{m} 2 \phi \phi' dx$. But for infinite potential, $\phi(0)=0$, so this gives 0. So I have an unwanted $\phi$ and a pesky $dx$ in my problem. I'm stumped for days, I'd appreciate all help. I'm fairly sure I should be getting an answer of force ~ $\phi'(0)^2$.


title: Symmetry and overlapping of ground states

text: In a quantum mechanics, there is the following formula to derive the zero energy $E_0$ of a perturbed Hamiltonian $$H = H_0 + V$$ knowing the zero energy $W_0$ of the free Hamiltonian $H_0$: $$E_0 = W_0 + i\frac{d}{dt}\text{ln}R(t)|_{t\rightarrow\infty(1-i\eta)}$$ The exponential killing the excited states faster than the lowest energy one. However, one needs to suppose a non-vanishing overlap of the two ground states $|\phi_0\rangle$ for $H_0$ and $|\psi_0\rangle$ for $H$. I read that if two have different symmetry they must be orthogonal but I didn't manage to derive why. Let's suppose that $G$ is a symmetry of $|\phi_0\rangle$ then $G|\phi_0\rangle=0$ and $\langle\psi_0|G|\phi_0\rangle=0$ and if $|\psi_0\rangle$ is not invariant under $G$ I still need to have $$G|\psi_0\rangle \propto |\psi_0\rangle$$ to derive $\langle\psi_0|\phi_0\rangle=0$. ($|\psi_0\rangle$ needs to be an eigenvector of $G$ with non-vanishing eigenvalue)


title: Electrical flow in a simple parallel circuit

text: I'm having trouble understanding something in one of my text books: > Let’s have a look at the implications of each circuit configuration. Figure > 3.13 shows the Conventional representation of a parallel circuit. If you > assume that the resistance of the wires can be neglected, then the voltage > drop across each bulb is equal to the e.m.f. of the source, the dynamo. The > Current flowing from the source is divided between each bulb depending on > its resistance (remember I = E/R), Removing one of the bulbs would not > affect the voltage drop across the other bulb and would therefore not affect > the Current in it, although the overall Current from the dynamo would drop > as the demand has been reduced. Specifically, the line about removing one of the bulbs not affecting the voltage drop. My understanding is that the sum of voltage drops in a circuit must be equal to the output of the emf, but the way I'm reading the text suggests that if you have three bulbs in a parallel circuit and you remove one of them, the voltage drop remains the same - this is what I don't understand, though. If you a lamp is removed, then that's one less lamp consuming emf. Does it not get redistributed to the other two lamps? Likewise, the text mentions the overall current from the dynamo dropping because demand has been reduced. My initial understanding was that current from an emf is only affected by the emf - not the demands of components further along the circuit, as in this case. What have I misunderstood?


title: What is the connection between Poisson brackets and commutators?

text: The Poisson bracket is defined as: $$\\{f,g\\}_{PB} ~:=~ \sum_{i=1}^{N} \left[ \frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} - \frac{\partial f}{\partial p_{i}} \frac{\partial g}{\partial q_{i}} \right]. $$ The anticommutator is defined as: $$ \\{a,b\\} ~:=~ ab + ba. $$ The commutator is defined as: $$ [a,b] ~:=~ ab - ba. $$ What are the connections between all of them? Edit: Does the Poisson bracket define some uncertainty principle as well?


title: Work done by spring over distance

text: I'm working through a problem involving energy conservation. Unfortunately, I cannot calculate the work done by a spring.               Before:          +------------+     |            |     |  spring    | d1     |            |     +------------+          After:          +------------+     |            |     |  spring    |     |            | d2     |            |     |            |     +------------+      Given the spring constant, d1, and d2, how can I determine the work done? Also, please explain how the formula was calculated instead of just posting an answer.


title: Quantum Field Theory Variants

text: I am a math guy, so sorry for the naivety. When I peruse the wikipedia I see many "variants" of quantum field theory...conformal quantum field theory, topological quantum field theory, axiomatic/constructive quantum field theory, algebraic quantum field theory, etc. Whether or not these are actually variants of something is unclear to me. I don't really have a specific question, but I was wondering if you guys could help me understand what these different things are and/or point me to somewhere to get a clearer picture.


title: The interpretation of mass in quantum field theories

text: Consider a free theory with one real scalar field: $$ \mathcal{L}:=-\frac{1}{2}\partial _\mu \phi \partial ^\mu \phi -\frac{1}{2}m^2\phi ^2. $$ We write this positive coefficient in front of $\phi ^2$ as $\frac{1}{2}m^2$, and then start calling $m$ the mass (of who knows what at this point) and even interpret it as such. But pretend for a moment that you've never seen any sort of field theory before: if someone were to just write this Lagrangian down, it's not immediately apparent why this should be the mass of anything. So then, first of all, what is it precisely that we mean when we say the word "mass", and how is our constant related to this physical notion in a way that justifies the interpretation of $m$ as mass? If it helps to clarify, this is how I think about it. There are two notions of mass involved: the mathematical one that is part of our model, and the physical one which we are trying to model. The physical mass needs to be defined by an idealized thought _experiment_ , and then, if our model is to be any good, we should be able to come up with a 'proof' that our mathematical definition agrees with the physical one. (Of course, none of this at all has anything to do with this particular field theory; it was just the simplest Lagrangian to write down.)


title: How can a sine wave represent a longitudinal wave?

text: I envision a longitudinal wave as a series of vertical lines like that drawn on the board in an introductory physics class. This image contains no angles. Sound is a longitudinal wave. Some audiovisual references claim that sound is composed of sine waves. I am trying to reconcile how longitudinal waves (no angles) can be composed of sine waves (dependent on angles). What maths or theory explains the relationship?


title: Has anyone theorized a connection between entropy and quantum uncertainty?

text: I apologize if this kind of idle theorizing is frowned upon here, but I was wondering if it is possible that the Second Law of Thermodynamics is a consequence of quantum uncertainty. I've heard entropy of a system defined as the number of micro-states that it can have to correspond to the macro-states it has. So that definition makes it sound like entropy is simply losing information. As we know, entropy increases as time goes on. Now this seems contradictory to me; we know more as time goes on, not less. Is it possible that, because you can gain more and more information about a system as time goes on as you can interact with it more that, some information needs to be "hidden" from you. And that this process of losing information is entropy? P.S. I know that what I "know" about any system does not approach the limits set out by the uncertainty principle. But as System A interacts with System B, over time System A's state is more influenced by System B and in that sense System A has gained knowledge of System B.


title: Could an ultra-relativistic particle tunnel directly through a stellar mass black hole?

text: It occurred to me in passing that the Lorentz contraction of a black hole from the perspective of an ultra-relativistic (Lorentz factor larger than about 10^16) particle could reduce the thickness of a black hole to less than the DeBroglie wavelength of the particle. It would seem to me that under those conditions the particle would have a non- insignificant probability of tunnelling right through the black hole rather than being adsorbed by it. Is this so? If not, why?


title: Must the action be a Lorentz scalar?

text: Page 580, Chapter 12 in Jackson's 3rd edition text carries the statement: > From the first postulate of special relativity the action integral must be a > Lorentz scalar because the equations of motion are determined by the extemum > condition, $\delta A = 0$ Certainly the extremeum condition must be an invariant for the equation of motion between $t_1$ and $t_2$, whereas I don't see how the action integral must be a Lorentz scalar. Using basic classical mechanics as a guide, the action for a free particle isn't a Galilean scalar but still gives the correct equations of motion.


title: Does a full freezer freeze items faster than an empty one?

text: Let's say we want to freeze a banana. Would it freeze faster if we insert it into an empty freezer, or into one that already contains many frozen bananas?


title: Writing $\dot{q}$ in terms of $p$ in the Hamiltonian formulation

text: In the Hamiltonian formulation, we make a Legendre transformation of the Lagrangian and it should be written in terms of the coordinates $q$ and momentum $p$. Can we always write $dq/dt$ in terms of $p$? Is there any case in which we obtain for example a transcendental equation and cannot do it?


title: Two clocks along different worldlines

text: I have been reading and watching videos about this subject for a while now. I just can not seem to grasp the idea. Let's say we have two clocks. I leave one at home and keep one in my pocket. Then, I started running at speed that is close to speed of light to my school then come back to my house. If I compare those two clocks how would they differ in time?


title: Circular motion, deciding what the tangential speed must be to maintain theta

text: A bob of mass m = 0.250kg is suspended from a fixed point with a massless string of length L = 25.0cm . You will investigate the motion in which the string traces a conical surface with half-angle θ = 21.0 deg ![enter image description here](http://i.stack.imgur.com/nTGlD.jpg) So what is the relationship between theta, mass and Tangential speed? An equation and an explanation would be nice as my text book is somewhat lacking when it comes to circular motion it only deals with orbit and im not sure if I can change one of those equations for this problem.


title: Atmospheric pressure in a mercury barometer in an upward accelerating elevator

text: I have an elevator accelerating upwards at an acceleration of $a$. A mercury barometer measures the atmoshperic pressure at this point. Will the reading be less than, more than or equal to $76 \ cm$ of $Hg$? I remembered from my class that the pressure in a liquid in an nonintertial frame accelerating upwards at $a$ is $\rho h (g + a)$. So, my first thought was it would be less that $76cm$ of $Hg$. But, then I realized that as you are accelerating upwards, you are hitting the air molecules faster and more often. So, technically, the atmoshperic pressure in our frame of reference should increase. But, then again I thought that air was compressible, so maybe that would skew off the results. What's the correct answer?


title: The quantum state can be interpreted statistically, again

text: Now there are two papers **The quantum state cannot be interpreted statistically** http://arxiv.org/abs/1111.3328 (It was discussed here the consecuences of this "no-go theorem") And this one (two of the authors are the same as the previous paper): **The quantum state can be interpreted statistically** http://arxiv.org/abs/1201.6554 I would like to note this: **titles give only poor information about the content** , and they seem even maliciously chosen, but the mere existence of the two papers is funny anyway.. The question is : **Which is more general!?** From the paper: _"Recently, a no-go theorem was proven [21] showing that a $\psi$-epistemic interpretation is impossible. A key assumption of the argument in [21] is preparation independence situations where quantum theory assigns independent product states are presumed to be completely describable by independently combining the two purportedly deeper descriptions for each system. Here, we will show via explicit constructions that without this assumption, $\psi$-epistemic models can be constructed with all quantum predictions retained"_ **About being general** As I understand the second one just _seems_ more general (because of "less assumptions"), but by no means Newton's dynamics is more general than Einsein's relativity because "it lacks of c=constant assumption". It's weird anyway, because it would mean that if " wavefunction is a real physical object" (a funny phrase from www.nature.com article) would depend on assumptions!, then what kind of realism depend on assumptions? Perhaps a point to discuss (assuming the theorem is well proven) is whether those assumptions have sense, if they come from experiments, or if they are just limiting the scope (toy model), or if those are random assumtions that have no source.


title: Why is it necessary for an object to have a bigger size than the wavelength of light in order for us to see it?

text: I keep hearing this rule that an object must have a bigger size than the wavelength of light in order for us to see it, and though I don't have any professional relationship with physics, I want to learn the explanation for this. Also I may have expressed my question wrong, but I hope you get the idea of what I'm trying to ask. Can you explain this as simple as possible for a non-physics person?


title: Dipole charge attractions while one of them is turning around other

text: There is a electric dipole which is fixed. So angular momentum isn't conserved. And there is charge $Q$ which has initial velocity $u$. My question is: What is the tangential velocity of the charge $Q$ as a function of $r$ and $\theta$ and beyond that, what is the $r$ and $\theta$ as a function of time? Here is what gives me trouble: I solved question when dipole and charge reversed. Because when they are reversed the dipole becomes aligned all the time along the $r$ axis freely, so I can write down angular momentum conservation equation. But in actual problem we are holding the dipole while it wants to get aligned along $r$ axis. That means we are applying torque to the system, due to that I have one less equation. And I can't solve the problem due to lack of info. ![Dipole charge attraction](http://i.stack.imgur.com/ttUXm.png)


title: Do all black holes have a singularity?

text: If a large star goes supernova, but not enough mass collapses to form a black hole, it often forms a neutron star. My understanding is that this is the densest object that can exist because of the Pauli exclusion principle: It's made entirely of degenerate matter, each particle of which cannot occupy the same quantum state of any other. So these objects are so massive that they gravitationally lens light. If you make them more massive, they bend the light more. Keep going and going until they bend the light _so much_ that light passing near the surface can barely escape. It's still a neutron star. Add a bit more mass, just enough that light passing just over the surface cannot escape. Now it's a black hole with an event horizon (I think?). Does this mean the neutron star has become a singularity? Isn't it still just a neutron star just beneath the event horizon? Why are black holes treated as having a singularity instead of just an incredibly massive neutron star at its center? Does something happen when an event horizon is "created?"


title: Association of financial phenomena/indications with the conservation laws of Black Scholes equation

text: For a while I've been doing research on methods of obtaining conservation laws via the symmetries of differential equations (DEs). I'm presently doing research on identifying financial indicators/phenomena that can be associated with the conservation laws of the Black Scholes problem. I've done some reading on econophysics and quantitative finance but there seems to be lots of contrasting and confusing views on this matter. Any contribution to shed light on this matter will be appreciated.


title: E&M and geometry - a historical perspective

text: Recently, I was contemplating the beautiful formulation of electromagnetism (specifically Maxwell's equations) in terms of differential forms: $$F=\mathrm{d} A\implies \mathrm{d}F=0 \hspace{1cm}\text{and}\hspace{1cm} \mathrm{d}\star\mathrm{d}F=\mu_0 J $$ I started thinking about the history of this way of looking at things, and realized that I don't know much about it at all. My first question was therefore: Was it known already at the time of Maxwell (or soon after) that electromagnetism could be cast in this geometric form? How was this first introduced and who did it? After consulting Maxwell's treatise, it became clear that at least Maxwell himself was not aware of this formulation. But maybe someone else immediately recognized the geometric formulation once Maxwell published his results... In modern times, one is - at least as a physicist - usually first introduced to the field strength tensor $F$ through the covariant formulation of Maxwell's equation using tensor calculus, where it is defined as $F_{\mu\nu}=\partial_\mu A_\nu -\partial_\nu A_\mu$. When one then learns about differential forms etc. it is then obvious that $F=\mathrm{d}A$ and the geometric formulation follows quite naturally. However, was this also the case historically? Did 'they' come up with the tensor calculus formulation of $F$ first, and did they only then recognize the geometric description? Or was the geometric description discovered first? Another possibility is that it took the introduction of Einstein's general relativity for anyone to realize that fields can be interpreted in terms of geometry. In conclusion, I am interested in a chronological description of the development of the different formulations of electromagnetism, with emphasis on the following points:   1. Who first came up with the geometric formulation in terms of differential forms?   2. Is it known at all how this person arrived at this?    3. Was the geometric interpretation discovered _before_ tensor calculus became popular, or only after it was know that $F_{\mu\nu}=\partial_\mu A_\nu -\partial_\nu A_\mu$? Was this after the introduction of GR, and was it at all influenced by Einstein's work?


title: Suns emission spectrum

text: I learnt that in astrophysical spectroscopy, the emission spectrum of distant stars is used to determine what they're made of. So why is it that our own Sun is emitting the whole spectrum ? (or is that information incorrect)


title: Why are we not affected by the radiation of the radioactive decay going inside the Earth?

text: I was reading the question Why has Earth's core not become solid?, and one of the answers says that > The core is heated by radioactive decays of Uranium-238, Uranium-235, > Thorium-232, and Potassium-40 Why are we not affected by the radioactive emission of the condition below? Is this due to the fact that there is a very thick layer of mantle and crust between us and the core? Or I am wrong and we suffer from it's radiation in everyday life up to some extent?


title: Entropy of a particle with two energy states

text: A particle has two energy states having energies $E_0$ and $E_1$ with degeneracies $g_0$ and $g_1$. The respective probabilities are $p_1$ and $p_2$. What is the entropy in terms of $p_1$, $p_2$, $g_1$ and $g_2$ ?


title: Why do my ice cubes stick together?

text: When I put ice cubes in a glass of water, I find that sometimes they will stick together and form a sort of "bridge" between them as they melt. There is usually a visible line where one ends and the other begins, and they break apart if pushed (but for the most part they stick together if they aren't interfered with). I'm wondering how they form this bridge in the first place if they're melting, and why it stays together.


title: Stagnation point from complex potential

text: I just wanted to see if I am doing this right. $$\Omega(z) = U(z+\frac{a^2}{z})$$ So to find the stagnation point: $$\Omega'(z) = U(1-\frac{a^2}{z^2})=0$$ Therefore stagnation points occur at: $z = +/-\sqrt{\frac{a^2}{U}}$ These both occur on the x-axis and I see the stagnation occurs on the circle, so I think it's right but not too sure. Thanks!


title: Follow up question on "Wilson Loops as Raising Operators"

text: This is a follow-up question on the topic that I opened a few days ago, Wilson Loops as raising operators. The paper > Topological Degeneracy of Quantum Hall Fluids. X.G. Wen, A. Zee. _Phys. Rev. > B_ **58** no. 23 (1998), pp. 15717-15728. arXiv:cond-mat/9711223. gives a nice derivation of the explicit ground states of the $U(1)$ Chern- Simons Theory on a torus in Section 2 on Abelian Quantum Hall States. In particular Eq. (12) gives the generic form of a ground state $\psi(y) = \sum_{n=-\infty}^{\infty} c_{n} \ e^{i\ 2\pi ny}$. Due to the fact that the theory lives on a torus the ground state manifold is found to be $k$-fold degenerate. My question: Is it possible (by direct calculation) to obtain the relations \begin{align} W(b)|n \rangle &= |n + 1 \text{ mod } |k| \rangle, \nonumber \\\ W(a) |n \rangle &= e^{2\pi i n /k} |n \rangle. \end{align} from the previous question? I don't have a particularly strong background in field theory so I am feeling somewhat uneasy when it comes to the explicit evaluation of the Wilson Loop (with its exponentiated gauge field and the path ordering) acting on the constructed state. I am looking forward to your responses.


title: Heat Kernel on Sphere for Vector Laplacian

text: Can somebody please provide me with a reference where the method of evaluating the heat kernel for spin-1 fields,i.e. vector laplacians on a 2-sphere is given? Please suggest some references accessible for physicists.


title: Moving in a heart!

text: You can find the symbol of love, the heart, by looking at the motion of a charged particle that's emitted from a hot wire in a specific electromagnetic field. The electric field is directed radially from the wire and has strength $1V/m$ everywhere. The magnetic field $B=1T$ is parallel with the wire axis. If the charged particle has a very small radial velocity with absolutely no velocity parallel to the wire direction when it escapes the wire, find how long the total length it has to travel to come back to the wire in meters? If you plot the orbit of the particle you'll find that it looks like a heart! Neglect the size of the wire. The electric charge of the particle is $1C$ and the mass is $1kg$. I am stuck on how to analyze the motion of the object.


title: Explaining valence with quantum mechanics

text: Can anyone give me a quantum mechanical explanation of the theory of valence? (i.e. why atoms bond just enough to have a complete orbital) EDIT: To clarify, I already have an idea of why atoms bond, and the molecular orbit makes sense to me. The problem is that the valence bond theory provides a simple and fairly accurate description for when a molecule is stable. To make this more concrete: why is CH_4 more stable than CH_3 or CH_5. Looking up the former on wikipedia, I see a better way of phrasing the question might be: why are free radicals reactive? (Should I change the title?)


title: Gravity of Light

text: I'm reading Quantum field theory in a Nutshell and I find a very interesting calculation that leads to the gravitational interaction between 2 light beam. Is this kind of interaction permitted in general relativity? (not necessarily a quantum gravity theory or the like) Is there a energy tensor $T_{\mu\nu}$ asscociated with a photon so that it creates $R_{\mu\nu}\ne 0$? It's awesome if someone can give a simple derivation in the framework of general relativity.


title: Simple kinematics excercise, throwing something upwards

text: I am trying to solve this simple excercise: **Question** _You throw a small coin upwards with_ $4 \frac{m}{s}$ _. How much time does it need to reach the height of_ $0.5 m$ _? Why do we get two results?_ **Answer** (We get two results for time, because the coin passes the 0.5m mark downwards too.) The equtation I used (for constant acceleration): $x = x_0 + v_0 t + \frac{1}{2} a t^2$ These values I know: $x = 0.5m$, $x_0 = 0$, $v_0 = 4 \frac{m}{s}$, $a = -9.81 \frac{m}{s^2}$ So, I get a quadratic equtation which I can solve for $t$. My two results are: $t_1 = 0.15s$ and $t_2 = 0.66s$, however the book has the results 0.804s and 0.013s. What am I doing wrong? **Thanks for your help**


title: Fermi level in disordered amorphous and/or organic semiconductors

text: So, the Fermi level in crystals is pretty easy to understand. Been using it and talking about it in terms of the highest occupied level forever. However, I'm now reading about disordered systems. A lot of researchers mention the existence of empty states randomly distributed above and _below_ the Fermi level. But isn't the Fermi level necessarily the energy at which all energies below are filled states? EDIT: So I suppose chemical potential is the more correct term to use (instead of Fermi energy) because not at T = 0. Anyways, consider this quote: "the localized gap states near $E_F$ are spread in energy with singly occupied gap states below $E_F$, doubly occupied states lying above $E_F$, and empty states distributed randomly."


title: Software to simulate dynamics of objects in a given gravitation field

text: I want to simulate and test set of **2D designs** that basically have **pulley/gear/chain-linked** systems under Gravity (For e.g. to check how a pulley would rotate given particular weights, of course I'm not talking about such small systems, but systems where different pulleys/gears/weights are linked together). _[Frictional/mechanical properties can be neglected for my purposes]_ Can anyone recommend any softwares **(Opensource/paid)** that can be used to easily design pulleys, gears, some chains(for e.g. to link a pulley to a gear) and simulate their behavior when the system is placed in a gravitational field? I can construct the physical replicas of the designs and test them but it's rather cumbersome and a waste of resources to do so. Your help is much appreciated.


title: Why is the transition into N proportional to N+1?

text: I am having trouble understanding the origin of the bosonic stimulated emission. How can I qualitatively understand why bosons Boson's attract each other into similar quantum states. The furtherst I was able to get was to simulate the feedback process, in my mind, but I don't have the foggiest of ideas why this rule must be the case. I haven't taken any classes on quantum or statistical mechanics. > Explicitly, if N bosons occupy a given state, the transition rates into that > state are proportional to (N + 1).


title: principle in a water Faucet

text: If you try to block with your finger the flow of the water out of the faucet or a water hose, the water's speed increases. But while you're blocking the water flow out of the faucet by turning the handle, the speed doesn't increase. So what's the difference between the two ?


title: Differences in the behaviour of pinching a garden hose and closing a tap

text: Let's say you have a garden hose connected to an ordinary water tap which is opened fully. If you pinch the end of the hose, water leaves the hose at a higher speed (and this can be useful while watering plants, to reach pots which are further away). However when a tap (with no hose connected) is opened only slightly, water flows out at a low speed, possibly even in drops. The actions of pinching the end of a hose and of almost-closing an open tap seem similar, so why the difference in behaviour?


title: Fast cool down of "things" in the kitchen

text: Is there any fundamental physical reason (thermodynamics/entropy?) behind the fact that there doesn't exist home appliance for fast cool down of food/drinks? I know that there are some methods (liquid nitrogen, etc.) used in the kitchen, but I mean something much more common, like microwave oven but with opposite function. **Update** Thanks for the responses so far. I understand that the temperature difference is the key. However, I do not understand why it is so much harder/slower to generate large temperature difference on the cool side?