title: The bizarre behaviour of superfluids! Climbing up walls and geting out of glass beakers

text: **SUPERFLUIDITY:** Superfluidity is one of the most amazing quantum phenomena, which we can sit and watch them happening before our eyes! Watch this video, it is only a couple of minutes long, which will bring you face-to-face with quantum mechanics in all its beauty. Then take a look at the questions below. http://www.youtube.com/watch?v=9FudzqfpLLs **QUESTIONS:** A superfluid has the amazing ability to climb up the walls of the glass container that it is in: **Does it defy gravity?** A superfluid can get out through the walls of the glass container: **Quantum tunnelling in action before our eyes?**


title: What pressure or tension occurs in a glass jar when I pour boiling water inside?

text: Sometimes it happens that when you pour a boiling water into a glass jar, it cracks. Since glass is very hard material and resilient to pressure, the tension must be very high. Is it possible to estimate what forces / pressure / tension occur in such a moment? Some supplementary questions:   * Is it true that a thin glass is less likely to crack than a thick glass?   * What other factors can influence cracking? (Like surface scratches etc.)


title: Electric field of a negative charge

text: Displacing something against the gravitational field, gains it potential energy. Moving something against the nature requires work. If the electric field of a negative source charge 'Q' points inward, then by definition, it would require some work to displace a negative test charge 'q' against 'Q'. According to the Coulomb's law, like charges repel and unlike attract. Two negative charges are like, and they are supposed to be repelling each other and no work is required to keep them apart. I think the electric field of a negative charge pointing inward is nothing more than a surmise. What does a theoretical physicist think?


title: Single Photon Hits A Linear Polarizer, What Happens?

text: If a linear polarized single photon strikes a linear polarizer such that its polarization is at 45 degrees to the polarization axis of the polarizer, what happens? There is a nearly 50% chance that the photon is transmitted, and assuming it is transmitted, it somehow rotates its polarization to match that of the polarizer axis. But the photon has energy defined by E=hv before and after it encounters the polarizer. So it cannot lose energy by projecting its amplitude onto the polarization axis, as per the normal explanation. Also assuming the linear polarizer is a dichroic type, then I understand that this means the long molecules in the film have their long axis aligned perpendicular to the polarization axis - so how does the photon encounter the molecules. Is it absorbed and then re-emitted orthogonal to the molecular axis somehow?


title: Compactifying on a circle and the exchange of R and NS sectors

text: I've noticed a general phenomenon in compactifying on a circle where if you start with, say, an NS field, then the KK fields with an index along the circle will be in the R sector, and those without will of course remain in the NS sector. I am wondering how to understand this phenomenon. What is the story for fermions? Their behavior under compactification is quite different, with the spinor bundle tending to split as a tensor product rather than as a direct sum.


title: How many equations are there to calculate distance?

text: I am an app developer and I am trying to build a physics app to calculate distance based on the quantities the user gives. for example if the user gives initial speed, time and acceleration, using Newton's 2nd equation, my program can calculate distance. So for example if I have six basic formulas which are:- $$s = \frac{d}{t}$$   $$d = ut + \frac{at^2}{2}$$   $$v^2 - u^2 = 2ad$$ $$s = \frac{u+v}{2}$$ $$a = \frac{v-u}{t}$$   $$v = u + at$$ where: $s$ = average speed $d$ = distance $u$ and $v$ are initial and final speed $t$ = time $a$ = acceleration Out of these, are there a definite number of equations I can derive to calculate distance if some combinations of quantities are given or will it be way too many as I might have some more equations.


title: Motion of a car rounding a bank

text: When a car is traveling round a banked track as fast as possible, it has a tendency to slip up the slope. Opposite in the case when the car travels slowly and has a tendency to slip down. Can someone please give me an intuitive reason as to why this "tendency to slip up or down" occurs.


title: Velocity in a pseudo-Riemannian manifold

text: Suppose we have a pseudo-Riemannian manifold (modeled by $\mathbb R^{p,q}$) with signature $$(\underbrace{+,+,\cdots,+}_p,\underbrace{-,-,\cdots,-}_q)$$ Meaning we have $q$ spacelike dimensions and $p$ timelike dimensions. For a given observer in this manifold, we can define the position vector $\mathbf S$ of an object by $$ \mathbf S = (\vec T,\vec X) $$ Composed of vectors $\vec X = (X_1,X_2,\cdots,X_q)$ (the spatial position vector of the object) and $\vec T = (T_1,T_2,\cdots,T_p)$ (the "temporal position" vector. Note $T = c\cdot t$). Given this, we can define the Jacobian of $\vec X$ with respect to $\vec T$, matrix $\mathbf B$ $$ \mathbf J (\vec X) = \mathbf B = \begin{bmatrix} \frac {\partial X_1}{\partial T_1} & \frac {\partial X_1}{\partial T_2} & \cdots & \frac {\partial X_1}{\partial T_p} \\\ \frac {\partial X_2}{\partial T_1} & \frac {\partial X_2}{\partial T_2} & \cdots & \frac {\partial X_2}{\partial T_p} \\\ \vdots & \vdots & \ddots & \vdots \\\ \frac {\partial X_q}{\partial T_1} & \frac {\partial X_q}{\partial T_2} & \cdots & \frac {\partial X_q}{\partial T_p} \\\ \end{bmatrix} = \begin{bmatrix} \beta_{11} & \beta_{12} & \cdots & \beta_{1p} \\\ \beta_{21} & \beta_{22} & \cdots & \beta_{2p} \\\ \vdots & \vdots & \ddots & \vdots \\\ \beta_{q1} & \beta_{q2} & \cdots & \beta_{qp} \\\ \end{bmatrix} \;\therefore\;d\vec X = \mathbf B\cdot d\vec T$$ Where $\beta = \frac{d(\lVert\vec X\lVert)}{dT} = \frac{d(\lVert\vec X\lVert)}{c\cdot dt} = \frac vc$. This matrix should then give a representation of the velocity of the object in all spatial dimensions with respect to all temporal dimensions, which must somehow be related to the velocity measured by the observer. Knowing that vector $\vec X$ defines a path through the spatial dimensions, and vector $\vec T$ defines a path through the temporal dimensions (which are related by the equation stated above), we can take the lengths of those paths to be $s$ and $w$ respectively. If we define their gradients over vector $\vec T$, namely $$ \nabla s = \left(\frac{\partial s}{\partial T_1},\frac{\partial s}{\partial T_2},\cdots,\frac{\partial s}{\partial T_p}\right)\\\ \nabla w = \left(\frac{\partial w}{\partial T_1},\frac{\partial w}{\partial T_2},\cdots,\frac{\partial w}{\partial T_p}\right) $$ We can say $$ ds = \nabla s\cdot d\vec T\\\ dw = \nabla w\cdot d\vec T $$ Knowing that the scalar velocity measured by the observer, $\beta^*$, is simply defined by the derivative of the spatial distance moved ($ds$) with respect to time as measured by the observer's clock (which would correspond to $dw$), we can derive $$ \beta^* = \frac{ds}{dw} $$ And therefore we can conclude the following $$ ds = \beta^*\cdot dw \;\therefore\; \nabla s\cdot d\vec T =\beta^*\cdot(\nabla w\cdot d\vec T) \;\therefore\; \nabla (s-\beta^* w)\cdot d\vec T = 0 $$ Is there any way to relate this last expression with the matrix $\mathbf B$? Much appreciated.


title: Why is $\left.\frac{\partial C_V}{\partial V}\right|_T$ different in these derivations?

text: I want to show that $\delta q$ is not an exact differential. Starting from $dE = \delta q - pdV$ and because $E := E(V, T)$ is a state function, which allows to express the exact differential as $$ dE = \left.\frac{\partial E}{\partial V}\right|_T dV +\left.\frac{\partial E}{\partial T}\right|_V dT, $$ the two expressions can be set equal giving after rearrangement $$ \delta q = \left[ \left.\frac{\partial E}{\partial V}\right|_T + p \right]dV + \left.\frac{\partial E}{\partial T}\right|_V dT $$ and therefore also $$ \delta q = \left[ \left.\frac{\partial E}{\partial V}\right|_T + p \right]dV + C_V dT. $$ Now, by definition $\partial E/\partial T|_V = C_V$, and so $$ \left.\frac{\partial C_V}{\partial V}\right|_T =\left[\frac{\partial}{\partial V}\left.\frac{\partial E}{\partial T}\right|_V\right]_T $$ and because $E$ is a state function, the sequence of partial derivatives can be exchanged (according to Schwarz' theorem, while I don't understand how it works), allowing to write $$ \left.\frac{\partial C_V}{\partial V}\right|_T =\left[\frac{\partial}{\partial T}\left.\frac{\partial E}{\partial V}\right|_T\right]_V. (*) $$ Also, multiplying the above expression for $\delta q$ by $1/\partial V$ at constant $T$, I obtain $$ \left.\frac{\delta q}{\partial V}\right|_T = \left[ \left.\frac{\partial E}{\partial V}\right|_T + p \right]\left.\frac{\partial V}{\partial V}\right|_T + C_V \left.\frac{\partial T}{\partial V}\right|_T $$ where $\partial V/\partial V = 1$ and the second term on the right hand side equals $0$ because $\partial T = 0$ at constant temperature. Multiplying the remaining equation by $\partial / \partial T$ at constant $V$ gives $$ \left[\frac{\partial}{\partial T}\left.\frac{\delta q}{\partial V}\right|_T\right]_V = \left[ \frac{\partial}{\partial T} \left(\left.\frac{\partial E}{\partial V}\right|_T + p \right)\right]_V. $$ Now _assuming_ $\delta q$ were exact, again the sequence of partial derivatives would not matter and I could write $$ \left[\frac{\partial}{\partial V}\left.\frac{\delta q}{\partial T}\right|_V\right]_T = \left[ \frac{\partial}{\partial T} \left(\left.\frac{\partial E}{\partial V}\right|_T + p \right)\right]_V $$ and by using $q=E$ since the "inner" differential on the left side is evaluated at constant volume, $$ \left[\frac{\partial}{\partial V}\left.\frac{\partial E}{\partial T}\right|_V\right]_T = \left.\frac{\partial}{\partial V} C_V\right|_T = \left[ \frac{\partial}{\partial T} \left(\left.\frac{\partial E}{\partial V}\right|_T + p \right)\right]_V. (**) $$ From this we find that $(*)$ and $(**)$ are different and thus the assumption must be wrong and therefore $\delta q$ is not an exact differential. Does this make any sense? * * * Exact wording from book: > Starting with $dE = \delta q - pV$, show that > > a) $\delta q = C_V dT + [P+(\partial E/\partial V)_T] dV$ > > b) $\left(\frac{\partial C_V}{\partial V}\right)_T = > \left[\frac{\partial}{\partial T} \left(\frac{\partial E}{\partial > V}\right)_T\right]_V$ > > c) $\delta q$ is not an exact differential. For c), the book states > If $\delta q$ were an exact differential, then by solution to a), $(\partial > C_V/\partial V)_T$ would have to be equal to $[\partial /\partial > T(P+(\partial E/\partial V)_T)]_V$ but it is not according to solution of > b), hence $\delta q$ is not exact.


title: Effect of gravity at near-lightspeeds

text: Let's say I'm in a space station, hurtling towards our galaxy nearly close to the speed of light. From my reference frame, I see the galaxy coming towards my ship at the same speed. I pass the Sun, and am affected by its gravity. From Earth's point of view, the gravity of the sun deflected my spaceship's trajectory. From my point of view in the spaceship, the trajectory of the entire galaxy changed very rapidly. From my reference frame, how did my space station cause an entire galaxy to change course? _Originally had multiple questions, removed all but one_


title: What exactly is the microgravity field in orbit?

text: The ISS and other objects in orbit still experience small acceleration outside from the perfect line of orbit (of the system CM). For instance, two objects in the ISS that are let to be at rest will pass by each other twice as the station makes one orbit because the two items are in separate orbits, and all orbits pass over the same point because they are great circles over the Earth. My question is how would you actually quantify this? Regarding the ISS, the entire craft could rotate just so it is effectively tidally locked with the Earth. If you assume it does that, then you have one axis along which it is totally acceleration-less relative to the craft. Looking forward along that line, moving to the left or right would create an acceleration back to the line. Moving up or down would also create an acceleration toward the line since they would assume more elliptical orbits. But I'm really curious as to whether there would also be a acceleration parallel to the line of orbit, and I'm also really curious if it would be unstable or stable. So if the line of orbit is x, down toward the Earth is the negative z, and right of the line of motion is y, then my intuition is that the system is stable on the y-axis, it is stable up-and-down for the z-axis, but movement up the z-axis would create acceleration in the negative x-axis. One major consequence would be if you left a hammer just outisde the airlock, the stability of these fields would dictate whether it sticks around or leaves. Could we find a simple $(x,y,z)$ equation for the acceleration? I can't find anything that quite answers this, and I my attempts result in more questions than answers.


title: Influence of Joe Rosen work, is it marginal, or significantly accepted?

text: I have prepared a paper that relies on work of Joe Rosen on symmetry (e.g. "Symmetry Rules: How Science and Nature Are Founded on Symmetry"). I am wondering about his influence. For example, when I once asked on Math.SE about status of Curie symmetry principle, the question was closed, being also repelled by physics.SE. So the topic seems to be perceived as unscientific. Then I found the Rosen book and papers, where he put much effort on giving Curie principle scientific rigor. Yet, the book seems to be unknown. Rosen proofs that dirrectly correlate symmetry and entropy seem to be ignored (the proof is given in The Symmetry Principle). But, the fact that Rosen's book is in Springer's Frontiers Collection seem to support his reputation? I have used Rosen's work in my paper and I am wondering e.g. if receiveing review only from Rosen-related group will not be too hermetic. I myself am a big fan of Rosen's work and of his determination on bringing symmetry-level reasoning to mainstream science (e.g. his first book on the topic was published in 1995).


title: Is the fine structure constant a rational number?

text: Since the fine structure constant (denoted alpha) is a pure real number, it just occured to me to ask if it is a rational number or not.


title: Where am I confused about force addition?

text: As far as my knowledge is concerned, a vector quantity should possess magnitude and direction & more over it should also obey the laws of vector addition. As we all know that the vector sum of 3 newtons in the x direction and 4 newtons in the y direction will acting at a point will produce a resultant of 5 newtons. Where did the remaining 2 newtons go? I mean we have applied a total of 7 newtons of force on a point sized particle but the output is only 5 newtons, so it appears as if a 2 newton force is disappearing here. In which other form does it reappear rather than the resultant? Or is it something like the remaining 2 newtons of force just vanishes and it doesn't appears in any other form? Please correct me if I am going wrong on this issue.


title: What determines how much energy a stone can hold?

text: Imagine you have a stone that is being hit by focused sunlight from a magnifying glass. Later you will place the stone into water to heat it. What type of stone will transfer the most energy into the water and why?


title: Ratio of position error of orbiter to the size of the orbit

text: This is an assignment question for online AP physics. As if it isn't already tough. This question is killing me. I even asked my physics teacher from last year and my calculus teacher. It stumped them, too. I would show some kind of attempt at solving the question, but I've got nothing. I don't even understand how to begin solving this. The question is: > The space shuttle tracking system predicts the position of the shuttle > orbiter with an accuracy that varies between 30 m and 100 m. Its orbital > radius is slightly larger than the radius of the Earth (average orbit > altitude is 340 km). What, approximately, is the ratio of the position error > to the size of the shuttle’s orbit? The orbiter is approximately 37 m long > and 17 high. ($R_{Earth} = 6378$ km)` Any help with this would be greatly appreciated!


If you have $N$ 1ohm resistors, how many distinct equivalent resistances can you create? Assume that only parallel and series and mixture of them is allowed and no bridging between two parallel connections is allowed.


title: Free-particle solution to Schrödinger Equation

text: The free particle solution in stationary state (with definite energy) to the Schrödinger equation is $$\psi(x,t) =Ae^{i(kx-\omega t)} + Be^{-i(kx+\omega t)}$$ Since the energy is definite, and hence the momentum is definite, the uncertainty in position must be infinite. How is this reflected by the probability distribution function: $$\Psi = |\psi(x,t)\psi^*(x,t)| $$ The book that I am using just look at the first term of the solution, and derive that the probability distribution function is $A^2$. However, I do not understand why we can do that? Does it imply that if wave function is made up of n terms such that each individual term has a constant probability distribution function, the whole wave function also has a constant probability distribution function? If so, how can I prove it? I know my question might be very vague but that is precisely the problem I am facing now, I don't even know how to ask about the things that I don't understand.


title: Uncertainty principle in Quantum mechanics

text: The Uncertainty principle says that "△x△p>h/2"; we cannot precisely obtain both position $x$ and momentum $p$ simultaneously. Is this because the uncertainty is the natural characteristic or it is because we do not know additional values? (ex. like additional 11 dimensions in superstring theory.)


title: Energy balance for beta decay of cobalt-60

text: I am confused by a simple fact about the $\beta^{-}$ decay of ${}^{60}{\rm Co}$ nucleus. According to Wikipedia, the most likely decay branch is to an excited state of ${}^{60}{\rm Ni}$, see the diagram: ![Decay scheme of Co-60](http://i.stack.imgur.com/cvidr.png) But the energy indicated on the diagram (0.31 MeV) is less than the electron rest mass (0.511 MeV)! How is that possible?


title: Observables in Quantum Mechanics

text: Studying on own quantum mechanics I came across: > **Preceeding text:** A basic postulate of quantum mechanics tells us how to > set up the operator corresponding to a given observable. Observables, > $\Omega$, are represented by operators, $\hat\Omega$, built from the > following position and momentum operators $$\hat x=x\times \;,\qquad \hat p_x=\frac {\hbar}i\frac d{dx}.$$ How are they given? I think they are been postulated, but how? Also related question is why the eigenvalue of the operator corresponding to an observable is the value of the observable?


title: Question on the preservation of information via mapping to free field states

text: In Hawking's paper, "Breakdown of predictability in gravitational collapse", the crux of Hawking's argument is as follows: > ...,one can extend the principle to treatments in which the gravitational > field is also quantized by means of Feynman sum over histories. In this one > performs an integration (with an as yet undetermined measure) over all > configurations of both matter and gravitational fields. The classical > example of black-hole event horizons shows that in this integral one has to > include metrics in which the interaction region (i.e. the region over which > the action is evaluated) is bounded, not only by the initial and final > surfaces, but by a hidden surface as well. Indeed, in any quantum > gravitational situation there is a possibility of "virtual" black holes > which arise from vacuum fluctuations and which appear out of nothing and > disappear again. One therefore has to include in the sum over histories > metrics containing transient holes, leading either to singularities or to > other space-time regions about which one has no knowledge. One therefore has > to introduce a hidden surface around each of these holes and apply the > principle of ignorance to say that all field configurations on these hidden > surfaces are equally probable provided they are compatible with conservation > of mass, angular momentum, etc... The setup for the argument he provides is to define three Hilbert spaces, $H_1$, $H_2$, $H_3$ for the initial, "hidden", and final space which contains all the data for each respective surface. He the defines a tensor $S_{ABC}$ with indices that refer to each space, with states in the each Hilbert space defined as: $$\xi_C \in H_1$$ $$\zeta_B \in H_2 $$ $$\chi_A \in H_3$$ such that: $$\sum \sum \sum S_{ABC} \chi_A \zeta_B \xi_C$$ defines the amplitude to have the initial state, final state and the hidden state on the hidden surface. The arguments is given the initial state, one is unable to determine the final state but, > only the element $\sum S_{ABC}\xi_C$ of the tensor product $H_1 \otimes > H_2$. This is the heart of the information loss problem discussed recently by Polchinksi. Here is where I have an issue. I see the vacuum as a type of black hole. So if one adds another hidden surface into the mix, it is essentially the same as mapping back to some vacuum state. The classical black hole might be distorting the path of particles from initial to final surface, but if I think of the initial and final surfaces as black hole surfaces as well, then it doesn't seem to be too much of a problem. In the most radical sense, the particles become free particles as far as the rest of the universe is concerned, so there simply isn't any way for them to interact inside the hole and decohere, so whatever information the particle is carrying is perfectly preserved to be spit out again when infalling Hawking radiation "liberates" the information during the evaporation process (e.g. perfectly preserved information of the past can now be passed back to the universe as it is once again allowed to interact with infalling particles, quantum mechanics ensures that state of the outgoing Hawking radiation will be completely consistent). Essentially, I think Hawking's insertion of a interim surface appears to be capricious fiction. I am curious as to what is wrong with this argument. UPDATE: I thought a link to Hawking's new paper is a worthwhile addendum.


title: The physics of breaking eggs

text: I have to to write an 4000 word research paper for my IB diploma in high school. It is called the extended essay. I was thinking about writing on the physics of breaking eggs. I came up with the idea that their might be some experiments I could do and find the best way to crack an egg. I'm having trouble finding sources. I think I need help with some directions I could take this topic as I find it very interesting.


title: Query into the cumulative velocity of mounted platforms

text: Consider throwing a stone at an object from rest, it travels at Vms-1. Now throw that stone whilst running at Ums-1. It seems in the latter scenario the total speed of stone is V + U. Now imagine Running at Ums-1, throwing a stone at Vms-1 whilst on a moving train with speed Wms-1 - total stone speed would be V+U+W. Let's extrapolate this to the case where you have a stack of moving platforms, the bottom platform begins to accelerate, once reaching top speed, the platform on top begins to accelerate, and so on and so forth. In a vacuum could it be theoretically possible to reach near infinite projectile velocities using these cumulative platform velocities? ![enter image description here](http://i.stack.imgur.com/G5wtQ.jpg)


title: Eigenvalue of $L_z$

text: In section 4.3 of Griffths' "Introduction to Quantum Mechanics", just below Figure 4.6, the sentence begins > _Let $\hbar \ell$ be the eigenvalue of $L_z$ at this top rung..._ Why is this valid? In the previous pages, there is no derivation of this fact. It's not surprising that this eigenvalue has $\hbar$ in it, but I don't see why I should expect it to be an integer multiple of $\hbar$.


title: Curvature of spacetime in only required to explain tidal forces?

text: I'm a bit confused about the equivalence principle in GR. I'm quoting from Wikipedia: > An observer in an accelerated reference frame must introduce what physicists > call fictitious forces to account for the acceleration experienced by > himself and objects around him. One example, the force pressing the driver > of an accelerating car into his or her seat, has already been mentioned; > another is the force you can feel pulling your arms up and out if you > attempt to spin around like a top. Einstein's master insight was that the > constant, familiar pull of the Earth's gravitational field is fundamentally > the same as these fictitious forces Later it is written: > The equivalence between gravitational and inertial effects does not > constitute a complete theory of gravity. When it comes to explaining gravity > near our own location on the Earth's surface, noting that our reference > frame is not in free fall, so that fictitious forces are to be expected, > provides a suitable explanation. But a freely falling reference frame on one > side of the Earth cannot explain why the people on the opposite side of the > Earth experience a gravitational pull in the opposite direction Here are some things I hope I understand correctly:   * A particle in free fall is in an inertial frame of reference   * Curvature of spacetime in only required in order to explain tidal forces, as long as you ignore tidal forces, you can explain gravity without curvature.   * Gravity is a fictious force experienced in a non-inertial reference frame My Questions (2 very related questions)   * 1) The statement that curvature of spacetime in only required to explain tidal forces seems weird to me. In the case that there is no curvature of spacetime, what explains gravity? I mean, if gravity is a "fictitious-force", what is the "real cause" of it? (Again this question stems from the statement that curvature is only needed to explain tidal forces, and not all of gravity). Last example from Wikipedia: > For gravitational fields, the absence or presence of tidal forces determines > whether or not the influence of gravity can be eliminated by choosing a > freely falling reference frame   * 2) If I'm in outer space and I'm freely falling towards earth, let's say I'm very small and I don't experience tidal forces, both me and earth are freely falling and thus in inertial reference frames, and yet I see the earth accelerating towards me, in my frame is it said that "gravity is eliminated"? just because I feel no tidal forces?


title: Difference b/w Kinetics & Kinematics w/concrete example

text: (I know whether I understand this or not doesn't matter much to my work & study but am just curious.) I still can't differentiate in my head kinetics and kinematics (similar thread is found but doesn't explicitly answer to my question yet What is the difference between "kinematics" and "dynamics"?). Some websites out there say (ex.) explain that force is only considered in kinematics. Does this mean for example Newton-Euler method is in kinetics and Lagrangian is in kinematics? I also prefer concrete examples in both category.


title: Can a force in an explicitly time dependent classical system be conservative?

text: > If I consider equations of motion derived from the pinciple of least action > for an _explicilty time dependend_ Lagrangian > > $$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$ > > under what circumstances (i.e. which explicit functional $t$-dependence) is > the force conservative? By force I understand here the term on the right hand side of the equation, if I shove everything to the right except the expression $mq''(t)$. * * * As a sidenote, besides the technical answer I'd be interested here in some words about the physical motivations involved. I'm somewhat unhappy with a formal $\text{curl}[F]=0$ condition, since it seems to be to easy to fulfill (namely we have to consider closed circles only at single points in time, respecively). The physical motivation behind conservative forces is the conservation of energy on closed paths, where any parametrization $q(s)$ of curves can be considered. But practically, only loops tracked in finite time are physically realizable, i.e. we would move in a circle while t changes. I guess as soon as one computes the r.h.s. for the equations of motion, one would also be able to define a more physical alternaltive to the above stated idea of conservative forces in this case. I.e. a ask-if-the-forces-integrate- to-zero-on-a-closed-loop functional for a rout between two points in time $t_1$ and $t_2$. This would be an integral where the momentarily force along the point in the path I'm taking would be taken into account. It wouldn't be path independend of course. (We could then even construct another optimization problem on its own, by asking for path with the smallest energy difference, which really would be a sensible question if friction is involved.)


title: Backward causality: A question/extension to Ma et al.'s "Experimental delayed-choice entanglement swapping"

text: In a philosophically rather interesting experiment, Ma et al. show that backward causality exists in quantum physics. An  Ars Technnica-article gives a less technical account. From Ars Technica: > Delayed-choice entanglement swapping consists of the following steps. (I use > the same names for the fictional experimenters as in the paper for > convenience, but note that they represent acts of measurement, not literal > people.) > >   * Two independent sources (labeled I and II) produce pairs photons such > that their polarization states are entangled. One photon from I goes to > Alice, while one photon from II is sent to Bob. The second photon from each > source goes to Victor. (I'm not sure why the third party is named "Victor".) > >   * Alice and Bob independently perform polarization measurements; no > communication passes between them during the experiment—they set the > orientation of their polarization filters without knowing what the other is > doing. > >   * At some time after Alice and Bob perform their measurements, Victor > makes a choice (the "delayed choice" in the name). He either allows his two > photons from I and II to travel on without doing anything, or he combines > them so that their polarization states are entangled. A final measurement > determines the polarization state of those two photons. > > > > The results of all four measurements are then compared. If Victor did not > entangle his two photons, the photons received by Alice and Bob are > uncorrelated with each other: the outcome of their measurements are > consistent with random chance. (This is the "entanglement swapping" portion > of the name.) If Victor entangled the photons, then Alice and Bob's photons > have correlated polarizations—even though they were not part of the same > system and never interacted. Now, this is rather interesting in itself. My interpretation is that the universe already "knows" whether Victor will entangle or not at the time of Alice's and Bob's measurements (since it controls Victor's random generator). This kind of avoids the paradox. The real interesting question, however, is why they haven't designed the experiment in the following way: Instead of letting Victor randomize whether to entangle, he should base his decision on the measurements of Alice and Bob: if they measured correlated polarizations, he should not entangle; if they measured uncorrelated polarizations, he should entangle. Seemingly, this would force the universe to produce correlated polarizations for Alice and Bob, despite there being no entanglement-chain connecting them. (Because, clearly, it would be contradictory if they were uncorrelated, despite there being a chain connecting them.) To me, this seems like a more interesting experiment/result. Any idea why they didn't do it this way? Update to answer @Nathaniel's comment: I don't think several measurements is necessary. Let's say that both Alice and Bob check for horizontal polarization: then if Victor decides to entangle, both Alice and Bob must get the same outcome (either fire, or don't fire). Obviously, it is not contradictory that they both get the same outcome even if there's no chain, but the experiment I'm suggesting would imply that they would _always_ get the same outcome, despite there _never_ being any chain.


title: Lunar twilight and sixth magnitude stars

text: Summary: when the Moon is x degrees below the horizon, it interferes with stargazing the same as astronomical twilight would. What is x (as a function of the Moon's phase)? We define civil, nautical, and astronomical twilight as when the sun is 0-6, 6-12, and 12-18 degrees below the horizon respectively. This corresponds roughly to what most people call twilight, the ability to distinguish a horizon at sea, and the ability to see 6th magnitude stars at the zenith. However, even when below the horizon, the Moon shines brightly enough to interfere with stargazing. What are the equivalent twilight angles for the Moon? I realize that even the full Moon overhead isn't bright enough for civil twilight, so my real interest is in astronomical twilight. Of course, this will vary greatly with the Moon's phase, and slightly with Moon's distance.


title: Orbital angular momentum of photon

text: People talk about orbital angular momentum (OAM) of photons. Is there some physical example that cannot be explained without assuming that photons have non-zero OAM? Does different photons have different values of OAM? If yes, then what determines the value of the value orbital angular momentum carried by individual photons?


title: Cause of Magnetic field

text: According to maxwell-ampere equation, the curl of magnetic field at that point equals the current density at that point + change of electric field at that point w.r.t. time. Now, the second factor i.e. change of electric field is also caused by some moving charge at some other point. $$ \nabla \times \vec B = \mu \vec J + \epsilon \mu \frac {\partial \vec E}{\partial t} $$ So is it correct to say that magnetic field are ultimately caused by currents ? ( and when the current isn't at the point where you calculated the current, you take the changing electric field factor due to that current) or can electric field be changed without reference to any charges and produce a magnetic field on its own.


title: Intuitive sketch of the correspondence of a string theory to its limiting quantum field theory

text: I'm looking for an intuitive sketch of how one shows the correspondence of string theory to a certain QFT. My best guess is that one calculates the scattering amplitudes in the string theory as a series in some parameter (string length?) and shows that the leading order term is equal to the scattering amplitudes in the corresponding QFT. If this is the case then my hope is that someone can elaborate and perhaps point me to some references. If I'm off base then my hope is that I can get a sketch and not be bogged down in heavy math (at this stage).


title: What does a unitary transformation mean in the context of an evolution equation?

text: Let be the unitary evolution operator of a quantum system be $U(t)=\exp(itH)$ for $t >0$. Then what is the meaning of the equation $$\det\bigl(I-U(t)e^{itE}\bigr)=0$$ where $E$ is a real variable?


title: How to charge an object with electricity

text: I know this is a rather basic question, but how do you charge an object? Not a battery, an object. I'm guessing it involves static electricity, but I'm not sure. Some resources I've been reading talk about charging two objects with opposing voltages, and I am trying to figure out how you do it. I think you do it with DC current, but past that, I'm not sure. Here is the paper I am talking about: http://www.avonhistory.org/school/gravitor.htm


title: Light filter for an experiment

text: I'm looking for a filter that lets through as many wavelengths as possible (from 200 to 5000 nm). Is that even possible?


title: How is acceleration computed in the leap-frog algorithm in computer simulations of particles?

text: I am reading the book _Computer Simulation of Liquids_ by Allen and Tildesley (here is another link). On page 80, the authors describe the leap-frog algorithm, which is used extensively in molecular dynamics (MD) simulations. The leap-frog algorithm is a modification to the basic Verlet algorithm. The authors state: > Modifications to the basic Verlet scheme have been proposed to tackle [the > deficiencies of the basic Verlet scheme]. One of these is a so-called half- > step 'leap-frog' scheme. The origin of the name becomes apparent when we > write the algorithm down: > > $$\textbf{r}(t + \delta t) = \textbf{r}(t) + \textbf{v}(t + \frac{1}{2} > \delta t) \delta t \; \; \; \; \textbf{(3.17a)}$$ > > $$\textbf{v}(t + \frac{1}{2} \delta t) = \textbf{v}(t - \frac{1}{2} \delta > t) + \textbf{a}(t) \delta t \; \; \; \; \textbf{(3.17b)}$$ > > The stored quantities are the current positions $\textbf{r}(t)$ and > accelerations $\textbf{a}(t)$ together with the mid-step velocities > $\textbf{v}(t - \frac{1}{2} \delta t)$. The velocity equation **(3.17b)** is > implemented first, and the velocities leap over the coordinates to give the > next mid-step values $\textbf{v}(t + \frac{1}{2} \delta t)$. During this > step, the current velocities may be calculated: > > $$\textbf{v}(t) = \frac{1}{2} \left[ \textbf{v}(t + \frac{1}{2} \delta t) + > \textbf{v}(t - \frac{1}{2} \delta t) \right] \; \; \; \; \textbf{(3.18)}$$ > > This is necessary so that the energy ($\mathcal{H} = \mathcal{K} + > \mathcal{V}$) at time $t$ can be calculated, as well as any other quantities > that require positions and velocities at the same instant. Following this, > equation **(3.17a)** is used to propel the positions once more ahead of the > velocities. After this, the new accelerations may be evaluated ready for the > next step. This is illustrated in Fig. 3.2. ![Leap-frog](http://i.stack.imgur.com/QQysm.gif) I have pasted Fig. 3.2 above; panel (b), framed in red, refers to the leap- frog algorithm. My question is, how is the acceleration computed in this algorithm? In Fig. 3.2(b), it appears that the first step (which I have personally highlighted in yellow) is to somehow compute $\textbf{a}(t)$ from $\textbf{r}(t)$. However, I do not see an equation for this. Do you know what equation the step highlighted in yellow would be? Thanks.


title: Is temperature an extensive property, like density?

text: I was thinking about it some time ago, and now that I've discovered this site I would like to ask it here because I couldn't work it out then. I know that the higher temperature the air in my room has, the more energy the molecules have. But temperature isn't energy because otherwise we'd be measuring temperature in joules, and we don't. And then temperature would depend on the number of molecules in the room, and that doesn't make any sense. So what I thought temperature had to be was the total energy that the molecules in the room have divided by something, for example the number of molecules or the volume of the room. If it was the latter, then temperature would be exactly like density, only with energy instead of mass. But in any case, I went to Wikipedia and tried to see if I could understand what they said about temperature. I didn't understand too much, but I saw that they used something called entropy to define temperature. I couldn't understand the article on entropy at all, but I think it means my thinking must have been incorrect because otherwise they would mention something simple like this in the article. Could you please explain it to me? EDIT: Here's why I thought it should be the total energy divided by the volume rather than by the number of particles: because if we divided energy by a number, it would still be energy, and we measure energy in joules, not kelvins.


title: If the earth has gravity, why don't we all collapse to the center?

text: I'm sorry if the answer is obvious for you guys, but why don't we all (including buildings, road, people, the ground) collapse to the center of the earth because of gravity? Is it because we have velocity, just like the earth not falling to the sun (or electrons not falling to the protons)? But that analogy doesn't sound right because those involve wide empty space.


title: Questions on electron orbits

text: I have three questions to ask:   1. Why do electrons (in an atom) specifically move in orbits and not some other type of motion?   2. Where does the energy comes from, for the electron to move at much higher speed, enough to create centrifugal force?   3. And when electrons enter an orbit, at which angle will it specifically enter?


title: Velocity dispersion of galaxies

text: I couldn't find on web how can I get the velocity dispersion and velocity maps of galaxies from the 3D data cube I get from integral field spectrograph.


title: Must the derivative of the wave function at infinity be zero?

text: I came across a problem in Griffiths where the derivative of the wave function (with respect to position in one dimension) evaluated at $\pm\infty$ is zero. Why is this? Is it true for any function that evaluates to zero at $\pm\infty$ or is there a special constraint on the wave function that I am forgetting?


title: Could the Periodic Table have been done using group theory?

text: These three questions are phrased as alternative-history questions, but my real intent is to understand better how well different modeling approaches fit the phenomena they are used to describe; see 1 below for more discussion of that point. Short "informed opinion" answers are fine (better, actually).   1. If Dmitri Mendeleev had had access to and a full understanding of modern group theory, could have plausibly structured the periodic table of chemistry in terms of group theory, as opposed to the simpler data-driven tabular format that he actually used?   2. If Mendeleev really had created a group-theory-based Periodic Table, would it have provided any specific insights, e.g. perhaps early insights into quantum theory?   3. The inverse question: If Murray Gell-Mann and others had not used group theory concepts such as $SU(3)$ to organize particles into families, and had instead relied on simple grouping and graphical organization methods more akin to those of Mendeleev, is there any significant chance they could have succeeded? Or less speculatively, is it possible to create useful, concise, and accurate organizational structures (presumably quark based) that fully explain the particle data of the 1970s without making _any_ reference to algebraic structures? * * * 1 Background: My perspective on the above questions is to understand the interplay between expressive power and noise in real theory structures. One way to explain that is to note that mathematical modeling of data sets has certain strong (and deep) similarities to the concept of data compression. On the positive side, a good theory and a good compression both manage to express all of the known data by using only a much smaller number of formula (characters). On the negative side, even very good compressions can go a astray by adding "artifacts," that is, details that are not in the original data, and which therefore constitute a form of noise. Similarly, theories can also add "artifacts" or details not in the original data set. The table-style periodic table and $SU(3)$ represent two extremes of representation style. The table format of the periodic table would seem to have low expressive power and low precision, whereas $SU(3)$ has high representational power and precision. The asymmetric and ultimately misleading emphasis on strangeness in the original Eight-Fold Way is an explicit example of an artifact introduced by that higher power. We now know that strangeness is just a fragment -- the first "down quark" parallel -- of the three- generations issue, and that strangeness showed up first only because it was more easily accessible by the particle accelerators of that time. * * * **2012-06-30 - Update on final answers** I have selected Luboš Motl's answer as the most persuasive with respect to the questions I asked. If you look at the link he includes, you will see that he has looked into this issue in minute detail with regards to what kind of representation works best, and why. Since that issue of "what is the most apt form of representation" was at the heart of my question, his answer is impressive. With that said, I would also recommend that anyone interested in how and to what degree group theory can be applied to interesting and unexpected complexity problems, even if only approximately, should also look closely at David Bar Moshe's fascinating answer about an entire conference that looked at whether group theory could be meaningfully applied to the chemical elements. This excellent answer points out a rich and unexpected set of historical explorations of the question. If I could, I would also flag this as an answer from a different perspective. Finally, Arnold Neumaier's answer shows how a carefully defined subset of the problem can be tractable to group theoretic methods in away that is predictive -- which to me is the single most fundamental criterion for when a model crosses over from being "just data" into becoming true theory. And again, I would flag this one as an answer if I could. Impressive insights all, and my thanks to all three of you for providing such interesting, unexpected, and deeply insightful answers!


title: Concept of relative speed

text: I am traveling on a train running at a speed of 100mph. If from the train I shoot a ball at a speed of 100mph in opposite direction then what would be the speed of the ball with respect to a person standing outside the train, ~~given that I shoot the ball as soon as the person standing out comes in parallel to my position in the train.~~


title: What is changing in latest light bulb technologies?

text: I'm confused with the latest home lightning bulbs. Understanding filament bulbs was easy. For example take 220V, 100W filament bulb: Power = $V^2/R$ Filament gets heated and emits energy in the form of light & heat. Whose sum is 100J per second. I'm getting a light energy of little less than 100J per sec. Its very clear! Now lets take latest CFL : ![enter image description here](http://7fff.com/wp- content/uploads/2008/09/cfl.jpg) How can it be equivalent to 6 filament bulbs in light and yet consume same amount of energy as a single bulb (or even less in some cases). Isn't conservation of energy getting violated here? Isn't More light implies, more light energy implies more electrical energy consumption?


title: The (co)algebra for the (co)monad of a light switch

text: If we take a light switch to embody an entire category, we could take the light switch to be a set with two elements and the morphisms are all endofunctions. Let's say, for fun, that we define the endofunctor for the monad as: > flip switch up $\rightarrow$ light turns on > > flip switch down $\rightarrow$ light turns off > > flip switch $\rightarrow$ light toggles > > do nothing to switch $\rightarrow$ light does nothing This looks like the identity endofunctor. Now, this endofunctor, in my mind, is deeply fundamental as it is used to test a causal relation between things like the light and the light-switch. The monad is nothing but the identity monad and so, I think, the algebra is nothing but an identity element. (I already asked at mathematics stack). One normally looks at this kind of thing as passing a signal from one system to another and this then goes up to information theory. If you have read my post correctly, though, you will see that I am trying to lift that whole idea up to where we talk only about morphisms and causal structure as opposed to systems of state and the information that encode them. It was a let down to find that the algebra was this trivial for such an important bit of behaviour, one that every physicist working in a lab will use every day. Can anyone take this thinking and get the first non-trivial algebra (it should be TINY!!!) and keep the spirit of "behaviours in a laboratory"? The co- algebra is also interesting. If anyone is wondering where this is coming from, consider the fact that one can construct a TQFT entirely within FDHilb by replacing the usual category of cobordisms with the internal category of comonoids. Thus, the background becomes the internal category of classical structures. The category of internal comonoids is defined with axioms that look like the copying and deleting of information. If you read this post carefully you will see that I am abstracting this idea to replace the category of internal comonoids with just comonads. To me, this then looks like an operationalist view of a topological quantum field theory.


title: If the graph isomorphism problem can't be solved in polynomial time, do spin-networks in loop quantum gravity violate the Church-Turing thesis?

text: If the graph isomorphism problem can't be solved in polynomial time, do spin- networks in loop quantum gravity violate the Church-Turing thesis? To determine whether or not two graphs are isomorphic (labelled in the case of spin networks, but this doesn't change anything essential) is conjectured to be unsolvable in polynomial time in the worst case scenario. It may or may not be solvable in polynomial time using quantum computers. To compute using spin- networks, we have to determine whether or not two components describe the same network when summing up over quantum states and computing bra-ket norms.


title: Commutator of scalar fields

text: So, in the calculation of $ D(t,r) = \left[ \phi(x) , \phi(y) \right] $, where $ t= x^0 - y^0,~ \vec{r} = \vec{x} - \vec{y} $ you need to calculate the following integral $$ D(t,r) = \frac{1}{2\pi^2 r} \int\limits_0^\infty dp \frac{ p \sin(p r) \sin \left[(p^2 + m^2)^{1/2} t \right]} { (p^2 + m^2 )^{1/2}} $$ For $m=0$, the integral is simple. We get $$ D(t,r) = \frac{1}{4\pi r} \left[ \delta(t - r) - \delta(t + r) \right] $$ I even know what the answer for $ m \neq 0 $. I have no idea how to calculate it though. Any help?


title: Is a signal traveling through fiber faster than a signal traveling through copper?

text: Does the transmission medium affect the speed of a signal? For instance does light traveling through a fiber cable get a bit from A => B faster than copper can transmit a bit the over the same distance?


title: Energy realized in fusion and electrons?

text: I was doing this question about the energy released in a fusion reaction: ![enter image description here](http://i.stack.imgur.com/Cogxc.jpg) In the mark scheme it included the mass of the electrons (for part cii) on the left and just used the mass of protons for the H. Do the H in this case not contain electrons and if so why do we not include them in the calculation but do the once on the left??


title: How does the hydrogen atom know which frequencies it can emit photons at?

text: At university, I was shown the Schrodinger Equation, and how to solve it, including in the $1/r$ potential, modelling the hydrogen atom. And it was then asserted that the differences between the eigenvalues of the operator were the permitted frequencies of emitted and absorbed photons. This calculation agrees with experimentally measured spectral lines, but why would we expect it to be true, even if we accept that the electron moves according to the Schrodinger equation? After all, there's no particular reason for an electron to be in an eigenstate. What would make people think it was anything more than a (very suggestive) coincidence?


title: How does an electron adjust itself to fit in an excited state that is completely filled?

text: According to quantum mechanics each state has a specific shape. So, how does the electron get into that shape of the orbital?


title: Capacitor charging, work done by battery on changing polarity

text: A uncharged capacitor $C$ is connected to a battery with potential $V$. It becomes fully charged and has a charge $Q=CV$ stored on it. Now the polarity of the battery is reversed. The capacitor will have the charge $Q$ still but with polarity reversed too. My question is: _What is the work done by the the battery?_ According to me, during 1st charging it will do a work of $QV$. The energy of the capacitor is also not changing, then what is the work done to change its polarity?


title: Calculating dust attraction to a charged surface

text: Even though dust particles are neutral, they tend to be attracted to a charged surface. I am guessing this is due to charge induction. Is there a way I can compute the attraction? how will it vary based on:   * **separation distance.** I think the distance will affect as inverse square law (1/r^2) [Coulomb's law]. But to calculate the force, I need to know how much charge has been induced ( how do I find that?) and does that vary due to separation distance.   * **type of dust.** Do all material act the same , or are some material gets more charge induced? ( metals, for example with more free electrons)   * **the size of dust particles.** Intuition suggests that bigger particles will be induced less, but I am not sure.


title: decoherence free subspace of a single photon

text: Take the state vector for a single photon as $\psi = \int \gamma_{\omega} | \omega \rangle \otimes (\alpha |H \rangle + \beta | V \rangle )d \omega$ $H, V, \omega$ are the horizontal polarization, vertical polarization and frequency components of the photon. We have a nice, big tensor product space of states for this photon. In particular, we have entangled single photon states! The entanglement of the single photon comes from entangling the polarization with its own frequency. Is it possible to use this effect to create decoherence free subspaces that would be useful in transmitting information within the polarization state of single photons?


title: Non-associative operators in Physics

text: Are non-associative operators (or other kind of elements) used in Physics? For example, in QM I'm looking for something like this: $A(BC)|\psi\rangle \ne (AB)C|\psi\rangle$ NOTE: I think that this question does not make much sense, in that case I will close it.


title: How do we measure meson decay constants?

text: I'm trying to understand how people actually measure decay constants that are discussed in meson decays. As a concrete example lets consider the pion decay constant. The amplitude for $\pi ^-$ decay is given by, \begin{equation} \big\langle 0 | T \exp \big[ i \int \,d^4x {\cal H} \big] | \pi ^- ( p _\pi ) \big\rangle \end{equation} To lowest order this is given by, \begin{equation} i \int \,d^4x \left\langle 0 | T W _\mu J ^\mu | \pi ^- ( p _\pi ) \right\rangle \end{equation} If we square this quantity and integrate over phase space then we will get the decay rate. On the other hand, the pion decay constant is defined through, \begin{equation} \left\langle 0 | J ^\mu | \pi ^- \right\rangle = - i f _\pi p _\pi ^\mu \end{equation} This is clearly related to the above, but it seems to me there are a couple of subtleties. In particular,   1. How do we get rid of the time-ordering symbol?   2. Since we don't have a value for $ W _\mu $ how can we go ahead and extract $f _\pi $ ?


title: Circuit analysis, calculating voltage across resistor

text: ![enter image description here](http://i.stack.imgur.com/vlpOb.jpg)![enter image description here](http://i.stack.imgur.com/SOeju.jpg) i'm solved this question, I'm sure that solution is right, but my instructor says that V1=116V, and also he said that he will not show how he get this result.Please help to identify who is right.


title: Need help in identification of formula

text: ![this equatio was just randomly given without any description ](http://i.stack.imgur.com/qlOgY.png) i would greatly appreciate it if someone could provide me with the concept to learn about this equation


title: Does a black hole have an interior or does the spacetime manifold itself end at the event horizon?

text: There have been a number of intriguing ideas over the years hinting at the possibility that a black hole might not have an inside, that it might consist of nothing but a surface and an external gravitational field. Here are some of the ideas that lead me to ask the question, in no particular order:   * Black hole firewalls---of which Raphael Bousso says: "In some sense, space and time actually end there." http://worldsciencefestival.com/videos/the_black_hole_mystery_that_keeps_physicist_raphael_bousso_up_at_night"   * According to the Cambridge astrophysicist, Professor Donald Lynden-Bell and Professor Emeritus, Joseph Katz, Racah Institute of Physics, in their paper _Gravitational field energy density for spheres and black holes_ , the total **coordinate-independent** field energy distributed in the gravitational field of a Schwarzschild black hole is mc^2. They conclude, explicitly, that **all** the mass of the black hole resides outside the event horizon. http://adsabs.harvard.edu/full/1985MNRAS.213P..21L   * The radial component of the Schwarzschild metric shows that, due to metric stretching, the energy density of space thins out and disappears at the event horizon.   * There is no ironclad rule that requires the spacetime manifold to continue past the event horizon.   * There is no way to verify (or falsify) what we think goes on inside the event horizon. These ideas, individually and collectively, point to the possibility that its surface and its external field might be all there is to a black hole. What's particularly interesting to me is that this "surface only" picture is entirely consistent with them being cutouts, or holes, in the spacetime manifold. Any thoughts would, of course, be most welcome. Update: Here's a quote from a recent, six minute NPR interview with Leonard Susskind and Joesph Polchinski. Polchinski, speaking for his research group, says :"Our hypothesis is that the inside of a black hole — it may not be there. Probably that's the end of space itself. There's no inside at all." Here's the link to the interview: http://www.npr.org/player/v2/mediaPlayer.html? action=1&t=1&islist=false&id=256897343&m=257674048 And a short article quoting from the interview: http://www.npr.org/2013/12/27/256897343/stretch-or-splat-how-a-black-hole- kills-you-matters-a-lot


title: Gauge-invariance of pole mass using Ward Identity

text: I am able to explicitly verify to one-loop order that pole masses are independent of the choice of gauge paramter. But how do I use the Ward-Identity/Taylor-Slavnov identity show that the position of the poles in Greens functions are gauge-independent to all orders? The difficulty I'm running into is in using the identities to make statements about the analytic structure of Green's functions.


title: Can we "safely" assume that quantum computing systems will be finite-dimensional?

text: This is a common assumption in the study of quantum computation to assume that the quantum systems involved are finite-dimensional, since qubits lives in the two-dimensional Hilbert space. According to Roman Gielerak and Marek Sawerwain, the quantum registers corresponding to a quantum computing machine with coherent pulses of light must have an infinite-dimensional character. I am looking for arguments for and against the hypothesis that finite- dimensional structures are sufficient to study quantum computation.


title: Elementary physics question...requires calculus?

text: A 2500.0kg car is going at a constant velocity of 14.0 m/s and hits the breaks to stop. It skids 25m. What is the coefficient of friction of the tires to the ground? So I have acceleration = -4.0 m/s^2 Normal force = 24525 N I got Fnet = -100,000 N And I don't know what to do now because normally I take the difference of Fnet between the amount of force applied and the amount of force that worked. But then what should have happened was that the brakes were hit and the car immediately stops but then distance = 0 and I can't divide by 0. So I'm probably forgetting something... Thanks


title: Acceleration in stationary spacetime

text: How would I show the acceleration vector $ a^\mu = u^\nu \bigtriangledown_\nu u^\mu = \bigtriangledown^\mu lnV $ for an observer instantaneously 'at rest,' where $u^\mu = dx^\mu/d\tau$ and $V^2 = -\xi_\mu \xi^\mu$ ($\xi^\mu$ is timelike killing vector field). I guess we're assuming that we have a stationary spacetime metric. I'm looking at Sean Carroll's Spacetime and Geometry, page 274 equation 6.15. They leave out the derivation for this. So V is the redshift factor.


title: Magnetic field distrotion

text: Does one exist, or do you think it would be possible to design a tracking magnetic field distortion detector to detect fast moving magnetic anomalies in our air space. ie; track a stealth aircraft or unidentified flying object at some distance by detecting the disturbance of the ambient magnetic fields?


title: Calculating decibel gain and loss

text: I'm doing a mobile/wireless networking subject and the physics aspect is giving me some trouble. I'm mainly confused about the conversion of dB, dBm and dBW and how to calculate the gain/loss from an input. The problem I'm trying to solve is what the resulting power (in milliwatts) is at certain points in a circuit (x and y). I've tried to describe the scenario as best I can (let me know if I need to clear anything or post a picture) In a circuit a 100mW input receives a 10 dB Gain and continues to point 'x' where it receives a 2 dB Loss. Then it receives another 2 dB Loss on the way to point 'y', where it receives another 2 db Loss. To simplify it I guess it would look something like 100mW --> +10 dB --> -2 dB --> Point 'x' --> -2 dB --> -2 dB --> Point 'y' Any help would be much appreciated, thanks in advance


title: Tower redshift paradox

text: If photons are emitted at intervals a, from the top of a tower of height $h$, down to earth, is this formula correct for the intervals b in which they are received at earth? $b=a(1-gh/c^2)$ If so, how does it not lead to a paradox, if say we wait a long time N, then at the top of the tower, N/a photons have been emitted. But a photon is received at earth every b seconds, so N/b>N/a, so eventually more photons have been received then emitted?


title: B physics and CP violation

text: So I am studying CP violation in SM. Experimentalists are trying to study B meson decays now a days. B meson systems involve quarks from the third generation and hence B physics gives more information than the Kaon system. Is there any other reason?


title: Alternative Critical Dimensions in String Theory

text: Is it possible to write down a Lagrangian for a string theory with a critical dimension different than the familiar 10 or 26? How could one find a string theory Lagrangian for a given dimension? Could you prove that no string theory exists for a given critical dimension?


title: Does the time to reach the highest point $P$ equal the time to reach the ground from $P$ in a trajectory, taking drag into account?

text: Assume a very simplified model without Corolis effect, the falloff of the local gravitational field and the like. My answer is _no_. It is sufficient to look at the vertical velocity of the projectile, because only that determines the time. The periods do not equal, because it is possible to vertically accelerate the projectile to a velocity which is greater than the terminal velocity $v_{term.}$ of the projectile in the medium. Therfore it may take longer for the projectile to come back down because it can only approach $v_{term.}$. I am not sure, though, how it behaves if the initial velocity is lower than $v_{term.}$. My guts say it behaves the same but a different explanation comes into effect. The projectile cannot reach the height which it would if there was no drag. Hence, the projectile cannot reach the initial velocity on the way back to the ground either and it takes longer.


title: Question about Hartle and Hawking's universal wavefunction?

text: My apologies in advance if this question is poorly worded or doesn't make any sense, however I have just finished reading into this theory and it seems as though Hawkings No Boundary Universe is basically emergent from a Universal Wave Function that is timeless. So no time took place before the big bang. However to the question- If the universal wavefunction is static how does a universe(or multiverse if you prefer) emerge at all? If it is static wouldn't nothing ever change?


title: Shielding RFID with aluminium foil

text: I've been playing around with some contactless bank cards and an RFID reader app on my phone. As expected, if I wrap the card in foil, the reader no longer detects it. But I was surprised to find that if I place a layer of foil on a flat surface, put the card on top of it and the phone on top of that, it also fails to detect the card. Why does placing a barrier behind the card prevent communication?


title: Is there a known equation for evolution of classical particle probability density?

text: Suppose we have some very imprecise knowledge of classical particle's coordinates and momentum: what we can only tell is the probability density to find it in some point of phase space. This is (almost?) all what is usually known by quantum state function. For quantum particle, there's an equation, which governs such initial state — it's Schrödinger equation. Is there any known equation, which would similarly govern evolution of classical particle in some external potential, given initial probability density in phase space?


title: Battery Capacity vs. Battery draw

text: Pardon my ignorance but I just can seem to find an Answer to my question and I hope that you can help me. What is the equation for calculating how long a Lithium Battery can supply a device? For instance a Lithium battery has a capacity of 5600mAh, and an Output of 5V 2A. The drawing device requires 350mA and 5Vdc. Is it as simple as dividing 350 into 5600 which would give me 16 hours of charge with optimal conditions? (This seems too easy.) or am I missing something?


title: Is Stephen Wolfram's NKS, an attempt to explain the universe with cellular automata, in conflict with Bell's Theorem?

text: Stephen Wolfram's _A New Kind of Science_ (NKS) hit the bookstores in 2002 with maximum hype. His thesis is that the laws of physics can be generated by various cellular automata--simple programs producing complexity. Occasionally (meaning rarely) I look at the NKS blog and look for any new applications. I see nothing I consider meaningful. Is anyone aware of any advances in any physics theory resulting from NKS? While CA are both interesting and fun (John Conway, Game of Life), as a theory of everything, I see problems. The generator rules are deterministic, and they are local in that each cell state depends on its immediate neighbors. So NKS is a local deterministic model of reality. Bell has shown that this cannot be. Can anyone conversant with CA comment?


title: Why does the low entropy at the big bang require an explanation? (cosmological arrow of time)

text: I have read Sean Carrol's book. I have listened to Roger Penrose talk on "Before the Big Bang". Both are offering to explain the mystery of low entropy, highly ordered state, at the Big Bang. Since the second law of thermodynamics is considered a fundamental law of nature, and since it states that in a closed system entropy either must stay the same or increase, the entropy at the time of the Big Bang must have been much lower than it is now. Also, the thermodynamic arrow was explained by Boltzmann in 1896 embodied in $S=k\ln W$ which was inscribed on his tombstone. $W$ is the number of distinct microstates of the system. It seems to me that trivially this number will be less in the past than in the future since entropy obeys the 2nd law. This determines the thermodynamic arrow of time. Why do we need more explanation of a "fundamental law"?


title: Zeolite-based oxygen concentrators

text: I wonder, what is content of output of zeolite-based pressure swing adsorption oxygen concentrators (both oxygen output, and exhaust output)? Yes, they can produce 95% oxygen. But what's the remaining 5%? Is it just argon and other noble gases, or some air contaminants could also be concentrated (like CO2, NO2, CO)? Any references to quantitative gas analysis results would be extremely useful (wasn't able to find any, probably bad google skills).


title: Effective aperture of isotropic antenna

text: I have always taken for granted that 'the aperture of a loss-less isotropic antenna is $\dfrac {\lambda^2} {4\pi}$'. On a whim, I tried to look up how this expression was derived, but so far I have not been able to find out a reference that works it out. Can someone outline the proof, or help me with any pointers to some on-line source? Hopefully this can be done using 3D vector calculus? Thanks...


title: Is this paragraph on probabilities of sub atomic partials accurate?

text: I am working on a concept for something and i want to make sure i understand something clearly before i start on everything else. Note, my project is more about the interactions of elements of complex systems rather than physics. Im just using this paragraph as an example, not doing a project on quantum mechanics. Is this paragraph accurate: The universe is built on probabilities. In the whole scope of the universe, absolute mathematics and absolute certainty do not exist. Its incorrect to say 1 + 1 = 2, the more accurate way to say it is 1 + 1 probably equals 2, but not always. It is all based on the probability that what you expect to happen, will. Its quantum probabilities that dictate that a group of sub atomic particles, at this exact moment in time, line up precisely in a certain way that allow an atom to exist. That atom lives in an environment (dictated by other probabilities) that has a calculable probability to grab onto another atom and form an object with mass. That object was hammered into a shape by a craftsman trusting that the probabilities dictating the actions of the subatomic particles allow it to not crack, or disintegrate, or break the tool. That object is now sitting on your desk holding your soft drink in the form of a can. The subatomic particles that are almost insignificantly small form a thread of interaction that leads up to that can sitting on your desk. If that thread breaks at any point, that can ceases to exist as you know it and your soda is running all over your desk. Thanks everyone, im not sure if this falls in the scope of this site, but i can't think of any other place to ask this question.


title: Casimir effect as an entropic force

text: When I first learned about the depletion interaction, my initial reaction was that it looks very similar to the Casimir effect. On making this remark to the professor, he replied somewhat mystically: "It **is** the Casimir effect." No further detail was supplied, however. Nevertheless, it really looks like both problems can be understood in terms of degrees of freedom maximising their positional entropy by reducing the volume of some "forbidden region" between two objects. For the depletion interaction, the fluctuating degrees of freedom are small particles, while in the Casimir effect, these degrees of freedom are long-wavelength modes of the free radiation field. However, a key difference is that in the first case the fluctuations arise thermally, while in the second case they are unavoidable quantum fluctuations of the vacuum. > Is it possible to derive the Casimir force between two conducting plates > from entropic considerations alone?


title: Speed of Light and Special Relativity

text: If light is travelling vertically upwards and I am travelling horizontally and perpendicular to light, the velocity of light in the vertical direction will get reduced. How does this happen? How does motion in x-direction cause a reduction in speed of light in y-direction ? Also, in Lorentz Transformation, suppose two observers measure a rod, can one of the observers see that the other person who is moving w.r.t. him, measure the rod to be less than his own measurement ? In other words, can the metre sticks of a moving observer get bigger than the observer who views the moving observer and sees himself to be at rest ?


title: Proof of Furry's theorem

text: i was wondering if anyone could give an explicit calculation or show a link that shows the proof to Furry's theorem. showing how the vacuum expectation value of any odd number of electromagnetic currents vanishes. in particular the case for n=3.


title: Relation between (super)integrability and closed orbits

text: Inspired by this recent question, I would like to understand from a more general and mathematical perspective why closed orbits are only found for the Kepler ($V(r) \sim 1/r$) or harmonic ($V(r) \sim r^2$) potential problems, as follows from Bertrand's theorem. There are two aspects that make these problems special, which I suspect may be related to the closed-orbit property. First, both problems are superintegrable. This property sits intuitively well with the idea that phase- space orbits should close "as quickly as possible", thus implying that real- space orbits close after a single revolution. Second, each problem possesses an additional "unexpected" conserved quantity, due to a larger symmetry of the problem than the obvious $O(3)$. For the Kepler problem, this is the Runge- Lenz vector, related to the $O(4)$ symmetry of the Hamiltonian. Meanwhile, the harmonic oscillator Hamiltonian conserves the Fradkin tensor: $$ F_{ij} = \frac{p_i p_j}{m\omega^2} + m\omega^2 q_i q_j, $$ which is related to an $SU(3)$ symmetry. In fact these symmetries and corresponding conserved quantities exist for _any_ central field problem (D. M. Fradkin, Prog. Theor. Phys. **37** (1967), p.798). However the conserved quantities only take a "nice" form for the Kepler and harmonic problems, which also allows the corresponding quantum problems to be diagonalised exactly by symmetry arguments alone. These considerations motivate the following question: > What specific physical/mathematical feature(s) do these two problems share > that gives them the property of closed orbits? Does this feature bear > relevance to the quantum counterpart?


title: Water level rise due to body in water

text: I recently came across a comment that when we push a rubber ball into water filled in a bucket, the water level rises because of the force applied by our hand (i.e. the more force we apply, the more water rises). But I do believe it's absurd, water rise occurs as a function of volume (of our hand). If water level rose with force applied, that would mean that if I moved my fingers in water, giving force to the body, without changing the immersed hand volume, then a water rise would occur. Isn't that creation of water from water?


title: A question on the property of proton and neutron?

text: The NOVA show on the string theory have mention once that the proton and neutron will be disappear in finite amount of time, then reappearing on somewhere else. Is there any experiment have shown that this is true?


title: Scalar two loop diagram in $\varphi^4$ theory

text: Could someone explain how, or at least show me a link that explicitly shows the calculation of a two-loop corrections to scalar’s two-point function in $\varphi^4$ theory in the massless limit.


title: Can we create invisible things?

text: We are able to see this beautiful world because of light. When light gets reflected from the object, the reflected light enters our eye retina and thus we are able see that particular object from which light was reflected from. In our daily life, we see certain things which are transparent, they appear transparent because most of the light is refracted instead of getting reflected. So, there will be only very less reflected rays which enters our eye and thus enables see up to certain extent. Suppose we have mirror or any other matter which is perfectly transparent, i.e it reflects no light incident on it. If this happens, we will not be able to see that particular object! So, if this is a possibility we can create invisible things like invisible robot, etc from those perfectly reflecting matter (like ideal transparent glass). Is this really possible? If yes what kind of things would be better to create in invisible form, like one may show their idea by displaying their model (ex. spy robot). Every one can give their idea, so that there will be value of saying why this site is for scientists. I don't know whether I have misunderstood anywhere, if so pardon me and explain.


title: What is the missing proportionality constant in the magnetic levitation formula?

text: The formula for magnetic levitation is $$ B \frac{dB}{dz} = \frac{ \rho g }{\chi} $$ but as always, I have a hard time figuring the units in SI. The left hand side is $\mathrm{T^2 /m}$, while $\chi$ has units of $\mathrm{m^3\,mol^{-1}}$, which makes the right hand side with units of.. $$\mathrm{kg\,m^{-5}\,s^{-2}\,(mol)}$$ Obviously there must be some constant, but I don't know what is it, as all texts use this natural unit system. Help? **Update:** using the permeability of free space as reported by Wikipedia, which seems to be Tesla-meter per Ampere, leaves the right hand side as $$\mathrm{kg\,T\,m^{-4}\,s^{-2}\,Ampere\,mol}$$ still far from being recognizable to the left side


title: Is emission/absorption of a photon lossy?

text: I recall vaguely that energy is absorbed/radiated in packets called quanta. Quanta were what are now known as photons. What I'm curious about - Is absorption/radiation vis-a-vis photon lossy? Do the total number of photons exactly match the energy acquired/released?


title: Theorem or Conjecture?

text: I understand the definitions "theorem" and "conjecture" in mathematics, but I wasn't sure for physics. I mean, if it's _proved_ mathematically, it's a theorem, otherwise it's a conjecture. But for physics (i.e. when the idea is meant to correspond to a physical reality - and - can only said to 'true' if tested experimentally), how does one make a distinction?


title: Problem understanding the capillary action equation

text: As you know the equation of capillary action id given by: > $h=\dfrac{2\gamma\cos\theta}{\rho gr}$ > > Where: > > $h$ is the height the liquid is lifted, > > $\gamma$ is the liquid-air surface tension, > > $\rho$ is the density of the liquid, > > $r$ is the radius of the capillary, > > $g$ is the acceleration due to gravity, > > $\theta$ is the angle of contact described above. > > Capillary action equation So my problem is I don't know what is the meant by $h$ the height the liquid is lifted? Picture 1 or picture 2? Picture 1: ![Picture 1](http://i.stack.imgur.com/46fCl.jpg) Picture 2: ![Picture 2](http://i.stack.imgur.com/7kdqU.jpg)


title: Why doesn't hydrostatic pressure glue objects to the seafloor?

text: Consider a cement block of the same density as sea-water resting on the (perfectly polished) seafloor. I also assume the side-faces of the cement block are highly polished, so that no vertical hydrostatic forces can attack on them. A cable is attached to the top of the block. My question ist: How much force must one apply to the cable before the cement block begins to lift off the seafloor? The normal response would be to say that only a negligible force is needed - as the block is practically suspended in the water. However, as the bottom surface of the cement block is not in contact with the water, it is NOT experiencing the hydrostatic pressure from below - only from above. Before the crane starts lifting, the (zero-sum) forces on the cement block are: $$F_{Seawater Pressure} +F_{Gravity on Cement Block} - F_{Seafloor Resistance} = 0$$ as the crane starts applying Force, the Seafloor will reduce its Resistance in the same measure, leaving the forces on the cement block zero: $$F_{Seawater Pressure} +F_{Gravity on Cement Block} - (F_{Seafloor Resistance}+F_{Crane}) = 0$$ Just before the Cement block lifts, the Seafloor will stop applying Force and the Crane will be applying the only upward Force: $$F_{Crane} = F_{Seawater Pressure} +F_{Gravity on Cement Block}$$ Once the Cement block lifts off the sea-floor, hydrostatic pressure kicks in on the lower cement surface, suspending the block, but before that - boy does it take a lot of force to lift it! What is wrong with this reasoning? ![Hauling up a Cement block from the sea- floor](http://i.stack.imgur.com/Ny5U8.jpg)


title: Kerr Metric in Orthogonal form

text: I've seen the Kerr metric usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any coordinates which express the Kerr metric in an orthogonal fashion. Is there ANY choice of coordinates that eliminates all cross terms/off-diagonal terms for the Kerr metric? If not, is it just a fact that you can never find such a coordinate transformation because of the inherent geometry of the Kerr space-time?


title: Fulvio Melia's linear Universe

text: ![Universe](http://i.stack.imgur.com/qay6o.jpg) I would be interested in what people think of Fulvio Melia's argument for a linearly expanding Universe. I realize that the experimental evidence seems to be pointing to an accelerating Universe but does Melia's argument have any merit? This is my version of his argument. Imagine that we are at point $P$ in a homogeneous, isotropic Universe. Point $P$ is on the surface of sphere $S_1$. Therefore, in Newtonian terms, there is an acceleration $g_1$ at point $P$ directed towards the center of sphere $S_1$ with magnitude: $$g_1 = \frac{G\ M_1}{R_1^2}.$$ But point $P$ is also on the surface of sphere $S_2$. Therefore one can construct another argument, independently of the previous one, that there is an acceleration $g_2$ at point $P$ directed towards the center of sphere $S_2$ with magnitude: $$g_2 = \frac{G\ M_2}{R_2^2}.$$ However since the Universe is homogeneous and isotropic then, again in Newtonian terms, there should not be any net acceleration vector at any point. How do we resolve this paradox? Either the Universe is empty so that $g_1 = g_2 = M_1 = M_2 = 0$ or General Relativity gives us another solution. In GR pressure also has "weight" so that the gravitational acceleration $g$ at the surface of a uniform density sphere of mass $M$ and radius $R$ with density $\rho$ and internal pressure $p$ is given not by: $$g = \frac{G\ M}{R^2} = \frac{4\ \pi}{3}G \rho R$$ but rather by: $$g = \frac{4\ \pi}{3}G (\rho + 3 p/c^2)R.$$ Thus if for symmetry reasons we require $g$ to be zero for all spheres touching point $P$ then we must have the equation of state: $$p = -\frac{\rho c^2}{3}.$$ When substituted into the Friedmann equations (without cosmological constant) this equation of state implies that $\ddot{a}=0$, where $a$ is the scale factor, so that the Universe can only be expanding linearly with time.


title: X-Ray crystallography using Bragg's Law

text: I was looking up X-Ray crystallography using Bragg's Law: $2d\sin\theta = n\lambda$ and I can understand the values of everything except this integer value $n$. As far as my research got $n$ is used to describe the atom spacing in the crystal lattice, but I don't understand how you'd express $n$ or how it would describe it. Could someone please explain this to me please? Note: diagrams tend to be very useful in developing my understanding and if anyone has any reference to a video that might help as well. Thanks.


title: Penetration of a bullet into a wall

text: ![Physics doubt](http://i.stack.imgur.com/xtzJm.png) In which of the following situation will the bullet of the pistol penetrate deeper in the wall? Why? Alternatively will the penetration in both cases be the same? Can you explain the concepts behind this?


title: Why does product of Moduli and Diff x Weyl Variation vanish?

text: According to equation 5.2.5 in Polchinski :- $$\int d^2 \sigma~ \delta^{'}g_{ab} \times [-2(P_1 \delta \sigma)_{ab} +(2\delta w - \Delta \cdot \delta \sigma)g^{ab}]=0$$ The assumption here is that " Moduli correspond to variation $\delta^{'}g_{ab}$ of the metric that are orthogonal to all variations of DiffxWeyl type given by the quantity in []" My question is that why are we imposing that orthogonality ? How can variation in the metric due to moduli be orthogonal to variation due to other Diff x Weyl ?


title: Why does this flashlight lens have this shape?

text: I pulled apart a flashlight and found a similar lens as the one shown below. ![enter image description here](http://i.stack.imgur.com/k4Vhh.jpg) I assume that the light starts off as a “point source” somewhere inside and the curvature and/or shape of the “lens” makes parallel wavefronts (or rays) exit the flashlight in a somewhat collimated beam. Is this approximating correct? Almost all of the websites really didn’t give any detailed information or was unclear that I found. I would love for someone to explain this in more detail if possible.


title: How to use The Schwarzchild Metric formula to get distribution representing "free-fall"

text: Given formula: ![enter image description here](http://i.stack.imgur.com/JsywY.png) How I can use to calculate distribution of points in space, so if i choose path which contains most of the points I get path that close to "free-fall path". As far as I know i should use square root of Determinant of given formula to do this, but i am not sure. Please, be gentle, I am computer scientist student that in process writing black hole simulation for academic purposes. NOTE: Simulation is in 2D. so some parameters may be irrelevant.


title: Are holograms like in this video possible?

text: http://www.youtube.com/watch?feature=player_detailpage&v=jfySIeS1XZE#t=118s If so, how are they created (roughly speaking). Earlier in the video he says that a laser scanned the surface of the object, which suggests that no physical object needs to be present at the time of viewing the hologram, like what is required for a Mirage toy (seen here: http://www.youtube.com/watch?v=lFqlQiTTHRs). Is this right? I am aware that this is a fictional show, so what they are saying should not be taken too seriously and the hologram effect could be added by CG effects, but I am interested in the actual workings of this type of hologram (as opposed to a "flat" hologram).


title: Constructive vs Algebraic Quantum Field Theory

text: I am interested to know how the (non)existence theorems of constructive QFT and algebraic QFT are related (or not). I have only a weak grasp of either, so I'm looking for something like a quick overview. Here's how I understand things: Constructive QFT has shown that quantum fields can be well-defined in $d$ < 4, by showing that the distributions and interactions exist in that case. Apparently there are specific examples, but this is an existence result for 1) techniques coming from analysis, 2) $d$ < 4, and 3) interactions are included. Algebraic QFT comes from looking at the canonical commutation relations on spacetime, and has shown that a single Hilbert space cannot represent both the interacting and non-interaction picture (I think this is one statement of Haag's theorem). So this is a non-existence result 1) based on the algebra of CCR and 2) includes interactions (apparently a way out is to assume periodic boundary conditions - I'm not overly interested in that part). So several specific questions - can I think of these as a Lagrangian vs Hamiltonian picture? What do these two results mean to each other - are they even related at all since they are essentially QFT in different dimensions? References with reviews of these theories would be nice - I've checked out Haag's book enough to know that if I spent time I could probably understand it, but I'd rather good review articles if anyone knows of any.


title: Notation in Quantum Mechanics

text: When we write equations in QM, in certain places, the wave function is represented as $\psi(x,t)$, which is the wave function in position space, and in some other places, it is written as $\Psi(t)$. What is the difference between the two?


title: Is our universe an emulation?

text: I was watching one of Neil Degrasse Tyson talks and there was a scientist (can't recall his name sorry) who was talking about a recent discovery: > _"Doubly-even self-dual linear binary error-correcting block code" has been > discovered embedded within the equations of superstring theory._ Is this for real? Does it imply that our universe just a sophisticated emulation running on some supercomputer? EDIT: Would it be possible to set up an experiment that would be able to test this hypothesis? I am thinking about World of Warcraft, for example, how would an elf in WoW test if his world is an emulation or not? Is it even possible?


title: Variations of S-matrix functional and Feynman diagrams in Weinberg QFT

text: Weinberg on p. 287 of his QFT vol. 1 introduces the extended interaction operator: $$ \tag 1 \hat{V}(t) \to \hat{V}(t) + \sum_{a}\int d^{3}\mathbf x \hat{o}_{a}(\mathbf x ,t)\varepsilon_{a}(x). $$   Here $$ \hat{S} = \hat{T}e^{i\int \hat{V}(t)dt}, \quad \hat{o}_{a}(\mathbf x, t) = e^{i\hat{H}_{0}t}\hat{o}_{a}(\mathbf x , 0)e^{-i\hat{H}_{0}t}. $$ Then he says that S-matrix arbitrary element $S_{\beta \alpha} = \langle \beta | \hat{S}| \alpha \rangle$ after extension $(1)$ becomes the $\varepsilon $-functional, and after that he introduces generalized Feynman rules by adding new vertexes corresponding to $\hat{o}_{a}$ with $n_{a}$ lines (the number $n_{a}$ coincides with the number of fields in $\hat{o}_{a}$) and c-factor $\varepsilon_{a}$. After that he introduces variational derivative $$ \tag 2 \left( \frac{\delta^{r}S_{\beta \alpha}}{\delta \varepsilon_{a_{1}}(x_{1})...\delta \varepsilon_{a_{r}}(x_{r})}\right)_{\varepsilon = 0} = (i)^{r}\langle \beta | \hat{T}\left(e^{i\int \hat{V}(t)dt} \hat{o}_{a_{1}}(x_{1})...\hat{o}_{a_{r}}(x_{r})\right)|\alpha\rangle $$ and notices that all $n_{a_{1}}, ..., n_{a_{r}}$ lines correspond to $\hat{o}_{a_{1}},...,\hat{o}_{a_{r}}$ respectively are internal, i.e. in case when $n_{a_{1}} = ... = n_{a_{r}} = 1$ they are compared to the propagators. Finally, he says, that if we want to get Feynman diagram with $r$ external lines with types $a_{1},...,a_{r}$ in momentum representation we need to do following with $(2)$: 1) to throw out of propagators $D_{a_{1}a_{r}}(x_{1} - x_{r})$, 2) to apply the Fourier transformation, 3) to add corresponding coefficient functions $u_{a_{1}},...$. Here is the question: сould you make the sense of introduction of mechanism 1)-3) clearer for me? Why do we need additional $r$ external lines which with corresponding vertexes which aren't connected to other vertexes (so the diagram is non-connected), as I think? I need to rephrase the question. I know that n-point Green functions $\langle \beta | \hat{T}\left(\hat{o}^{H}_{a_{1}}(x_{1})...\right)|\alpha \rangle$ where the operators are in Heisenberg picture are equal to $(2)$. Also these functions are widely used for derivation of some non-perturbative results for scattering processes. But I don't understand how to apply these non- perturbative results for S-matrix, because we need to set $r$ to zero for obtaining the exact sets of Feynman amplitudes $S_{\beta \alpha}$, but I'm not sure that it is possible without loss of nonperturbative results. Here is some incorrect understanding of Weinberg method, so it will be very good if someone help me.


title: Longitudinal waves in a large (infinite) solid block

text: Specifically, I am trying to roughly determine the sound produced by a ball when it hits the floor and bounces. If the ball exerts a pressure onto the floor, then certainly this pressure will go on to create a sound wave in the floor (infinite block) and the air. I was just wondering if there is any way to find the sound wave (or the energy of the sound wave) released by the ball, thus finding the energy lost and the ball's approximate rebound height. Is the velocity of the sound wave given as follows?: ![](http://i.stack.imgur.com/r3bgq.gif) or is it more complicated than the basic equations provided in most physics textbooks?


title: How can one diagonalize the second variation of action?

text: Suppose we have action $S[q]$ and its stationary path $q_s$, I want to find the orthonormal paths $\psi_n$ that can diagonalize the second variation of the action $S[q]$. How to do that? Thanks


title: Will my car consume more if I plug in my laptop?

text: I drive a Volvo v40 with a 110hp diesel engine. It usually use 4.6L/100km. If I plug my laptop which is 85W, will this change the fuel need? If so, by how much?


title: Which is the biggest object which can interfere with itself?

text: I've heard that scientist proof that viruses of the Tobacco mosaic virus could interfere with themselves. I'm referring to quantum interference-- the same as photons. Unfortunately, I couldn't find any material on this problem on the Internet , so I don't know if it's true. Viruses have a width between 20nm and 1000nm, so they should be applied to mesoscopic physics, where that phenomenon is possible. Is there proof that some species of virus can interfere with themselves? If not, which is the biggest object where we may observe that interference?


title: Can anyone explain to me why light is not dispersed into a spectrum through a parallel glass slide, but only through a prism?

text: The question pretty much sums up what I need to know. Why is it that light only gets dispersed into a spectrum when travelling through two non-parallel sides(like a prism) and not through something like a glass slide with parallel slides. And how does this experiment(an experiment conducted by Newton) explain this? Because this is what is in my school textbook. Newton's Two Prism Experiment


title: shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula

text: shouldn't be the quantization formula (in one dimension) equal to $ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ?? where the Oscillating term is just the correction from Gutzwiller trace formula or a sum over Orbits why is just the oscillating term ignored ..


title: Potential of surface charge

text: I have a question about the $ \hat{n} $ in this formula $\sigma = P \dot{}\hat{n}$. Why do sometime in my book they get $\sigma = P \cos{\theta}$ for a sphere. Isn't $\hat{n} = r$ ? And then in another problem, where $P = \cfrac{k}{r}\hat{r}$ and r = a (inner) and r = b (outer) they get $\sigma =\cfrac{k}{a}$ and $\sigma =\cfrac{k}{b}$. $\sigma$ = surface charge density $P$ = polarization


title: Validity of the holographic principle

text: Is the holographic principle applicable everywhere, e.g. is it possible to learn everything about any whatsoever volume of space everywhere in the universe from the boundary of it or does it have to be bounded by some special feature like an event horison? And do the same thing always apply in the reverse direction too, from the perspective of investigating from inside the same volume? Do these questions depend on the nature of space(time), it for example being de sitter one place or the other. The question is intented as a generalization of Holographic principle "inside-out view"


title: How to find the angle of elevation and launch speed?

text: A particle is projected from a point on level ground with a speed of $u$ meters per second and an angle of elevation $\theta$. The maximum height reached by the particle is $42$ meters above the ground and the particle hits the ground $196$ meters from its point of projection. Find the values of $\theta$ and $u$.


title: Simulating electrical sublimation of aluminium foil

text: When i apply high voltage (through a capacitor bank) across an aluminium foil, it gets converted into plasma. I want to simulate this process and study the properties of the plasma produced henceforth. I would then like to change my experimental parameter and see if my simulation predicts the correct output. How do i proceed to do so? I am an absolute beginner in plasma physics.


title: Can light travel slower than the maximum?

text: First of all, I know that light does indeed travel slower in a medium like air or water, but that's because the photons are bouncing off of the medium's particles and in different directions so the light beam as a whole is slowed down (or at least that's the classical explanation I've read somewhere). But my question is about light traveling freely in the vacuum.   What if an astronaut during a spacewalk switches on a flashlight towards the opposite direction he is moving. Will that light travel slower than normal? If not, is there another way to make light move slower?   For example, can you make a beam of light move so slow that you can visually perceive it being affected by gravity?


title: Four vector manipulation

text: I have started doing _Relativistic Quantum Mechanics_ from _Greiner_. I'm having difficulty understanding the following derivation for commutation relations (page 4): $$[\hat{p}^\mu, x^\nu] = i\hbar[\frac{\partial}{\partial{x_\mu}},g^{\nu \sigma}x_\sigma]=$$ $$= i\hbar g^{\nu \sigma}\frac{\partial x_\sigma}{\partial x_\mu}=$$ now this is the part I don't understand, how did we got from last equation to next one: $$=i\hbar g^{\nu \sigma}\delta^{\mu}_\sigma$$ Why is: $$ \frac{\partial x_\sigma}{\partial x_\mu}= \delta^{\mu}_\sigma$$ where $$\delta^{\mu}_\nu = g^{\mu \sigma}g_{\sigma \nu}$$


title: Studying Quantum Electrodynamics?

text: As an electrical/computer engineer, I already have a relatively thorough understanding of classical electromagnetism. From what I understand though, classical EM is only an approximation to quantum electrodynamics. I'm very curious about how it all _really_ works though. So as an ECE engineer, what would be the best way to approach quantum electrodynamics? (assuming taking a course at a community college is not an option)