title: Non-existence of gluon singlets: Any recent theoretical progress?

text: An unanswered question from last year (2012) on gluon singlets asked whether there is any theoretical explanation for the experimental absence of the ninth or colorless (singlet) gluon. This is the gluon that, if it existed, would give allow the strong force to extend far beyond the range of atomic nuclei, with catastrophic results. (Non-experts can find an explanation of the singlet gluon in the Addendum below.) Qmechanic partially answered the question with a link to this 1996 paper by J.J. Lodder, which proposed that the singlet gluon exists but is so massive that its effects are negligible. However, Lubber's massive-singlet idea seems to have gone nowhere. On an cursory search I could not find any references to the 1996 draft, even though it was written seventeen years. I also do not find Ludder's approach very plausible. Theoretically he had to do a bit of mayhem to Standard Model symmetries to come up with his model. More importantly, though, its seems unlikely that the idea holds water experimentally. The mass of the singlet gluon would have to be astronomical indeed for it not to have shown up in high-energy experimental results, especially in the post-Higgs era. So, my version of the singlet question is this: Do there exist any plausible, Standard Model compatible theories for the observed absence of the singlet gluon, other than the apparently non-starter idea that the singlet exists but is very massive? Or alternatively, have searches for the Higgs boson produced any evidence that the singlet gluon state may in fact exist and have a very large mass? * * * **Addendum for non-experts: What is a "gluon singlet" and why is it important?** One way to understand the "colorless" gluon singlet is through an analogy with how photons work for the electric force. Photons interact with electrically charged electrons, but do not carry any electric charge themselves. Because they have no charge, even low-energy photons can easily escape an atom or electron and travel infinite distances. Imagine, however, what would happen if photons did carry electric charge. Such photons would have the same energetic difficulties leaving a neutral atom as an electron, dramatically altering and limiting how they behave. (I should probably mention that electrically-charged photons in one sense really do exist: They are more-or-less the $W^\pm$ particles of electroweak theory.) Curiously, the charged situation is reversed for the otherwise photon-like gluons. It is the gluons that convey the strong force, and thereby hold quarks together to form protons and neutrons, as well as secondarily binding protons and neutrons together within atomic nuclei. There are eight types of gluons instead of just one, due to there being more than two types of charge in the strong force. However, in sharp contrast to photons, all of the eight gluons _normally_ carry strong (color) charge. The color charges of gluons cause them to interact strongly with the quarks that emit them and with each other. As in the earlier hypothetical example of how electrical charges would dramatically limit the range of photons, the presence of color charges on gluons similarly limits the distances over gluons can convey the strong force. Consequently, the strong force has almost no impact beyond the scale of atomic nuclei. However, the same mathematical model that predicts the eight color-charged gluons also predicts a ninth neutral or strong-charge-free gluon, called the singlet gluon, that has never been seen experimentally. Its lack of color would make its impact far greater than that of any of the eight other gluons. In particular, just as charge-free photons can carry the electric force far beyond the range of atoms, a charge-free gluon, if it existed, would allow the strong force to extend far beyond the range of nuclei. The repercussions would be huge. In fact, the non-existence of the singlet gluon is best demonstrated by the fact that we exist at all. My best guess (only that, since I have not seen any papers on it) is that if the colorless singlet quark really did exist, every clump of two or more atoms in the universe would melt together into an amorphous sea of quarks. Even if that is not correct, I assure you it that the consequences of the existence of singlet gluons would be... very bad indeed! That is also why I find I think the non-existence of the singlet gluon is a truly interesting question, one that probably deserves more theoretical attention than it has received over the decades since strong force theory was first codified.


title: What's the difference between 'least count' and 'smallest division'?

text: I'm wondering the difference between the 'least count' and the 'smallest division' of an instrument. Can you explain that for me, plz?


title: Lightcone singularity of a 3 point function in CFT

text: I had a quick question regarding the title of the question. In e.g. 2D CFT (for simplicity), the three point function of three operators with conformal dimension $a$, $b$ and $c$ are given as $$ \langle\mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\mathcal{O}_3(x_3)\rangle~=~\frac{c_{123}}{(x_1-x_2)^{a+b-c}(x_2-x_3)^{-a+b+c}(x_1-x_3)^{a-b+c}} $$ Now, I will expect that this correlator shows UV divergences when any two of these operators are coincident. But from the RHS, it seems that e.g. for $c>a+b$, there's no light cone singularity for $x_1=x_2$. What am I missing here?


title: Dealing with environment in a CHSH game

text: I am reading arxiv:1209.0448. I understand that my questions could be highly trivial. I would appreciate if anyone helps me to resolve my confusions. In a CHSH game, Alice and Bob cannot have classical communication channel between them. According to the case of the second paragraph of page 6, Eve chooses to stop playing with either Alice or Bob selectively without notifying the other party. Let us consider the case when Alice has stopped while Bob is still playing. I am confused whether 'not having a classical communication channel with Alice' also includes 'not having access to the environment Alice is in'. Because, if Alice receives the input it will change the entropy of Alice's system which eventually effects the entropy of Alice's environment. If Bob cannot communicate with Alice but has access to the environment where Alice is in, he may try to analyze the thermodynamic footprint and guess what is going on. I understand that ideally Alice and Bob can be in two isolated environments but in real life it is not feasible, right?


title: a metal bar on a pair of conducting rails that carries a current

text: This is a homework question, and I solved it already, but something bugs me. So the problem is stated as following: A metal bar of mass M sits on a pair of long horizontal conducting rails separated by a distance $\mathcal{l}$ and connected to a device that supplies a constant I to the circuit, also the bar has length l. There is a constant magnetic field $\vec{B}$ that points into the screen where this whole setup is. The current is following in clockwise direction. Now if there is no friction on the rail, the bar will move to the right because of $$F = I\vec{L} \times \vec{B}$$ This is easy. And since there is no friction, the acceleration will be $$a = \dfrac{F}{M}$$ and hence the magnitude of the velocity at any later time $t$ will be $$v(t) = at = \dfrac{IlB}{M}t$$ The question is asking for the velocity at time $t$. However, what bugs me is that since the bar is moving to the right, thus the flux through the closed loop of the powersource, rails and the bar will be increasing, which means that there will be an induced electric potential trying to push back the current `I`. However, the problem does not give the resistance of the bar, and I assume that in this hypothetical situation, the whole thing has 0 resistance. So how does the electric potential make sense in this case? Since I am not given a resistance, I cannot calculate the "pushing back" current caused by the change in flux. Thank you!


title: General Relativity Equivalence

text: Is Einsteins Equivalence theorem in General Relativity correct? It seems to me that it neglects the fact that gravitational acceleration depends upon separation distance squared, thus neglecting the effect of tidal forces. For example, as I sit on earth, I experience the affect of earth's gravity; Although the acceleration on my head is slightly less than the acceleration acting on my feet. If I make the claim that my frame is equivalent to me being in a space ship traveling at `g`, doesn't that mean my whole body is accelerating at `g` uniformly? This is contrary to the previous statement though.


title: Carbon in the form of graphite a conductor?

text: Well, it happens a I have a glucose test strip (One Touch Ultra) which has three electrodes (Counter, Working and Reference) and I'm guessing this electrodes are made from graphite mixed with a binder. If graphite is a conductor why the continuity tester registers there is no conduction?


title: Parallel Transport of a 4-vector

text: ![enter image description here](http://i.stack.imgur.com/aEqXf.jpg) Why does the parallel transported $4$-vector change from $X^a(x)$ to $X^a(x) + \bar{\delta}X^a(x)$ ? This is also discussed in D'Inverno's relativity book [page - 72]; but the reason is not clear.


title: Quark Radius Upper Bound

text: If quarks had internal structure (contradicting current beliefs), what is the lowest upper bound on their "radius" based on current experimental results? If possible, I'd prefer to only consider experiments which probe protons and neutrons (not other shorter-lived particles since their interpretations get biased more by the standard model). My only understanding is that this radius must be less than roughly 0.2 fm since spacings are found to be 2 fm in high-energy proton scattering experiments. I imagine "higher-energy scattering experiments" and "excited angular momentum experiments" have probed this further, but am not familiar with any other results. Or, is there some other reason why this radius must be zero? Honestly, with the surprise of quarks 10,000x smaller than the electron cloud, it wouldn't be surprising if we found some internal structure after another 10,000x zoom.


title: Phase space appellation

text: Does anyone know why they called the momentum-position space the phase space in the first place? To clarify what I mean a bit more, I'll give you an example: The name configuration space for the position space makes perfect sense to me as it represents the configuration of individual particles of a system. But what type of phase does the phase space represent?


title: Modulus of action-reaction forces

text: I read somewhere that action-reaction forces satisfy the form $$ \mathbf{F}_{12}=-\mathbf{F}_{21}=f(|P_1-P_2|)(P_1-P_2) $$ meaning that the modulus can only depend on the distance between the two points $P_1$ and $P_2$. Is that right?   Cannot the modulus depend on, say, $|\mathbf{v}_1-\mathbf{v}_2|$?


title: SU(N) symmetry and its representations

text: If a Lagrangian containing an N-multiplet of fields is invariant under global $\mathbf{SU}(N)$ transformations, does that necessarily imply it is invariant under $\mathbf{SU}(N-1)$, $\mathbf{SU}(N-2)$,... all the way down to $\mathbf{U}(1)$ as well, where the representations in each case are $N$x$N$ matrices? Also, given a symmetry group $\mathbf{SU}(N)$, do representations involving $M$x$M$ matrices exist for all $M \geq N$?


title: Is the quantum state or information of a particle is all that differentiates it from another particle?

text: So I have learned in my QM classes that you can't tell one electron from another electron. They are indistinguishable. I also learned that the wavefunction of a particle includes the spacial part and the spin part. (There might be other parts I don't know! Please don't fault me for not knowing.) I have also learned that it is possible to use the quantum teleportation protocol to retrieve exactly, 100%, the spin state of one particle in another particle after particular measurements. http://en.wikipedia.org/wiki/Quantum_teleportation My question is, if you can teleport the spatial state and the spin state and whatever other state left there is that describes the particle, then wouldn't you be **effectively teleporting the original particle?** A sub question directly related to this is; Is matter/particles just a changeable glob of stuff that acts differently, thus being a different particle, depending upon what quantum state its in? (This kinda sounds like string theory to me... Oh no!!) Also, what's never answered is, **What state does the original particle assume when its state is teleported to the new particle?** Does the two particles, the original particle and the particle retrieving the quantum information, switch states?


title: Forces in a Pendulum

text: ![pendulum](http://i.stack.imgur.com/2RWJU.gif) Help me visualise the forces found in a pendulum. I know weight can be decomposed into $F_x$ and $F_y$. Centripetal force, acceleration and velocity are three words that I'm confused. Centripetal force is in L and is equal to acceleration ? it's the gravity that move the pendulum, the weight, but there is a rope, so it's not the same situation that happens to a satellite.


title: How is the observable universe mapped?

text: As I was looking at how big earth was relative to everything else in the universe, this picture boggles my mind. http://en.wikipedia.org/wiki/Observable_Universe#Horizons We're like the size of an atom relative to earth in relation to the universe. Is this picture just an interpretation or is it how things really are? How is it possible to map things like this? Up to the Solar Interstellar Neighborhood seems understandable to me. Then it shows that this neighborhood is only a tiny tiny little dot in the Milk Way in this specific location relative to the other little dots. Then it shows our galactic group part of the local galactic group, to the Virgo Supercluster, to the Local Superclusters, etc.


title: Condensate fraction and momentum distribution in cold atom experiments

text: In ultrcold atom experiments, people usually use time-of-flight technique to measure the momentum distribution, then get the condensate fraction information from the interference pattern. What is the exact relationship between the momentum distribution and the condensate fraction? How to exactly measure the condensate fraction in optical lattice experiments?


title: Transmission Line above infinite plane connected by impedance line - Is my drawing correct?

text: Okay, I was doing a question on transmission lines. The setup is a wire placed at distance $d$ above an infinite conducting plane. The impedance of such a line is $Z_0$. Then there is an impedance $Z$ connecting the wire and the plane. For a wave propagating along the line above, I'm supposed to find the impedance of $Z$ that gives maximum transmission. I got an answer of $Z = \sqrt Z_0$ which looks familiar when a $\frac{\lambda}{4}$ line is placed inbetween - I'm not sure if this is the same as that setup. Here's what I think the setup is: ![enter image description here](http://i.stack.imgur.com/z0kvr.png) I know the wire above the conducting plane has impedance $Z_0$, but am I right to "assign" impedance $Z_0$ to the plane as well? Or do they "share" the impdance like a pair of resistors in series; i.e. each has impedance $\frac{Z_0}{2}$?


title: Can a broken light filter shift the wavelength of light exiting it?

text: I've measured the wavelength of light emitted from a red Helium–Neon laser passing through a red intensity filter (indirectly, by fitting a function to a single slit diffraction pattern, then forcing the fit to the theoretical values). It came out around 735nm, whereas the theoretical value for He-Ne is 632.8nm (looked it up online, I don't have manufacturer specs). The light cannot receive any energy from the filter so the wavelength can only be shifted up. The filter is visibly worn out and cracked, and it does a poor job filtering the intensity. There is nothing wrong with the fitting method as it works well with a green laser. And I tried fitting with 3 different data sets for the red one, to no avail. What phenomena shifts **exiting light** wavelength in general? (apart from relativistic corrections)


title: Josephson effect - fractional or not

text: It is well known that a current proportional to $J\propto\sin(\phi_1-\phi_2)$ flows when two superconductor with phases $\phi_1$ and $\phi_2$ are connected. Also, a current which depends on the phases according to $\sin[(\phi_1-\phi_2)/2]$ is claimed to be fractional Josephson effect (which is believed to be a signature of Majorana fermions). But I see that even with two s-wave superconductors connected through a barrier, the current could be proportional to $\sin[(\phi_1-\phi_2)/2]$ (see for instance - http://arxiv.org/abs/cond-mat/9811026) when the barrier is zero. I do not understand this well. Does it mean that $J\propto\sin(\phi_1-\phi_2)$ is true only in the large barrier limit ? Then, what is holy about fractional Josephson current?


title: Calculation of energy eigenvalues of $\hat{x}^4$

text: I would appreciate help in calculating the energy eigenvalues associated with $\hat{x}^4$, with $\hat{x}$ expressed using the ladder operators for harmonic oscillators. > $\hat{x} = \sqrt{\hbar/2m\omega} (\hat{a} + \hat{a}^{\dagger})$ Neglecting the constant term, I multiplied out $(\hat{a} + \hat{a}^{\dagger})^4$. I am familiar with the steps to compute $\hat{x}^2$, but would appreciate help in getting $\hat{x}^4$. I would presume that due to orthogonal considerations, as in the case of $\hat{x}^2$, the only terms that contribute are those with the same number of $\hat{a}$'s as $\hat{a}^{\dagger}$'s. To the extent this is accurate, I would say $\hat{a}^{\dagger}\hat{a}\hat{a}^{\dagger}\hat{a}^{\dagger}= n^2$. And $\hat{a}\hat{a}^{\dagger}\hat{a}\hat{a}^{\dagger}=(1-n)^2$. I am especially stuck as to how to deal with, e.g., $\hat{a}\hat{a}\hat{a}^{\dagger}\hat{a}^{\dagger}$ and other combinations. Thanks for your help and any general principles I am overlooking or incorrect about. Especially I was wondering if there is a particularly efficient way to approach this.


title: Rutherford Experiment - practical and theoretical questions

text: I performed the Rutherford experiment the other day, using Au thin foil of $2\,\mathrm{\mu{}m}$, a source/gun of α particles (241Am) and a detector/counter. α particles were shot from the source through a slit of $20\,\mathrm{mm} \times 1\,\mathrm{mm}$ (presumably attached to the foil, thus narrowing the effective area). In the first part of the experiment I was trying to measure the scattering angle without the foil for $0^\circ \ll |\theta| \ll 7^\circ$, where $\theta$ was the scattering angle and also the angle between the foil and the detector. For each angle I noted the number of counts and the time elapsed (in order to calculate the capacity=number of counts/time). The angles at which the capacity decreased by around 90% were $4^\circ$ and $-7^\circ$. Before I move on to describe the second part of the experiment using the foil, I'd like to pose a few questions as some things are not sufficiently clear to me. Our booklet for this experiment instructs us to calculate $\mathrm{d}P_0(\theta)=\frac{n}{t}$ for each of the angles, then divide it for each angle by the angular width of the detector in order to determine $\frac{\mathrm{d}P_0}{\mathrm{d}\theta}$. If I understand the instructions correctly, $\frac{\mathrm{d}P_0}{\mathrm{d}\theta}$ is then apparently to be used to plot a Gaussian, which is to be integrated between $-\infty$ and $+\infty$ to yield the total $P_0$ (i.e. the "background" measurement, without the foil). Does that make sense? Normally it is the capacity itself which is plotted against the scattering angle to yield the Gaussian, and not the capacity divided by the angular width, isn't it? Furthermore, how exactly do I determine the angular width? The booklet indicates that in order to determine the angular width one must measure the width of the slit and the distance between the detector and the source/gun. However, I am not really sure I understand. I was under the impression that the angular width was simply given by $\Delta \theta=\Delta \Omega/(2\pi \sin\thetaθ)$, whereas $\Delta \Omega$ is the area of the slit used. Isn't it? I'd sincerely appreciate some feedback.


title: Electric potential of spherical water droplet

text: I'm trying to answer the following: > 1000 spherical water droplets, each of radius $r$ and each carrying a charge > $q$, coalesce to form a single bigger spherical drop. If $v$ is the electric > potential of each droplet and $V$ that of bigger drop, then find > $\frac{V}{v}$. It is not mentioned here whether $v$ is potential at a point outside or on the surface of sphere, where should I take the potential? As water is a good conductor of electricity so water droplet can be regarded as spherical shell.Potential due to spherical shell is *** $\frac{kq}{r}$.*** where **_k_** is constant and **_q_** is charge on the shell and **_r_** is the distance between the centre of spherical shell and point on which **_P_** is to be calculated and at a point inside or on the surface of shell **P** is constant and is equal to *** $\frac{kq}{r}$.*** here **_r_** is the radius of shell. So **_P_** depends on the distance between the centre of spherical shell and point on which **_P_** is to be calculated.So in the above problem **_P_** on which point should I need to consider. I am unable to understand what is meant by the potential of water droplet.I know potential at a point due to point charge,system of charge and due to continuous charge distribution.But they are calculated at point,I mean we calculate potential at point due to different charge distributions.How can we calculate potential of a body! I want to know what is meant by( " $v$ is the electric potential of each droplet" )this line of the question.


I am trying to understand how to formulate classical dynamics on group manifold SU(2). This will be an exercise for me to the more advanced subject of path integral on group manifold. Does someone know of good (pedestrian) lecture notes on classical dynamics on SU(2)? For example, why the free particle Lagrangian look like that: $L=\frac{1}{2}tr\dot{U}\dot{U}^\dagger$? why the trace , whats the role of $U$?


title: Why does inverting a song have no influence?

text: I inverted the waveform of a given song and was wondering what will happen. The result is that it sounds the exact same way as before. I used Audacity and doublechecked if the wave-form really is inverted. The second thing I tried was: I removed the right channel, duplicated the left one and set the duplicated layer as right channel. This way I made sure that both channels are exactly the same. Then I inverted the second channel only. I thought that this would create some kind of anti-noise, but it didn't. Why is that?


title: Improved energy-momentum tensor

text: While still dealing with this issue, I've stumbled upon this answer to a question asking about the conserved quantity corresponding to a scaling transformation. It mentions that in accordance with Noether's theorem, an improved energy-momentum tensor and Noether current can be found for a large class of (scale invariant) theories, such that the conserved charge can be calculated. Unfortunately, apart from these short remarks, the OP of the answer I cite left no reference with further information about this issue. For example I'd like to know how such an improved energy-momentum tensor can be derived generally, what form it and the corresponding conserved charge would take for some example theories, how this conserved charge can be physically interpreted, etc. Finally I'm interested in applying these ideas to fluid dynamics,I'd like to know how to construct the conserved quantity corresponding to the scale invariance of the Navier Stokes equations for example. But references wherein this concept is explained dealing with QFTs I'd appreciate too :-).


title: "+" and "-" sign in Maxwell Stress tensor

text: I have trouble in determining the "+" and "-" sign of momentum per unit time, per unit area of the following question. Why in the second part, $d\vec{a}$ is pointing in the $ -\vec{z} $ direction? I mean, the normal vector is pointing upwards, so the area vector should point upwards, so $d\vec{a}$ is pointing $ +\vec{z} $ direction, right? And for (b), why it is negative? Is it because $ \vec{T_{zz}}$ and $d\vec{a}$ point in the different directions? And for (c), this is the most confusing part for me. $ -{T_{zz}}$ should be minus, becasue in (a), we get the component of the tensor matrix to be "+". I just get really confused about the sign "+" or "-" of this problem; yet, the calculation is pretty easy for me. ![enter image description here](http://i.stack.imgur.com/2StCb.jpg) ![enter image description here](http://i.stack.imgur.com/w5zr0.jpg) ![enter image description here](http://i.stack.imgur.com/cwK23.jpg)


title: What does the Pauli Exclusion Principle say about a superposition of spin states?

text: Suppose we have an atom. It is commonly said that because of the PEP, two electrons can't be in the ground state unless they have opposite spins, because no two electrons can have the same wavefunction. What bugs me is that spin up and spin down aren't the only possible spin states. There's a whole continuum of linear combinations of them, and as far as I can tell the PEP wouldn't exclude the possibility of having lots of electrons, all sharing the same spatial wavefunction but with different combinations of $\mid\uparrow \rangle$ and $\mid\downarrow\rangle$. Why doesn't this happen?


title: What would be the resulting effect of two ships passing near each other while using a Alcubierre drive

text: So, I don't have any formal background in physics or space. but I read about the Alcubierre drive, and now I'm curious. If two ships passed one another, what sort of interference would be generated? How dangerous would it be? I'm thinking it would actually neutralize the effect of warp for either ship since their fronts would be generating opposite forces. Also, am I correctly interpreting what a warp drive travel path would look like? If not, my question is pretty irrelevant. The arrows are supposed to indicate the ships travel path. ![Ship traveling in a warp. Arrows indicate direction of travel](http://i.stack.imgur.com/N7vtd.jpg)


title: Thermodynamic potentials and approach to equilibrium

text: I have seen some material which tries to show that when approaching equilibrium upon different constraints, the changes in some thermodynamic potential is always positive or negative (for example, that Helmoltz free energy decreases for constant temperature and volume). I cannot make sense of these arguments, however, because the quantities these thermodynamic potentials depend on are only defined at equilibrium. I think, that what one should show is that if there are several equilibria, the one which minimizes/maximizes the appropriate potential is the one which maximizes entropy. Is this the right way to think about thermodynamic potentials?


title: Multiplication of 3-vector operators

text: I've started reading "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine and have some trouble understanding how to handle 3-vector operators (i.e. an operator $\mathbf{A}$ with $\mathbf{A} = (A_{1}, A_{2} , A_{3})$) like the position operator $\mathbf{Q}$ and the momentum operator $\mathbf{P}$ when it comes to multiplication. **General problem** Do I multiplicate those vectors componentwise, i.e. \begin{equation} \mathbf{Q} \mathbf{P} = \sum_{\alpha = 1}^{3} Q_{\alpha} P_{\alpha} \end{equation} or do I have to do it another way? **Specific problem** The context in which my problem arises is the following: On pp. 77 and 78 of the book by Ballentine one finds (I added some explanatory notes to the original text): > We assume the position operator for the particle to be $\mathbf{Q} = (Q_{1}, > Q_{2}, Q_{3})$, where by definition > > \begin{equation} Q_{\alpha} | \mathbf{x} \rangle = x_{\alpha} | \mathbf{x} > \rangle \qquad (\alpha = 1, 2, 3)\tag{3.36} \end{equation} > > has an unbounded continuous spectrum. [...] > > The space displacement $\mathbf{x} \rightarrow \mathbf{x}^{\prime} = > \mathbf{x} + \mathbf{a}$ involves a displacement of the localized position > eigenvectors, > > \begin{equation} | \mathbf{x} \rangle \rightarrow | \mathbf{x} > \rangle^{\prime} = e^{−i \mathbf{a} \cdot \mathbf{P}} | \mathbf{x} \rangle = > | \mathbf{x} + \mathbf{a} \rangle\tag{3.40} \end{equation} > > where $i$ is the imaginary unit and $\mathbf{a}$ is a space displacement. > [...] > > The displaced observables bear the same relationship to the displaced > vectors as the original observables do to the original vectors, as was > discussed in Sec. 3.1. In particular, > > \begin{equation} \mathbf{Q} \rightarrow \mathbf{Q}^{\prime} = e^{−i > \mathbf{a} \cdot \mathbf{P}} \mathbf{Q} e^{i \mathbf{a} \cdot > \mathbf{P}}\tag{3.41} \end{equation} > > with > > \begin{equation} Q_{\alpha}^{\prime} | \mathbf{x} \rangle^{\prime} = > x_{\alpha} | \mathbf{x} \rangle^{\prime} \qquad (\alpha = 1, 2, > 3).\tag{3.42} \end{equation} > > But since $ | \mathbf{x} \rangle^{\prime} = | \mathbf{x} + \mathbf{a} > \rangle$, a comparison of (3.42) with (3.36) implies that > > \begin{equation} \mathbf{Q}^{\prime} = \mathbf{Q} − \mathbf{a} I\tag{3.43} > \end{equation} > > where $I$ is the identity matrix. [...] > > Equating terms of first order in $a$ from (3.43) and (3.41), we obtain > > \begin{equation} [Q_{\alpha}, a \cdot \mathbf{P}] = i_{\alpha} I,\tag{3.44} > \end{equation} > > (where $[A, B] = A B - B A$ is the commutator of the operators $A$ and $B$) > which can hold for arbitrary directions of $a$ only if > > \begin{equation} [Q_{\alpha} , P_{\beta}] = i \delta_{\alpha \beta} > I\tag{3.45} \end{equation} > > where $\delta_{\alpha \beta}$ is the Kronecker Delta. I'm not sure whether the result $[Q_{\alpha}, a \cdot \mathbf{P}] = i_{\alpha} I$ is correct or contains typos. Ballentine doesn't say what $i_{\alpha}$ means and usually he adds a "$\cdot$" between two variables only when he wants to indicate an inner product between two vectors, so maybe the $a$ should be the vector $\mathbf{a}$ and not its norm. Furthermore when I do the Taylor expansion of $e^{−i \mathbf{a} \cdot \mathbf{P}} \mathbf{Q} e^{i \mathbf{a} \cdot \mathbf{P}}$ to the first order in $\mathbf{a}$ I get \begin{equation} e^{−i \mathbf{a} \cdot \mathbf{P}} \mathbf{Q} e^{i \mathbf{a} \cdot \mathbf{P}} \approx \mathbf{Q} + i [\mathbf{Q}, \mathbf{a} \cdot \mathbf{P} ] \end{equation} so that I come to the result \begin{equation} [\mathbf{Q}, \mathbf{a} \cdot \mathbf{P}] = i \mathbf{a} I . \end{equation} I have some problems getting to equation (3.45) from this point. Especially I'm unsure how to get from the general product of the 3-vector operators, $\mathbf{Q} \mathbf{P}$, to the componentwise one, $Q_{\alpha} P_{\beta}$, and whether I can move the vector $\mathbf{a}$ around like a scalar, i.e. \begin{equation} [\mathbf{Q}, \mathbf{a} \cdot \mathbf{P}] = \mathbf{a} \cdot [\mathbf{Q}, \mathbf{P}] \end{equation} or not. I hope I have made clear what my problems are without being unnecessarily wordy.


title: Event-by-Event Simulation of Quantum Phenomena

text: I just recently stumbled over http://rugth30.phys.rug.nl/dlm/ and http://www.sbfisica.org.br/bjp/files/v38_26.pdf As the title suggests these are presentations of mathematical models capable of simulating quantum "effects" on an event-by-event basis using "Deterministic Learning Machine" Models. What is the state of discussion regarding this? Is this bad science? or really accepted alternative way to tackle the pure output side of the experiments? What does this add to the available interpretations of quantum-phenomena?


title: Why does 'proper length' exist as a notion?

text: $$\text{proper time}= \tau= \sqrt{dt^2-d\mathbf{s}^2}$$ $$\text{proper length}= L= \sqrt{-dt^2+d\mathbf{s}^2}$$ What tangible benefit is brought about by calling $i \tau$ 'proper length' (applying when $\Im(L)=0$ (the spacetime intervals are spacelike))? Could one extend the notion of the interval to simulatneusly cover both proper time and distance? Call this $\text{Interval}=dt^2-d\mathbf{s}^2$, _which can be imaginary_. Is it impossible to merge proper time and length because they are fundamentally different things, as proper time is a explicitly measurable quantity, but proper distance must be determined implicitly? My problem is that I don't understand the rationale behind having proper length, rather than a cheap mathematical trick to make the interval real when $ dt^2-d\mathbf{s}^2<0$.


title: Definition of "intensive" and "extensive" properties

text: Today I was asked what does it mean for a physical property of a system to be intensive. My first answer, loosely speaking, was: > _"It is a property that is local."_ I was specifically thinking about density and, by "local", I meant "that is unaffected by the dimension of the system". Ofcourse this is a very ambiguous answer, so after that I said (shifting to extensivity's definition): > _"A property is extensive if it depends on the volume of the system > observed._ " To be honest, I said _if it's proportional to the volume_ , but I'm not sure the this is correct. Now, that I'm still thinking about it, I've come to the conclusion that a good definition could be: > _"A property is extensive if it depends on the **quantity of matter** of the > system observed._" Looking on wikipedia I realized that this is exactly the definition given. But I'm somewhat still uncomfortable with that: if a gas is kept in a recipient of volume $V$ at a temperature $T$, his pressure is function of the number of moles of the gas:$$p=n(RT/V).$$ And, as we know, pressure is an intensive property. So (to me) it is not really clear what does "does not depend on the quantity of matter" mean. I also thought that one could use an operational definition (if this is the good term) of extensivity/intensivity: one example might be: > "Suppose to measure a quantity $q(S)$ relative to a system $S$. Now > reproduce a copy of $S$ and measure the same quantity for the system $S+S$ > given by the two identicaly systems joined. If $q(S+S)=q(S)$, then $q$ is an > intensive quantity." This seems to give a more precise sense to the "does not depend on the quantity of matter" in the above definition, but there are gaps to fill. Maybe I will try to develop better this in a second time. Now, ofcourse, the question is: what is the definition of extensivity/intensivity in rigorous and unambiguous terms?


title: Magnetic force and work

text: If the magnetic force does no work on a particle with electric charge, then: How can you influence the motion of the particle? Is there perhaps another example of the work force but do not have a significant effect on the motion of the particle?


title: Special Relativity - Relativistic Dynamics

text: I've been wrestling with this problem but to no avail. I'm hoping that someone here can give me a little nod in the right direction. **Problem statement:** A thrust-beam space vehicle works bearing a sort of sail which feels the push of a strong steady laser light beam directed at it from Earth. If the sail is perfectly reflected, calculate the mass of light required to accelerate a vehicle of rest mass $m_0$ up to a fixed value of $\gamma$. **Attempt at a solution:** OK. Since the sail is perfectly reflective I view as if the vehicle is emitting photons. I also realize that the momentum of the light is $p = mv = mc = m$ (since I define $c=1$). This is where I get stuck. I have been using A.P. French's Special Relativity book and read his chapter on photon emission countless of times but the solution still evades me. Any pointer will be appreciated! Thanks. edit: I should add that I've calculated the relativistic mass of the ship as $m = m_0 \gamma$ and the momentum as $p = m \gamma = m_0 \gamma ^2$


title: Why cosmic background radiation is not ether?

text: why cosmic background radiation is not ether? I mean it's everywhere and it' a radiation then we can measure Doppler effect by moving with a velocity.


title: How plausible is a subsurface ocean on Pluto?

text: According to this article on physorg.com, it's likely that Pluto has a subsurface ocean of liquid water. It suggests that the ocean would be about 165 km deep, under an equally deep crust of solid ice, topped by a thinner layer of solid nitrogen. The heat to keep the water liquid would be provided by the decay of radioactive potassium. The article doesn't explicitly say so, but I presume that would be potassium-40, which has a half-life of about 1.25 billion years (which suggests that there would have been a lot more of it a few billion years ago). Measurements of meteorites believed to have formed in the early Solar System show 10 times as much potassium as needed. The New Horizons spacecraft, when it arrives at Pluto in 2015, should be able to see surface features that will indicate whether this hypothesis is correct. I haven't seen any mentions of this other than that article (and references to it). My question is, how plausible is this idea? Has anyone else crunched the numbers and confirmed or denied the possibility? Is there some fatal flaw in the argument? (And a followup: _How freakin' awesome would this be??!!_ )


title: How can I prevent my son building up static on his trampoline?

text: Whenever my three year old son plays on his trampoline, it doesn't take very long for him to start building up a significant amount of static electricity. His hair stands on end (which is quite amusing), but when I help him down we both get a nasty static shock (which is not amusing). He finds the shock upsetting, and I'm concerned that it will discourage him from enjoying his trampoline. How can I prevent the build-up? One suggestion I have seen on a parenting forum is to ground the trampoline frame with a cable and a metal stake. However my understanding is that this would enable him to discharge by touching the frame (rather than me), but it would not prevent the static occurring in the first place. If it's relevant, it's this trampoline and is on a grass lawn. My son bounces in his socks, no shoes. In case of link rot, it is an 8ft trampoline with a net enclosure.


title: How can I vizualize and understand curved spaces in general relativity?

text: I'm taking a basic physics class and the teacher described space with a special table that has curves and black holes etc. He would throw a metal ball down onto it and the class would watch it circle around a black hole and this showed the warping of space. The instructor said that it is actually more like a table cloth because the ball would cause a warping as well. The problem I have is transferring this image of 3d objects on a warped 2d plane to actual actual space. Another way to look at my dilemma: There is space above the 3d object on the table, and on the sides of it. If we were on the 3d object and left if in any direct but down, we would be in space, but how is this space described? I can only picture the one "bottom" portion of space. Help me understand the rest.


title: Why don't we have a better telescope than the Hubble Space Telescope?

text: The Hubble Space Telescope (HST) was launched in 1990, more than 20 years ago, but I know that it was supposed to be launched in 1986, 24 years ago. Since it only took 66 years from the fist plane to the first man on the Moon why don't we have a better telescope in space after 24 years?


title: How to measure the diameter of a star?

text: I am thinking about something I read somewhere (if only I could find it again) in a textbook. It is about the size of a star and its ER peaks. It has to do with the waves coming off the edge (maybe) and arriving later than those from "head on" and therefore you can know something about its diameter. It has been puzzling me but I can't quite remember it. Just yesterday I was reading about a black hole that pulses at a minimum of 10 minutes and so it is at least 10 light-minutes across. (I probably am not getting it just right, but help me out!) Is this the same principle? Anyone know what I'm talking about? I would love to have this explained and/or would like to know what it is called, so I can look it up.


title: What sort of equipment would I need to take a photo like this?

text: I'm interested in doing some astrophotography and I'm looking into the equipment needed to get a photo like this: http://www.flickr.com/photos/cscunha1984/6619321531/in/faves-heyvian/ I'm not looking for brands or anything, just the recommendations on what a beginner* should be looking for in a telescope/tracking mount and so on. Would entry level equipment get me the photo above? If not, could you provide an example of what I could expect please? How would these recommendations differ if I weren't interested in taking photos but just looking? I assume I wouldn't need the tracking mount. I ask because if the photography part makes it too expensive, I would be happy to just look. * _beginner meaning not only someone new to the field but also someone not looking to make a large initial investment._


title: How fast will the sun become a red giant?

text: I've read many accounts of our sun's distant fate, but what I've never heard is on what time scale these events occur. For instance, when the sun runs out of hydrogen, I presume it doesn't just WHAM! become a red giant suddenly, engulfing the inner planets in seconds. But how long would it take for the sun to expand? Would anyone left on Earth have days, weeks, months, years to escape? Centuries? What kind of time scales _are_ we talking about, here?


title: Why isn't sunset time in sync with solstice?

text: The winter solstice in the Northern Hemisphere in 2011 is on December 22. But if I look at the sunset times for a location such as Washington, DC on the USNO site, the sunset time starts reversing much earlier (around December 6th). Shouldn't the sunset time start reversing (from earlier to later) on the same date as the solstice? **Update:**   Omega Centauri's explanation is correct.   * The Royal Observatory gives a similar account of this oddity on this page under the section titled "The apparently odd behaviour of sunrise/set times near the winter solstice".   * Cornell University provides more details here.


title: what sort of set up would i need to create an electro magnetic chair with no legs

text: I am a furniture design student therefore please keep it simple. a system strong enough to hold the avergae male of say 90 kg is this possible even....


title: Magnetic moment and other invariants of Lorentz System

text: It's a standard fact that the quantity $\mu = v_{\perp}^{2}/B$ is approximately conserved in the system $d_{t}\mathbf{v} = \gamma (\mathbf{v}\times\mathbf{B})$. The paper _Magnetic Moment to Second Order for Axisymmetric Static Field_ by C. Gardner claims that this is actually just the first term in the series expansion of a function ("the" magnetic moment) whose time derivative is exactly zero, but he only finds the second term (which is a huge mess.) This sort of thing fascinates me, and I have a few questions:   1. Lets call this exact magnetic moment $M$; it has the property that $d_{t}M = 0$. We know that $\mu$ is an adiabatic invariant, but $M$ is, in some sense, "more" invariant than that, so what kind of function is it?   2. What guarantee is there that $M$ won't just be a function of the kinetic energy and some conserved momenta (which have time derivatives equal to zero?) In other words, how do we know that $M$ is independent of invariants we already know?   3. This is an old paper. Has anyone figured out $M$ since then, or has any more progress been made?


title: Convergence of Light on the Retina

text: So, I've learned about lens ray diagrams-but the problem I'm having is that when ray diagrams are drawn for a point of an image, they converge to another point, but there are two problems that I see with regards to our eyes: 1) In the simplest drawn case it's at least three rays converging to the same point, but our eye would only have once receptive cell at a point, how does it take in all of them? 2) At any given time, isn't there more than one point being sent to the same point on the back on the retina? We draw 2D cases in high school physics, but I feel like there should be more than one point that gets sent to the same point. In any case, part one is the more pressing matter.


title: Relative Velocity problem

text: I was solving many problems on relative velocity and observed that when the question asks, "what is the minimum time taken by the boat/man to cross the river.?" ![enter image description here](http://i.stack.imgur.com/3E19I.png) so the solution says that he should swim perpendicular to the river, and then time taken will be $\frac{w}{v}$. Here lies the problem... the distance is not w, but it is the hypotenuse I have drawn (in a crazy manner), and the speed is $\sqrt{v^2 - r^2}$...so what is right and why? Moreover, why is the fact that- he needs to swim perpendicular to the river-true??


title: Behavior of black holes in higher- and lower-dimensional space-times

text: The behavior of black holes in 3+1 dimensional space-time as our own is rather well known: formation, event-horizon size, mass, spin, radiation etc. However, my question is what would black holes behave like in universes with different number of space-time dimensions, such as 2+1 dimensional or 4+1 dimensional space-time? Would they be able to form? Would the event horizon radius be smaller or larger? Would their densities be higher or lower? Would they spin, and how quickly? Would they emit Hawking radiation? How would the space-time behave close to it compared to in 3+1 dimensional space-time?


title: When taking a sequence of exposures for stacking/coaddition, what dither patterns are most commonly desired? Why?

text: When taking a sequence of exposures for stacking/coaddition, what dither patterns are most commonly desired? When visiting a telescope, what default dither patterns would a visiting astronomer like to see in the observing software (assuming custom patterns are also supported)?


title: Numerical Ising Model: Swendsen–Wang algorithm, Percolation theory?

text: When you look at the original paper of Swendsen and Wang in 1987: **"Nonuniversal critical dynamics in Monte Carlo simulations"** it is somewhat mentioned that the proposed algorithm uses percolation theory and the autocorrelation time is significantly reduced: > In this paper, we present an unusal type of dynamics, which violates dynamic > universality, and greatly reduces relaxation times in the computer > simulation of large systems. Large clusters are changed in a single move, so > that the profcess is not local in the usual sense, allowing z to be less > than the lower bound... After proving the necessary condition of _detailed balance_ , they spread some words about the origin of this behavior, > The percolation clusters behave as Fisher droplets and contain a great deal > of information". but only from the publication I cannot understand why this is working. I followed some sources, but obviously not the right one. My question: Can someone outline how percolation theory comes into play? That the algorithm is working due to the detailed balance condition is not a surprise, but that its autocorrelation time is reduced like this seems curious to me. the next question would be: What are the main differences between the Wolff and the Swendsen-Wang algorithm? As far as I see it Wolff uses a good choice of the probability so that there are no rejections, is this true?


title: How are newly discovered objects (stars, planets, galaxies...) named?

text: When a new astronomical object (star, planet, galaxy, comet, etc.) is discovered, what is the official procedure to name it? Who decides about the name of it? Can they be changed in time? Extra question: How were the areas on the surface of the Moon and planet Mars named?


title: When "weight" of an object is listed, is it really the mass or the weight?

text: I Have read an earlier post regarding this, but the answer wasn't perfect enough or I didn't understand so! Let me put it to clear, I know difference between weight and mass. Also I know the conventional method of denoting "Kg" and "Kgf" as units of weight in some countries. My question is, say for example of a car. It is said that Toyota corolla has a curb weight of 2800 pounds or 1270 Kg. Does the above spec actually denote the weight(mass x g) or mass of the car?


title: If maximal work is extracted, in what manner does the heat flow between bodies?

text: There are two bodies starting with different temperatures and specific heat capacities (for simplicity assume that the bodies are solid to the volumes are constant). Let the rate of heat flow from the body with the highest temperature be called $Q(t)$. If the work extracted from the system is maximal, what is $Q(t)$? I'm not sure whether (apart from the evident problem of finding a closed form for it):   * $Q(t)$ is unique, and whether   * assuming a different model of how the heat transfer actually occurs (e.g. Newton's cooling equation) will affect the allowed form(s) of $Q(t)$.


title: Mechanics Newtons third law

text: > _In the system suppose that the mass of the lower cylinder is $12 kg$. The > system is held at rest in the position shown, with the tape taut and then > released. Find the acceleration of_ > > _a) the lower cylinder,_ > > _b) the $5 kg$ mass._


title: Why is stainless steel a poor conductor of electricity?

text: I recently had a metal plate put in my shoulder and was wondering why stainless steel isn't a good conductor (At least I hope it isn't). Does the alloy just lack free electrons? Why is that?


title: Why does the speed of light have no uncertainty?

text: I could understand that the definition of a second wouldn't have an uncertainty when related to the transition of the Cs atom, so it doesn't have an error because it's an absolute reference and we measure other stuff using the physical definition of a second, like atomic clocks do. But why doesn't the speed of light have uncertainty? Isn't the speed of light something that's measured physically? Check out that at NIST.


title: I don't understand the idea of perpendicular vectors being independent of each other?

text: So problem 71-75 is about vectors. The problem says: > _A river has a current flowing with a velocity of 2.0 meters per second due > east. A boat is 75 meters from the north riverbank. It travels at 3.0 meters > per second relative to the river and is headed due north. In the diagram > below, the vector starting at point P represents the velocity of the boat > relative to the river water._ http://www.jmap.org/JMAP/IJMAP/Physics/RegentsExams/0612ExamPH.pdf Then it says, > _Calculate the time required for the boat to cross the river._ Apparently I'm suppose to d=vt where d = 75m, v = 3.0m/s and solve for t. Why is it that I use 3.0 m/s and not sqrt(13) m/s which is the resultant? I know it says that perpendicular vectors are independent of each other but that doesn't really make sense to me. If I'm crossing some distance and I'm getting pushed horizontally, then I'd be travelling diagonally which is a longer distance then a vertical distance? Also what does "relative to the river" in the problem?


title: State with non-zero angular momentum - cannot be described by spherical harmonic?

text: For a state with non-zero angular momentum, why is it that it cannot be described by the spherically symmetric spherical harmonic?


title: Pressure $p$ in the Bernoulli equation

text: I know the Bernoulli equation that states that the energy along a streamline is constant: $$ \frac{v^{2}}{2}+gh+\frac{p}{\rho}=C $$ However I can't seem to figure out what exactly $p$ is in this equation. In every book I look and also on Wikipedia it only says _"$p$ is the (static) pressure"_. I always considered $p$ to be the internal pressure of the liquid, i.e. the pressure exerted by the fluid on its surroundings (that includes covering fluid). But this raises a problem that I wasn't sure of how to solve. ![enter image description here](http://i.stack.imgur.com/cjR80.png) Lets assume that the flow in the picture is an incompressible flow, like water. When the water flows from the wide to the narrow part of the tube, the speed $v$ increases, lowering the pressure $p$ (as $gh$ and $\rho$ remain constant). As this is an incompressible fluid, the volume cannot change. But if the pressure is lowered and the volume does not change, doesn't that mean that the temperature is lowered too? This just seems weird to me. What goes wrong in this thought process?


title: Euclidean functional Integrals

text: In the chapter "Uses of Instantons" from the book "aspects of symmetry" by Sidney Coleman I have come across the euclidean version of the path integral in semi-classical approximation. To evaluate the sum over paths, each path is written as the sum of the classical path (for which action is an extremum) and the sum of a set of orthonormal functions obeying the boundary conditions with respective co-efficients. Now action is invariant under time translation. My confusion is that, it is written that due to time translation symmetry, the operator appearing in the path integral formula (whose determinant has to be evaluated) must have a zero eigen value, where the eigenfunctions are those orthonormal functions obeying the boundary condition. I can not understand this arguement.


title: Is the observable region of the universe within the event horizon of a super-massive black hole?

text: Observations:   1. I have read that for a free-falling observer within the event horizon of a black hole that all lines of sight will end at the singularity which is black.   2. I also look up and see that the sky is mostly black.   3. I also know that by measuring the red-shifts of the galaxies that they are all accelelerating towards that blackness. (rather than accelerating away from a big-bang event, which makes less intuitive sense)   4. The red-shifts are greatest for those galaxies closest to the singularity (i.e. furthest away from us). I therefore conclude from these consistent observations that all the matter in at least the finite observable region of the universe in which we are located, is accelerating due to gravity towards the singularity of a super-massive black hole. In the spirit of good science I will happy accept being wrong, but I need to understand why I am wrong. Predictions from the theory: The light from the universe outside the event horizon of the black hole should be visible as a small disc or point light source in the direction facing away from the singularity. Of course, if this happens to be inconveniently located on the far side of the milky way's core from us, then we will be unable to observe it. Further Speculations: It may be that in regions of the universe far ouside the influence of this black hole (e.g. >50 billon light years away) that the sky is white hot due to Olber's paradox. The black hole may have been formed from a large quantity of anti-matter, which might explain the local perponderance of ordinary matter. The microwave background radiation may be a result of Hawking radiation at the event horizon (which we are viewing fromn the inside), or, depending upon the non-euclidian geometry, we may be observing the result of matter being destroyed at the singularity.


title: Telescope "blue book"

text: I have a telescope that I may be in the market to sell in the near future and am wondering if there is a good source to find its value in the used market. Although it's never been out of the box, it was given as a gift nearly 10 years ago and I have no idea what it might be worth. It's a Meade 114EQ-DH and I see a few on eBay that look similar but none that are in-box and in brand new condition. Is there a source of prices similar to a blue book for cars?


title: Chemical effect on gravitation?

text: We know, that gravitation field of charged black hole is different than one of uncharged. I this true only for objects with singularity or is true for all objects? If true, then may we say, that gravitation field of chemical molecule has footprints of it's chemical composition and state and, in principle can be registered? I know it is very small.


title: Why a black hole sucks nearly everything, but emits gravitons?

text: What is so inherently different to the idea of gravitons from other particles, that a black hole draws everything possible including massless photons, but emits gravitons the more the stronger it grows? If this is something obvious like "^%#^& magnets, how do they work?" please close the question but at least point me to the direction in which should I look.


title: Wavefunction of a Baryon

text: How to write the total wavefunction of a Baryon including space part, spin part, isospin part and color part such that the net wavefunction is anti- symmetric? What is the difference in wavefunctions of two different baryons but of same quark content say proton $p$ and $\Delta^+$ baryon?


title: Visible light through a single-mode optical fiber?

text: If I understand things correctly, the optical fibers used for (long-range) data transmissions are generally single-mode fibers, transmitting light in the 1300-1500 nm spectrum. Now, could such a fiber transmit visible light (~400-700 nm) a short distance, say a few meters? Or does the fiber have a property that prohibits transmission of shorter wavelengths?


title: Simple Quantum Mechanics question about the Free particle, (part1)

text: I am reading Introduction to Quantum Mechanics by David Griffiths and I am in Ch2 page 59. He starts out writing the time dependent Schrödinger equation and the solution for $\psi(x,t)$ for the free particle, > $$\psi(x,t) = A e^{ik(x-(\hbar k/2m)t)} + B e^{-ik(x + (\hbar k/2m)t)}$$ Then he goes and says the following, > Now, _any_ function of $x$ and $t$ that depends on these variables in the > special combination $x \pm vt$ (for some constant $v$) represents a wave of > fixed profile, traveling in the $\pm x$-direction, at speed $v$. What does this sentence mean?


title: Do Alkaline batteries, $\mathrm{NiMH}$, rechargeable alkaline, Lithium $\mathrm{AA}$, all have similar MAX POWER?

text: So in physics, one smart teacher told me, $$ V = IR $$ or $$ I = \frac{V}{R} $$ but it is not always true, because $P = VI$ and each power supplying device (such as battery) has a "maximum power" it can provide. So $I = V/R$ is true as long as $P = VI$ doesn't exceed the maximum power the battery can supply. So will old style $\mathrm{AA}$ batteries, Alkaline $\mathrm{AA}$ batteries, and $\mathrm{NiMH}$, rechargeable alkaline, Lithium $\mathrm{AA}$ (Energizer) all have similar MAXIMUM POWER? I am suspecting my Mario Kart Remote (fit in a wheel) for playing Mario Kart Wii not behave the same when using different batteries. The best seems to be the Duracell Ultra Alkaline, and then the Duracell rechargeable pack for Wii remote ($2.4V$ only) works also flawlessly (but can it be, because it is very snug?) Otherwise, sometimes I turn left and do a drifting and the console thinks that I am drifting right... so it does seem that different batteries have different outcome... and I am suspecting can the Wii need more power than some batteries can provide? and so how do they work really?


title: Are small speakers inherently limited to higher frequencies?

text: I am hoping to build a subwoofer using multiple smaller speakers (165mm) instead of a single larger speaker (380mm). My theory is that the displaced air volume is what matters, not the individual speaker's diameter.   The surface area of a 380mm speaker is $\approx900cm^2$.   The surface area of a 165mm speaker is $\approx140cm^2$.   Presuming the speakers are capable of being driven to the same $X_\max$, six or seven 165mm speakers should be roughly equivalent to a 380mm speaker.   Taken to an extreme, an array of 100 $9cm^2$ speakers should be equivalent to a single $900cm^2$ speaker. Is this correct, or do smaller speakers have some other limiting factor that limits their low-frequency reproduction?


title: How is barometric light porduced?

text: A shaken sealed glass tube containing liquid mercury in a dark room will glow. This has been know since the 17th century and is called barometric light. How does the addition of potassium permanganate crystals to the mercury influence the production of light?


title: Does Lyapunov exponent equate to exponential inflation?

text: Physics can be modeled by dynamical systems $f^t(x)$ as well as by PDEs. The most common dynamical system has hyperbolic fixed point and can be an attractor or a repellor. The dynamics at repellors and attractors are simple exponential expansion or contraction and are represented by a Lyapunov exponent. My question is how could one prove or disprove that exponential inflation is just an example of a repellor with a Lyapunov exponent?


title: Photomagnetic effect

text: I just saw an article on wikipedia: http://en.wikipedia.org/wiki/Photomagnetic_effect "This article appears to contain unverifiable speculation and unjustified claims. Information must be verifiable and based on reliable published sources. Please remove unverified speculation from the article." Ok, but there is also link to the article: http://physicsworld.com/cws/article/news/2011/apr/21/solar-power-without- solar-cells Could someone tell me if this is some serious science or just a hoax?


title: Klein factors and Conformal Field Theory

text: Consider the mode expansion of a (chiral) scalar field confined to a disc with circumference L: $$ \phi(x) = \phi_{0} + p_{\phi} \frac{2\pi}{L} x + \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} e^{-(k_{n}a)/2} \left(e^{-ik_{n}x} \ b_{n}^{\dagger}+e^{ik_{n}x} \ b_{n}\right) $$ with $k_{n}=\frac{2\pi n}{L}$ , $\phi_{0}$ some "zero-mode", $p_{\phi}$ some "conjugate momentum" and $a$ some short-distance cut-off. The operators fulfill the following bosonic commutation relations $$ \left[b_{n}^{\dagger} , b_{n'}\right]=\delta_{n,n'} \quad\text{and}\quad \left[\phi_{0},p_{\phi}\right]=i $$ (Fermionic) Vertex operators are defined by $$ V_{\alpha}(x)=:e^{i\alpha\phi(x)}: $$ with $: \ ... \ :$ denoting normal ordering. Inserting the mode expansion of $\phi(x)$ into the definition of the vertex operator yields to lowest order in $\frac{a}{L}$: $$ :e^{i\alpha\phi(x)}: = \left(\frac{L}{2\pi a}\right)^{\Delta(\alpha)} e^{i\alpha\phi(x)} $$ with the "scaling dimension" $\Delta(\alpha)=\frac{\alpha^{2}}{2}$. The pre factor on right side in front of the exponential is sometimes called "Klein factor". Now here are my questions (They may really be "Newbie"-CFT-questions;) ) :   1. Since the right hand side is only an approximation of of $:e^{i\alpha\phi(x)}:$ to lowest order I am wondering whether the left hand-side reproduces the correct (say) fermonic commutators in all cases and whether hand side only partially reproduces the correct fermonic commutators?    2. If the right-handside only indeed only partially reproduces the correct commutation relations how can we say that a certain product of fermionic operators (say a product of 3 fermionic operators) indeed obeys the correct sermonic commutators when written in the "bosonized language"?    3. What is the importance of the higher-order terms in $\frac{a}{L}$ in the "expansion" of the vertex operator?    4. Is all this a more general construction in CFT?  I am looking forward to your responses!


title: Will a wave packet undergo dispersion when traveling down a hanging rope?

text: Suppose I tie one end of a rope to my ceiling and the other end to a spot on my floor directly underneath it. Because the rope has some mass, the tension varies along the rope, from highest at the ceiling to lowest at the floor. If a wave packet begins propagating down the rope, will its shape change? If so, it is possible to calculate the shape of a Gaussian wave packet as it travels down the rope? Intuitively, it seems to me that the wave packet will change shape for two reasons. First, the portions higher up the rope have higher tension, and therefore higher speed. They will "catch up" to portions of the wave packet further down. Second, because the tension is changing, the wave equation now has a term related to the first derivative of the displacement of the rope. Specifically, I tried assuming that the displacement of the rope is only horizontal and that the slope of the rope is never far from vertical. I made $y$ a coordinate measuring up from the floor and $x$ a coordinate to the right. Letting the tension be $T(y) = T_0+\lambda g y$, with $\lambda$ the mass per unit length, I got the wave equation ( **edit:** important typo corrected) $$\frac{\partial^2{x}}{\partial t^2} = g \frac{\partial x}{\partial y} + \frac{T_0+\lambda g y}{\lambda} \frac{\partial^2 x}{\partial y^2}$$ but I don't know what to do with it.


title: What are the normal modes of a vertical rope?

text: Closely related to this question on traveling waves on a hanging rope, I would also like to know what the normal modes are on a rope that hangs vertically, fixed at both ends. Tension in the rope increases with height, so I expect that the wavelength of standing waves decreases as we move up, and nodes are clustered somewhat more towards the top of the rope than the bottom. Is this correct? The wave equation I found was ( **note** : important typo corrected) $$\frac{\partial^2{x}}{\partial t^2} = g \frac{\partial x}{\partial y} + \frac{T_0+\lambda g y}{\lambda} \frac{\partial^2 x}{\partial y^2}$$ so mathematically, my question is about how to find the eigenfunctions of this equation with the boundary conditions $x(0) = x(h) = 0$ with $h$ the height of the ceiling. (I was able to locate a reference, but don't have access to it.)


title: Finding the voltage of an inductor in a RL series circuit

text: ![enter image description here](http://i.stack.imgur.com/f9tbl.png) Here is the solution: ![enter image description here](http://i.stack.imgur.com/lj9Eg.png) This assigned question is an odd one since it doesn't seem to have anything to do with phasors which is the chapter I am currently studying. I know that that the phase relationship in a RL circuit is that voltage leads current but I'm not sure why they used Pythagorean theorem.


title: Scientific value of timing total lunar occultations

text: Is there still scientific value in timing and reporting **total** lunar occultations? Why would I time total lunar occultations (grazing occultations are out of the question)? When I reported observations to ILOC many years ago I never got any feedback. Is the situation better today? There are apparently new arrangements, but are they actually working, for example, how is feedback provided to observers?


title: What is an asterism compared to a constellation?

text: I'm doing an astronomy exam tomorrow and in the practice paper it asks for the difference between constellation and asterism. It seems asterism is a group of recognizable stars; however I thought that is what a constellation is. So what exactly is the difference?


title: Is this scene from the A Team explainable by Physics?

text: This scene (youtube link) from the movie _The A-team_, the four members are in the tank and its falling from the air, they fire the canon and it slows the tank from falling for a moment before falling again. Is this possible from a Physics point of view? I am looking at this from a recoil point of view. Can the tank firing the rocket produce enough recoil for it to counter the force of gravity?


title: Was Max Born the first to notice a connection between quantum mechanics and randomness?

text: Max Born introduced the Born Rule in a paper from 1926. But was this really the first time that a connection between quantum mechanics and randomness was noticed? Today, quantum mechanics and randomness seem to be so closely connected that it's hard to imagine that 21 years should have past between Einstein's 1905 paper on the photoelectric effect, and the realization that randomness might be involved if "energy is exchanged only in discrete amounts".


title: A vector field $\vec{F}$ from cartesian to spherical

text: I have a vector field F that has the same magnitude and directions at all points in space. If I choose $z$-axis parallel to $\vec{F}$, so the cartesian coordinate of $\vec{F}$ is $\vec{F}=F\hat{z}$, How can I express $\vec{F}$ in spherical coordinates? My guess = $\vec{F}=\cos(\theta)\hat{r} - \sin(\theta)\hat{\theta}$ I think?


title: What is the mass of the universe?

text: Working with a flat and infinite model of the universe (which seems to be the most popular serious model these days), the density of the universe is 3e-28 kg/m^3 [1]. When added to the cosmological principle, it would imply that the mass of the universe is infinite. Yet, the same umass.edu link [1] reports _"...that the number of atoms in the Universe is at least about 4e78, but perhaps as many as 6e79."_ What am I missing here? Note that, before this statement, no-where am I referring to the observable universe. If you know where I have erred, it would be great if you could restrict it to the flat and infinite assumption and also talk in the context of the entire universe (and entirely skip references to the observable universe).


title: How do I correctly scale down a space capsule for testing its physical behaviour on splashdown?

text: Kristian von Bengtson (on twitter, on Wikipedia) of Copenhagen Suborbitals is building a downscaled test item to test the design for their space capsule. He notes that as volume and area scale down differently, he has to make sure that his test results sre still applicable to the full-scale item. He asks on Wired if the following assumptions he makes on the physical properties of his 1:3 scale model of a space capsule are correct:   * to test buoyancy behaviour (does it swim, in what position does it come to rest), he has to keep the volume to mass ratio (i. e. the density) constant.   * to test the forces on impact in the water, he has to keep the ratio of inertia to impact area constant, and therefore add mass to the model (because the volume, and therefore the mass, scales down more quickly than the craft's cross section) Are those assumptions correct?


title: Frequency Modulation

text: If FM radios work by modulating the frequency, how is it that we can tune into a specific channel, and hear a song or station? Wouldn't the channel need to be modulated along with the varying frequency?


title: Limit on velocity in Minkowski Spacetime geometry

text: Let A be a rocket moving with velocity v. Then the slope of its worldline in a spacetime diagram is given by c/v. Since it is a slope, c/v = tan(theta) for some theta > 45 and theta < 90. Does this impose a mathematical limit on v? If so what is it? As in, we know tan(89.9999999999) = 572957795131. And c = 299792458. Using tan(89.9999999999) as our limit of precision, the smallest v we can use is: c/v = tan(89.9999999999) => 299792458 / v = 572957795131 Therefore, v = 1911.18 m/s What is the smallest non zero value of v? Is there a limit on this?


title: Electron Fermi gas

text: My question is about 2-dimensional Fermi gas of electrons.   1. What is magnetic susceptibility when $T<<T_F$ (where $T_F$ is Fermi Temperature) and,   2. What is the ratio between Pauli and Curie spin susceptibilities?


title: Is there any analogy between electron positron annihilation and brane anti-brane annihilation?

text: I would like to know if there is any similarity between electron positron annihilation and brane anti-brane annihilation? Is it there then can we use electron positron annihilation knowledge to study more about brane anti-brane annihilation and there by string theory?


Spontaneous (exothermic) chemical reactions often require a push from the addition of externally supplied energy. This energy is often called activation energy. What does activation energy actually do? What is the energy hill that the activation energy surmounts?


title: Why does hair stand up when standing under power lines?

text: My initial guess would be the immense electric field around the lines, that causes hair to get charged and due to each hair having the same charge they start to repel each other. So what is exactly happening here?


title: Why is it wrong when I try to use Newton's Law?

text: > A 25 kg block is connected to a 30 kg block by a light string that passes > over a frictionless pulley. The 30 kg block is connected to a light spring > of force constant 195 N/m, as in Figure P13.59. The spring is unstretched > when the system is as shown in the figure, and the incline is smooth. The 25 > kg block is pulled 15 cm down the incline (so that the 30 kg block is 35 cm > above the floor) and is released from rest. Find the speed of each block > when the 30 kg block is 20 cm above the floor (that is, when the spring is > unstretched). ![image of blocks on ramp and spring](http://www.webassign.net/sf/p13_59.gif) I wrote out all the equations For the 25kg mass $$\sum F_x = T- mg\sin\theta = ma$$ $$\sum F_y = n = mg\cos\theta$$ For the 30kg mass $$\sum F_y = kx + Mg - T = Ma$$ Using energy, I got v = 0.91m/s, but using Newton's Law I got 0.95m/s EDIT: **Energy** $E = Mgh + \frac{1}{2}kh^2$ $E' = mgh\sin\theta + \frac{(M + m)}{2}v^2$ $E = E'$ Solving, $v = \sqrt{\frac{2Mgh + kh^2 - mgh\sin\theta}{m + M}}$ **Forces** $T- mg\sin\theta = ma$ $kh + Mg - T = Ma$ Add the two equations $kx + g(M - m\sin\theta) = (M + m)a$ $\frac{kh + g(M - m\sin\theta)}{M + m} = a$ $v^2 = 2\frac{kh + g(M - m\sin\theta)}{M + m}h$ $v = \sqrt{2\frac{kh + g(M - m\sin\theta)}{M + m}h}$ The source of the mistake seem to lie with the 2 in front of the kh


title: storing energy (as mass)

text: When chemical energy is released mass is reduced, if only by a negligible amount. Presumably that's true for all energy. And presumably that works in reverse as well: storing energy involves an increase in mass. It seems to follow that moving some object against a gravitational gradient, increases the mass of the object -- potential energy is being stored. Somehow that's difficult to understand. Is it really true?


title: Can I use the reduced mass principle in a spring-damper system?

text: http://hyperphysics.phy-astr.gsu.edu/hbase/orbv.html#rm I want to know, if I can use the reduced mass principle to solve a two object spring-damper system. In the books and webpages that I have check out, this principle is used only with simple spring systems; without any damping. I know that this principle is a consequence of the 3th Newton's Law. I just want to be sure if this principle can be also be used when the objects are connected using a spring and a damper?


title: Do green stars exists?

text: I asked a university lecturer why we don't observe green stars, and he said the blackbody curve averages at that frequency such that the cones in our eyes don't recognise it. I have a hunch that white stars emit shades of green, and this is reflected by chlorophyll, but this paper throws confusion on the matter "AEGIS: THE MORPHOLOGIES OF GREEN GALAXIES AT 0.4 < Z < 1.2" http://arxiv.org/pdf/1101.3353.pdf What is green about 'Green Valley' galaxies, if anything? My hunch is that they're called green to emphasise the fact that they're some kind miscellaneous class, i.e. not particularly white and not particularly yellow, just somewhere in between blue and red.


title: Does time dilation correct for the Doppler effect?

text: Knowing that a body in motion experiences time dilation, "also" knowing when two objects travel at a great speed away from one an other, both observers experience the others clock as moving slower relative to themselves due to the Doppler effect "I presume". So is it safe to speculate that if observer A where stationary and observer B where in motion (disregarding time dilation for observer B) that they would mutually experience each other's time as slowing down due to the Doppler effect alone? However; taking time dilation into account for observer B, wouldn't the observed Doppler effect of observer A's slowing clock combine with the time dilation of B's to be an in-sync operation? Where if B looking back at A's clock would appear to B as time moving normal? (just to clarify: I realize this would have the reverse effect if B where to travel towards A rather then away, meaning B's time dilation combined with its more frequently emitted light pulse would then appear to A as B's time moving normally instead).


title: Is the Mendeleev table explained in quantum mechanics?

text: Does anybody know if there exists a mathematical explanation of Mendeleev table in quantum mechanics? In some textbooks (for example in F.A.Berezin, M.A.Shubin. The Schrödinger Equation) the authors present quantum mechanics as an axiomatic system, so one could expect that there is a deduction from the axioms to the main results of the discipline. I wonder if there is a mathematical proof of the Mendeleev table?


title: Quantity with approximate lognormal distribution

text: I am studying a quantity $x$ for which $\log( x)$ is nearly (although not exactly) lognormal. What would be the appropriate "typical" value: the mean $\langle x\rangle$ or rather $e^{\langle\log(x)\rangle}$?


title: Why is copper a metal?

text: **Context** : Solid state physics **Question** : Can it be reasoned in the context of solid state physics (perhaps within the band theory of solids?) that copper is a metal ?


title: What is the relationship between Luminosity, Intensity, and Flux?

text: I am always confused by the terminology: In high energy particle scattering, and in particular, in the context of collider physics, what is the relationship between luminosity, intensity and flux? What are the (SI _and_ natural) units for these quantities? And finally, how do they relate to the cross section and to the event rate? There are so many quantities to keep track of--I think it's easy to get lost!!


title: Does a coronal mass ejection change solar neutrino emission rates?

text: Does the CME and neutrinos have any relation? CME is measured by Corona graphs.. How do they measure neutrinos coming from the sun? Does any of these have effects on earth's magnetic field or atmosphere..?


title: Positive emf? What does positive emf mean?

text: ![enter image description here](http://i.stack.imgur.com/YTJOr.jpg) Could someone please explain to me why we want to take the "magnitude" of the emf?


title: Is quantum entanglement functionally equivalent to a measurement?

text: I saw the following talk the other day: http://www.youtube.com/watch?v=dEaecUuEqfc&feature=share In it, Dr. Ron Garret posits that entanglement isn't really that "special" of a property. He argues (and shows) that the mathematics behind it is analogous to the math behind measurement. Is this true? There seems to be a lot of hoopla around quantum entanglement (including people that argue it could facilitate faster-than-light (FTL) communication). Is this excitement about the entanglement properties of some elementary particles unwarranted? Just looking for some clarification.


title: Beta Decay Energy

text: Consider $\beta ^-$ decay. \begin{align*} ^{198} Au \rightarrow ^{198} Hg + e^- + \bar{v_e} \end{align*} The decay energy is given by the difference in mass between multiplied by the speed of light. So, you'd take the mass of the Au nucleus - the mass of the Hg nucleus - the mass of the electron to find the change in mass (I think we leave out the mass of the antineutrino since its really small, therefore the equation for the decay energy is actually an upper limit). My textbook goes on to say that the decay energy can be written in terms of the mass of the atom, and not the nuclear mass. \begin{align} \frac{Q}{c^2} = M_p - M_D \end{align} where $Q$ is the decay energy, $M_p$ is the mass of the parent atom, and $M_D$ is the mass of the daughter atom. My book derived this by adding $Z$ electrons to both the parent nucleus and the decay products. If we take the initial example above, \begin{align} ^{198} Au + 198e^- \rightarrow ^{198} Hg + 198e^- + e^- + \bar{v_e} \end{align} which becomes, Mass of Au atom $\rightarrow$ Mass of Hg atom + $e^- + \bar{v_e}$ or \begin{align} M_p \rightarrow M_D + e^-1 \end{align} (I leave out the antineutrino here). So my question is, why is the decay energy just $M_p - M_D$ and not $M_p - M_D -e^-$? For $\beta ^+$ decay, my textbook says that the decay energy is \begin{align} \frac{Q}{c^2} = M_p - (M_D -2m_e) \end{align} They derived this in the same fashion. So my question also applies to this decay process as well.


title: The equation of the location of L1

text: On http://en.wikipedia.org/wiki/Lagrangian_point#L1 it says that the location of L1 can be determined as $\frac{M_1}{(R-r)^2}=\frac{M_2}{r^2}+\left(\frac{M_1}{M_1+M_2}R-r\right)\frac{M_1+M_2}{R^3}$, but how can I deduce this equation myself? From which equations is this derived?


title: Why do rolling disc (coin) move in circular path?

text: We have a coin that is rolled such that it's tilted at an small angle $ \theta $. **Question::** What turns around rolling disc so that it traces circular motion (spiral as it's speed decreses)? **Problem statement::** In the following figure, what turns the disc so that it follows the circular path? ![image 1](http://i.stack.imgur.com/0Mp7R.jpg)   **Solution::**   I interpreted the problem incorrectly. Only a sliding body would have a torque like that.


title: Will it start rolling?

text: Suppose you have a wheel standing stationary on a rough horizontal surface. Now you apply a horizontal force at the top of the wheel. Now, will the wheel experience any force or will it just start rolling smoothly? I am a beginner to physics and hence, slightly confused. Please help


title: Is pressure distribution affected by shape

text: We have two iron (assume real-life stiffness) manhole covers resting on friction-less, perfectly smooth shims on flat ground. One is circular and the other square. If a force F is applied vertically downwards at the center of each manhole cover, is the pressure on the manhole shim distributed uniformly in each case? i.e. is the downward force at any given cover-contact-point on the shim the same for both manholes.


title: expectation vaules of commutator and anti commutator (momentum and position)

text: what is expectation vaules of commutator and anti commutator when the case is momentum and position. when the case is commutator: $$\langle i\hbar\rangle=?$$ when the case is anti commutator: $$\langle - i\hbar \rangle=?$$


title: How does a strobe lamp stop a fast moving object?

text: A strobe lamp can be used to seemingly stop a fast moving object when calibrated.   Commonly used in quality assurance during production to inspect otherwise non- observable assembly line activity. What causes this effect in observations?


title: what is physical meaning of this partial derivative?

text: what is physical meaning of this partial derivative: $$\frac {\partial p_x}{\partial x}$$ i know how do i solve it when the case is just derivative but partial derivative is a bit Hectic!.


title: What is a Lorentz boost and how to calculate it?

text: I know very little special relativity. I never leaned it properly, but every time I read someone saying: "if you boost in the x-direction, you get such and such" my mind goes blank! I tried understanding it but always get stuck with articles that assume that the reader knows everything. So, what is a Lorentz boost, and how to calculate it? And why does the direction matters?


title: Why Are Maxwell's Equations Preferred Before Those Proposed by H. Hertz?

text: In a recent exchange it was pointed out that in certain situations Maxwell's equations need Lorentz force as a patch (the latter not being part of those equations neither is it derivable from them). It appears that the equations proposed by H. Hertz lack that deficiency while retaining Lorentz invariance. What might be the reason for using Maxwell's equations instead?


title: What are typical values of the critical thickness of insulation?

text: As most people who've had any elementary heat transfer course are aware, when insulating a pipe, wire, etc, there is a critical thickness for the insulation below which it causes greater heat transfer than no insulation would. In actuality, since the critical radius is a minimum, one needs to go even farther before it catches up to the uninsulated case. This effect is due to the thermal resistance from the added insulation (a function of material and thickness) being less than the decrease in thermal resistance to convection brought about by the increased surface area due to the thicker insulation. A more detailed explanation is found here What I wonder is how large this critical thickness typically is for realistic cases such as an electrical wire, a steam pipe, or a water pipe (all cases in STP air)? I realize exact answers aren't possible given the fact that it will vary with material type, temperature diff., and size. The motivation for this is that it theoretically could prevent wasting insulation or provide a practical avenue for energy dissipation, but Fundamentals of Heat and Mass Transfer 6e by Incropera et al. indicates that the effect is usually too small to be of practical importance.


title: How does the weak force between two neutrinos compare with their gravitational interaction?

text: In short, are there cases where the weak interaction between two neutrinos is actually smaller, in (absolute) magnitude, than their gravitational interaction? There is no principle that forbids this. But is it ever the case?


title: Negative radiation pressure from negative refractive index?

text: I see this claim being originally made by Vesselago (the discoverer of the principles of metamaterials) and indeed in contemporary papers. It means that such a metamaterial would be pulled towards its illuminating light source. Why does this not violate conservation of momentum?


title: Principle of Caratheodory and The Second Law of Thermodynamics

text: **Background** _Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:_ > In every neighborhood of any arbitrary initial state $P_{0} $ of a physical > system, there exists neighboring states that are not accessible form $P_{0} > $ along quasi-static adiabatic paths. The above statement is taken from 'Heat and Thermodynamics' 8th Ed by Zemansky and Dittman and it provides a very concise discussion on the topic which I did not find very illuminating. Moreover, Wikipedia states it slightly differently as: > In every neighborhood of any state S of an adiabatically enclosed system > there are states inaccessible from S. _With this formulation he described the concept of adiabatic accessibility for the first time and provided the foundation for a new subfield of classical thermodynamics, often called geometrical thermodynamics._ **My questions are:**   * What is the exactly meant by _Adiabatic Accessibility_ and how is this relevant to the formalism of The Second Law?   * How is this formalism equivalent to the Kelvin Planck and Clausius statements of the Second Law?   * Except for the satisfaction of having an axiomatic approach, does this provide any advantage over the Kelvin-Planck formalism using heat engines? P.S: The text in _italics_ has been copied from Wikipedia.


title: Does a second similar source of white noise increase the overall noise level?

text: If I put next to my cooler another similar cooler that produces similar white noise, will the overall noise level increase? I want to point out that I am speaking about adding another independent, non- correlated white noise source, not just another pair of speakers that produce sound of the same phase and curve. It is evident for me that adding another speaker will increase amplitude twofold compared to one speaker, but this is not evident for coolers which produce non-correlated sound.


title: Is there a theoretical upper bound on the mass any new particles can have?

text: One possible outcome of the collision experiments at LHC is the discovery of new elementary particles with large mass. Is there a theoretical way to derive an upper bound on the mass of elementary particles? For example, we have the electron, the muon and the tau particle. Can we be sure that there are no heavier elementary fermions with charge $e$? (Maybe there are some symmetry arguments?)


title: General Relativity Paradox: Holding a string across a gravitational gradient

text: The paradox I envision involves two objects that exist in very different gravitational potentials -- one very high (eg: close to a black hole) and one very low (eg: far away from a black hole). Now, imagine these objects are actually little spaceships that are blasting their engines so that they remain a constant distance away from the black hole. Also, imagine they are lined up with each other (the black hole, the near spaceship, and the far spaceship form a line). Would it be possible to lower a string from the further spaceship to the spaceship which is closer? **That is, will the distance between the two spaceships be measured to be a constant?** _If it's not.._ please explain this! It seems odd that the distance between the two ships wouldn't be constant. _If it is_ , then it seems like there would be a paradox. First, let's label the spaceship nearer to the blackhole "A" and the one further "B". Next, let's say the string's length is exactly 1 light second. Now, let's start a light clock between "A" and "B" -- "A" will send a light pulse to "B", and upon receiving this, "B" will send a light pulse to "A", and so forth. Since both "A" and "B" know that their distance is 1 light second apart, each time they receive the pulse, they will add 2 seconds to their clock. While we're at it, they might as well send along their recorded time with the light pulse. The paradox is that from the perspective of B viewing A, A should appear to be moving in "slow motion" -- everything will be redshifted, and everything will transpire slower. From the perspective of A viewing B, B will be blueshifted and moving in "fast motion". Yet, this cannot be the case, because both will be receiving ticks at 2 second intervals, and each tick will represent 2 seconds of elapsed time on the other party. So, what gives? I'm assuming you cannot have a constant distance between two objects if their gravitational potentials are different. But that just seems very strange. Thanks. Edit: It would be very helpful if the answers could give an example of what it would be like to be onboard A and onboard B. If you're on A, and you send the pulse, how much time will you measure before you hear back from B? If you're on B, and you send the pulse, how much time will you measure before you hear back from A?


title: Thermodynamics, chaperones : How to model polymer fragmentation

text: Living polymers are well described by equilibrium statistical physics. Now I would like to consider a case were living polymers undergo fragmentation due to chaperones. I can think of a kinetic description, but can I still use equilibrium statistical mechanics? **Edit :** I'd like to make the question a bit more general. Here are my interrogations : When there is no chaperone activity, i.e. polymers polymerize and de polymerize freely, I am comfortable with equilibrium statistical mechanics because I can define a free energy, accounting for polymer binding energy, and entropy. See for example the Flory-Huggins theory. When it turns to chaperone activity, it seems to me obvious that non equilibrium physics is adapted to this case : it looks like a dynamical system, and I don't see how to define an energy in the context of equilibrium stat mech. In an other hand, for the former case (no chaperone), I can also think of a kinetic model, with association and dissociation rates, leading, at equilibrium, to the same result as equilibrium physics. So, what is fundamentally different between the two cases? Why one can be described by equilibrium physics, while the other can't (assuming it can't, that was actually my first question). In the case with chaperone activity, I see that energy is spent to break each polymer. In the dynamic description, this is not a problem, as long as we can define reaction rates, but if one wants to use equilibrium description, I think the crucial (and difficult) point is to consider this energy used by chaperones. Thanks for any comment that could make me understand a bit more the boundaries between equilibrium and non equilibrium systems **Edit 2** After some reflections, I think I got what's make the difference. With chaperone activities, at time +infinite, you expect an equilibrium state, with a polymer size distribution. But this equilibrium is intrinsically dynamic : energy is continuously provided by the chaperones, breaking the polymers. This input of energy is clearly not described by equilibrium stat mech (see micro- canonical, canonical, grand canonical ensembles) **Any comment, reading suggestion is more than welcomed.**


title: Covariant derivative of a vanishing tensor component

text: Is the covariant derivative of a vanishing tensor component necessarily zero?


title: what is QCD Background?

text: I am looking at some papers in particle physics and came across 2 terms called QCD Background and ABCD method (control region and signal region). When I searched them on Google, could not get much information about them. Could someone either of those terms in a simple way for a non-physicist?


title: Third-order susceptibilities of metals?

text: Can anyone point me to a source for measurements of the third-order nonlinear electric susceptibilities $\chi^{(3)}$ of various metals? Specifically in relation to the AC Kerr effect, so measurements of the second-order index $n_2$ would do as well. For example, Bloembergen published measurements in 1969 (Opt. Comm. 1(4), 195) of the $\chi^{(3)}$ of silver and gold determined using THG, but I'd like to know if there's any data for other metals, and whether they are any different when studying the Kerr effect.


title: Luminescence when ripping (answered) and when pouring (not answered)

text: As a father to a small child, I have often observed this phenomenon but have until i posted this question not found the vocabulary to Google for it. Can you explain what I am seeing? In a darkened room I see a faint light appearing when:   1. pouring a quantity of urine from a potty into a toilet (I will spare you the image) **Update** possibly urine chemiluminescence - however I think that is when it gives off light on its own - without being poured   2. pulling something apart ( **UPDATE** it is called Triboluminescence) that was taped together on purpose such as   a) the fasteners on a modern diaper   b) opening a _band-aid_ "envelope" ![Band- aid](http://i.stack.imgur.com/pgdij.jpg) (please note that I had not used the word "band-aid" until I was looking for an image to describe what I was pulling)


title: The FRW universe is NOT asymptotically flat? Its mass?

text: The Friedman-Robertson-Walker (FRW) metric in the comoving coordinates $(t,r,\theta,\varphi)$ which describes a homogeneous and isotropic universe is $$ ds^2\,= -dt^2+\frac{a(t)^2}{1-kr^2}\,dr^2 + a(t)^2 r^2\,\Big( d\theta^2+\sin^2 \\!\theta \,d\varphi^2 \Big) $$ where $k$ is the curvature normalized into $\\{-1\,,0\,,+1\\}$ which refers to a closed, flat and open universe, respectively; and $a(t)$ is the scale factor. My question is, this FRW metric is NOT asymptotically flat at spatial infinity $r\to+\infty$, isn't it? Thus, we can not calculate the so-called ADM mass (Arnowitt-Deser-Misner), right? If so, how to get **the mass of the matter content** from the metric? Note: I do not mean the trivial $m=\rho V$, I mean the mass obtained from the FRW metric. The matter/material content determines geometry/metric, and reversely the metric reflects the matter content. So I'm trying to recover the material mass (not including the gravitational energy) from the FRW metric.


title: How do I calculate DC motor speed for a given load?

text: Suppose I have a robot of a given mass, and I'm choosing between 2 different wheels and 2 different motors to put on it. For each wheel I have the diameter, and for each motor I know the stall torque and free speed. How would I figure out which motor and wheel combination will make the robot move the fastest? My calculations show to use the big motor with the big wheels, but the small motor with the small wheels goes faster than the big motor with the small wheels. I am not sure my calculations are correct, I need to know the correct way to work this problem.


title: Quantization of orbital angular momentum

text: Probably a very simple question, but I can't find the answer on the Internet. I know nearly to nothing about quantum mechanics, but in statistical physics I'm confronted with the idea that the orbital angular momentum is quantized as $$ L = \sqrt{(n(n+1)}\hbar, $$ with $n$ being an integer. But in the Bohr description of the hydrogen atom I was also confronted with $$L = n\hbar,$$ with $n$ being an integer, which seems to contradict the first one. (If I look for it on the Internet, it is stated that the first $L$ is the norm of the angular momentum, while the second $L$ is only the $z$-component. But I don't see how those two can be different.) And what I'm also wondering about is, if the electron of the hydrogen atom is in ground state, which one will be its rotational momentum? And because $ \mu = \frac{eL}{2m}$, with $ \mu$ being the magnetic momentum, what will be the magnetic momentum? It seems that both formulas give different values. I hope it's possible to give a simple (intuitive) explanation for this, because I have no experience at the moment with quantum-mechanical operators, ...