title: What is actually universe? only matter or both matter and space?

text: I have googled for the "meaning of universe" where I found the following: "all existing **matter and space** considered as a whole; the cosmos. The universe is believed to be at least 10 billion light years in diameter and contains a vast number of galaxies; it has been expanding since its creation in the Big Bang about 13 billion years ago." Now,I have heard about big bang theory which tells that universe was initially a point of infinite density .But in the above definition I see space is also included in the universe. so if the universe was initially a point then **what was outside that point?** And **how this point is expanding if there is nothing outside it?** That is why I don't understand the balloon analogy also which is expanding in space. But here the universe itself contains the space according the google definition. Probably I have this question in my mind because I couldn't visualize how the space meets on itself in 3 dimension like earth's surface does on 2 dimension.


title: Problem with experiment results on drag force

text: I am trying to investigate the relationship between velocity and drag force of falling object in air. I used video analysis from logger pro to determine the displacement of the falling object at different time, and then differentiation to find velocity and acceleration. Drag force at each time interval is found by subtracting the resultant force from the weight. I found a smooth relationship between velocity and drag force, but it is similar to a hyperbolic tangent function which is totally different from the drag equation.   How come??


title: relation between Schrodinger equation and wave equation

text: I have always been confused by the relationship between the Schrödinger equation and the wave equation. $$ i\hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2}{2m} \nabla^2+ U \psi \hspace{0.25in}\text{-vs-}\hspace{0.25in}\nabla^2 E = \frac{1}{c^2}\frac{\partial^2 E}{\partial^2 t} $$ Because of the first derivative, the Schrödinger equation looks more like the heat equation. Some derivations of the Schrodinger equation start from wave-particle duality for light and argue that matter should also exhibit this phenomenon. In some notes by Fermi, it was derived by comparing the Fermat least time principle $\delta \int n \;ds = 0 $ and Maupertuis least action principle $\delta \int 2T(t) \; dt = 0 $. Was this ever clarified? How can we see the idea of a matter-wave more quantitatively? * * * To summarize, I am trying to understand why the Electromagnetic wave equation is hyperbolic while the Schrodinger equation is parabolic.


title: Are Feynman's Hamiltonian computers unitary?

text: In this paper, Feynman gave the idea of creating a time-independent Hamiltonian from a quantum circuit. Is there anyway to say that these Hamiltonians will always be Hermitian? Moreover, will these Hamiltonians be always unitary?


I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the next chapter which is about path integral for boson and fermion. Here, I am confused for a long time. Could you please tell me the difference between the two kind of path integrals? What is the point of path integral for boson and fermion? I find that there are big differences in forms between single particle, boson and fermion. I am not understand why the book uses different forms to discuss them. Even the path integral for the spin system has a new form to discuss. In my opinion, I think the biggest difference between single particle and boson (fermion) is statistics, but how to consider about the statistical properties in path integral? Just using one symbol for differential, $D$, to take the place of the original symbol, $d$, is enough?


title: Airy Pattern as infinite sum of Fraunhoffer Patterns

text: Is there a way to view the Airy Pattern as an infinite sum of Fraunhoffer diffraction patterns? I don't know where the 1.22 would come from then. Is there something inherently wrong with collapsing diffraction slits to infinitely small slits?


title: microcausality and locality

text: There is this thing I got confused: Microcausality is the statement that spacelike separated local field variables commute so that we can specify field variables on a spatial slice as a complete base. It is usually referred to as a statement about locality---if microcausality is broken then the "local" operators are not that "local". There is another statement about the notion of "locality" in S-matrix language ---an S-matrix have poles corresponding to particle exchange, and the residue factorizes into S-matrices of sub scattering processes in the limit that these processes happen far from each other. It is in the line of cluster decomposition principle. So my question is: do these two statements somehow have connections to each other, or even are equivalent? Or they are simply two very different statement and not connected at all?


title: Spacetime Diagrams

text: > > Suppose an observer $\mathcal{O}$ uses the coordinates $t$, $x$, and that > another observer $\mathcal{O}'$, with coordinates $t'$, $x'$, is moving with > velocity $\mathbb{v}$ in the $x$ direction relative to $\mathcal{O}$. Where > do the coordinate axes for $t'$ and $x'$ go in the spacetime diagram of > $\mathcal{O}$? >> >> $t'$-axis: This is the locus of events at constant $x'=0$ (and $y'=z'=0$, too, but we shall ignore them here), which is the locus of the origin of $O'$'s spatial coordinates. This is $O's$'s world line, and it looks like that shown in the figure below. ( _A First Course In General Relativity_ , Bernard Schutz, Second Edition, p. 6) Since an observer is at the origin of his coordinate system, and $\mathcal{O'}$ is moving with a relative velocity of $v$ in the $x$ direction relative to $O$, I am perfectly fine with the fact that the line which we call $t'$-axis in the diagram is the worldline of $\mathcal{O'}$ in the spacetime diagram drawn by $\mathcal{O}$. However, I do not at all get the point of why we say that this worldline of $\mathcal{O'}$ is the "$t'$-axis" of $\mathcal{O'}$ in the spacetime diagram drawn by $\mathcal{O}$, and why it has to be that way; "tilted". Can someone please explain the reasons to me? ![enter image description here](http://i.stack.imgur.com/liU96.jpg)


title: Do COBE, WMAP, and Plack have design flaws?

text: MRI expert Pierre-Marie Robitaille on the design flaws of COBE, WMAP, & Planck and the violation Kirchhoff's Law: Here are his talks: **Pierre-Marie Robitaille: The Cosmic Microwave Background** **Pierre-Marie Robitaille: On the Validity of Kirchhoff's Law** Robitaille holds the world record for highest resolution MRI imaging. An interesting point he makes is that cosmological sources would not vary over time, yet the COBE, WMAP, and Plank data are highly variable. Here are his papers detailing the design flaws of COBE, WMAP, and Planck: Robitaille P.-M. WMAP: A Radiological Analysis http://www.ptep- online.com/index_files/2007/PP-08-01.PDF Robitaille P.-M. COBE: A Radiological Analysis http://www.ptep- online.com/index_files/2009/PP-19-03.PDF Robitaille P.-M. The Planck Satellite LFI and the Microwave Background: Importance of the 4K Reference Targets http://www.ptep- online.com/index_files/2010/PP-22-02.PDF


title: Energy Required to Rip Spacetime

text: I have heard that the presence of an extremely strong gravitational field possesses the capacity to warp or tear spacetime and to potentially create a wormhole. Is any energy lost when spacetime is ripped, and if so is there a constant energy per volume required to 'rip' a given region of spacetime? Otherwise, is there some minimum gravitational field strength required to rip spacetime?


title: Estimation of the internal electric field strength in the pn-junction

text: I would like to compare my result in an order of magnitude. So, How can I estimate the strength of the electric field in a typical Si PN-junction?


title: Capacitor with dielectric between the plates

text: Let's assume we have a capacitor of capacitance $C$ and potential difference $U$. After charging it we disconnect it. Then we put a dielectric between the plates. I know that capacitance will increase by $C * k$, however what happens with the charge and potential difference on it. Let's say $k = 2$. Will $q$ double or will $ U $decrease to a half ?


title: Charge residing on an overpolished surface

text: I had very well read that when charge is stored on a rough surface, the leakage is very high from the pointed tips of such surfaces, by a phenomenon called action of points. But now, I've come to know that if a surface is over- polished (or say ideally polished), it becomes very difficult to store charge on it. I'm confused with this. What might be the reason to say so? I do think that by over polishing, you destroy the dielectric layer on the surface of such object (where we tend to store charge) and charge can't be stored easily. But I'm not satisfied with my own logic. So, can someone please clarify it?


title: Question about the Noether charge algebra

text: I'm reading these notes \- page 8 and 9 - and I'm a bit confused. If we consider a field $\phi$ (which can be either bosonic or fermionic) transforming as: \begin{equation} \phi(x) \rightarrow \phi(x) + \delta \phi (x) \end{equation} with: \begin{equation} \delta \phi^a = t^a \phi(x) \end{equation} where $t^a$ is the generator of the transformation. The generators satisfy the Lie algebra: \begin{equation} [t^a,t^b] = if^{abc} t^c \tag{$*$} \end{equation} Let us suppose that the above transformation is a symmetry transformation such that the Noether charge corresponding to this symmetry is given by: \begin{equation} Q^a = \int \mathrm{d}^3 \mathbf{x} \; \pi \delta\phi^a = \int \mathrm{d}^3 \mathbf{x} \; \pi t^a \phi \end{equation} where $\pi$ is the canonical momentum density. It is then possible (but tedious) to show that the charges satisfy the so-called charge algebra: \begin{equation} [Q^a,Q^b] = i f^{abc} Q^c \tag{1} \end{equation} Until this point I understand it. But then the notes say on page 8: > [...] the charges generally have to satisfy the same algebras as the > generators – in fact it is only because of this that the symmetry has any > useful physical meaning. In particular it is the charges which are the > physical observables that participate in interactions rather than gauge > fields for example. I don't really understand what is meant with the above statement. What does the quote have to do with the fact that Noether charges obey equation $(1)$? Edit: I understand that the charges satisfy the same Lie algebra as the generators. But according to the quote above, if understand it correctly, we should also expect this based on logical/physical reasons. Apparently, according to the notes, "it is only because of this that the symmetry has any useful physical meaning." I don't understand why this is the case.


title: Frames, Tetrads and GR

text: Given a general metric, $g_{ab}$ I can select an orthonormal basis $\omega^{a}$ such that, $$g_{ab} = \eta_{ab}\omega^a \otimes \omega^b$$ where $\eta_{ab}$ = $\mathrm{diag}(1,-1,-1,-1).$ We may conveniently compute the spin connection and curvature form by employing Cartan's equations. The problem I have lies in getting back to the coordinate basis. I know the general formula, $$R^{\mu}_{\nu \lambda \tau} = (\omega^{-1})^{\mu}_a \, \omega^b_\nu \, \omega^c_\lambda \, \omega^d_\tau \, R^{a}_{bcd}$$ where the l.h.s. $R^{\mu}_{\nu \lambda \tau}$ is in the coordinate basis. The objects $\omega^b$ are familiar, they're just the orthonormal basis, so what is the object $\omega^b_\nu$ (with the extra index)? The $(\omega^{-1})^{\mu}_a$ are the inverse vielbeins? How are these obtained? I've visited several sources, including Wikipedia, but it's still not 100% clear. I'd appreciate any clarification, especially a small explicit example if possible.


title: Why doesn't a gaussian surface pass through discrete charges?

text: I have read that **Gaussian surface** cannot pass through discrete charges. Why is it so? I have even seen in application of Gauss' Law when we imagine a Gaussian Surface passing through a charge distribution, e.g. in case of infinite plane charge carrying sheet . If it cannot pass through discrete charges how do we use it in continuous charge distributions as same ' _objection_ ' must be there for it also. Please explain the reason. ![](http://i.stack.imgur.com/t7Yjt.png) Here $E \rightarrow \infty$ as, $r\rightarrow 0$ If this is ambiguity then this must be same in continuous charge distribution , otherwise please state it more clearly because we can define charge to be a spherical ball and half charge can be considered inside surface (as in pic and even agreed by @JoshuaBarr).


title: What are the Implications of Bell's Theorem?

text: Consider the following game show: two friends Tom and Jerry (X and Y) are selected from an audience to compete for a grand prize, a brand new Ferrari. The game description:   1. The two contestants are space-like separated.   2. Each contestant will be asked one of three questions {A, B, C} and the questions which are asked of the two contestants need not be the same. Each of these questions has two possible answers, which we will quantify as {+1, -1}.    3. Repeat 2 a large number of times.   4. When the two contestants are asked the same question, they must always give the same answer.    5. When the two contestants are asked different questions, they must agree $ \frac 14 $ of the time.  Now, how can Tom and Jerry win this game? It's simple: They create a strategy, whereby they pre decide on a set of answers to give to the three questions {A, B, C}. This will guarantee that they always give the same answer when they are asked the same question. For example, they may decide on {+1, +1, -1} to {A, B, C}. Let us denote these answers as $v_i(\alpha) = \pm1$ for $\mathcal i$ = X, Y, $\alpha$ = A, B, C. This will not allow Tom and Jerry to satisfy 4. $\mathscr Theorem:$ There do not exist random variables $v_i(\alpha), \mathcal i$ = X, Y, $\alpha = A, B, C$ such that: $$ 1. v_i(\alpha) = \pm1 $$ $$ 2. v_X(\alpha) = v_Y(\alpha)\forall \alpha $$ $$ 3. Pr(v_X(\alpha) = v_Y(\beta)) = \frac 14 \forall \alpha, \beta, \alpha \neq \beta $$ $\mathscr Proof:$ Assume for contradiction that there do exist random variables $v_i(\alpha), \mathcal i$ = X, Y, $\alpha = A, B, C$ such that (1-3 hold). Since $ v_i(\alpha)$ can only take on the two values $\pm1$, we must have $Pr(v_X(A) = v_X(B)) + Pr(v_X(A) = v_X(C)) + Pr(v_X(B) = v_X(C)) \geq 1 $ By condition 2, we then have $Pr(v_X(A) = v_Y(B)) + Pr(v_X(A) = v_Y(C)) + Pr(v_X(B) = v_Y(C)) \geq 1$ Now, by condition 3, we have $ \frac 14 + \frac 14 + \frac 14 \geq 1$ a contradiction. But, if you look at the predictions of quantum mechanics, it is possible to satisfy (1-3). Experiments have validated quantum mechanics, thus the correlations achieved cannot be due to a pre existing strategy. Then we must wonder how could Tom and Jerry always assure that property (2) holds, if they can not simply pre decide on a set of answers to give to the three questions {A, B, C}. It must be that when Tom and Jerry are asked a question, they communicate with each other what question is being asked, and agree to an answer, for if not, one would have $Pr(v_X(\alpha) = v_Y(\alpha)) = \frac 12$ $\mathscr Bell's\; Theorem\; Implication:$ Quantum mechanical correlations are not due to pre existing properties $\Rightarrow$ there must exist an exchange of information between entangled subsystems about what properties are being measured on them, and what values of these properties are to be taken on. Combining this with rule (1) of the game implies that this must take place faster than light, recent experiments overwhelmingly suggest instantaneously. My question is why is this salient point so muddled in the literature? Bell's theorem is often stated as follows. $\mathscr No\; theory\; of\; local\; hidden\; variables\; can\; produce\; the\; predictions\; of\; quantum\; mechanics$ That's missing the point. The hidden variables (pre existing properties) are a derived consequence of no exchanging of information about what properties are being measured and what values to take on. Bell simply showed that pre existing properties fail as an explanation. Consequently, we must have the implication above. Credit to Tim Maudlin for the game description.


title: Does the Alcubierre drive use negative energy to compress space infront of it?

text: The contraction in most images looks like a gravity well. Is it that you use negative energy to BOTH contract and expand space or positive and negative to contract (positive energy) and then expand with then negative energy?


title: What does "causally connected" or "causes" really mean?

text: In a different thread, a user stated the following in respect of events preceding or following other events: > However, if the two events are causally connected ("event A causes event > B"), the causal order is preserved (i.e. "event A precedes event B") in all > frames of reference. My question is what does "causally connected" really mean? What does "causes" mean? Further, given that we know that we can have instantaneous effects in typical quantum processes (e.g. flip the polarizer, effect on another a reading light years away, even though we cannot transmit useful information with this), does that not constitute "causing" for the purpose of this statement?


title: Can matter be excited into energy and then be turned back into matter?

text: I was wondering the other day about teletransportation (human). And I had the idea that as far as I know, matter is energy. So I was wondering if it's possible to excite matter so it turns into energy, energy which may be could be moved to another physical location and then it would be allowed to return to it's original form. Is this just plaint stupid or is it theoretically possible?


title: Elastic collision of point particle and rod

text: > A 1 meter long rod on the ice with mass $m_2=1$ kg is perpendicularly hit on > one end by a point particle with mass $m_1=0.1$ kg. The collision is elastic > and the point particle is bounced back in the same direction. After the > collision the rod's frequency is $\nu =2$ Hz. What was the initial velocity > of the point particle? My attempt: Since the collision is elastic, the kinetic energy of the system is the same before and after the collision: $$0.5m_1v_1^2=0.5J_2 \omega_2^2+0.5m_2v_2^2+0.5m_1v_3^2$$ Where $v_3$ is the velocity of the point particle after the collision. Now, in the case of a rod: $$J=\frac{1}{12}L^2m$$ And, we also know: $$\omega_2=2 \pi \nu$$ And there are also no external forces, therefor the momentum of the system is the same before and after the collision: $$m_1\vec{v_1}=m_1 \vec{v_3}+m_2\vec{v_2}$$ Here $v_1$ is the quantity we're looking for, $v_3$ is the point particle's velocity after the collision and $v_2$ is the velocity of the rod's center of mass. It follows: $$\vec{v_2}=\frac{m_1 \vec{v_1}-m_1 \vec{v_3}}{m_2}$$ From this it follows: $$0.5m_1v_1^2=\frac{1}{24}L^2m_2 4 \pi^2 \nu^2+0.5m_2 |\frac{m_1 \vec{v_1}-m_1 \vec{v_3}}{m_2}|^2+m_1v_3^2$$ This is 1 equation with 2 unknowns, and this is where I get stuck. Any help is appreciated.


title: Propeller Force & Momentum

text: An air stream is created by a propeller at velocity $\nu = 93.6\frac{m}{s}$ To calculate force applied by the propeller I used this formula: $$F=\frac{1}{2}\rho\nu^2A$$ where:   * $\rho = 1.29 kg/m^3$ is the air density   * $\nu = 93.6\frac{m}{s}$ is the air velocity   * $A = 0.54m^2$ is the area swept by propeller's blades (This is for simplicity reasons) Is this a correct way? I think it's correct because the answer results in $kg.m/s^2 = N$. By plugging the numbers I got a force of $F = 3051$ N **How do I calculate momentum?** I tried this: $$p = m\cdot\nu$$ where $m$ is air mass. I calculated the mass this way: $$m = \rho.A.\nu$$ Although this would give $kg/s$ because of velocity, but I'm working on 1 second, we simply eliminate the $s$ by multiplying by $t = 1$ sec, thus the mass is $m = 65.2kg$ $$p = 6102 \frac{kg.m}{s}$$ This is **twice** the force. Where did it go wrong?


title: Make air reflect light

text: Is there any way in which air can be made to reflect light? By making air denser or by any other way? The task is to project images in air...


title: Normal reaction - force without acceleration

text: When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero. However, how can the body exert a force on the ground when it does not have any acceleration? Since force equals mass times acceleration how does a body without acceleration experience a force?


title: Can I see the light from 10 million km away?

text: If **light** is switched ON, only for a second, and the distance between the observer and the light source is 10 million kilometers, can I still see the light spark? For example, let's assume that the source is the Sun and the observer is a human eye.


title: Can entropy of Universe be constant?

text: If I understand entropy correctly, then for example two objects orbiting a centre of mass have lower entropy than when said objects eventually crash into each other and form a new one. So let's say that a typical galaxy spirals around its centre of mass and eventually objects within it will fall into the center thus increasing its entropy. But if the entropy of the Universe was somehow to be constant, then maybe that's why space is expanding? As each galaxy becomes more chaotic while objects are going closer and closer together these galaxies are at the same time becoming more and more spread apart thanks to expansion of space. I don't know the exact calculations of entropy, but is it possible that there is a mechanism triggering space expansion as a reaction to gravity increasing local entropy? Also gravity is increasing in intesity when the distance between objects is shorter, so the longer two masses are gravitating, the shorter the distance between them and then the more intensive gravity becomes over time. This might correspond then to the increasing speed of expansion of Universe, as it has to compensate faster to keep entropy constant. Forgive me if what I said above is completely incorrect; I've been thinking about entropy and came with this idea, but I'm no professional physicist and would like to know if any of the above make sense.


title: Direction of friction on particle placed on a rotating turntable

text: If a particle is placed on a rotating turntable then the particle has a tendency to slip tangentially with respect to the underneath surface... So the friction should act tangentially to the particle... Why then does it act towards the center... Please explain with respect to inertial frame Friction opposes relative slipping between surfaces... When the particle is initially placed on the rotating turntable... the surface under it has a tangential velocity. So, in order to oppose this slipping friction must act tangentially... How then does it act radially inward?


title: O(N) sigma model renormalization

text: Does anyone know, is a model with lagrangian $\mathcal{L} = \frac{(\partial_{\mu}\phi_a)^2}{2}-\frac{m^2 \phi_a^2}{2}-\frac{\lambda}{8N}(\phi_a \, \phi_a)^2$ renormalizable? I'm using BPHZ scheme and everything is OK in one loop. But it seems to me (may be I'm mistaken) that the scheme breaks down even in two loops. I will be grateful for links on books or lectures where such a model is considered.


title: Do some half-lives change over time?

text: I was recently doing some physics tuition on radioactivity and the student claimed her chemistry teacher had said that radioactive substances can be grouped into two divisions: those whose half-life is constant and those whose half-life changes over time. I had never heard of this before and can't think of any reason why a half-life should change, so does anyone else know anything about this? (I know some half-lives can be altered under certain conditions, but I'm talking about a natural change over time).


title: Gauss-Bonnet theorem in the Hawking/Ellis book

text: At the page 336 of Hawking, Ellis: _The Large Scale Structure of Space-Time_ , the Gauss-Bonnet theorem is stated as $$\int_H \hat{R}\ d\hat{S} = 2\pi \chi(H) \qquad (1)$$ with $$\hat{R} = R_{abcd} \hat{h}^{ac} \hat{h}^{bd}$$ and induced metric on the horizon $\hat{h}_{ab}$, $$\hat{h}_{ab} = g_{ab} + \ell_a n_b + n_a \ell_b \ ,$$ where $\ell^a$ and $n^a$ is a pair of future-directed null vectors on the horizon. Is there a missing factor of **2** on the RHS of equation (1)? The (2-dimensional) Gauss-Bonnet theorem in the literature is usually stated using "Gaussian curvature" $K = R/2$, so I'm suspecting in this "hidden factor" (compare it, for example, with Heusler: _Black Hole Uniqueness Theorems_ , equations (6.23)--(6.26)).


title: Kinetic energy of alpha-particle in $^{212}$Po decay

text: Admittedly, Nuclear Physics is not my strength. I'm writing a simulation to model alpha-decay. So far, I have looked up the values of the kinetic energy of the alpha particles that are emitted in a certain decay. Now I have seen this a lot of times, for instance for 212-Polonium: **$^{212}$Po -10.3649 MeV** the the value given is the mass excess. Then I looked into a Nuclear Physics book (Krane) and found: $T_\alpha = \frac{Q}{1 + m_\alpha / m_{x'}}$ where $T_\alpha$ is the kinetic energy of the alpha particle, Q is the Q-value, $m_\alpha$ is the mass of the alpha particle and $m_{x'}$ is the mass of the daughter nucleus. First I thought, Q and $\Delta M$ are simply related by a factor of $c^2$. But that does not seem to be the case, since my calculations are wrong. How can I calculate the kinetic energy of the alpha-particle **only given the information above**?


title: Isometries and Kaluza Klein theories

text: I am reading Bailin and Love's review on Kaluza Klein theories. On section 4.1 they start talking about infinitesimal isometries generated "with a particular generator $t_a$ of the isometry group". $I+id\sigma{}t_a$ $y^n\to{}y'^n=y^n+d\sigma{}\xi_a^n(y)$ where the $\xi_a^n(y)$ are just killing vectors. Immediately thereafter it says > For any representation of the non-Abelian isometry group, the eigenvalues of > a diagonal generator $t_a$ will be integral multiples of some lowest > (positive) eigenvalue $g_{min}$ Why is that so? And also, I have a suspicion that where it says representation of the non- Abelian (Lie) group it really means representation of the Lie algebra associated. Is my suspicion right?


title: Applied / environmental question: direction of exhaust fumes

text: I'm not sure the Physics StackExchange is the perfect place for this environmental/applied physics question, but as I found no forum more fitting I ask my question here. Otherwise please move my question. **Main Question** **In which direction will the fumes move when leaving the exhaust of a car?** No aerial movement or wind is assumed. On cold winter days it can be seen that the initial direction is horizontal or downwards, forming small fume clouds behind the car. Where to will the fumes move from there on? The fumes assumingly have a higher temperature than the surrounding air, indicating they will rise. Nevertheless cooling effects and density may eliminate or surpass this effect. **Sub-question** My office is in 3rd floor next to a main traffic road. Will parts of the fumes enter the room when I open the window? (This is where my initial inspiration to this question comes from)


title: Group velocity of localized wavepacket

text: This is a Homework problem so please feel free to not answer and just give pointers. A localized wavepacket is given as: $$\Phi(r,t=0 ) = \frac { e^{-\large\frac {r^2}{2s^2}} e^{\large\frac{i\pi x}{4a}} } {(2\pi^{\frac{3}{4}}s^\frac{3}{2})}$$ Find the group velocity (given by: $v_g = \frac{d\omega}{dk}$ (I can't see how this will help)) Also, given a time-dependent homogeneous electric field in z-direction $E_z(t) = E_0sin(\omega t)$, give the center of mass movement $r_0(t)$ of the wavepacket for $t>0$, neglecting all the scattering events.


title: How does a thermal temperature gun work?

text: I once worked as a kitchen porter over a winter season.   We had fun with thermal temperature guns (like these) which I learned can be used for measuring the temperature of something a reasonable distance away (aside from the obvious use of laser tag), which to my mind is pretty impressive. How do they work?


title: Which form of the first law of thermodynamics should I use?

text: I usually wonder which thermodynamics first law is better to use ? The one given by physics : $\Delta U=Q-\Delta W$ or the one by chemistry : $\Delta U=Q+\Delta W$ * * * In other words, should I take the gas as my system and take every parameter in its terms?


title: Help for orbits of planets

text: Suppose that an asteroid) that moves at a velocity $v$ passes near to a planet: now I know that the gravity force of the planet will curve the trajectory of the asteroid so I tried to make a draw of the asteroid while passing near the planet using vectors but as result the planet **ALWAYS** falls into the planet that is obviously wrong because the asteroid in real life can also pass the asteroid. Can someone please help me and maybe show some math to calculate the orbits?


title: Which side of wave-particle duality to choose in a given situation

text: How does one know whether, in treating a certain problem, one should consider particles as waves or as point-like objects? Are there certain guidelines regarding this?


title: Applying Ehrenfest's theorem to Hamiltonian

text: It maybe a stupid question, but from the Ehrenfest's theorem, we have \begin{eqnarray*} \frac{d\langle A\rangle}{dt} &=& \left\langle\frac{\partial A}{\partial t}\right\rangle + \frac{1}{i\hbar}\left\langle[A,H]\right\rangle \end{eqnarray*} The if we apply it to the Hamiltonian, \begin{eqnarray*} \frac{d\langle H\rangle}{dt} &=& \left\langle\frac{\partial H}{\partial t}\right\rangle + \frac{1}{i\hbar}\left\langle[H,H]\right\rangle \end{eqnarray*} But since the last term vanishes \begin{eqnarray*} \frac{d\langle H\rangle}{dt} &=& \left\langle\frac{\partial H}{\partial t}\right\rangle \end{eqnarray*} But in general cases, the expectation value of the time derivative of the Hamiltonian is not zero, i.e. in the infinite potential well. $$ \left\langle\frac{\partial H}{\partial t}\right\rangle=\int\Psi^*\frac{\partial H}{\partial t}\Psi dx=\int\sum_n c_n^* \psi_n^*e^{iE_n t/\hbar}\frac{\partial H}{\partial t}\sum_m c_m \psi_m e^{-iE_m t/\hbar}dx$$ $$ =\int\sum_n c_n^* \psi_n^*e^{iE_n t/\hbar}\sum_m c_m (H \psi_m) \frac{\partial }{\partial t}e^{-iE_m t/\hbar}dx$$ $$=\int\sum_n c_n^* \psi_n^*e^{iE_n t/\hbar}\sum_m c_m{1\over{i\hbar}}E_m^2\psi_m e^{-iE_m t/\hbar}dx$$ $$={1\over{i\hbar}}\sum_n\sum_m e^{i(E_n -E_m) t/\hbar}c_n^*c_m\int E_m^2 \psi_n^*\psi_m dx$$ $$={1\over{i\hbar}}\sum_n |c_n|^2E_n^2 $$ But since the expectation value of the Hamiltonian in the infinite well is a constant, it is obviously a contradiction. Is it impossible to apply the Ehrenfest's theorem to the Hamiltonian, or is there any mistake in my calculation?


title: Details of the new solutions to the three-body problem

text: > This question is part of this week's Journal Club session. * * * These systems look ridiculously fun to construct. Could someone explain the particulars? What are the various types of solutions, and what are their dynamics? How are they different from previously discovered solutions? ![enter image description here](http://i.stack.imgur.com/2DPJi.jpg) It's been a while since I first saw the article, which is described nicely in > Physicists Discover a Whopping 13 New Solutions to Three-Body Problem. Jon > Cartwright, Science Now news, 8 March 2013. The original paper is at > Three Classes of Newtonian Three-Body Planar Periodic Orbits. Milovan > Šuvakov and V. Dmitrašinović. _Phys. Rev. Lett._ **110** no. 11, 114301 > (2013). arXiv:1303.0181.


title: Normal Coordinates for Quantum Coupled Oscillators

text: Thanks if you take the time to read this. Here is the problem statement: ![problem statement](http://i.stack.imgur.com/Xne8Y.png) The problem I'm getting is that I'm not getting the kinetic energy diagonal when I convert to the coordinates that diagonalize the potential energy. If you scroll all the way down you should see there's a cross derivative term involving the partial derivatives w.r.t $q_1$ and $q_2$. I haven't been able to spot any significant mistakes. So is there some other way to simultaneously diagonalize potential and the conjugate momenta in the new coordinates? Is there something I'm missing? How does the $\frac{1}{2(2M + m_2)}$ factor come into play? First we make a transformation in the x coordinates so that the $a$'s go away. Namely $$\begin{bmatrix} x_1^\prime \\\x_2^\prime \\\ x_3^\prime\end{bmatrix} = \begin{bmatrix} x_1 \\\x_2 \\\ x_3 \end{bmatrix} - \begin{bmatrix} a/2 \\\\-a/2 \\\ -3a/2\end{bmatrix} $$ And I will refer to the $x_i^\prime$ coordinates without the prime hereafter. $$(x_2 - x_1)^2 + (x_3 - x_2)^2 = x_1^2 +x_2^2 - 2x_1x_2 + x_2^2+ x_3^2 - 2x_2x_3 $$ There are multiple choices for the matrix which below which would produce the above algebraic expression. We want to choose the one which Hermitian, so that the corresponding transformation is unitary. $$= \begin{bmatrix} x_1 &x_2 & x_3\end{bmatrix}\begin{bmatrix} 1 &-1 &0 \\\ -1 &2 &-1 \\\ 0 & -1 & 1 \end{bmatrix}\begin{bmatrix} x_1 \\\x_2 \\\ x_3\end{bmatrix} $$ $$det\begin{bmatrix} 1 - \lambda &-1 &0 \\\ -1 &2- \lambda &-1 \\\ 0 & -1 & 1- \lambda \end{bmatrix} = \left(1 - \lambda \right)^2\left(2 - \lambda \right) - \left(1 - \lambda \right) - \left(1 - \lambda \right) $$ \begin{align*} = \left(1 - \lambda \right)\left[\left(1 - \lambda \right)\left(2 - \lambda \right) -2 \right] &= \left(1 - \lambda \right)\left[2 - 3\lambda + \lambda^2 -2 \right] \\\ & =\lambda\left(1 - \lambda \right)\left(\lambda - 3 \right) \end{align*} So the set of eigenvalues is $\left\\{0, 1, 3 \right\\}$. $$U = \begin{bmatrix} 1/\sqrt{3} &1/\sqrt{3} &1/\sqrt{3} \\\ 1/\sqrt{2} &0 &-1/\sqrt{2} \\\ 1/\sqrt{6} & -2/\sqrt{6} & 1/\sqrt{6} \end{bmatrix}$$ $$ U^{T}\begin{bmatrix} 0 &0 &0 \\\ 0 &1 &0 \\\ 0 & 0 & 3 \end{bmatrix}U = \begin{bmatrix} 1 &-1 &0 \\\ -1 &2 &-1 \\\ 0 & -1 & 1 \end{bmatrix}$$ $$\begin{bmatrix} q_1 \\\q_2 \\\ q_3\end{bmatrix} = U \begin{bmatrix} x_1 \\\x_2 \\\ x_3\end{bmatrix}$$ Next begins the calculation of the partial derivatives of $x_i$ in the new coordinate frame, as the first step to finding the KE in terms of the momenta conjugate to the new coordinates $q_i$. $$\begin{bmatrix}\frac{\partial }{\partial x_1} & \frac{\partial }{\partial x_2} & \frac{\partial }{\partial x_3}\end{bmatrix} = \begin{bmatrix}\frac{\partial }{\partial q_1} & \frac{\partial }{\partial q_2} & \frac{\partial }{\partial q_3}\end{bmatrix}U$$ $$KE = -\hbar^2\begin{bmatrix}\frac{\partial }{\partial x_1} & \frac{\partial }{\partial x_2} & \frac{\partial }{\partial x_3}\end{bmatrix} \begin{bmatrix} \frac{1}{2M} &0 &0 \\\ 0 &\frac{1}{2m_2} &0 \\\ 0 & 0 & \frac{1}{2M} \end{bmatrix} \begin{bmatrix}\frac{\partial }{\partial x_1} \\\ \frac{\partial }{\partial x_2} \\\ \frac{\partial }{\partial x_3}\end{bmatrix} $$ $$ = -\hbar^2\begin{bmatrix}\frac{\partial }{\partial q_1} & \frac{\partial }{\partial q_2} & \frac{\partial }{\partial q_3}\end{bmatrix}U \begin{bmatrix} \frac{1}{2M} &0 &0 \\\ 0 &\frac{1}{2m_2} &0 \\\ 0 & 0 & \frac{1}{2M} \end{bmatrix}U^{T}\begin{bmatrix}\frac{\partial }{\partial q_1} \\\ \frac{\partial }{\partial q_2} \\\ \frac{\partial }{\partial q_3}\end{bmatrix} $$ $$ U \begin{bmatrix} \frac{1}{2M} &0 &0 \\\ 0 &\frac{1}{2m_2} &0 \\\ 0 & 0 & \frac{1}{2M} \end{bmatrix}U^{T}$$ $$= \begin{bmatrix} 1/\sqrt{3} &1/\sqrt{3} &1/\sqrt{3} \\\ 1/\sqrt{2} &0 &-1/\sqrt{2} \\\ 1/\sqrt{6} & -2/\sqrt{6} & 1/\sqrt{6} \end{bmatrix}\begin{bmatrix} \frac{1}{2M\sqrt{3}} & \frac{1}{2M\sqrt{2}} &\frac{1}{2M\sqrt{6}} \\\ \frac{1}{2m_2\sqrt{3}} & 0 &-\frac{2}{2m_2\sqrt{6}} \\\ \frac{1}{2M\sqrt{3}} & -\frac{1}{2M\sqrt{2}} & \frac{1}{2M\sqrt{6}} \end{bmatrix}$$ $$ = \begin{bmatrix} \frac{1}{3M} + \frac{1}{6m_2} & 0 & \frac{1}{3\sqrt{2}}\left(\frac{1}{M} - \frac{1}{m_2} \right) \\\ 0 & \frac{1}{2M} & 0 \\\ \frac{1}{3\sqrt{2}}\left(\frac{1}{M} - \frac{1}{m_2} \right) & 0 & \frac{1}{6M} + \frac{1}{3m_2} \end{bmatrix} $$ $$\frac{KE}{-\hbar^2} = \begin{bmatrix}\frac{\partial }{\partial q_1} & \frac{\partial }{\partial q_2} & \frac{\partial }{\partial q_3}\end{bmatrix} \begin{bmatrix}\left(\frac{1}{3M} + \frac{1}{6m_2} \right)\frac{\partial }{\partial q_1} + \frac{1}{3\sqrt{2}}\left(\frac{1}{M} - \frac{1}{m_2} \right)\frac{\partial }{\partial q_3}\\\ \frac{1}{2M}\frac{\partial }{\partial q_2} \\\ \frac{1}{3\sqrt{2}}\left(\frac{1}{M} - \frac{1}{m_2} \right)\frac{\partial }{\partial q_1}+ \left(\frac{1}{6M} + \frac{1}{3m_2} \right)\frac{\partial }{\partial q_3}\end{bmatrix} $$ $$= \left(\frac{1}{3M} + \frac{1}{6m_2} \right)\frac{\partial^2 }{\partial q_1^2} + \frac{1}{2M}\frac{\partial^2 }{\partial q_2^2} + \left(\frac{1}{6M} + \frac{1}{3m_2} \right)\frac{\partial^2 }{\partial q_3^2}$$ $$+ \frac{\sqrt{2}}{3}\left(\frac{1}{M} - \frac{1}{m_2} \right)\frac{\partial^2 }{\partial q_1 \partial q_3} $$ So to me the fact that there is a cross term means that I won't able to express the Hamiltonian in terms of three independent oscillators.


title: Black-hole firewall and holographic principle

text: Can the firewall be viewed as the holographic boundary? Naively a hologram 3d image can not cross the hologram 2d surface that produces that image. According to the metaphor the boundary - 2d field quantum theory without gravity - could act as a firewall for the enclosed space - 3d string theory with gravity and black holes. Yet information won't be lost by the presence of the firewall, because the digital bits would be just the pixels of that firewall/boundary. Doesn't this settle the paradox of entanglements non- locality with quantum gravity? " we must carefully impose the laws of thermodynamics and/or statistical physics to Maxwell's Demon himself and when we do so, his miraculous abilities to create a paradox evaporate." In the same way I'm asking to impose the boundary S matrix unitarity to the firewall ;-) The entangled partner behind the firewall is then a kind of fictitious hologram according to the Wheeler DeWitt diffeomorphism of quantum gravity, isn't it?


title: X-Ray/Gamma Ray shielding: density versus conductivity

text: When talking about gamma ray or x-ray propagation in media, we usually talk about the mass attenuation coefficient, and we desire high density materials for shielding. This seems probabilistic: we increase the shielding to maximize the chance of EM radiation interacting with the media. However, conductivity is a part of the attenuation coefficient. Why not use highly conductive materials? What justifies using high density lead over high conductivity?


title: More efficient far-future means of keeping the earth alive?

text: In about 7 Billion years our planed will be consumed by the ever-growing sun, life would have become extinct long before that. That means that in several hundred thousand years we have a deadline to either: 1) Move earth to a higher orbit to keep it from heating up   2) Move our civilization to Mars and beyond Of course we are only beginning to understand some of the technologies which would be at work, but what do you think is the more efficient/likely solution to this issue?


title: Anharmonic oscillator solution function

text: I am solving a CLASSICAL an-harmonic oscillator problem with Hamiltonian given by $H= (1/2)\dot{x}^2+(1/2)x^2-(1/2)x^4$ with all the constants (k's) and mass being taken as 1 (one). I find that $x= \tanh(t/\sqrt{2})$ is satisfying the equation of motion. But my question is how to incorporate the Hamiltonian, $H$ in to this solution so that by providing $H$ we can control the initial conditions of this problem. Or any other solution function that can have $H$ in it. thanks in advance. PS= In SHO (m=k=1) lets say $x=A\sin(t)$ then $A= \sqrt{2H}$, where $H$ is the total energy or the Hamiltonian. So $x=\sqrt{H}\sin(t)$. I need a solution function like this.


title: Why is this charge distribution in correct? Capacitors in parallel and series

text: Please consider the circuit diagram below, in particular, look at the capacitors enclosed by the green loop. ![enter image description here](http://i.stack.imgur.com/dybm1.jpg) *Note that the green loop and the (+) and (-) charges on the plates were drawn by me, the original circuit has none of these. Is the charge distribution on the plates correct? The two capacitors in the green loop have a + and - plate connected by a wire, which by definition should be in series. The three -s that joins up at point **d** and evenly distribute itself (split) into two paths and adds charge to the two plate near point **b** (sorry for poor terminologies here) But the book treats the green loop capacitors in parallel, which must imply the configuration. ![enter image description here](http://i.stack.imgur.com/3fzyw.jpg) I am awfully confused how $\ C_1$'s right (+) plate managed to induce $\ C_2$'s right plate to (-) and how the left plate of $\ C_2 $ has (+) plate when it's connected to the negative terminal of the battery. Also, I've noticed that a lot of people often just attack these problems based on the geometry of the circuits and I think they would make the same mistake as my book.


title: Sun revolves around the Earth

text: What if somebody says that **Sun revolves around the Earth** and not Earth revolving around the Sun? What would be the _consequences_?


title: Why do we say that the earth moves around the sun?

text: In history we are taught that the Catholic Church was wrong, because the Sun does not move around the Earth, instead the Earth moves around the Sun. But then in physics we learn that movement is relative, and it depends on the reference point that we choose. Wouldn't the Sun (and the whole universe) move around the Earth if I place my reference point on Earth? Was movement considered absolute in physics back then?


title: Relative Motion and orbiting planets

text: if all motion is relative to the frame of reference determined by an observer, why would the view that planet earth revolves around the Sun more correct than the view that the Sun revolved around planet Earth and all the other planets revolve around the Sun? Is there a mathematical proof?


title: What made us think that Earth moves around the Sun?

text: Trying to observe the night sky for a few weeks, the motion of the Sun and the stars pretty much fits into the Geocentric Theory i.e. All of them move around the Earth. **What then, which particular observation, made us think that it could be the other way around, that all the planets move around the Sun?**


title: Why was Galilei "right"?

text: Considering that all frames are equivalent, isn't it up to the observer to say "The earth turns around the sun" or "The sun turns around the earth"? Isn't this more or less like arguing about which meridian should be considered the null-meridian, or whether time should be counted according to years before/after Jesus Christ or the conquest of Mecca?


title: heliocentricity and the theory of relativity

text: > **Possible Duplicate:**   >  Why do we say that the earth moves around the sun? I should preface by stating that I'm not a physicist and my knowledge of the theory of relativity is limited to what Encarta told me in the 90's (does everyone know what Encarta was?) and I don't even understand the Wikipedia entry! Encarta had a video on the theory of relativity that basically explained in part that (i suppose in vacuum) there's no way to tell which body is in motion relative to another (without observing from outside the space in which they are moving i suppose). so my question is whether this warrants a reassessment of our reliance on a heliocentristic model. is it possible the planets do not revolve the way we've modeled them? i'm not necessarily talking geocentric, just different from our current model. should we be exploring this? ps -- while researching this question i came across geocentricity.com, the first sentence of which starts "Of all the sciences, the Holy Bible..." I'm really not interested in starting a religious debate so please keep answers strictly physics related (though i hope i don't have to even say that on **_physics_**.stackexchange.com!)


title: Revolution of Earth

text: If all motion is relative, how do we know that the Earth revolves around the sun? Or we are just making the above statement from the frame of reference in which Sun is at the origin?


title: Does the earth really move round the sun?

text: Is there really any empirical proof that the earth moves round the sun? I've read simple explanations using mass-gravity relation. But then some questions remain, is gravity a function of mass alone? Is mass a function of size alone? if the earth is revolving round itself, and the sun is revolving round and moving towards the black hole in the centre of the Milky Way, how can we be sure that these two movements alone do not suffice to explain night and day or change in the position of the stars with time? Thanks.


title: How do we know the Earth orbits around the Sun and not the other way around?

text: I know that describing the trajectory of all planets in the solar system around the Earth is much more complicated than if we take the Sun as the reference point. But besides this, what is the simplest experiment that can prove that the Sun is a more "inertial" point of reference than the Earth? Do we have to look at the stars in the background or something like that?


title: Heliocentric Worldview

text: Isn't the whole historic Discussion of Heliocentric vs. Geocentric Worldview just about a Calculation-Technique. I mean I could also choose my coordinate- center to be in the middle of Earth and setup my differential Equations and starting points and it would still describe all Movements correctly, right? Now if I want to solve this it might be pretty wise to choose the Sun as my coordinate origin. But nevertheless I could transform the resulting curve so that the origin is within earth and I can claim that the Sun is (in a fancy possibly self-intersecting way) rotating around Earth, and even the whole Universe is ( in a very fancy way) rotating around the Earth. What's the Problem here? Isn't this the General Principle of Relativity in Physics? How do we have to define Rotation, so that we get the Heliocentric Worldview? If we don't allow self-intersections, we would get a Problem with double-star- systems and Planets which rotate around both stars. It seems that the current Definition relies on the Masses of the involved Objects. But this seems to be a very naive View neglecting the Fact that Forces aren't imposed by the "stronger" Object ( = Human Intuition) but that they are just caused by "Physics itself".


title: Dynamics question. Please help, exam coming soon

text: I'm trying to solve this elementary problem. I'm studying mathematics, but there is a compulsory course in physics that has to be passed. I'm having an exam in 5 days and I have some doubts on problems like this: > ![enter image description here](http://i.stack.imgur.com/Y72Td.jpg) > > In the above system, both 1 and 2 have the same mass. 2 has an initial > velocity of $2 \frac m s$ (meters over second) > > $(a)$ Graph the free body diagram of each block. Indicate it's reaction- > action pair. > > $(b)$ Calculate the acceleration of 1 and describe analytically and > graphically it's movement as a function of time. $(a)$ isn't too difficult: ![enter image description here](http://i.stack.imgur.com/68gEN.jpg) What is getting me a little troubled is $(b)$. My professor says we should take a "curved" $x$-axis in following the rope. I suppose then I take the $y$-axis as perpendicular to the $x$-axis. I decompose the problematic $\vec w$ vectors via the angles given. I use $\sin 37º \approx 0,6$ and $\cos 53º \approx 0,8$. ![enter image description here](http://i.stack.imgur.com/jbZcn.jpg) EDIT: The normal vectors are wrong. They should be. $$\eqalign{ & \vec N = mg\sin 37\hat j \cr & {{\vec N}_0} = - mg\sin 37\hat j \cr & \vec N' = - mg\sin 37\hat j \cr & \vec N{'_0} = mg\sin 37\hat j \cr} $$ (there is a $-$ missing in $\vec w$, before $\cos 37$ which should be $i$, not $j$.) Now I apply Newton's law, $\sum \vec F = m \cdot \vec a $, to my system. I'm interested only in $x$, so I have to use $\sum \vec F_x = m \cdot \vec a_x $. Since the conditions are ideal, $a$ is constant in all the system, $t$ is also constant. The equations are: $$\eqalign{ & t - \left| w \right|\cos 37 = {m_1}a \cr & \left| w \right|\sin 37 - t = {m_2}a \cr} $$ Now $|w| = m_2 g=m_1g$, so $$\eqalign{ & t - m \cdot g \cdot \cos 37 = m \cdot a \cr & m \cdot g \cdot \sin 37 - t = m \cdot a \cr} $$ So I find $a=-0.1 g\approx 1 \frac{m} {s^2}$ This means the acceleration of $1$ is in the positive direction of the $x$ axis. Is this correct? How can I move on with the problem?


title: How do you explain the observed fact that "black hole" objects move?

text: As per Newton objects with mass attract each other, and per Einstein this is further explained by saying that mass warps space-time. So a massive object makes a "dent" into space-time, a gravity well. I have taken to visualizing this as placing a object on a rubber sheet and the resulting dent, being the gravity field. So obviously placing two objects on the sheet not to far from each other will make the dents overlap, and the object will roll towards each other. BUT for a BLACKHOLE, this is not a dent. It's a cut or rupture in the rubber sheet. Furthermore, space-time is constantly falling INTO the blackhole, and everything else that exists in space-time, including light. So a blackhole is not just a super-massive object, it's really a hole, and how can a hole move? How does it react to the gravity pull of a nearby object, when everything just falls thru it? Thanks!


title: Where can I get a gfortran i386 (option -m32) compatible version of CERNlib library .a files?

text: I'm using CERN library's libmathlib.a and libkernlib.a, downloaded from this site, and running on Ubuntu linux to do Mellin-Barnes integrals with f77 fortran code in i386 mode (hence the `-m32`): gfortran -m32 -O -o output MBpart1ep0.f -L. -lmathlib -lkernlib -Lcuba But I'm getting errors like: //usr/local/lib/libmathlib.a(cgamma64.o): In function `wgamma_': cgamma64.F:(.text+0xd1): undefined reference to`s_wsfi' It seems to be caused by an incompatibility to gfortran. Does anyone know where I can download a gfortran compatible version of `libmathlib.a` and `libkernlib.a`?


title: Is the concept of inertia still used? When is it useful as a fictitious force?

text: Is the concept of inertia still used? When is it useful as a _fictitious force_? Can you list a few situations in which, if we didn't use this tool we might be in difficulty?


title: Time travel and nuclear decay

text: Reading a previous closed question an interesting variation has come to my mind. Suppose that time travel to the past was possible:   * I wait for an atom to decay and measure the time, $t_{1a}$    * I travel back in time at $t_0<t_{1a}$   * I wait for the same atom to decay and measure the time, $t_{1b}$ Let's think about the two values, $t_{1a}$ and $t_{1b}$. If they coincide, then from my point of view the measured $t_1$ time would not be governed by chance (the second time I would know $t_1$ _a priori_ ). It would therefore prove some form of existence of hidden variables. Would this violate any known laws of quantum mechanics? Would this prove the existence of hidden variables (e.g. Bohm's interpretation)? If they are different, then what to make of $t_{1a}$ and $t_{1b}$? Which would be the _correct_ value? To me this doesn't make any sense, but maybe it could be compatible with the multiverse interpretation (I don't know how though). In other words, does this gedankenexperiment:   1. ...help us select viable QM interpretations and exclude others? Which?   2. ...lead us to conclude that backwards information time travel is incompatible with QM?


title: Can a human throw a football over the Matterhorn at Disneyland?

text: Some friends and I were at Disneyland this past week. We spent an hour arguing back and forth whether it is possible for someone to throw an NFL football over the Matterhorn? I think it is, but no one else really thought it was possible. What do you guys think? Is this humanly possible? The Matterhorn is 146 feet (44.5 metres) tall. Not sure how wide the base of the mountain is. It's ok if the football hits the other side of the mountain (as long as it clears the top).


title: Why does the work done by an internal force differ from the work done by external force?

text: Let's consider the following situation. We put a body of mass $m$ at a distance $A$ from the center of Earth. We let the Earth attract the body and analyze the situation at a point $B$, closer to the Earth. Now, the work done by the gravitational force (a conservative force, which seems to be important) is given by: $$W = GMm\left(\frac{1}{r_B} - \frac{1}{r_A}\right)$$ This work equals the change of the kinetic energy of the system (approx., the Earth didn't budge too much) and the negative change of the potential energy of the system. The mechanical energy hasn't changed, the system is isolated. What bothers me is this: why doesn't the work done by the gravitational force change the overall energy? It seems inconsistent to say "the work done equals the energy change, BUT not when the work is done by a conservative/internal force". Why does one work differ from another?


title: motion of an electron near a conducting wire

text: An electron is ejected from the surface of a long thick straight conductor carying a current, initially in direction perpendicular to the conductor. The electron will: a) ultimately return to the conductor b) move in a circular path around the conductor c) gradually move away from the conductor along a spiral d) move in helical path with the conductor as the axis According to me, $$mv^2/r=qvB\implies r=mv/qB$$ since B is the magnetic field due to the conductor, $B=\mu i/2\pi R$ where R is the distance from a conductor. So$$r=2\pi mvR/\mu qi$$ Since the force will always be perpendicular to the velocity, the electron moves in a circle. As the electron moves, $R$ increases since the electron has to move outwards first to complete the circular motion. As $R$ increases, $r$ also increases. So I think the electron should move away from the conductor along a spiral. What is the correct answer?


title: Chern bands and HEP Lattice Fermions: the emergence and the exact map

text: **Chern bands or Chern insulators** in 2 spatial dimensional(2D) are a way to construct the bulk insulating gap, but with edge or surfaces with **gapless fermions**. Such gapless fermions are emergent, and which seems to be different than the **High Energy Physics Lattice Fermions approach**. There in **HEP Lattice Fermions** , people try to discretizes the continuum Lagrangian on the lattice. Here in **Chern insulators** , the lattice model is _NOT_ written from discretizing the continuum Lagrangian, and the 1D edge gapless fermions fields $\hat{\psi}$ are emergent which degree of freedom does not directly mapped from the fermion hopping operator $f$ in the 2D bulk. Questions-   1. Can we compare the two kinds of schemes (Chern bands from 2D bulk $f$ to 1D $\hat{\psi}$, and HEP Lattice Fermions from 1D $\Psi$ fields to $\hat{\Psi}$) and their mapping more rigorously? How are their difference?   2. If we add **interaction terms** on the edge, such as $\Psi_L^\dagger \Psi_R^\dagger \Psi_L \Psi_R$; the HEP Lattice Fermions again just discretize the Lagrangian to $\hat{\Psi}_L^\dagger \hat{\Psi}_R^\dagger \hat{\Psi}_L \hat{\Psi}_R$; but in the Chern bands scheme, for a rigorous mapping, do we get more correction terms, beyond a simply adding $\hat{f}_L^\dagger \hat{f}_R^\dagger \hat{f}_L \hat{f}_R$ on 1D edge? (where $L$ and $R$ can be two different copies of Chern insulators.) Is there extra terms $...$, how are these terms derived. Any good and rigorous Ref on **adding gapping terms on the edge of the Chern insulators** and comparing the discretized lattice to a continuum theory is very welcome.


title: Gamma functions integral identity

text: In Srednicki's QFT book, eq. $14.27$ is a result used over and over again for computing loop correction. It is the following integral evaluated in terms of gamma functions: $$ \int d^dq \frac{(q^2)^a}{(q^2+D)^b} = \frac {\Gamma (b-a-\frac{1}{2}d)\Gamma (a+\frac{1}{2}d)} {(4\pi)^{d/2}\Gamma(b)\Gamma(\frac{1}{2}d)} D^{-(b-a-d/2)} $$ Where $q$ is a $d$-dimensional vector, and $q^2$ denotes the square of its norm. I want to know how to obtain the above result. Since $q^2$ is the only variable in the integrand, we can use hyper-spherical coordinates, where the integral is non-trivial only for the radial component. The factor from the angular components is the volume of the unit $d$-sphere: $$\frac {2\pi^{d/2}}{\Gamma(d/2)}$$ Then the above expression is then a equation for the radial component, let's call it $r$: $$ \int dr \frac{r^{(2a+d-1)}}{(r^2+D)^b} = \frac {\Gamma (b-a-\frac{1}{2}d)\Gamma (a+\frac{1}{2}d)} {(8\pi)^{d}\Gamma(b)} D^{-(b-a-d/2)} $$ Where the extra $r^{d-1}$ in the numerator comes from the volume element of the $n$-sphere. I would like to know how to obtain this result.


title: Generator of Velocity Transformations - Galilean Transformations

text: Under a Galilean transformation, the coordinates and momenta of any system transform as: $$ t \rightarrow t',\\\ \vec r\:' = \vec r + \vec vt,\\\ \vec p\:' = \vec p + m\vec v $$ where $\vec v$ is velocity of frame moving w.r.t it. Now, what will be unitary transformation that can that will carry out this transformation. Let us say the total momentum of the system is $\vec P$ and its mass $M$ and its position $X$. I know how to write a single coordinate translation, but am not able to put all these together. **An Attempt** : The transformation should contain : $ \bf e^{i \vec p.\vec x} $ for translations and $ \bf e^{iHt}$ for time translations, **but what about generators of Velocity transformations ?**


title: How to differentiate between ferri-magnetic and para-magnetic substances?

text: Both are feebly attracted by a magnetic field. I know the difference between these substances(on why these get attracted to magnetic field) but as both get feebly attracted how to find out whether a given substance is ferri-magnetic or para-magnetic? Is it that all ferri-magnetic materials are compounds of different metals like magnetite and we can differentiate in this way?


title: Scalar field transformation and generators

text: When we do a transformation (norm preserving one) for a given quantity, from what I have understood it seems like there is a representation of the group element for each quantity depending how they transform (eg : scalar, vector, rank 2 tensor spinor.. ). Considering a normal rotation in 2-D plane (associated to $\mathrm{SO(2)}$ group), if a scalar field $\psi(x,y) \rightarrow \bar\psi(\bar x, \bar y)$ transforms, the representation for the group (which I derived from my arguements of infinitesimal rotations) : $$ \psi(x,y) = (1+ L_z\delta\theta)\bar\psi(\bar x, \bar y) $$ Now I am just wondering what exactly remains unchanged here (since it is a scalar field) or am I just understanding it in the wrong way ? Also is there a general way of finding a representation given a quantity (a field, vector, tensor ...) in group theory. Since I derived the above scalar representation unlike how find the representation in Lie groups. PS : Is it probably the form of the field remains invariant, (like how Lorentz covariance gives us spinor transformations) $$ x^2 +y^2 \rightarrow \bar x^2 +\bar y^2 $$ EDIT 1 : If I wanted to derive this infinite dimensional representation from its Lie group (like I do for the vector case), how can I do it ? EDIT 2 : I am not able to see the Representation for transformation of Quantum mechanical operators from group directly.


title: Golf: spin direction resulting from striking out of the toe

text: If a golf club strikes the ball out of the centre of the club face with the club path on the target line through impact, and the face square to target, the ball will move towards the target with no side-spin. If the same shot is played but the impact is towards the toe of the club, the club face will open slightly as a result, and side spin will be imparted. The question is: for a right handed golfer is the spin clockwise (ball path bends right) or anti-clockwise (ball path bends left). I ask this question because my golf coach and I disagree on the answer. He is a very experienced and highly qualified coach. I know nothing about golf but I have a degree in physics. I'm looking for an answer with a link to a respected reference which backs it up.


title: Cause for Power Transmission Tower "Breathing"

text: OK, this question is not your usual one: Last night while hiking solo from the mountains back to my car at the mountain/desert interface (Lone Pine, CA), I had a rather bizarre -- and downright spooky -- experience. The last half-mile of my return was in total darkness, which wasn't a problem since I had prepared for that unintended possibility. Partway into that last portion of the hike, with my LED flashlight piercing the remote, desert darkness, I began hearing a slow, distinct and loud "breathing" sound, both inhaling and exhaling, which became more pronounced the closer I got to my car. The source seemed to be perhaps a couple hundred feet away. I'll skip the whole middle part which had a Blair Witch vibe to it -- at one point I froze in my tracks in the darkness for a minute or two, pondering what to do. Ultimately I realized the sound was coming from a large, steel, high-voltage power transmission tower. I had noticed earlier that that particular tower had been louder than the others in the daylight, buzzing and cracking, but nothing more than that. The loud, rhythmic "breathing" noise began after the sun-baked tower began cooling down, with a modest 5 MPH wind present. It sounded EXACTLY like an animal slowly "breathing." I'm familiar with the corona discharge effect of such towers. But anyone have any insight into the pitch-black desert "breathing" phenomenon?


title: Why is the critical state in the Mean Field Bak-Sneppen Model a global attractor?

text: Simulations of the Bak-Sneppen Model of Species Evolution (introduced in http://link.aps.org/doi/10.1103/PhysRevLett.71.4083) show that it exhibits Self-Organized Criticality where after a transient only mutation through barriers of height $B_i < B_C$ where $B_C = 0.67 \pm 0.01$ occur spontaneously. As far as I can tell two studies attempt to show the SOC property of the Bak- Sneppen Model in the Mean Field approximation:   1. Flyvbjerg et al. (1993, http://link.aps.org/doi/10.1103/PhysRevLett.71.4087) formulate the evolution equation for the probability distribution of the barrier values $P(B, t)$ but the argument for the existence of a global attractor is given very tersely as: > Our mean field dynamics is an approximation to the master equation for the > Markov process of the random neighbor model, both having one unique > attractive fixed point. (Page 4088, last paragraph left column)   1. In de Boer et al. (1994, http://link.aps.org/doi/10.1103/PhysRevLett.73.906) the Markov Process hinted at in the previous publication is studied by deriving the Master equation $P_{n,\lambda}(t)$ where $n$ is the number of sites with a barrier value less than $\lambda$. However as $\lambda \rightarrow \frac{1}{2}$, $P_{n,\lambda} \rightarrow 0$, which I interpret as meaning that there exists a $B_C \ge \frac{1}{2}$. But I do not see how this proves that the critical state is an attractor. Therefore what is the argument for the critical state being a global attractor in the Mean Field Approximation?


title: Sterile Neutrinos as Dark Matter

text: There has been recent activity by astrophysicists to determine whether a fourth flavor of neutrino, a sterile neutrino, exists. It would likely be more massive than electron, muon or tau neutrinos. However, it wouldn't be affected by the weak force, only by gravity. It would therefore have similar characteristics to dark matter. The LHC is looking for evidence of supersymmetry, and the existence of the stable neutralino, another dark matter candidate. Can the LHC be of any assistance in helping determine the existence of the hypothetical sterile neutrino?


title: cm^3/g as a unit of adsorption

text: I recently saw cm^3/g as a unit for amount adsorbed. Usually, you see either kg adsorbate/kg adsorbent or mole adsorbate/kg adsorbent. Does anyone know the meaning of this unit?


title: Do mechanical waves travel in straight lines?

text: Electromagnetic waves travel in straight lines but do all waves travel in straight lines?


title: spectral function

text: How do you obtain the spectral function for advection equation in one dimension? 2.How about 2D? thanks a lot


title: Condition for the magnetic field

text: Let $B$ be the magnetic field. If $$\nabla \times B = 0$$ and of course $$\nabla \cdot B= 0$$ Can we conclude that $B=0$? For a general field it is wrong because every constant vector will satisfy those conditions. But for the magnetic field is it enough?


title: Does electron-electron scattering contribute to resistivity?

text: Electron-phonon and electron-defect scattering clearly contributes to resistance, but pure electron-electron scattering conserves the total momentum (and energy) of all the electrons. Then, how is it possible for electron- electron interactions to contribute to electrical resistance?


title: Is there any way to find difference between two same sounds of different people?

text: I am trying to understand and find a way to distinguish two same sounds of different people by some physics formula, so could you guys help me? OK I'll try to explain my question in this way that, for example, there are two people A and B are reading this sentence aloud. _"Crackers are Cracking for Crown"_. And if we want to find difference by applying any kind of physics, maths or computer science formula, so and then later we can say this was person A sound or B etc. But while finding the difference these points should not matter:               1- volume of the sound     2- pronunciation(obviously it understandable)     3- speed of the sound      4- same voice or different


title: Geodesic devation on a two sphere

text: So the geodesic deviation equation gives the relative acceleration between two geodesics in motion. But given a pair of geodesic (let's say on the two sphere) that start at the equator, separated by some distance. Is there a way to compute their separation as a function of time without using the geodesic equation? Let's say they're moving at northward toward the pole along a line of constant longitude at unit velocity.


title: Projectile trajectory with linear air resistance

text: I have the following equations $$\ x′′(t)=−\frac km x′(t)$$ $$\ y′′(t)=−\frac km y′(t) - g$$ where $k$ is the drag, $m$ is the mass of the object and $t$ is the time. $g$ is the gravity constant. After integrating the functions twice, I end up with the following equations $$\ x(t) = C_1 e^{\frac {-kt} {2}} + C_2$$ $$\ y(t) = C_3 e^{\frac {-kt} {2}} + C_4 - \frac {gmt}{k}$$ How should I determine the constants $C_1$, $C_2$ etc? I want to be able to set the angle $\alpha$ and velocity $v_0$. For example $y'(0) = 30 \sin(\alpha)$


title: Does non-conservation of number of particles imply zero chemical potential?

text: In the systems like photon gas in a cavity and phonon gas in a solid number of particles is not conserved and chamical potential is zero. Is this a general rule? If yes, how zero chemical potential is obtained from number non- conservation?


**Question:** What isotope has the shortest half life?


title: Stratospheric ship

text: Let's assume that we build a giant steel hull in a shape of cube with open top (2km long edge) and lift it to the top of stratosphere and then pump air out of it. Would it float on the outer layer of stratosphere like a ship floats on the surface of water?


title: How to calculate mass from compound lever?

text: A class 1 lever and a class 2 lever are connected in series, on the resistance end of the class one lever is a 500g weight. On the 2nd class lever sits a weight of an unknown mass. From the end of the 1st class lever to the center of the known mass is 46cm, from center of the known mass to fulcrum is 4cm. On the left side of the fulcrum the lever arm is 50cm. The 2nd class lever sits on the force end of the 1st class lever and their arms overlap 2cm. From the end of the 2nd class lever to the center of the known mass is 47cm. From the center of the unknown mass to the 2nd class fulcrum is 45cm. From Fulcrum to the right is 8cm. Calculate the unknown mass. (The answer should be 200g) Picture representation: ![Picture](http://i.stack.imgur.com/b4oBL.png) I can't seem to get this to work, I've tried using the $\frac{m_k}{d_k} = \frac{m_?}{d_?}$ with this but to no avail. I've discussed with some others about using the torque of the levers but I can't get that to work either. (Where $t = FL$ and $t_1-t_2 =0=t_3-t_4$ and I can't get that to work either.) Any help would be appreciated!


title: Why neglect friction when computing torque?

text: There is a block of wood on a plank, with friction, and the block is moving down with **uniform speed**. They are asking what is the **torque acting through the center of the block**. ![Force diagram of block on plank](http://i.stack.imgur.com/RicWP.jpg) My doubt is that since the block is moving with **uniform speed** that means that downward force is exactly balanced by force upward due to friction so the **net torque about the center should be zero** but the answer they have given takes into account the downward force $mg \sin \theta$ to calculate the torque, friction is totally neglected. **And why is the net torque not zero?**


title: Tsunami dampening mechanisms

text: Encouraged by the zeitgeist let me ask the following: **Is it feasible (now or in the future) to build systems a certain distance of a vulnerable coastline which can serve to dampen a tsunami before it reaches the coast itself?** The following picture comes to mind. We have some device which is small enough to be mounted on a buoy. An array of such buoys can be anchored some distance off the coastline, controlled by computers which are linked into the global tsunami warning network. This setup is quite feasible given what a cell phone can do today. On the detection of an oceanic earthquake or other tsunami generating event (such as a piece of the Rock of Gibraltar falling into the sea) and given present environmental conditions one can calculate the expected path of the tsunami and its intensity. If a TDS (Tsunami Dampening System) of the type I describe above happens to be deployed in range of the tsunami, all relevant information is conveyed to the TDS controllers by the global tsunami warning system. All this happen in a matter of moments. This leaves plenty of time (25min - 2hr) for the devices in the TDS array to be activated and to do their job. The question in this case would be - what form could such devices take? Perhaps mini-turbines which could dissipate the incoming energy into the ocean by first converting it to electrical energy. Any such undertaking involves physical estimates for the size and shape of such an array, the precise capabilities of each device, etc. Many of these concerns involve simple physical questions. Can you come up with the details of such a system or alternatively outline your own design? If you think that this idea would never work in the first place - for technological, physical or some other reasons - please explain what you think would be the prime obstacle and why?


title: Big Bang, Heat Death, and cause and effect

text: If the Universe has two 'end points', one being the Big Bang, and the other being heat death, is there anything in the laws of physics which forbid a random fluctuation in the heat death state from being the reason for the Big Bang? My thinking is this: we know that moving along the time axis from the Big Bang to Heat Death, the various states of the Universe are separated by probabilistic quantum mechanical events. We also know from experience that moving in the opposite direction, the states are linked deterministically (if we prepare the state of an electron by measuring its spin along the x-axis, we find there is a 50/50 chance that the spin is +/-1/2. But once we make the measurement, we know that the outcome - say +1/2 with total certainty because it happened. If we then make a measurement along the y-axis, we again have a 50/50 chance of +/-1/2 but after the measurement we again know the result with 100% - say -1/2 for the 2nd measurement. But if we run the process in reverse, we know with 100% certainty the outcomes of both measurements because the future state of the Universe contains the information of the previous states). This is depicted in the picture below. ![enter image description here](http://i.stack.imgur.com/ttVDx.png) Each point is a possible state of the Universe at a given time. An infinite amount of time after the Big Bang, we end up in a state of Heat Death which looks the same no matter what path was taken. From what I understand, there is no sense of direction for the time dimension in space-time (i.e. in general relativity, all the events on the worldline 'exist' together - there is no 'flow of time', future states only contain the information of previous states). So I'm wondering is: Is there any fundamental physical law that prevents us from concluding that a random fluctuation in the Heat Death state, which would result in one of the infinite number of high entropy states that 'preceded' it, is the 'cause' of the Big Bang and the specific worldline of the Universe we experience (because if there is no sense that something 'happens', but rather all events are simply connected by a world line, if one of those states must exist due to a random fluctuation, then all states causally linked to it must also exist - i.e. trace the specific deterministic worldline back toward the Big Bang and you define the complete unique history of the Universe)?


title: Spin drift velocity?

text: I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf j_{\pm} = n_{\pm} \mathbf V_{\pm} - D \nabla n_{\pm},$$ where $n$ is the number of spins(up/down). Now the second term is clear, as this one comes from Fick's first law, but the first one is strange. He claims that $V_{\pm}$ is the velocity of positively(negatively) oriented spins (he restricts himself to spin 1/2). Does anybody know what this drift velocity could mean?


title: Strain energy density in index notation

text: The strain energy density is defined as $$dU = \int_0^{\epsilon_{ij}} \sigma_{ij} d \epsilon_{ij}$$ (see Reddy "Energy Principles and Variational Methods in Applied Mechanics", 2nd Ed, 4.11). Assuming a linear stress-strain relationship, I get $$U = \frac12 \sigma_{ij} \epsilon_{ij}$$ which is consistent with the literature. Now, if I do the summation and assume symmetry of the stress and strain tensors, I get $$ U = \frac12 (\sigma_{11} \epsilon_{11} + \sigma_{22} \epsilon_{22} + \sigma_{33} \epsilon_{33} + 2 \sigma_{23} \epsilon_{23} + 2 \sigma_{13} \epsilon_{13} + 2 \sigma_{12} \epsilon_{12})$$ However, in Soedel "Vibration of Shells and Plates", 2nd Ed, 2.6.1, all the "shear terms" (i.e. terms with indices 23, 13, 12) are not multiplied by two. Did I make a mistake, is there some assumption in the Soedel book I might have missed or is this possibly a typo in the book? **Edit:** There is still some confusion on my part. For elastic materials the stresses can be derived from the strain energy $$ \sigma_{ij} = \frac{\partial U}{\partial \epsilon_{ij} }$$ For orthotropic materials the constitutive relation is $$ \begin{bmatrix} \sigma_{11} \\\ \sigma_{22} \\\ \sigma_{33} \\\ \sigma_{23} \\\ \sigma_{13} \\\ \sigma_{12} \end{bmatrix} = \begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\\ C_{12} & C_{22} & C_{23} & 0 & 0 & 0 \\\ C_{13} & C_{23} & C_{33} & 0 & 0 & 0 \\\ 0 & 0 & 0 & C_{44} & 0 & 0 \\\ 0 & 0 & 0 & 0 & C_{55} & 0 \\\ 0 & 0 & 0 & 0 & 0 & C_{66} \end{bmatrix} \begin{bmatrix} \epsilon_{11} \\\ \epsilon_{22} \\\ \epsilon_{33} \\\ \epsilon_{23} \\\ \epsilon_{13} \\\ \epsilon_{12} \end{bmatrix} $$ So when I try to get $\sigma_{11}$, that works fine $$ \begin{align} \sigma_{11} = \frac{\partial U}{\partial \epsilon_{11} } &= \frac12 (\frac{\partial \sigma_{11}}{\partial \epsilon_{11}} \epsilon_{11} + \sigma_{11} + \frac{\partial \sigma_{22}}{\partial \epsilon_{11}} \epsilon_{22} + \frac{\partial \sigma_{33}}{\partial \epsilon_{11}} \epsilon_{33}) \\\ & = \frac12 ( C_{11} \epsilon_{11} + \sigma_{11} + C_{12} \epsilon_{22} + C_{13} \epsilon_{33}) \\\ & = \frac12 (\sigma_{11} + \sigma_{11} ) \end{align} $$ However, for $\sigma_{12}$ I get $$ \begin{align} \sigma_{12} = \frac{\partial U}{\partial \epsilon_{12} } &= \frac12 \cdot 2 (\frac{\partial \sigma_{12}}{\partial \epsilon_{12}} \epsilon_{12} + \sigma_{12} ) \\\ & = ( C_{66} \epsilon_{12} + \sigma_{12} ) \\\ & = 2 \sigma_{12} \end{align} $$ which is obviously wrong. This works out fine if you leave out the 2s of the strain energy, as Soedel did. Any clarification would be greatly appreciated.


title: How is the width of a slit related to the intemsity of light passing through it?

text: Here's a question I got in my final exam this morning. "If in a Young's double slit experiment setup, the ratio of intensity of the bright spot to the dark spot is 25:9, what is the ratio of the width of the slits?" Here's what I did. Since the ratio of intensity at the bright and dark spots is 25:9, the ratio of amplitudes there must 5:3. Which means the amplitude of one wave is 4 times the other. Now, knowing that the amplitude of light through the wider slit is 4 times the amplitude of light through the narrower slit, how can I determine the ratio of the slits' width? I'd appreciate any help even though I skipped the question in my exam, it's been bugging me all day.


title: What makes an abstract physical system describable by a "fluid" equations of motion?

text: We can describe (some of) the dynamics of many systems using fluid mechanics. Of course these include classical fluids like water, more exotic fluids like photon gases and the universe as a whole and even solid(ish) things over long times, like glasses and ice. Further still we can treat general classical systems in phase space using a phase fluid, quantum systems (e.g. Madelung equations) and with a little bit of hand waving anything that happens on a symplectic manifold (which gives us a Hamiltonian and hence a flow and Louiville's theorem). So what is it about a system that makes it obey a fluid model? Are there systems that definitely do not fit a fluid model? (I realise that I haven't said exactly what I mean by "fluid model", this is somewhat deliberate. If you like you can take it to mean "having equations of motion which are (almost) identical in some form to the Euler equations".) **edit:** Since admittedly, the original question wasn't quite clear I'll try to clarify a bit. I'm not looking for a high-school answer, or one which describes only actual literal physical fluids, e.g. "a fluid doesn't support a shear stress", "a fluid is something you can wash your hair with". I've given some examples above of situations that fit this description, and without further explanation I think it's non-obvious what a "mean free path" or similar would mean in a generalised fluid. What I'm really looking for (and there may not be any) is some overarching physical or mathematical principle, or failing that an argument as to why there isn't one. I'd even be quite happy to be directed to a book or more appropriate forum. I apologise for not being clearer before and appreciate the answers already given.


title: Quantization of electrostatic $\vec E$ field?

text: Can a electrostatic field $\vec E=\vec E(x,y,z)$ (time-independent) or electrostatic potential $\phi=\phi(x,y,z)$ be quantized? If yes, will these quanta be photons again? But we don't have an electromagnetic field here.


title: What would cause a spinning fluid to stop spinning?

text: I once saw a demonstration where an electric current caused a drop of mercury to spin. The drop contained bits of iron, which could be seen flowing around in a circular pattern. As soon as the current was turned off, the spinning slowed fairly quickly. What caused the circular motion within the drop to slow? It seems to me that there would be very little friction within the drop, and that the motion should be similar to that of a gyroscope. Why was this not the case?


title: Why isn't this working?

text: I just broke a 120mm computer fan in name of science and now I'm pissed; can anyone explain why this doesn't work? : ![enter image description here](http://i.stack.imgur.com/rfwqo.jpg) The battery should create a potential difference across the motor, causing the fan to spin up, right?


title: Would equations for a spinning top be an (x,y,z) vector

text: I am following the equations on this page, and for torque it is $mgr\sin\theta$, but I am curious about $r$. I am working on a game and I want to correctly model the top, and am curious if $r$ should be the distance from the tip of the top to the center of mass as an $(x,y,z)$ vector, or should it just be the scalar version?


title: How can counting the number of cracks in glass tell you about the speed of impact?

text: A recent article, Counting cracks in glass gives speed of projectile (Andrew Grant, _Science News_ , May 1 2013) indicates that the number of cracks in a broken glass can tell you information about the speed of the impact that broke it. ![enter image description here](http://i.stack.imgur.com/w6h32.jpg) However, I'm not quite clear on how this is done and what the physics behind this mechanism is. Can someone explain it to me?


title: Proper time for an accelerating object

text: As far as I have read so far, proper time is the time measured on the clock of an inertial frame moving uniformly with respect to another inertial frame. The concept and the mathematical expression for proper time is originated from the concepts of relativity of simultaneity and time dilation, both of which are evident from the fact that the quantity "interval" between two events remains constant in all the inertial frames. The conclusion is that the quantity proper time has a meaning only when we are talking about an inertial frame of reference. > I encountered a question in my exam: $$ x(t) = \sqrt{(b^2)+((ct)^2)} $$ The > equation of motion of a particle in the ground frame of reference is given > by the above equation. Calculate the expression for proper time. (This > question is taken by Griffiths, Electrodynamics book). I have two doubts about this question: _Does it make sense to define proper time for an accelerating object?_ Assuming that the answer for Q1 is yes, then is it calculated by transforming coordinates into a new reference frame moving with velocity **v** for every small time **dt**? i.e., for every small change in dt there is a change in velocity of the particle as seen from ground frame. So, do I have to change my frame for every dt time, and sum up the **dT**? **_dT** \- infinitesimal proper time._


title: Crystal diffraction for waves vs particles

text: I thought that I understand the "Bragg's Law" understanding of crystal diffraction, but recently I read something that made me confused. I understand that if the planes in the crystal have sufficiently small spacing relative to wavelength (more specifically, such that $sin \theta$ in Bragg's Law >1 even for lowest order), then there would be no angles for which constructive interference occurs. Now, I read that if I shoot neutrons at the crystal of sufficiently large corresponding wavelength, then the neutrons will make it through. Why did I get confused by this statement? Because, suppose we are shooting waves. I would think that scattering still occur, just that at every angle, the waves "cancel" each other out so nothing is observed. In particular, there is still nothing that makes it to the end of the crystal because the wave is scattered as it moves through the crystal. But apparently this is not the case for neutrons. So my question is:   1. Is my understanding with shooting of waves correct? [That the waves are still scattered in all directions, but not observed due to destructive interference.]   2. Am I right to conclude that the wave model is therefore not an adequate description of neutrons? [I think I can see why neutrons make it to the end if I use probability amplitude analysis instead of thinking of the neutrons as waves.]   3. What about something like light which can be understood as a wave and as a stream of photons?


title: What keeps mass from turning into energy?

text: I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force holding a subatomic particle together? What keeps mass in it's state? I hope this is not a silly question but I am clueless. Thanks


title: Can matter be created from energy?

text: > _The small, hot, dense early universe the size of an atom was made up > entirely of energy, it wasn't until after the expansion began and the > universe cooled down some of that energy began converting into the first > atomic nuclei._ This quote seems a little dubious but I think this is worth asking anyway: Can someone explain the atomic process, if it even exists, of how this would work to convert energy in to matter, and what form of energy was initially present, and what is required to cause this change?


title: Application of $E = mc^2$

text: We very well know that mass-energy equivalence is given by $E = mc^2$. My question however is how would we actually convert an object or some mass into its pure energy state and then if possible even back to its original state. The answer needs to state the requirements for conversion into pure energy. We all know its possible theoretically but how would it be done in a practical world. Just assume that the mechanism required for the process is possible. In short I want the process/mechanism for how to go about it.


title: Deriving Bernoulli's equation via conservation of E

text: So I'm not OK with how some people derive this equation. These people consider a pipe whose endings have cross-sectional areas and heights which are different. They then use the conservation of energy principle by saying $dW = dK + dU$ (Where $W$ is work, $K$ is kinetic energy, and $U$ is potential energy). For this they consider that the work done on the system would be due to external pressure forces exerted on the whole system of water along the pipe. And here comes the part where I disagree: they use this Work to calculate the change in Potential and Kinetic energy for just a small slab of water within the whole system. This is completely invalid isn't it? I mean you would have to consider the entire system, I think. My way of interpreting the derivation is if you consider just one slab the whole time. Is this a valid way of thinking? Thanks! edit: In fact, in one video I saw, the person just says "the middle chunk of water stays the same the whole time, so we can just ignore it".


title: Is there a physical interpretation to invariant random matrix ensembles?

text: **Disclaimer.** I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any misconceptions present in my question. * * * **Background.** From readings I have done online (mainly on Wikipedia and online lecture notes), I understand that according to the theory of quantum mechanics, the possible energy levels of a quantum system are sometimes described using the eigenvalues of a Hermitian operator $H$ called the **Hamiltonian operator** on a (possibly infinite dimensional) Hilbert space, which is (for convenience) sometimes approximated using a large $n\times n$ Hermitian matrix $\widehat{H}_n$ (i.e., with $n\gg0$). Furthermore, I understand that for many very complicated and rapidly fluctuating systems (such as heavy atomic nuclei), one is often mostly interested in a _generic_ or _typical_ hermitian operator, which can be modelled by defining our approximation $\widehat{H}_n$ as a random hermitian matrix. According to what I have written so far, I understand at least partially the interest of studying the spectrum of large Hermitian matrices for applications in physics. However, when applications in physics are mentioned in random matrix theory, there is usually a lot of emphasis on the _invariant_ random matrix ensembles, which are ensembles of random matrices $M$ whose distributions are invariant under conjugation by matrices from one of the classical matrix Lie groups. For example, the random matrix $M$ is said to belong to a _unitary ensemble_ if the probability distribution of $M$ is equal to the probability distribution of $UMU^*$ for every unitary matrix $U$. This leads me to the following question: * * * **Question.** Is there a _physical_ reason why physicists are especially interested in the invariant ensembles? While researching this, I came across the following paragraph in a paper which seems to address this question > Physically, an invariant random matrix ensemble describes extended (but > phase-randomized) states, where the localization effects are negligible. In > contrast to that any non-invariant ensemble accounts for a sort of structure > of eigenfunctions (e.g. localization) in a given basis which may be not the > case in a different rotated basis (remember about the extended states in the > tight-binding model which are the linear combinations of states localized at > a given site). but given my lack of knowledge of physics jargon, I don't quite understand what is meant by "localization effects are negligible".


title: Why does a water drop on a hot plate at $150^o C$ evaporate faster than on a plate at $200^o C$?

text: I recently read that: > "A drop of water landing on a hot plate at $150^o C \:(300 F)$ evaporates in > a few seconds. A drop of water landing on a hot plate at $200^o C \:(400 F)$ > survives a whole minute." How would you explain this observation using physics principles?


title: Significant error conversion

text: So here is my question: Say we have measured something to be 15,67 mm and the significant error is $\pm 0,01$mm. then we convert the measurement to meter to be 0,01567m would the significant error then be $\pm 0.00001$m?


title: What does this term G+G'->G' mean?

text: In this document, what does the line "Write $\vec{G}_i + \vec{G}_i' \rightarrow \vec{G}_i'$" after equation (25) actually mean?


title: In a theory of quantum gravity, does the gravitational coupling "constant" actually depend on the scale of the systems involved in the interaction?

text: In the following I will give some arguments that will indicate that the gravitational coupling "constant" actually depends on the scale (space and time) of the interacting systems. The question is: Question 1. Which of the following arguments are invalid? The following arguments are inspired by the following article: "Loops, trees and the search for new physics", by Zvi Bern, Lance J. Dixon and David A. Kosower, Scientific American, Special Edition, "Extreme Physics". The unitarity method (presented in this article and others), is a way of analysing particle processes that bypasses the complexity of Feynman's technique. Virtual particles are the prime reason why Feynman diagrams get so complicated. Virtual particles have both real and spurious effects, but the spurious effects cancel out of the final result (we can call this interference). The key to the success of the unitarity method is that it avoids the direct use of virtual particles. In this approach, it seems that each graviton behaves like two gluons stitched together. Heisenberg's uncertainty principle will allow transitory fluctuations of energy that would allow processes involving multiple virtual particle loops to occur. These processes will have a very low probability of occurrence p. The average waiting time for such a process to occur will be around 1/p (the less likely the process is, the longer we have to wait, on the average, for it to occur). we also note that there are also many possible combinations, for a fixed number of gravitons and a fixed number of loops. In QCD, it has been noticed that at very short distances (including distances relevant for collisions at LHC), the coupling diminishes in value, so theorists can get away with considering only uncomplicated diagrams. A similar phenomenon (but at different relative scales) will appear in quantum gravity (when following the unitarity method, for example), when estimating the gravitational coupling constant (through actual measurement). The waiting time for the occurrence of processes associated with complex Feynman diagrams (that will affect the calculated value of the gravitational coupling constant) will be much longer than for the simple processes. Here I assume that in a theory of quantum gravity, the gravitational coupling constant can be estimated through measurement, and calculated based on the theory (as is the case for the electromagnetic coupling constant in QED). Related to the dark matter problem, when scientists study the rotational speed of stars in a galaxy as a function of their distance from the galactic center, the system involves distances around thousands of light years (or more), and observation time of months or years. In this case, the gravitational coupling constant will have a greater value than in the case of systems at a lower scale. These scales leave plenty of room for the processes associated to complex Feynman diagrams to occur, thus affecting the value of the gravitational coupling constant (as compared to the Planck length 10^(-35) m, and Planck time 10^(-43) s). The force of gravity will seem stronger at larger scales. The conclusion is that the gravitational coupling constant actually depends on the scale (in space and time) at which the act of measurement (observation) is performed. This does not exclude the possible existence of massive compact halo objects, WIMP particles, or other attempts to solve the dark matter problem, but I think that it plays a major role in this. Question 2. Could this solve that dark matter problem?


title: Leonard Susskind's videos. Which order?

text: As a mathematics student with almost no modern physics background (just an introduction to relativity when I was in secondary school) I find Leonard Susskind's lectures videos (freely available in Youtube) very interesting but I am wondering, in which order should I watch them? Which courses first? These are the ones I have found in Youtube:   * Modern Physics: Quantum Mechanics (https://www.youtube.com/watch?v=2h1E3YJMKfA)   * Modern Physics: Special Relativity (https://www.youtube.com/watch?v=BAurgxtOdxY)   * String Theory and M-Theory (https://www.youtube.com/watch?v=25haxRuZQUk)   * Einstein's General Theory of Relativity (https://www.youtube.com/watch?v=hbmf0bB38h0)   * Quantum Entanglements (https://www.youtube.com/watch?v=0Eeuqh9QfNI)   * Modern Physics: Classical Mechanics (https://www.youtube.com/watch?v=pyX8kQ-JzHI)   * Cosmology (https://www.youtube.com/watch?v=32wIKaLkvc4)   * The Theoretical Minimum (https://www.youtube.com/watch?v=iJfw6lDlTuA) I would also appreciate if you could give links to more lectures from him (I mean full courses, there are plenty of talks available) P.D. Sorry about the bad Tags, but i couldnt find something like 'student, learning, modern-physics'


title: Understanding emergent phenomena in the block universe. (Reworded question)

text: Each person exists as an unchanging 4D worldtube in the block universe. At each slice of the worldtube there is a present, past and future. However, there is a black box* which appears to exist in only one slice of the block universe at a time. How could this be explained? I am not trying to attack the block universe concept, I am not trying to get into metaphysics and I am not trying to come up with my own crack-pot theory. I would just like to know how a world tube can contain something, a black box, that exists throughout the whole worldtube, and yet creates the illusion of only existing in one slice of the universe at a time. Is it an imaginary force like the centrifugal force? Or an emergent phenomena such as temperature? Something else? *The black box is consciousness, but I don't want to use that word as it seems to make physicists run away screaming.


title: Are there any restrictions on building the topology of spacetime out of the complement of open balls?

text: I assume that for a Lorentzian manifold (i.e. with Minkowski signature), the analog of an open ball is the interior of a light cone. My question is motivated by the observation that whereas any point on the boundary of an open ball on a Rimannian manifold (i.e. with Euclidean signature) can be considered to be simultaneously interior to an infinite number of other open balls (and exterior to an infinite number of others) the boundary of a light cone is associated with a metric interval that is distinct from the timelike and spacelike intervals. For that reason, I wonder whether this introduces additional subtleties/restrictions on constructing a spacetime topology. Related to this question is under what circumstances (if any) can individual points be associated with certain kinds of intervals (e.g. Spacelike, timelike, null).