title: Question on quantum computation, entanglement and speed of information propagation

text: Imagine a following thought experiment. Suppose we have a large amount of entangled particle pairs, several million or billion. Now suppose there are two observers, each carrying one member of particle pair - a slower-then-light spaceship and mission control on Earth, for example. Before departure, both spaceship crew and Earth crew agreed to order their entangled pairs by into sets of 100 (or 1000,10000, ...), ordered by the time of particle pair creation or any other way, as long as the order is the same on both Earth and spaceship. Now, spaceship departs Earth with v << c, so relativistic effects are negligible and the clocks on the ship and Earth are more-or-less in sync for the foreseeable future. Each day mission control on Earth is using the their particles in the pre-determined pair set to construct a quantum computer (can entangled particle in a pair be used as qubit? used for quantum gate?) and runs a specific quantum algorithm that should give some defined answer (Shor's, or Grover's). Afterwards results are measured, breaking the entanglement and then compared against the expected one. Each day next set of particle is used and discarded. The spaceship crew does nothing, except noting which particle set has been used up by Earth team. Now, suppose after many hundreds years of flight spaceship is several light- years away from Earth, but there are still entangled particle sets available for both crew and Earth team and both team know which sets have been used and what set is going to be the next one for the next day. Now, imagine our spaceship encounter hostile aliens. On that day and all the subsequent ones as long as the spaceship crew survives, they _observe_ all remaining particle pair sets, breaking the entanglement with the matching ones on Earth. Earth team is not aware of the encounter and they still attempt to construct quantum computer from their matching half of the particle pair sets every day. But each day as they try to run the quantum algorithm on their half of particle pair set, their computation FAILS as their particles are no longer in a quantum superposition state and can no longer be used for quantum computation. So, after a few days, Earth team learns that spaceship crew sent them a 1-bit distress signal, even though a ship is several light-years away, receiving this information faster then light. Now question: where is the mistake in my chain of thought?


title: Can a discrete dynode mass spec detector get "tired?"

text: In an electron multiplier (discrete dynode detector), one electron triggers the release of more electrons in a cascade. Is it possible that a "large" number of electrons hitting the detector can temporarily (course of hours) reduce the number of electrons available to amplify future incident electrons? (E.g. is there a cumulative recharge time?) Or is it possible for the anode to have temporarily reduced sensitivity if the electrons are not flushed quickly enough? (Assume real-world, non-ideal physics. This is an actual mass spec we're talking about. Something is causing reduced sensitivity over the course of hours of usage, aside from reduced transmission and ionization due to dirt.)


title: Anyons as particles?

text: I'm trying to understand the basics of anyons physics. I understand there is neither a Fock space they live in (because Fock is just the space of (anti-)symmetrized tensor product state, see _e.g._ Wikipedia), nor a (pseudo / fictitious) commutation relation for them, as discussed at this Phys.SE post. But still I've a few questions regarding their statistics:   * Can we associate a creation / destruction operator to an anyon mode ? Does it make sense to talk about _mode_ of anyons?   * Is there a general occupation function like Fermi-Dirac or Bose-Einstein for fermions or bosons ? Is it model dependent, _i.e._ does it depend on the type of anyon ? Does it make sense to discuss _number_ of anyons?   * What is the ground state of anyons, like a Fermi sea or a Bose-Einstein condensate for fermions or bosons ? Does it make sense to talk about a _ground state_ of a gas of anyons? I believe this bunch of questions can all be contracted to   * **Does it make sense to talk of the anyons as particles ?** Because in principle a particle exists independently of the Fock space construction, isn't it ? We could still construct a space of the tensor product of non (anti-)symmetrised states. I realised that a perhaps better approach on the question would be:   * **To which extend is the anyon statistic a (quantum) statistic ?** provided the two other quantum statistics I know (Bose and Fermi) provide a ground state, an occupation number, and some second-quantised version of operators. _Post-scriptum :_ This Phys.SE question is partially related to mine.


title: Complex masses for Dirac and Weyl spinors

text: I'm trying understand how to rotate Dirac fields to absorb complex phases in masses. I have a few related questions:   1. With Weyl spinors, I understand, $$ \mathcal{L} = \text{kinetic} + |M|e^{i\theta}\xi\chi + \textrm{h.c.} $$ The phase removed by separate left- and right-handed rotations, e.g. $\xi \to e^{-i\theta/2}\xi$ and $\chi \to e^{-i\theta/2}\chi$. These phases cancel in the kinetic terms. Is it correct that with Dirac spinors, $$ \mathcal{L} = \bar\psi |M|e^{i\theta\gamma_5} \psi = \text{Re}(M)\bar\psi\psi +i\text{Im}(M)\bar\psi\gamma_5\psi $$ and the phase is removed by $\psi \to e^{-i\theta\gamma_5/2}\psi$? The appearance of the $\gamma_5$ in the phase troubles me a little - I suppose this is telling us that Weyl spinors are a more suitable basis than Dirac spinors?   2. If the field is Majorana, $\xi = \chi$, and the field can still absorb a phase? I think I must be making a trivial mistake.  For example, Majorana neutrino fields cannot absorb phases, leading to extra CP violation. And in SUSY, the gaugino Majorana soft-breaking masses are e.g. $M_1e^{i\theta}$. Can their phases be re-absorbed via a field redefinition? I don't think they can. So I must have a mistake.


How is Fermat's least time principle proven? Or it is what usually is observed and is basis for the theories?


title: Is particle entanglement a binary property?

text: Is the particle entanglement a boolean property? That is, when we consider two given particles, is the answer to the question "are they entangled" always either "yes" or "no" (or, of course, "we are not sure if it's yes or no")? Is there such thing as partial entanglement?


title: Representation of Hamiltonian in terms of "creation" and "destruction" operators

text: Let's have Schrodinger equation or Dirac equation in Schrodinger form: $$ i \partial_{0}\Psi = \hat {H}\Psi . $$ Sometimes we can introduce some operators $\hat {A}, \hat {B}$ (the second is not always Hermitian conjugate to the first) for which $$ \hat {H} = \hat {B}\hat {A} + \varepsilon , $$ which is look like rewriting $\hat {H}$ through destruction and creation operators. Right commutation or anticommutation laws $[\hat {B}, \hat {A}] = 1, \quad [\hat {B}, \hat {A}]_{+} = 1$ are not necessarily too. I heard that it helps to simplify the way of solution of equation. But I don't know what physical sense of $\hat {A}, \hat {B}$, so I don't understand how to use these operators fo finding energy spectra and functions for corresponding state. What do you know about this? An example. For electron in Hydrogen atom Schrodinger equation can be rewritten in form $$ \partial^{2}_{\rho}\kappa + \frac{2m\alpha}{r}\kappa - \frac{l(l + 1)}{\rho^{2}}\kappa = -E\kappa , $$ where $\kappa$ is $R(\rho)\rho$ and $R(\rho )$ is the radial part of Schrodinger equation. So $\hat {H}\kappa = E \kappa$, and we may construct some $\hat {A}, \hat {B}$ operators, for which $$ \hat {A} = \partial_{\rho} + \omega , \quad \hat {B} = -\partial_{\rho} + \omega, \quad \omega = \gamma + \frac{\beta}{\rho }, $$ and $$ \hat {H} = \hat {B}\hat {A} + \epsilon = -\partial^{2}_{\rho} - \frac{2m\alpha}{r} + \frac{l(l + 1)}{\rho^{2}}, $$ from which it is possible to find $\gamma , \beta$. I heard that this representation also can help to find the spectra and state functions, but I don't know why, because physical sense of introduced operators is incomprehensible for me.


title: Is there a general systematic approach how to calculate the individual terms in an operator product expansion?

text: Is there a general systematic procedure or approach to obtain the analytic functions $c_{ijk}$ as well as the corresponding operators $$A_i(z)$$ that appear in the operator product expansion (OPE) $$ A_i(z)A_j(w) = \sum\limits_k c_{ijk}(z-w)A_k(w) $$ for any given two operators $A_i(z)$ and $A_i(z)$? I have followd (a limited number of) examples of OPE calculations that involved things like expanding until some correlators for which the expression is known appear and power series expansions of derivatives of operators, but from this I was not able to discern the general way to go.


title: Temperature limit of the increase in heat

text: If the sun is the hottest known thing to humans is it possible to have a temperature greater than the sun?


title: Why is the Fermi surface stable?

text: As a condensed matter physicist, I take it for granted that a Fermi surface is _stable_. But it is stable with respect to what? For instance, Cooper pairing is known as an instability of the Fermi surface. I'm simply wondering what makes the Fermi surface stable? Possible way of thinking: Is it a topological property of the Fermi gas (only of the free one ?, only robust against disorder?)? What is the modern, mathematical definition of the Fermi surface (shame on me, I don't even know this, and all my old textbooks are really sloppy about that, I feel)? What can destroy the Fermi surface, and what does _destroy_ mean? Any idea / reference / suggestion to improve the question is welcome. _Addenda / Other possible way to discuss the problem:_ After writing this question, I noted this answer by wsc, where (s)he presents a paper by M. Oshikawa (2000), _Topological Approach to Luttinger’s Theorem and the Fermi Surface of a Kondo Lattice_ PRL **84** , 3370–3373 (2000) (available freely on arXiv), and a paper by J. Luttinger & J. Ward _Ground-State Energy of a Many- Fermion System. II._ Phys. Rev. **118** , 1417–1427 (1960). An other interesting reference to start with is a paper by J. Luttinger, _Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions_ , Phys. Rev. **119** , 1153–1163 (1960), where he shows (eq.33) that the volume of the Fermi surface is conserved under interaction, using analytic properties of the Green function including the self-energy as long as the total number of particles is conserved. I'm not sure if it's sufficient to proof the _stability_ of the Fermi surface (but what does _stability_ means exactly, I'm now confused :-p ) Is there absolutely no modern (topological ?) version of this proof ?


title: Background Fields in String Theory

text: In "String theory and M-theory" (K. Becker, M. Becker and H.Schwarz) page 81, they said that among the background fields, the fields associated with massless bosonic fields are especially significant. My question is, why is that? What's the most general form for the action in bosonic string theory with background theory if all fields are included? Thank you!


title: Hollow stone columns provide more support?

text: In history class in elementary school I remember learning that the Greeks would build their stone columns hollow because they thought this provided more support. Is it true that a hollow column is stronger? Thanks!


title: what is the electric field intensity inside a charged metallic shell if there is a point charge inside the shell?

text: What I know so far: \- Charges (electrons) inside a conductor will repel (Coulomb's law). \- The charges will experience repulsion which results in maximum separation distances between the charges. \- The charges will then redistribute along the surface of the conductor in order to achieve electrostatic equilibrium (ie. net force of zero on each charge) \- Thus, no electric field exists inside the conductor. Please feel free to correct me if I am wrong in any of the above statements. Appreciate the help. Thanks.


title: Why don't you see multiple images of an object?

text: Consider the ray model of light. Let's say an object such as a pencil is illuminated, and consider one point on that pencil. Since there could be many rays of light bouncing off the same point on the pencil, one ray could hit the left side of your eye and another ray from the same point could hit the right side of that same eye. Why don't you see that point in 2 different places then? Thanks!


title: Explanation that air drag is proportional to speed or square speed?

text: A falling object with no initial velocity with mass $m$ is influenced by a gravitational force $g$ and the drag (air resistance) which is proportional to the object's speed. By Newton´s laws this can be written as:   1. $mg-kv=ma$ (for low speeds)    2. $mg-kv^2=ma$ (for high speeds).  I assume that $k$ is a positive constant that depends on the geometry of the object and the viscosity. But how can one explain that the air resistance is proportional to the velocity? And to the velocity squared in the second equation?


title: Resisting force depends on velocity?

text: Why does resisting force depend on velocity? I think there is no relation between resisting force and velocity of object. Please speak about it logically.


title: Confused about the theoretical origin of quadratic air drag

text: Though the mathematical concepts underlying quadratic air drag are quite straightforward (a single variable differential, just like the linear drag equation), my text book (and online text books) completely ignore the reasoning behind why the "drag" at high speeds on a trajectory through a fluid is proportional to the velocity squared. I know that this could not just be an empirical result. Is there an intuitive reason for this (perhaps like momentum transfer or kinetic energy?). If possible, I would also like to ask for an intuitive reason behind the units $m^2/s^2.$


title: Use and understanding of higher-order correlation functions

text: The correlation function g1 is pretty easy to understand and the relation to young's double slit experiment is also clear to me. In every quantum optics book I read so far correlation functions $g^n(x_1, ... , x_{2n})$ of an order greater than 1 are defined, but not related to an experiment or explained any further. What is an example for an experiment that requires a correlation function of a higher order? In my understanding $g^1(x_1,x_2)$ gives the similarities between two functions for different $\tau$. How is this possible for more than one function, if $g^n(x_1,...,x_{2n})$ is still scalar? The definitions I used can be found in any book an quantum optics or here http://www.matthiaspospiech.de/files/studium/skripte/QOscript.pdf (p 64)


title: Can Divergences in Nonrenormalizable Theories Always Be Absorbed by (An Infinite Number of) Counterterms?

text: For example, consider the $\phi^3$ theory in $d=8$, with Lagrangian: $\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}-\frac{1}{3!}\lambda_{3}\phi^{3}$. In 8 dimensions, the box diagram now diverges. We would need to add a $\lambda_{4}\phi^{4}$ coupling to our Lagrangian. Then, this box divergence is thought of as the one-loop correction to our 4-point vertex. Now, what if the $\phi^4$ term was not allowed in our Lagrangian due to some symmetry constraints? Can we argue that we wouldn't see the box divergence in the first place? That the same symmetry forbids the divergence? This is not terribly realistic, but if you look at 't Hooft and Veltman's 1-loop Gravity paper, we see that we can't write down a counterterm due to Gauss-Bonnet. Could we stop there and immediately say that there will be no 1-loop graviton divergence without even calculating? Punchline: No allowed counterterm $\Rightarrow$ No relevant divergence? Edit: Here's a more relevant example: http://www.conferences.itp.phys.ethz.ch/lib/exe/fetch.php?media=qg11:ld.ethz.qg.pdf. Check out slides 6 and 7. It argues that in SUGRA at two loops in 4 dimensions, the only possible counterterm, $R^3$, "cannot be supersymmetrized." He implies that it follows that no divergence is allowed at two loops; however, at three loops, since we can write down a $R^4$ counterterm, a divergence is allowed but not necessarily present. Edit 2: Signs seem to be pointing me to the BPHZ Theorem. Weinberg (Vol. 1, Chapter 12) says, "...the cancellation of ultraviolet divergences does not really depend on renormalizability; as long as we include every one of the infinite number of interactions allowed by symmetries, the so-called non- renormalizable theories are actually just as renormalizable as renormalizable theories." The disconnect may be coming when I try to relate the BPHZ subtractions method to the counterterm method, which appears to be explained in http://prd.aps.org/abstract/PRD/v25/i2/p392_1.


title: Does the mass point move?

text: There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at $t=0$ its position is $0$, i.e., $x(t=0)=0$, same for its velocity, i.e., $\dot{x}(t=0)=0$, its acceleration, $\ddot{x}(t=0)=0$, its rate of change of acceleration, $\dddot{x}(t=0)=0$, and so on. Mathematically, for the trajectory of the mass point one has \begin{equation} \left. \frac{d^{n}x}{dt^n}\right|_{t=0} = 0 \textrm{ for } n \in \mathbb{N}_0\mbox{.} \end{equation} My physical intuition is that the mass point is not going to move because at the initial time it had no velocity, acceleration, rate of change of acceleration, and so on. But the mass point not moving means that $x(t) \equiv 0$ since its initial position is also zero. However, it could be that the trajectory of the mass point is given by $x(t) = \exp(-1/t^2)$. This function, together with all its derivatives, is $0$ at $t=0$ but is not equivalent to zero. I know that this function is just not analytical at $t=0$. My question is about the physical understanding: How could it be that at a certain moment of time the mass point has neither velocity, nor acceleration, nor rate of change of acceleration, nor anything else but still moves?


title: why are two higgs doublets required in SUSY?

text: I can't really understand why two higgs doublets are required in SUSY. From the literature, I have found opaque explanations that say something along the lines of: the superpotential W must be a holomorphic function of the chiral supermutiplets and thus we need to introduce another chiral supermutiplet. I also know that this is somehow related to an anomaly cancellation. Can somebody help to make this a bit more clear?


title: Wavefunction collapse and gravity

text: If gravity can be thought of as both a wave (the gravitational wave, as predicted to exist by Albert Einstein and certain calculations) and a particle (the graviton), would it make sense to apply quantum mechanics (which I understand only applies to mass/energy) and therefore wavefunction collapse to gravity? In other words, does gravity exhibit wave-particle duality as light does, and thus is it susceptible to wavefunction collapse? If so, what would the implications of the wavefunction collapse of a gravitational wave be? To better sum up my question: could a gravitational wave be described as a wavefunction? I would appreciate it if anyone could help me understand if this is a valid concept, or if there are any other theories and concepts that would help me understand gravity and quantum mechanics combined (quantum field theory?).


1. What is background independence and how important is it?   2. In order to be a theory of everything, will the final string-theory/m-theory have to be background independent?    3. Does the current lack of background independence show string theory is currently _NOT_ a theory of everything?  My understanding from Wikipedia is that the ADS/CFT shows hopeful hints. Are there any recent papers that have made progress in this direction? I've tried google but get haven't been able to get a definitive answer to this question. I found this interesting post by Lubos Motl, but it is from 2005.


title: Does General Relativity encompass Special Relativity?

text: Can all of the predictions made in Special Relativity (SR) also be made in General Relativity (GR)?


title: Low-scale supersymmetry

text: One of the major reasons SUSY was adopted in particle physics is to Naturally have a Higgs boson (a fundamental scalar) at the weak scale. If we abandon this argument, what other motivation for low-scale ($\mathcal{O(1)}$ TeV) SUSY exists?


title: The example of relativity of simultaneity given by Einstein

text: I understand (supposedly) the mathematics concerning the relativity of simultaneity in Special Relativity, but I have a nagging question regarding the original example given by Einstein supporting it (I'm only disagreeing with this specific example, not the concept). It is normally given as a person on an embankment and a person on a train. There is a relative speed between them (usually presented as the train passing the embankment). Now, when both people are at the same x-position (x=0), there is a flash of light at x = +dx and x = -dx. The argument as I keep seeing it is that the person on the embankment will say that both flashes reach him at the same time, whereas the person in the train will say that the flash in front of him reaches him before the other because he was moving toward it, and thus the observers will disagree on the simultaneity of the flashes. But given that the flashes occurred at the same distance from each of them, the speed of light is constant in both frames, and either one can claim to be at rest, then won't they, according to SR, necessarily see the flashes as simultaneous (both flashes have to travel the same distance in both frames since at the time of emission, the sources of both flashes were equidistant from both observers). I agree that the person on the embankment will say that the person on the train shouldn't see them as simultaneous (and vice versa) since either observer will see the other moving relative to the sources, but in each of there own frames, they must see the flashes as being simultaneous shouldn't they? Am I just misunderstanding the example? Thanks.


title: Mode of vibration comparing Classical and Quantum waves

text: I'm now studying Quantum Mechanics, and I took a course on Vibration and Waves last year. I have been trying to make an analogy between classical and the quantum waves. Is it true that both the modes of a quantum and classical wave can not be excited individually? Whenever you pluck a classical string, its motion can be described as a superposition of many different modes , n=1,2,3... you can never excite a single mode. In analogy, can we say that whenever you try to measure the wave function, the measured value will be a composition of different eigenvalues? Any ideas or contributions much appreciated.


title: If energy is only defined up to a constant, can we really claim that ground state energy has an absolute value?

text: Sorry if this is really naive, but we learned in Newtonian physics that the total energy of a system is only defined up to an additive constant, since you can always add a constant to the potential energy function without changing the equation of motion (since force is negative the gradient of the potential energy). Then in Quantum Mechanics we showed how the ground state of a system with potential energy $V(x) = \frac{1}{2} m \omega^{2} x^{2}$ has an energy $E_{0}=\frac{1}{2} \hbar \omega $. But if we add a constant to $V(x)$ won't that just shift the ground state energy by the same constant? So in what sense can we actually say that the ground state energy has an absolute value (as opposed to just a relative value)? Is there some way to measure it? I ask this in part because I have heard that Dark Energy might be the ground state energy of quantum fields, but if this energy is only defined up to a constant, how can we say what it's value is?


title: Does topology have any role in classical physics?

text: I've seen many applications of topology in Quantum Mechanics (topological insulators, quantum Hall effects, TQFT, etc.) Does any of these phenomena have anything in common? Is there any intuitive explanation of why topology is so important? Is there a similar application of topology in Classical Mechanics?


title: How does a noseblow counter detect alpha radiation?

text: After working in air fed suits,operatives are required to give samples from their nasal passages by blowing their nose into a tissue,which is then counted in a noseblow counter. How does this work?


title: is it possible to condense an object to a point?

text: When matter is condensed the mass stays the same and we also know that only the volume and density are the only other two effected variables. But is there a point in which the matter cannot condense anymore? Or a point in which the volume cannot decrease anymore?


title: When an object casts a shadow, why are there different shades of that shadow?

text: Let's imagine that there is a lamp on the floor. There is a dice on that same floor casting a shadow from our light source, the lamp. Why is it that there are different shades of the shadow phasing from darkest to dullest (darkest being closest to dice and dullest being farthest)?


title: How does faster than light travel violate causality?

text: Let's say I have two planets that are one hundred thousand lightyears away from each other. I and my immortal friend on the other planet want to communicate, with a strong laser and a tachyon communication device. I record a message on the tachyon communication device and release the message at exactly the same time as I activate the laser, both of which are directed to the other planet which is one hundred thousand lightyears away. Say it is the year 0 for both of us at the time I did this. If tachyons existed, then the message would arrive to my friend before the photons in the laser. It would arrive, say, a thousand years earlier. From my vantage point, that message will arrive to her at year 99,999; the same would be true for my friend's vantage point. However, she will only see the laser at year 100,000. So since she got the message at year 99,999, she immediately sends me a reply back going through the same procedure as I did. She records a message and releases it at the same time as the laser. The tachyons will arrive 1,000 years earlier than the laser, so for me, I will receive the message at year 199,998. I will receive the laser, however, at year 199,999. It seems to me that communication this way does not violate causality. I will still have received the message after I had sent it. If tachyons truly violated causality, though, I realize it should arrive at year -1 for her, and so she can reply to me at year -2, which would mess me up by year 0 as I will ask her how she knew I was planning on sending her a message before I sent it. I could send her a different message, which she would end up receiving at year -1, and will end up confusing her as she would have received one message asking her out, and the other asking her how did she know I was asking her out. She then decides I am crazy and sends me a message at year -2 that she does not want to date me, and so she will have both turned me down and entertained me before I have even asked her out. On the other hand, let's go back to year 0 and add a third device to our list: an Alcubierre drive. After I send out the message and the laser, I get impatient and do not feel like waiting 99,999 years, so I get on my Alcubierre drive spaceship and arrive on her planet at the same year 0. My friend is not in her office, so I leave a note to her also immortal secretary saying I dropped by and that she should expect a message for her in year 99,999. I then get back on my Alcubierre drive and land back on my planet, still on year 0. Meanwhile, the tachyons and photons I sent out are still racing to arrive to her. By year 99,999, she receives the message just as I Alcubierre drive back to her, and I pick her up for dinner. But the point of my question is, it seems to me that just going faster than light, if that alone was what you had, would not violate causality. It must be something else. I understand time dilation and that things with mass cannot travel at the speed of light, but using the Alcubierre drive, hypothetically speaking, I was still able to outpace the photons while also having mass. It still did not produce causality problems. Alcubierre drives are also valid solutions to GR. It seems circular to me to say that what makes traveling faster than light violate causality is because it violates causality (if faster than light communication was divorced from causality problems, then the causality problem would cause itself -- thereby violating causality and, hence, we would scrap it and conclude that there is no causality problem after all). What is it that I am missing? If someone could help me out, that would be excellent. I've been itching to ask my friend out for a few millenia now. :)


title: Is self gravitation theoretically impossible?

text: Is it theoretically possible to create some system such that the energy distribution creates a gravitational potential offset from its center of mass (or energy?) so that the body continually 'falls' into its own potential (i.e., as the body moves, the center of the potential moves with it such that it constantly falls forward)? I get the feeling that this doesn't make sense in the context of GR so I'd like to know why (I'm trying to understand the frame dependance of gravitational effects).


title: Deriving D'Alembert's Principle

text: The wiki article states that D'Alembert's Principle cannot derived from Newton's Laws alone and must stated as a postulate. Can someone explain why this is? It seems to me a rather obvious principle.


title: The relation between classical and quantum vacua

text: First let me clarify what I mean by vacuum. Suppose we are concerned with a theory of fields $\phi ^i$ defined on a stationary globally hyperbolic spacetime $M$ (I want the spacetime to be stationary so that I have a canonical choice of time-derivative and I want the spacetime to have a Cauchy surface so that I can speak of the Lagrangian) by an action functional $S(\phi ^i)$. For $\phi ^i$ stationary (i.e. $\dot{\phi}^i=0$), we define the potential by $V(\phi ^i):=-L(\phi ^i)|_{\dot{\phi}^i=0}$, where $L$ is the Lagrangian of $S$. A _classical vacuum_ (the definition of quantum vacuum is a part of the question) of this theory is a solution $\phi _0^i$ to the equations of motion $\tfrac{\delta S}{\delta \phi ^i}=0$ such that (1) $\phi _0^i$ is stationary and (2) $\phi _0^i$ is a local minimum of $V(\phi ^i)$ (by this, I mean to implicitly assume that $V(\phi ^i)<\infty$). In what way do these vacuum solutions of the classical equations of motion correspond to quantum vacuums? For that matter, what is a quantum vacuum? In particular, I am interested in theories with interesting space of vacua, for example, how $SU(3)$ instantons relate to the QCD vacuum.


title: How to solve fixed-fixed beam with finite difference method?

text: What equations to use on this system to form a matrix $A$ with dimensions $[n,n]$ and load vector $q$ with dimension $[n]$ ? I am trying to get vertical displacement $w$. $$w = A^{-1}\times q$$ Boundary conditions are as follows: $$w(o) = 0 $$ $$w(L) = 0 $$ $$\phi(o) = 0$$ $$\phi(L) = 0$$ It is becouse in any point of beam I can't make equation: $$d^2y/dx^2*E*I=M=0$$ so I can't get the exact values of displacement. The problem is that everywhere I look for solution it is done on a beam with continous load over entire beam or with at least one joint and I have only half of the beam covered with continous load and no joints. From $d^4y/dx^4*E*I=q=0$ again I have too many unknown values. ![Scheme](http://imgur.com/YkIdCAI.jpg)


title: Electrostatic charge leakage

text: What are the ways electrostatic charged objects leak charge in humid conditions? Can airborne particles pick up charge by contact, then be repelled hence removing charge? If so would it be a significant factor?


title: Car tires wearing in dependence on breaking system

text: Lets say I have two cars.   They are identical in every way, except that Car A has a normal breaking system, where most of the breaking power is inflicted on the front wheels, and some on the back, and Car B has a breaking system where all of the power is inflicted on the front wheels and none on the back. In the long run, in which car will the tires on the back wheels experience more wearing?   (For the sake of comparison, let's say we measure wear by the weight lost from the tires.)


title: Calculating energy U from $\partial U/\partial q$

text: Imagine $N$ oscillators with only two possible energies, $\epsilon_0$ and $ \epsilon_1$, with $\epsilon_1 > \epsilon_0$. Taking $\epsilon_0 = 0$ for now I showed $\Omega(q\epsilon_1) = \frac{N!}{(N-q)!q!}$ and then $$\frac{\partial S}{\partial q} = k \log(N/q - 1) $$ How can I use the above equation to show that $$U = N\epsilon_1\frac{e^{-\epsilon_1/(kT)}}{1+e^{-\epsilon_1/(kT)}} $$ I tried moving the $\partial q$ over to the right, and then have $dS = dU/T$, but i wasn't getting anything meaningful.


title: Calculating the Neutron Stopping Power of complex materials

text: Is there a fast and convenient way of calculating the neutron stopping power of materials, consisting of multiple elements (e.g. doped crystals) without the need for Monte Carlo Simulation, that is more exact than simple cross- section additivity?


title: In the diode equation, why the exponential $\exp$ and the ideality factor $n$ are there? What do they represent & what is their significance?

text: In the Shockley diode equation, why the exponential $\exp$ and the ideality factor $n$ are there? What do they represent & what is their significance? I have to work on Solar Photovoltaics, and I need to understand the Shockley diode equation clearly.


title: What objective criteria distinguish between valid science, fringe science and pseudoscience in physics?

text: Plenty of research activity in physics have been vigorously opposed by their opponents as pseudoscience or fringe science, while other research are mainstream. It is possible some topic is pseudoscience if the experts claim it is so, but they could potentially be biased. For the nonexperts out there, short of appealing to authority, what objective criteria can be used to distinguish between valid science, fringe science and pseudoscience, i.e. topics which are a waste of time compared to topics worth pursuing.


title: Difference between spin-orbit coupling and LS coupling (Russell-Saunders)

text: I'm having some trouble understand what the difference is between these two. It seems as though there are kind of the same, but that spin-orbit coupling reduces to LS coupling under certain circumstances. But, I can't seem to make sense of it. So I was hoping anyone could explain the difference briefly, and maybe explain when you use one of them, instead of the other. Thanks in advance.


title: What does transport equation represent in terms of physical quantities?

text: In my math course we're taught to solve PDE (partial derivative equations) like transport equation: $$ c\frac{\partial u}{\partial x} +\frac{\partial u}{\partial t}~=~0. $$ If $u(x,t)$ is the quantity transported and $c$ has speed dimension (according to my book), $\frac{\partial u}{\partial t}$ must be speed too. What does $\frac{\partial u}{\partial x}$ represent? Does anybody have a good physical example to help me understand?


title: Planetary model of atom still valid?

text: When I was in school, I learned (from Democritus) that an atom was similar to a solar system, with the nucleus being the sun, and the electrons being the planets. Of course, there are some differences:   * The "sun" isn't a single entity, but a collection of protons and nuetrons.    * Two planets can share an orbit (which might be possible in a solar system too, but it doesn't happen in our solar system).  Is this model still valid? Here are my problems with it:   * In "Surely You're Joking, Mr Feynman", Richard Feynman implies that electrons are more a theoretical concept than real objects.    * I have trouble understanding atomic bonds (ionic and covalent) in this model.    * I also have trouble understanding electron "orbit jumping" in this model, as well as several other things.  Is there a better model for someone learning this for the first time?


title: How to smooth a path (and speed calculation) based on randomly timed coordinates?

text: first my actual problem. then my try on improving the current way of solving this with the wish for feedback or even a solution :) gpx file with lat/long, elevation and time. wanna calculate speed... easy! when visualizing the speed on a chart you would figure it needs a little smoothing. done you have a pretty accurate speed, average-speed, max-speed... ...but i want more ;) 1) the coordinates are from an object that is adjusting there direction in a more or less smooth/curved fashion (aka. car, bike,...). thus smoothing the path would/could be nice. right? maybe something like a Bézier curve? but the path should still follow thru the actual measured points. any ideas? 2) smoother path would be generated by creating more points...right? so how do i split the time to the newly create points along the path in a similar way (so the new points along the path are timed like the measured ones)? 3) as long as the resulting data isn't less accurate i'm happy with it. still, feedback about how much or little improvement those calculations might bring are highly appreciated. thx.


title: Magnetic Field and the Speed of Light

text: Is it just a historical choice that both magnetic field and the Lorentz force equation include the speed of light? I figure that whoever wrote up the equations (in cgs!) could have put both factors of $c$ in either the force equation, or have define the magnetic field as being smaller by a factor of c- but they didn't. Any ideas why?


title: How many fundamental forces could there be?

text: We’re told that ‘all forces are gauge forces’. The process seems to start with the Lagrangian corresponding to a particle-type, then the application of a local gauge symmetry leading to the emergence of the force bosons via the associated symmetry group. But where did _exactly four forces_ come from? Could new, perhaps supersymmetric particles hint at new fundamental forces? Is there a deeper theory which predicts what final set of forces we’ll eventually end up with? Finally, is the concept of force in unified physics really that fundamental at all?


title: Is it viable to convert nuclear waste into safe isotopes?

text: I read that powerful pulsed lasers can change isotopes: J. Magill, et. al.: "Laser transmutation of iodine-129". Did anyone estimate what would be the energy costs to transmutate 1 kg of fission product from a conventional reactor using such a laser or an accelerator? Is it even possible to transmutate a mixture of isotopes? Would that be a viable alternative to long term storage if we find a way to get enough energy? Right now I seriously doubt that we could ever process 100s of kilograms using such techniques.


title: Energy storage and battery banks

text: Why is it not possible to store windfarm energy in battery banks? A lot of energy isn't being used when wind farms are at peak and we have no way of storing it. This is wasteful. So why don't we use battery banks?


title: One way insulation?

text: I know from basic physics lessons that a box painted black will absorb heat better than a box covered in tin foil. However a box covered in tin foil will lose heat slower than a black box. So what is the best way to conserve the temperature of a box? (aiming for 0 degrees Celsius inside the box when it's -60 outside). I mean would painting the outside of the box black, and having tin foil on the inside work? So the box can absorb heat better (black paint) and the tin foil making it harder for heat to escape?


title: Ozone generation

text: Another crazy question: 1) I will need to generate some ozone for chemical reactions, and what seems to be the most straightforward way is using germicidal lamps, but the question is how to estimate how much ozone is produced (for let's say 100W of lamps) and what should be inlet oxygen flow for maximum ozone concentration? 2) Also, I see that there are ozone-generating & non-ozone generating germicidal lamps - based on whether their glass absorb 193nm line or not. If anyone worked with non-ozone producing lamps - do you ever feel ozone odor when working with them, or ozone generation is 0? For example lamps I have nearby give ozone odor in few seconds after turning on at the distance of 1 meter (with no air movement) - but that might not mean anything as humans are very sensitive to ozone. 3) And finally, how many centimeters of oxygen under normal conditions is needed to absorb half of 193nm light? If it's more than few centimeters, I guess I will have to build box with reflectors - as far as I see, aluminum foil should reflect 193nm light back, right? PS. Oxygen is to be generated by electrolysis of ultra pure water, so I guess it will be 100% wet. I cannot mess with compressed oxygen, that's a little over my danger tolerance :-) , and chemical oxygen generation might give me too much contaminants in line with other difficulties (hard to maintain low constant flow for hours, especially when not using water). PPS. I know that both germicidal lamps & ozone is very dangerous. PPPS. I guess this is still not chemistry question, as it mainly focuses on UV light. Anyway, we don't have such stack-exchange site...


title: Does coverslip thickness matter for high NA oil immersion objectives?

text: This question is related to Impact of covering glass on lens performance. I use a 63x TIRF objective with a numerical aperture of 1.46 and oil immersion. The immersion oil has an index of $n_e=1.518$. I'm observing green eGFP fluorescence at around 510 nm. Does it matter if I use a coverslip (BK7 glass) with 140 $\mu$m thickness instead of 170 $\mu$m? Edit: The objective is a Zeiss Objective alpha "Plan-Apochromat" 63x/1.46 Oil Corr M27 ![Zeiss Objective](http://i.stack.imgur.com/zgRpH.png)


title: Understanding the math behind velocity-dependent conservative forces, Part 1

text: In a notable answer to this question, Qmechanic formulates conditions for "conservative" velocity-dependent forces (e.g. the Lorentz force, but not velocity-proportional friction) that are analogous to those for traditional velocity-independent conservative forces. To wit, in a simply-connected domain (for the velocity-independent case, anyway), two sets of three equivalent conditions for a force to be conservative are presented: $$ \begin{array} {cccc} \text{ } & \text{velocity-independent force } \boldsymbol{F}( \boldsymbol{r}(t)) & | & \text{velocity-dependent force } \boldsymbol{F}(\boldsymbol{r}(t),\boldsymbol{\dot{r}}(t)) \\\ 1) & F_i = - \frac{\partial U}{\partial x^i} & | & F_i = -\frac{\partial U}{\partial x^i} + \frac{d}{dt} \left( \frac{\partial U}{\partial \dot{x}_i} \right) \\\ 2) & \boldsymbol{\nabla \times F} = 0 & | & \frac{\delta F_i(t)}{\delta x_j(t')} - \frac{\delta F_j(t')}{\delta x_i(t)} = 0 \\\ 3) & \oint_{S^1} dt \, \boldsymbol{F}(\boldsymbol{r}(t)) \boldsymbol{\cdot \, \dot{r}} (t) = 0 & | & \oint_{S^2} dt \wedge ds \, \boldsymbol{F} ( \boldsymbol{r}(t,s), \boldsymbol{\dot{r}}(t,s)) \boldsymbol{\cdot \, r'}(t,s) = 0 \end {array} $$ where $\delta$ denotes a functional derivative, the final integral is over any "two-cycle $r: S^2 \rightarrow \mathbb{R}^3 \,$", and "a dot and a prime mean differentiation wrt. $t$ and $s$, respectively". I have changed the formulation somewhat; I hope I didn't introduce errors. I get the maths for the velocity-independent force conditions, but, for the velocity-dependent case, I am a bit puzzled by the functional derivatives and totally baffled by the two-cycle integral. My question:   * What is this "two-cycle integral", which looks like no surface integral I've ever seen, and how is it evaluated? (and how did $\boldsymbol{r}$ acquire two arguments?).  > \- How is this functional derivative evaluated? \- Why are the functional > derivative and two-sided integral equivalent to each other and to the > potential formula for the force? I suspect this is a rather large subject; references would be appreciated.


title: About SU(2) gauge symmetry of the large U limit of the Hubbard model

text: I have been studying about the SU(2) symmetry in Heisenberg Hamiltonian with a paper 'SU(2) gauge symmetry of the large U limit of the Hubbard model' written by Ian Affleck et al(Phys. Rev. B 38, 745 – Published 1 July 1988). In the paper, they represent the spin in terms of fermionic operators with constraint that number of particle at each lattice is 1. $$S_{x}=\frac{1}{2}c^{\alpha\dagger}_{x}\sigma_{\alpha}^{\beta}c_{x\beta}, \\\constraint: c^{\dagger\alpha}c_{\alpha}=1$$ And they re-express the Hamiltonian using matrix $\Psi_{\alpha\beta}\equiv\left(\begin{array}{cc}c_{1}&c_{2}\\\c_{2}^{\dagger}&-c_{1}^{\dagger}\end{array}\right)$(where number denotes the spin up and down) to show the SU(2) symmetry of the Heisenberg Hamiltonian explicitly. Also the constraint can be re-expressed as follows: $$\frac{1}{2}tr\Psi^{\dagger}\sigma^{z}\Psi=\frac{1}{2}(c^{\dagger}_{1}c_{1}+c_{2}^{\dagger}c_{2}-c_{1}c_{1}^{\dagger}-c_{2}c_{2}^{\dagger})=c^{\dagger}_{1}c_{1}+c_{2}^{\dagger}c_{2}-1=0$$ At this time $c^{\dagger}, c$ are operators. And they write the lagrangian of this Hamiltonian. $$L=\frac{1}{2}\sum_{x}tr\Psi^{\dagger}_{x}(id/dt+A_{0x})\Psi_{x}-H$$ where $A_{0}=\frac{1}{2}\mathbf{\sigma}\cdot\mathbf{A_{0}}$. Here components of $\mathbf{A_{0}}$ are Lagrangian multipliers. This lagrangian has time dependent gauge symmetry. Here I have a problem. As far as i know $c^{\dagger}, c$ in Lagrangian are not operators anymore but grassmann variables. Therefore constraint of $(\mathbf{A_{0}})_{z}$ in the Largrangian becomes   $$\frac{1}{2}tr\Psi^{\dagger}\sigma^{z}\Psi=\frac{1}{2}(c^{\dagger}_{1}c_{1}+c_{2}^{\dagger}c_{2}-c_{1}c_{1}^{\dagger}-c_{2}c_{2}^{\dagger})=c^{\dagger}_{1}c_{1}+c_{2}^{\dagger}c_{2}=0$$ This is different from the original constraint condition!! I am really confused about this. Can anyone help me to solve this problem?


title: Superstring theory and renormalization

text: > **Possible Duplicate:**   >  Does the renormalization group apply to string theory?   >  Renormalization in string theory QED and some quantum theories require renormalization techniques and take it as somehow granted. I did not study string theories yet, but I would like to whether renormalization similar to QED and some quantum theories is required in superstring theory.


title: Renormalization in string theory

text: I'm taking a course in string theory and have encountered renormalization for the first time (and I suspect it isn't the last). Specifically, while quantizing the bosonic and spinning strings, an ordering ambiguity in the mode expansion gives us a constant (called 'a' in the notes I'm reading) which is a divergent sum. The constant is then fixed to 1 (at least for the bosonic string in light-cone quantization - don't remember the others at the moment) by some very convincing physical arguments reminiscent of renormalization in good ol' QFT. My question is: why would we expect something like this to be necessary? Isn't the whole philosophy of renormalization that the necessity for adjustment of parameters comes out of the fact that your QFT is an effective low-energy approximation of some complete theory? If this complete theory is a string theory, then why do we still encounter the need for renormalization?


title: Maximum speed of a rocket with a potential of relativistic speeds

text: > Ultimately, the factor limiting the maximum speed of a rocket is: > >   1. the amount of fuel it carries >   2. the speed of ejection of the gases >   3. the mass of the rocket >   4. the length of the rocket > This was a multiple-choice question in a test I've recently taken. The answer was (1), however, is this disputable, for if we assume that this rocket can potentially achieve relativistic speeds, what implications would this present to the limiting factor on maximum speed?


title: If strings are infinitely extended, are they nonlocal?

text: To completely localize a string within any bounded region of space, no matter how large, requires an infinite energy. Does this mean strings modes are inherently nonlocal?


title: How will the Twin Paradox become, for Time Dilation, if no acceleration was ever involved?

text: I think one catch in Twin Paradox was about the big acceleration that can turn back the traveling twin from light speed outward bound, to become light speed inward bound. What if there is strictly no acceleration?   1. Peter is on a space ship, traveling 99% of light speed. He is exactly 20 years ago.    2. Michael is on Earth ( **or a planet similar to Earth, but with a radius so small that any centripetal acceleration is negligible**... or consider him standing just on a piece of concrete in space with oxygen supply)   3. Michael is also exactly 20 years old.   4. According to time dilation, Peter's clock in the spaceship is slowing than Michael's clock.   5. According to time dilation, Michael's clock on Earth is slower than Peter's clock. (since motion is relative, if we consider Peter to be stationary, and Michael is traveling)   6. Peter's spaceship is traveling towards Michael.   7. After 30 years on Earth, Peter's spaceship went past Michael's face, so Peter and Michael is 1 cm apart, face to face and eye to eye.   8. Now, would Peter see Michael quite older than him, and also, Michael sees Peter quite older than him?


title: How to construct the radial component of the momentum operator?

text: I'm having trouble doing it. I know so far that if we have two Hermitian operators $A$ and $B$ that do not commute, and suppose we wish to find the quantum mechanical Hermitian operator for the product $AB$, then $$\frac{AB+BA}{2}.$$ However, if I have to find an operator equivalent for the radial component of momentum, I am puzzled. It does not come out to be simply $$\frac{\vec{p}\cdot\frac{\vec{r}}{r}+\frac{\vec{r}}{r}\cdot\vec{p}}{2},$$ where $\vec{r}$ and $\vec{p}$ are the position and the momentum operator, respectively. Where am I wrong in understanding this?


title: How does the electron electric dipole moment (EDM) depend on supersymmetry?

text: I have read a recent paper that says that limit on the EDM of the electron has now been measured to 12 times better accuracy. According to that paper, as I understood, there should be a difference in the measured value of the EDM depending on whether or not supersymmetry exists. What is the reason behind that? calculations are always my preference.


title: What will happen when measuring unmeasurable object?

text: There is a set called Vitali Set which is not Lebesgue measurable. Analogously, there also exists a Vitali set $Y$ in $\mathbb R^3$ which is a subset of $[0,1]^3$ and $|Y\cap q|=1$ for all $q\in \mathbb R^3/\mathbb Q^3$. However, I'm curious about if it fulfilled a kind of isotropic uniform medium, let this isotropic uniform medium has density $\rho$, and put it on a electronic scale to weigh, **what reading can we get**? Note that $m_Y=\rho V_Y$ but $V_Y$ seems to be undefined... So it seems we cannot get any real reading. But on the other hand, since we are using a electronic scale, it also seems we must get a reading...A paradox?


title: Deriving Birkhoff's Theorem

text: I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the vacuum, and that $g_{00}*g_{11}=f(t)$. But the next question is: Show that you can get back to a Schwarzschild metric by a certain mathematical operation. I am thinking at a coordinate change (or variable change on $r$) to absorb the $t$ dependence of $g_{11}$, but I can't see the right one. Does someone has a tip to share? Also one further question is to explain if an imploding (spherically) star radiates gravitationally, based on a quantum mechanical argument. I would say that under the isotropy hypothesis we have $[H,J]=0$, so the total angular of the star is conserved, or if gravitons would be emitted, they would carry angular momentum from their spin 2 and violate this conservation, so my answer would be no. Is this wrong?


title: Do the trigonometric functions preserve units?

text: I saw an exercise where you had to calculate the units of $C_i, i=1,2$ from an equation like this:   * $v^2=2\cdot C_1x$ and   * $x=C_1\cdot \cos(C_2\cdot t)$ where   * $x$ means _meters_ ,   * $t$ means seconds and   * $v$ means velocity. For $C_1$ I got $C_1=m/s^2$. But coming to $C_2$ the cosinus irritates me somehow: $$x=C_1 \cdot \cos(C_2 t)\Rightarrow m=m/s^2 \cdot \cos(C_2 s)\Rightarrow s^2 = \cos(C_2 s)$$ Does this mean, that $C_2$ must have the unit $s$? Thanks a lot!


title: Expected Energy Production From High Efficiency Solar Cells

text: First, a bit about my thoughts. I believe we have the capability today to provide energy, water, food, education, and transportation to every man woman and child on the planet. To that end, I would like to become a force that brings about this change. In trying to meet the first goal, which is to provide energy, I have come across two technologies which greatly interest me, the first of which must be in place to begin the second. The first is the high efficiency solar cells developed by Patrick Pinhero at the University of Missouri. Assuming that said solar cell captures 80% of available light, how much energy can I expect them to produce per meter of cell? How would this vary betweeen environments such as the Nevada desert and central Florida, how did you come to these conclusions, and is there any formula I can use to calculate an expected energy output?


title: question about derivative of momentum = force proof***

text: I was trying to prove it 2 ways, 1st way: $$p=mΔV$$ $$a=ΔV/t$$ $$ΔV=at$$ $$p=m*a*t$$ Remember $$F=ma$$ $$F(t)=p$$ The derivative of momentum just gives us the "regular force" since b4 that momentum = force as a function of time. NOT SURE IF THIS PART IS CORRECT thus, $$dp/dt = F$$ 2nd way: if mass was constant $$p = mv$$ $$dp/dt = m(dv/dt) + v(dm/dt)$$ $$dp/dt = ma + 0, dp/dt = f$$


title: Data requirement to determine proportionality

text: A common result of theoretical analysis in physics is some sort of relation derived from physical parameters and typically expressed in the form of a non- dimensional parameter. These scale relations are not equalities but proportional relationships. For instance, in turbulence you end with with $$ \frac{\eta}{l} \sim Re^{-3/4}$$ Assuming that some derivation results in: $$f(\Pi_1,\Pi_2,\dots,\Pi_i) \sim C$$ where $C$ is the experimental measure, $f$ is a function of non-dimensional parameters, and $\Pi_i$ are the independent non-dimensional parameters, is there a minimum number of experiments to determine the constant of proportionality $a$ such that: $$f(\Pi_1,\Pi_2,\dots,\Pi_i) = aC$$ sufficiently? I would expect that the number of experiments required is in some way related to the combination of all possible parameters. For instance, if $i = 2$ then I would expect a minimum of 4 experiments would be required. But is the minimum based on combinations sufficient or are more values needed?


title: When did Voyager-1 achieve Solar System escape velocity?

text: Wikipedia's page on escape velocity puts the escape velocity for an object travelling out of the Solar System at ~525km/s. This figure is slightly higher than the tentative velocity of Voyager-1 at ~17km/s. Why is the vehicle spoken of as being on an interstellar course? When did the vehicle achieve Solar Escape velocity? What am I missing?


title: Why do light disappears the moment we switch off the source (inside the wooden box)?

text: I am failing to explain why light won't remain inside the wooden box in the following situation. I considered a wooden box closed from all the sides, with a bulb inside it. If we switch on the bulb, light will be emitted from the bulb inside the box, if we switch off the bulb, I assumed the light to disappear, which I practically assume to be true. If I am wrong here, please explain. So, practically I assumed light to disappear if we switch off the bulb, after being switched on for a while. I got a question here, _why light has to disappear the moment we switch off the bulb?_ Thinking about the above situation, I considered the case of bullet being fired into the wooden face from the inside of the same box. No doubt, bullet smashes the wooden face into pieces and comes out. Here bullet has high speed and even has mass, so that, it disappears out of the wooden box. I considered the photons now, I thought photons have high speed much greater than bullet, but they have very less mass (I am not sure with rest or relativistic), so I thought that, photons should remain into the wooden box after colliding the wooden face. If they would had, I thought that there should have been light inside the box even after the bulb was switched off, but it is not. _Is it that photons are piercing into the voids between the atoms with high speed to get out of wooden box?_ If we say photons are getting out of the wooden box piercing into the voids, why won't it be in total internal reflection phenomenon. If we assume light to be incident at the interface from the denser medium to the rarer medium, at an angle greater than critical angle, photons should even then pierce into the voids. But, my teacher has taught me that, in total internal reflection there would be no refraction. By this even my assumption of photon getting out of the box from the voids also falls down. As radiation is a form of energy, it can't be lost with out being utilised or else it can't be lost without getting emitted out of the box so as to avoid violation of conservation of energy. _Is here, the light absorbed inside the box by the medium?_ I don't know whether I have misunderstood here or whether we could explain from wave nature of light, so as to _why light disappears from the box?_


title: Hybrid Inflation and Supergravity

text: Is it necessary to add a constant term in the superpotential of hybrid inflation within supergravity in order to cancel SUSY vacuum energy at the end of inflation?


title: Reason for considering the positive root

text: In eqn. (3.11) of Srednicki's QFT book only the positive root is considered; i.e., $ \omega = + \sqrt{(k^2 + m^2 )} $ Why the negative root is not considered? And what is the $\omega$?


title: Calculating the $\frac{dp}{dT}$ slope using Clausis-Clapeyron

text: I've produced experimental data over how the boiling point of water varies with pressure and temperature and plotted this in a PT graph. I would like to verify my results using theory. The Clausius-Clapeyron equation appears to be exactly what I want. I did manage to find a table over heat of vaporization depending on pressure, so that this version of Clausius-Clapeyron is almost applicable: $$ \frac{dP}{dT}=\frac{L}{T\Delta v} $$ However, I don't have any values for $\Delta v$. So what are my options? Is there some approximation I can make to find the value for $\Delta v$ or is there another version of Clausius-Clapeyron I can use to find $\frac{dP}{dT}$ using freely available tables? Or would someone suggest another way of verifying my results?


title: Why does the power in an inductor equal what it does?

text: I understand that power is that rate at which work is done and that because of this the power in an inductor is equal to $$P=\frac{d}{dt} \left(\frac12Li^2\right).$$ I also understand that the power is also equal to $$P=Li\frac{di}{dt}$$ since $L\,\frac{di}{dt}=V$ and $Vi$ is power. I understand that since the power is equal to both of these equations that they are equal to each other. The part that I don't get is mathematically how to get from one to the other.


title: the poles of impurity system's Green's function

text: Denote the pure system as system 1, with both continuum and discrete eigen energy. $G_0$ is its Green's function. After introducing some impurities, we call the resultant system system 2 with new Green's function $G$, and $T$ is T matrix. We have $G=G_0 + G_0 T G_0$ My question is, since the poles of Green's function are eigen energy of the system, and from the above equation, we find that all the poles of $G_0$ will also be the poles of $G$, does this mean the eigen energy of system 2 share the same eigen energy as its pure counterpart system 1? That is to say, both system 1's continuum and discrete eigen energy do not change in the presence of impurity? Is there any possibility the $T$ matrix can cancel some of $G_0$'s poles?


title: Noether theorem and classical proof of electric charge conservation

text: How to prove conservation of electric charge using Noether's theorem according to classical (non-quantum) mechanics? I know the proof based on using Klein–Gordon field, but that derivation use quantum mechanics particularly.


title: What are thermal energy distributions?

text: I am trying to understand the photoelectric-effect deeply. My teacher used the Planck's law and integrated it to deduce the Stefan-Boltzmann law. He somehow showed some quantum-physical characteristic -- something that intensity did not increase the energy of photon as expected classically but the stopping voltage. Now let's take a step back. He started with Planck's law and I want to understand how it is connected to other thermal equilibriums such as Bose- Einstein distribution, Fermi-Dirac distribution and Maxwell-Boltzmann distribution. **What are the thermal energy distributions? How to remember them? Some mnemonics? Are they somehow connected? I know BE and FD are the quantum- physical descriptions while MB is a classical approximation but I don't how Planck's law is related to them, how?** **Wikipedia about Planck's law** > _As an energy distribution, it is one of a family of thermal equilibrium > distributions which include the Bose–Einstein distribution, the Fermi–Dirac > distribution and the Maxwell–Boltzmann distribution._


title: Generalized quantum mechanics

text: I wonder if it's possible to discover another version of quantum theory that doesn't depend on complex numbers. We may discover a formulation of quantum mechanics using p-adic numbers, quaternions or a finite field etc. Also, physical states lives on a Hilbert space. What if we consider the infinite dimensional Hilbert space to be the tangent space of an infinite dimensional manifold at some point? Is it possible to make these generalized theories and if it's possible can it lead to new predictions or resolve some of the difficulties that are present?


How to explain Tsirelson's inequality using extended probabilities? Some people have tried explaining the Bell inequalities using extended probabilities. For instance, a pair of entangled photons are created and sent off to Alice and Bob. Alice can set her polarizer to $0^\circ$ or $+30^\circ$. Bob can set his to $0^\circ$ or $-30^\circ$. If both polarizers are aligned, both outcomes always agree. If only one is rotated, 3/4 of the time, there's agreement. If both are, there's only agreement 1/4 of the time. Extended probabilities. Assume each photon "secretly" has "actual" values for both polarization settings prior to measurement. WLOG, just consider the cases where the "hidden values" between the two Alice polarizations either (A)gree or (D)isagree. Ditto for Bob's. Then, (A,A) prob 3/8 (A,D) prob 3/8 (D,A) prob 3/8 (D,D) prob -1/8 "explains" the violation of the Bell inequality. This still leaves open the question why we can't have (A,A) prob 1/2 (A,D) prob 1/2 (D,A) prob 1/2 (D,D) prob -1/2 violating Tsirelson's bound.


title: Glueball mass in non-abelian Yang Mills theory

text: How can the glueball mass be calculated in Yang Mills theory?


title: Why is average velocity the midpoint of initial and final velocity under constant acceleration?

text: Since average velocity is defined as$^1$ $$\vec{\mathbf v}_\mathrm{av}=\frac{\vec{\mathbf x}-\vec{\mathbf x}_0}{t-t_0},$$ where $\vec{\mathbf x}$ denotes position, why is this quantity equal to $$\frac{\vec{\mathbf v}+\vec{\mathbf v}_0}{2},$$ where $\vec{\mathbf v}=\frac{d\vec{\mathbf x}}{dt}$ and $\vec{\mathbf v}_0=\left.\frac{d\vec{\mathbf x}}{dt}\right|_{t=t_0}$, when acceleration is constant? What in particular about constant acceleration allows average velocity to be equal to the midpoint of velocity? $^1$: Resnick, Halliday, Krane, _Physics_ (5th ed.), equation 2-7.


title: Convergence of quantum effective action to finite loop order

text: Consider the quantum effective action of a fixed QFT. If we compute it perturbatively to finite loop order $\ell$, we get a sum over an infinite number of Feynman diagrams. For example, the 1-loop quantum effective action of QED contains contributions from all diagrams in which a single electron loop is connected to k external photon legs. What is known about the convergence of this sum? Does it converge "on the nose"? Does it at least converge after some formal manipulations a la Borel summation? Also, are there examples where the quantum effective action can be written down "explicitely", in some sense? I.e. as an analytic expression of a (non- linear) functional? EDIT: Evidently I haven't expressed myself clearly. Let's take $\phi^3$ theory for example. It's inconsistent beyond perturbation theory because the vacuum is unstable but it doesn't matter. The effective action is a functional $I(\phi)$ given in perturbation theory by an infinite sum over 1-particle irreducible Feynman diagrams. For example, consider a diagram with a loop to which 4 external legs are attached. The diagram evaluates to a function $f(p_1, p_2, p_3, p_4)$ of the external 4-momenta. If the function was polynomial the resulting term in the effective action would be the integral of a quartic differential operator. Otherwise something more complicated results. To describe it we need to consider the Fourier transform phi^ of phi. The diagram's contribution is roughly $$\int f(p_1, p_2, p_3, -p_1-p_2-p_3) \phi^{p_1} \phi^{p_2} \phi^{p_3} \phi^{-p_1-p_2-p_3} dp_1 dp_2 dp_3$$ If we compute the effective action to some fixed finite order in $\hbar$, it corresponds to restricting the sum to diagrams of limited loop order. However, the sum is still infinite. For example, to 1-loop order we have all of the diagrams with a loop and $k$ external legs attached. The question is whether this sum converges to a well-defined functional $I(\phi)$. In other words, I want to actually evaluate the effective action on field configurations rather than considering it as a formal expression.


title: Is there precision experimental evidence for Furry's theorem -- that only even degree VEVs are non-zero?

text: Is there precision experimental evidence for or contradicting Furry's theorem -- that only even degree VEVs are non-zero, specifically for the EM field?


title: AdS/CFT at D = 3

text: AdS/CFT at D = 3 (on the AdS side) seems to have some special issues which I bundled into a single question   * The CFT is 2D hence it has an infinite-dimensional group of symmetries (locally). The global (Mobius) conformal transformations correspond to isometries of AdS. What is the meaning of the other conformal transformations on the AdS side?   * Is it possible to apply the duality to CFTs with non-zero central charge?   * The CFT can be regarded as a string theory on its own. Hence we get a duality between different string sectors. Is there another way to describe/interpret this duality?


title: Simulation of QED

text: Can anyone point me to a paper dealing with simulation of QED or the Standard Model in general? I will particularly appreciate a review paper.


title: Extensions of DHR superselection theory to long range forces

text: For Haag-Kastler nets $M(O)$ of von-Neumann algebras $M$ indexed by open bounded subsets $O$ of the Minkowski space in AQFT (algebraic quantum field theory) the DHR (Doplicher-Haag-Roberts) superselection theory treats representations that are "localizable" in the following sense. The $C^*-$algebra $$ \mathcal{A} := clo_{\| \cdot \|} \bigl( \bigcup_{\mathcal{O}}\mathcal{M}(\mathcal{O}) \bigr) $$ is called the quasi-local algebra of the given net. For a vacuum representation $\pi_0$, a representation $\pi$ of the local algebra $\mathcal{A}$ is called (DHR) **admissible** if $\pi | \mathcal{A}(\mathcal{K}^{\perp})$ is unitarily equivalent to $\pi_0 | \mathcal{A}(\mathcal{K}^{\perp})$ for all double cones $K$. Here, $\mathcal{K}^{\perp}$ denotes the causal complement of a subset of the Minkowski space. The DHR condition says that **all expectation values (of all observables) should approach the vacuum expectation values, uniformly, when the region of measurement is moved away from the origin.** The DHR condition therefore excludes long range forces like electromagnetism from consideration, because, by Stokes' theorem, the electric charge in a finite region can be measured by the flux of the field strength through a sphere of arbitrary large radius. In his recent talk   * Sergio Doplicher: "Superselection structure in Local Quantum Theories with (neutral) massless particle" at the conference Modern Trends in AQFT, it would seem that Sergio Doplicher announced an extension of superselection theory to long range forces like electromagnetism, which has yet to be published. I am interested in any references to or explanations of this work, or similar extensions of superselection theory in AQFT to long range forces. (And of course also in all corrections to the characterization of DHR superselection theory I wrote here.) And also in a heads up when Doplicher and coworkers publish their result.


title: Acceleration of particles in a pipe with variable cross section

text: I am currently making an exercise from Paterson,1983, IV.3.ii. It goes as follows > Water flows steadily and incompressibly along a pipe whose area cross > section $A(x)$ varies slowly with the coordinate $x$ along the pipe. Use the > conservation of mass and/or incompressibility to calculate the mean velocity > along the pipe at $x$, and calculate the acceleration of a moving particle > moving with this mean velocity. Take the mean velocity to be along the pipe > and depending only on $x$. I would solve the first part of the question as follows. Let $A(0)$ and $v(0)$ be the cross section and the velocity at the begin of the pipe respectively. Since the medium is incompressible, it holds that $A(0) v(0) = A (x) v(x)$ for every $x \in [0, L]$ where $L$ is the length of the pipe. The local velocity in the x-direction at any point $x$ therefore is $$v(x)=\frac{A(0) v(0)}{A(x)}$$ So the average velocity of a fluid particle therefore is $$\langle v(x)\rangle=\frac{1}{L}\int_0^L \frac{A(0) v(0)}{A(x)} dx $$ So far so good. It's the second part of the question I don't get: How can I know where the particle attains its average velocity and what the local acceleration is. I only know that it exists (intermediate value theorem for differentiable functions).


title: Calculate vector forces on object being affected by wind

text: I am wondering how you calculate the vector forces of the wind on an object? The information I have is the bearing direction of the wind and the speed of the wind. So how do I calculate the _x_ and _y_ vector forces of the wind as shown in the diagram below? Also I do realise that using trig I can do a straight calculation but that only works out the speed not the force. ![enter image description here](http://i.stack.imgur.com/J4GHi.png)


title: Effect of space time relativity on the age of the universe?

text: So we all heard about the twins paradox to explain einstein's time space relativity. Wikipedia Quote :" In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly. " So what if the universe has been travelling at varying speeds (increasing or descreasing), wouldn't this effect our measurements on age of the universe?


title: Mass eigenstate of neutrinos

text: Isn't mass a fixed and an intrinsic property of a particle? How can we talk about eigenstates of the mass in the context of neutrinos?


title: What are mass eigenstates?

text: According to Wikipedia > _Neutrino oscillation arises from a mixture between the flavor and mass > eigenstates of neutrinos. That is, the three neutrino states that interact > with the charged leptons in weak interactions are each a different > superposition of the three neutrino states of definite mass. Neutrinos are > created in weak decays and reactions in their flavor eigenstates. As a > neutrino propagates through space, the quantum mechanical phases of the > three mass states advance at slightly different rates due to the slight > differences in the neutrino masses. This results in a changing mixture of > mass states as the neutrino travels, but a different mixture of mass states > corresponds to a different mixture of flavor states. So a neutrino born as, > say, an electron neutrino will be some mixture of electron, mu, and tau > neutrino after traveling some distance. Since the quantum mechanical phase > advances in a periodic fashion, after some distance the state will nearly > return to the original mixture, and the neutrino will be again mostly > electron neutrino. The electron flavor content of the neutrino will then > continue to oscillate as long as the quantum mechanical state maintains > coherence._ What are these mass eigenstates?


title: Total Angular Momentum of deuteron

text: I'm studying for my nuclear physics exam and the book we use is Introductory Nuclear Physics by K.S. Krane. In the chapter on Basic Nuclear Structure, we research the deuteron. However, when discussing the total angular momentum of the deuteron, something confuses me (p84 if someone has the book). I'll copy the paragraph: > **Spin and Parity** > > The total angular momentum $I$ of the deuteron should have three components: > the individual spins $s_n$ and $s_p$ of the neutron and proton (each equal > to $\frac{1}{2}$), and the orbital angular momentum $l$ of the nucleons as > they move about their common center of mass: $$I = s_n + s_p + l $$ [...] > > The measured spin of the deuteron is $I = 1$ [...]. Since the neutron and > proton spins can be either parallel (for a total of $1$) or antiparallel > (for a total of zero), there are four ways to couple $s_n$, $s_p$, and $l$ > to get a total of $1$: > > (a) $s_n$ and $s_p$ parallel with $l = 0$ > > (b) $s_n$ and $s_p$ antiparallel with $l = 1$ > > (c) $s_n$ and $s_p$ parallel with $l = 1$ > > (d) $s_n$ and $s_p$ parallel with $l = 2$ Unfortunately, this is not explained deeper and options (b) and (c) are shown to be invalid because the measured parity is $1$, whereas those options have parity $-1$. Now, (a), (b) and (d) seem okay with me to get total angular momentum $1$, but I don't understand how we can get to $1$ in (c): $I = 1$ if $l=1$ and $s_n + s_p = 1$. This gives either $0$ or $2$? Or can $I$ take all values between $l-s_n-s_p$ and $l+s_n+s_p$ rather than just those two extremes?


title: What are the largest thermal gradients achievable in a lab environment?

text: I am looking for a system capable of creating a gradient of $100\, \mathrm{K}/\mathrm{\mu \textrm{m}}$ on a $30\, \mathrm{\mu}\textrm{m}$ spacing of a system mounted on a Si-N membrane. My so-called nanoheater is not up to the task.


title: Dynamic simulation of surface tension

text: Is there any substantial body of work in physics on dynamically simulating effects of surface tension on liquids? The texts i found so far on fluid dynamics all seem to ignore surface tension, probably because they concentrate on liquids without free surfaces and fluid mechanics texts consider only special cases, like how far water edge raises in a glass. What i want to do is simulate something like droplets of water on flat glass. The problem seems very different from typical fluid dynamics, first the mass of liquid is very small in comparison to cohesive forces between glass and liquid and liquid molecules with themselves(surface tension), which means there should be virtually no movement in absence of external forces, once surface tension resolves into equilibrium with weight of liquid. Besides there are free surfaces around water droplets. How would you even approach simulating cohesive forces? As negative pressure? I know about causes of surface tension, but I don't understand how it relates to computational fluid dynamics. Is there an article, book or anything that could serve as example? My knowledge of fluid dynamics is pretty limited thus far, but I'm planning to spend considerable time catching up to anything I need, I just wanted to find out if someone has already done what I'm trying to do and save me few years of study :).


title: How to multiply Celsius and kilograms?

text: I have something like this: $$\frac{0.04\,\text{kg} \times 90\,^{\circ}\text{C} + 0.06\,\text{kg} \times 50\,^{\circ}\text{C}}{0.1\,\text{kg}} = T_k$$ Where $T_k$ is a temperature, in Celsius. But I have no idea how to multiply Celsius times kilograms. How do I do it?


title: Approximating mean daily and hourly temperature beyond Fourier series

text: Summary: What "well-known" and short parametrized mathematical function describes daily and hourly temperature for a given location? If you look at the mean daily temperature graph for a given location, it looks like a sine wave with a period of one year. Similarly, the hourly temperature for a given day for a given location also looks like a sine wave with a period of one day. However, closer inspection (Fourier analysis) shows that they're not. There are fairly strong components of frequency 2/year and 3/year for the daily temperature, and the hourly temperature also has strong non-single-period terms. Is there a parametrized function that reasonably describes the daily mean temperature and (a separate function) the hourly mean temperature? The parameters would be location-based. I realize I can keep taking more Fourier terms to increase accuracy, but I was hoping for something more elegant. For example, maybe the graph is a parametrized version of sin^2(x) or some other "well-known" function.


title: Computing delta temperature based on radiation and heat loss

text: Is there a formula that gives me the instantaneous change in temperature under ideal circumstances? Details: On a cloudless day, temperature is affected by two major things(?):   * While the Sun is up, incoming solar radiation, which increases the temperature at a known rate(?) depending on the sun's angle.    * Heat loss to "outer space". "Outer space" is colder than the ground, so heat is always flowing away from the ground into outer space. The hotter it is on the ground, the faster the heat flows away.  Is there a semi-accurate mathematical function that models these temperature changes for a given location on a given cloudless day?


title: Math for Thermodynamics Basics

text: I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present. There is a section that i can not understand: ${Fj|j=1,..,N}$ $S= \sum_{j=1}^{N} F_{j}$ $<S>=< \sum_{j=1}^{N} F_{j}> = \sum_{j=1}^{N} <F_{j}>$ $\sigma^{2}_{S} =<S^{2}>-<S>^{2}$ line a: $=\sum_{j=1}^{N}\sum_{k=1}^{N} <F_{j}F_{k}> \- \sum_{j=1}^{N} <F_{j}>\sum_{k=1}^{N}<F_{k}>$ line b: $=\sum_{j=1}^{N}\sum_{k=1(k\neq j))}^{N} <F_{j}><F_{k}> +\sum_{j=1}^{N} <F_{j}^{2}> \- \sum_{j=1}^{N} <F_ {j}>\sum_{k=1}^{N}<F_{k}>$ line c: $=\sum_{j=1}^{N} (<F_{j}^{2}>-<F_{j}>^{2})$ $=\sum_{j=1}^{N} \sigma_{j}^{2}$ My question is what happened after line a to line b and after that to line c? My other question is, i have a little math, what should i study to understand such thermodynamics root math studies, calculus 1 or 2 or what else, can you specify a math topic? Thanks


title: Value of Ramanujan Summation In Quantum Mechanics

text: In mathematics, sum of all natural number is infinity. but Ramanujan suggests whole new definition of summation. "The sum of $n$ is $-1/12$" what so called Ramanujan Summation. First he find the sum, only Hardy recognized the value of the summation. And also in quantum mechanics(I know), Ramanujan summation is very important. **Question.** What is the value of Ramanujan summation in quantum mechanics?


title: Increase thermal efficiency of combustion engine by using heat of coolant/exhaust?

text: I can't be the only one who's ever thought of this, but obviously it hasn't caught on: In terms of energy density, fossil fuels are the best thing around short of enriched uranium (and, flammability aside, a _lot_ safer). The biggest two problems with using fossil fuel as an energy source are the low thermal efficiency of combustion, and the production of CO2 gases. The second problem is the more publicized, but it can be mitigated to a very large extent by solving the first. One idea, which may catch on in industrial power generation, is the "carbon- conversion fuel cell", which at least in the lab gives a thermal efficiency of about 80% of the theoretical energy potential of the fuel. However, the energy density (1kW of generation capacity per square meter of fuel cell surface area) and the operating temperature (750*C) make it impractical at the small scale. However, we currently have technologies that can improve efficiency of combustion engines, we just aren't using them. ICEs typically top out at about 30% thermal efficiency; the rest is lost, primarily as heat, some as kinetic energy of expanding gas. We even go so far as to build cars with water coolant loops and mufflers to more efficiently waste that heat and kinetic energy. Well, what if we instead harnessed that energy to do more work for us before it leaves the car? Imagine a parallel hybrid with two additional generators in addition to the one powered directly off the drivetrain of the engine. One would be powered by steam from the superheated coolant (anyone who's opened the radiator cap on a hot engine will tell you this system is perfectly capable of producing copious amounts of pressurized steam), and the other would work much like a turbocharger, using the pressurized exhaust to turn a turbine, but instead of an intake compressor the turbine would power another generator. To my knowledge, no car manufacturer has ever fielded a production passenger vehicle that utilizes these additional energy sources to charge the battery system. But these technologies are decades old; one would think that we have the technology to pass the breakeven point on power to weight with these systems. Does anyone have documentation showing these additional avenues of energy capture have at least been considered, and if so, why they're not being pursued more aggressively?


title: Two Different Sorts of Inertia: Inertial Mass and Moment of Inertia

text: There are two different sorts of inertia: inertial mass and moment of inertia. I am currently reading about moment of inertia. Now, I know inertia is an important concept; with it, we can determine how difficult something is to move. For linear motion, the difficulty of altering an object's position is dependent upon the mass of the object being moved. For rotational motion, the difficulty in rotating an object around an axis is dependent upon the mass, and the radius of that mass to the the axis of rotation?   1. Why do we need to different measures of inertia?    2. And for rotational motion, why is the inertia dependent upon mass, and its radial distance from the axis of rotation?


title: Fractal Cosmology and Misner's Chaotic Cosmology

text: I have a question pertaining to the ideas behind the considered homogeneity and isotropic nature of the universe (at a grand scale) versus the theory of a chaotic and anisotropy structure of the universe. I am particularly ignorant on this subject, but I am assuming that the idea of fractal cosmology expresses that the universe has some sort of fractional pattern to it, which is the nature of fractal construct, and implies homogeneity. The Chaos Theory, which is tied to fractal pattern indicates that even the movement of chaos has a significant pattern. If so, wouldn't Misner's chaotic cosmology theory also result in a level homogeneity? If not, I would appreciate if someone could explain why or where I've made the wrong assumptions. Thank you


title: Direct nuclear reactions problems

text: can anyone explain Multi-step nuclear reactions in terms of direct nuclear reactions .


title: What practical issues remain for the adoption of Thorium reactors?

text: From what I've read on thorium reactors, there's enormous benefit to them. Their fuel is abundant enough to power human civilization for centuries, their fission products are relatively short-lived, they're far less prone to catastrophic failure, and they don't produce anything you could feasibly use as a source of material for nuclear weapons. So what technical issues need to be resolved so that Thorium reactors become practical and put into wide use? Is it purely engineering issues that need to be overcome? Or are there problems of physics as well? If so, what are the technical problems and what research is occurring to overcome them? If none of the problems that face thorium reactors are insurmountable, then why aren't they the focus of research and development that nuclear fusion is? Are there real environmental issues? (If so what are they?)


title: The speed of light and unstable matter

text: Mr.E is on a luxury spaceship travelling about 1/2 the speed of light and finds a cubic lump of unstable matter(attached to a bomb) in his cabin. He of course is an expert with bombs but this device is based on the unstable matter's critical mass. The lump of matter fluctuates a tiny amount constantly but if it is more than 2k.g, (say for the sake of argument) it will cause the bomb to explode. Right now it is at 1.9999k.g., if the ship accelerates making it over 2kg relative to the people anxiously monitering the ship from Earth they would think it should detonate yet relative to Mr.E and the fellow passengers its mass is still under 2kg?? Is this loose reasoning valid?


title: Why, in EXAFS spectrum, does the absorption coefficient monotonically decrease with increasing photon energy?

text: In atomic physics, it is common knowledge that following the absorption edge, where the photon energy equals the binding energy of a core electron, a monotonic decrease in the absorption coefficient with increasing photon energy is observed. Obviously it is so common, that everyone mentions it, but nobody cares to explain. For example: ![absorbtion spectra graph](http://i.stack.imgur.com/ns5sv.gif) As I understand, in EXAFS (Extended X-Ray Absorption Fine Structure) case, a core electron is excited to the conduction band, and photons with higher energy should just excite it to the higher energy level in the conduction band. So why does absorption decrease?


title: Is energy "destroyed" when walking?

text: Conservation of energy states energy can't be destroyed, but isn't energy used up when walking in a straight line? If your not walking up a slope, kinetic energy isn't converted to gravitational potential energy, so what is it converted to?


title: Phonon wavevector $q\le 2k_{F}$ for Electron-Phonon Scattering

text: I am reading "Supercollision cooling in undoped graphene." There the authors write: ``Above $T_{BG}$ (the Bloch-Gruneisen temperature), only a fraction of acoustic phonons with wave vector $q\le 2k_{F}$ can scatter off electrons." I assume the condition $q\le 2k_{F}$ for electron-phonon scattering is a basic result, but I couldn't find it proved anywhere. Could anyone point me in the right direction, or state the proof here? Thanks.


title: Example of diffusion process without a gradient

text: A book I was reading stated that diffusion can exist without a gradient of a physical quantity. Heat is an example of diffusion because of temperature gradient and similar is the case of mass flow in chemistry. Can anyone give me an example for a gradient less diffusion process?


title: How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?

text: This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.) > Show, by explicit calculation, that $(1/2,1/2)$ is the Lorentz Vector. I see that the generators of SU(2) are the Pauli Matrices and the generators of SO(3,1)is a matrix composed of two Pauli Matrices along the diagonal. Is it always the case that the Direct Product of two groups is formed from the generators like this? I ask this because I'm trying to write a Lorentz boost as two simultaneous quatertion rotations [unit quaternions rotations are isomorphic to SU(2)] and tranform between the two methods. Is this possible? In other words, How do I construct the SU(2) representation of the Lorentz Group using the fact that $SU(2)\times SU(2) \sim SO(3,1)$? Here is some background information: Zee has shown that the algebra of the Lorentz group is formed from two separate $SU(2)$ algebras [$SO(3,1)$ is isomorphic to $SU(2)\times SU(2)$] because the Lorentz algebra satisfies: $$\begin{align}[J_{+i},J_{+j}] &= ie_{ijk}J_{k+} & [J_{-i},J_{-j}] &= ie_{ijk} J_{k-} & [J_{+i},J_{-j}] &= 0\end{align}$$ The representations of $SU(2)$ are labeled by $j=0,\frac{1}{2},1,\ldots$ so the $SU(2)\times SU(2)$ rep is labelled by $(j_+,j_-)$ with the $(1/2,1/2)$ being the Lorentz 4-vector because and each representation contains $(2j+1)$ elements so $(1/2,1/2)$ contains 4 elements.


title: How does locality decouple the UV and IR behaviour of a QFT?

text: I came a comment in this paper: Scattering Amplitudes and the positive grassmannian in the last paragraph of page 104 which says: "One of the most fundamental consequences of space-time locality is that the ultraviolet and infrared singularities are completely independent." How do I understand this?


title: Impervious nature of solid matter due to quantum degeneracy pressure

text: On Wikipedia the following statement is made without reference: > Freeman Dyson showed that the imperviousness of solid matter is due to > quantum degeneracy pressure rather than electrostatic repulsion as had been > previously assumed. Can anyone find the appropriate reference(s)?


title: Coherences in the density matrix

text: It is said that the off-diagonal elements of density matrix are `coherence`. When a system interacts with its environment the off-diagonal elements decay and the final density matrix is the diagonal one, a statistical mixture. This process is called decoherence. We know that every density matrix can be diagonalized in some basis. I want to know that what decoherence would be when the density matrix is diagonal in some basis?


title: What is the height of different layers of the atmosphere?

text: I have a confusion regarding the height of different layers of atmosphere. I have searched for this in some books but the information varies.


title: What symmetries does a lattice calculation need to preserve?

text: I've heard that it is impossible to have a properly Lorentz-invariant lattice QFT simulation, as the Lorentz invariance is spoiled by the nonzero lattice distance $a$. I've also heard that there are other symmetries that _must_ be preserved for a lattice simulation to be realistic. What symmetries must a lattice simulation preserve to be realistic? Why must they be preserved?


title: Influence of air resistance in space

text: Consider the following situation: You are locked inside a cylindric container allowing you to move around freely without being in contact with any of the items or surfaces aboard. The container is floating in space, far from any gravitational field, and is spinning around - like a washing machine would do, at a constant speed. My question is: Is there any speed limit that would make air resistance inside the container substantial enough so that you would start spinning also? How about the same situation, but in vacuum? Are there any factors that could cause you to start the spinning motion at all?


title: Chemical potential in terms of temperature and pressure

text: ![enter image description here](http://i.stack.imgur.com/63qqd.jpg) For part (a), I know how to take the partial derivatives of S to get chemical potential, pressure. But there seems that I still need one equation to correctly express chemical potential in terms of T and P. The biggest problem for me is that the gas is not an ideal gas, so I can't use the equation of state to finish the job. Can anyone give me a hint?


title: Simulating Gravity in 3D Game?

text: Alright, I am writing a space simulator for a 3D game and I would like to implement gravity of objects into it. Is there a nice way to find a velocity vector which can be added to my engine output vector to create the effect of gravity. In addition, how would I be able to find the velocities required to get object A into orbit around object B at a certain distance?


title: What is Diffraction?

text: Diffraction is just light interacting with small objects, and bending, but this seems like a very imprecise definition to me. What is diffraction, actually? I was confused because there are at least two diffraction gratings, that I know of. One being actually slits, through the standard diffraction I learned about in class, and then there are spaced grooves which can also diffract. This latter one, I thought, would just be reflection and interference, but I was told it's the same phenomenon. So again, what is diffraction?


title: What is the name of the molecule HCCO?

text: I have a very hard time finding information about $HCCO$. I don't even know what it's name is. I'd like to know what its main features are, where it shows up and/or what it's used for?


title: Potential energy from opposing magnets repelling each other with a gap of 1 mm

text: I have two powerful rare earth magnets, that are separated by a distance of 1 mm. I applied energy to bring them closer to each other, hence increasing the potential energy. Now, when one of the magnets is released(other is fixed) there is acceleration, with time force = 0 since the gap(D) is increased, yet there is massive kinetic energy. Assuming from position X( where the air gap is 1 mm) we could calculate the repulsive force, knowing m of course. From the initial acceleration we could calculate the time + velocity, since the distance is known as well. **Can the KE of that moving magnet being repelled be calculated**? This magnet is easily moved around (attached with wheels & low friction), and the force is known over certain positions, beyond those points F = 0 since D is very large, and there is no magnetic force being applied yet we know acceleration = 0. But there is kinetic energy? I'm a bit confused as to what might happen. Can anyone explain with great detail of the outcome of such an experiment?


title: How to keep the clock of a spaceship synchronised to the clock of an observer?

text: I read that the clocks of GPS satellites seem to run slower than the clock of stationary observer, because of their speed (special relativity) and seem to run faster than the clock of stationary observer because of their altitude (general relativity) . http://osg.informatik.tu- chemnitz.de/lehre/old/ws0809/sem/online/GPS.pdf From this, can you model the speed $\upsilon(t)$ and the altitude $r(t)$ of a **spaceship** launched from the ground vertically at $t=0$ such that the clock of the **spaceship** will always seem to be synchronised to the clock of the observer on the ground (from the observer's frame of reference) ?


title: Understanding drift velocities in currents

text: I have a doubt about the understanding of drift velocities in a current. My problem is that the textbook speaks very loosely about this. It's like: "well, if we apply a field $E$ then the charges will experience a force due to this field, aquire acceleration, colide between then and because of that there will be a small resultant velocity for each particle called drift velocity". But wait a moment, how can we be so sure of all of that? For me it's a little counterintuitive, and even if it was intuitive, how can we show that this really occurs? In other words, I feel that the first step to understand the meaning of drift velocity is to be really sure that this velocity _will_ exist. And once we've shown it exists, what's is this velocity anyway? Is the velocity of the particle in the direction of the current? Thanks a lot in advance for your help!


title: Number of particles in a microcanonical ensemble

text: Is it always assumed that, in a microcanonical ensemble, the number of particles is $N \gg 1$ ? If no, are all the theorems related to the microcanonical description true even if the number of particles is small ?


title: Weird integration of gaussian wave packet

text: I have been learning Fourier transformation of a gaussian wave packet and i don't know how to calculate **this** integral: ![enter image description here](http://i.stack.imgur.com/G579S.png) In the above integral we try to calculate $\varphi(\alpha)$ where $\alpha$ is a standard deviation, $\alpha^2$ is variance, $x'$ is average for $x$, $p'$ is average for $p$ and: $$\psi_\alpha = \frac{1}{\sqrt{\sqrt{\pi} \alpha}} \exp \left[ - \frac{(x-x')}{2 \alpha^2} \right] $$ For some reason author of this derivation swaps $p$ with $(p - p')$ (red color) and from $=$ sign (yellow color) forward i am completely lost. Could anyone please explain why did author did what he did? It is weird...