title: what is the relationship between the dynamical casimir effect and virtual particles?

text: Since virtual particles are disturbances in a field, and not particles in any sense, as explained here, how is it that true photons arise from them when excited with kinetic energy via the dynamical casimir effect? While the effect is described here, I was hoping to get an answer that touches more with the virtual particle's role in the effect, if it is of sigificance.


title: Looking for review articles on big bang nucleosynthesis

text: Can someone point to a good review article covering contemporary developments in big bang nucleosynthesis, beyond what's covered in Kolb and Turner's _The Early Universe_? Thanks.


title: What in Newtons three laws of motion original to himself and not a paraphrasing of his predecssors

text: The three laws are: First law: The velocity of a body remains constant unless the body is acted upon by an external force. Second law: The acceleration a of a body is parallel[disambiguation needed ] and directly proportional to the net force F and inversely proportional to the mass m, i.e., F = ma. Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear. The first law had already been formulated by some philosophers prior to Newton, Hobbes said in the Leviathan '...[the proposition] that when a thing is in motion it will eternally be in motion unless somewhat else stay it, though the reason be the same (namely that nothing can change itself)...', given his reasoning, I think it safe to mean constant speed and direction, otherwise change is occuring and he explicitly rules that out. I think the same proposition is mentioned in Lucretious's De Rerum Natura. Are there any antecedents for the second and third law?


title: How is the energy of a lightning calculated?

text: I was wondering how is the energy of a lightning measured? Is it based on the luminous intensity and/or the generated sound? What about the generated heat and energy spent in the production of ozone? Is it taken into account? I looked here and here, but I didn't find an answer that satisfies me.


title: Why should fluids be confined for Pascal's Law to be applicable

text: When is Pascal's law about fluid pressure propagation applicable? Is it applicable to a closed circular pipe with a pump rotating the fluid, but not to a tub of water. Most statements require only confinement of the fluid. Or is the question irrelevant ? This law is no longer used or taught ? Here is my full story about it. You do not have to read it all to answer. Your choice. # The question and its context Being a bit surprised by a dismissal on this site of the applicability of Pascal's Law because the fluid was not **confined** (well, it was an ocean), I took my favorite browser and asked: **Pascal Law** , then I took the answers in order, more or less. I do skip youtube. According to Wikipedia (quoting a book): > Pascal's law or the principle of transmission of fluid-pressure is a > principle in fluid mechanics that states that pressure exerted anywhere in a > **confined incompressible** fluid is transmitted equally in all directions > throughout the fluid such that the pressure variations (initial differences) > remain the same. which is confirmed by the Wiktionnary: > The law that states that a **confined** fluid transmits externally applied > pressure uniformly in all directions Then according to NASA (who seems to equate fluid with liquid): > Pascal's law states that when there is an increase in pressure at any point > in a **confined** fluid, there is an equal increase at every other point in > the container. The Q&A system of the Physics Dept at University of Illinois at Urbana- Champaign agrees (quoting a book): > Pascal's Law (also called Pascal's Principle) says that "changes in pressure > at any point in an **enclosed** fluid at rest are transmitted undiminished > to all points in the fluid and act in all directions." insisting further that it must be " _a closed container_ ". And the sciencefair site confirms for the layman: > Pascal's Law states that when you apply pressure to **confined** fluids > [...], the fluids will then transmit that same pressure in all directions > within the container, at the same rate. While the Hyperphysics site insist for the professional with this statement of Pascal's Principle: > Pressure is transmitted undiminished in an **enclosed** static fluid. To be fair, the Free Dictionnary defines Pascal's law as follow: > The principle that external static pressure exerted on a fluid is > distributed evenly throughout the fluid. Differences in static pressure > within a fluid thus arise only from sources within the fluid (such as the > fluid's own weight, as in the case of atmospheric pressure). Maybe because it is not a science site. My main question is: **Why should the fluid be enclosed ?** (for the law to be applicable) A side question is, **why do most statements ignore compressibility ?** Well, Pascal did too, afaik, but he was in a much different context. Also we should remember that not all fluids are liquids. Forgetting that fact may lead to death by drowning, or by diving in empty pools. # My own clarification of the issue _Maybe I should not answer myself, so as to better encourage other answers. But then, why pretend I am too stupid to answer it when I can actually prove that I am ?_ As I said, I would like some clarification on this, and check my own understanding, which is not quite in agreement with the above definitions. If this law is considered in a uniform gravity field, the requirement of incompressibility is needed only to preserve a constant density, so that the pressure difference between different heights in the liquid does not change. If correct, this also means that **the incompressibility requirement can be lifted regarding the transmission of pressure change between two points at the same height.** _Note that if pressure change is small, there is little compression and density variation so that the incompressibility requirement can be lifted as first approximation. That was, I guess, the situation of Pascal as he was analysing atmospheric pressure and its variation under limited height changes._ In free fall, the weight of the fluid no longer matters, and the compressibility should not matter either. However the fluid has to be confined if a non-zero pressure is to be applied. _It is actually more complex, as there may be surrounding pressure from the environment, or surface tension in various cases (e.g., a bubble of gas in a liquid). Also, enclosure may be necessary to prevent mixing of the liquid or gaz with surrounding medium, though that does not require a rigid enclosure, and is not related to Pascal's law itself._ However, I do not see the need for the confinement constraint in a gravity field. A container is certainly needed, as is usual for liquids (especially when it is hot coffee), but nothing requires that it be a closed confinement. The top can perfectly well be open to atmospheric pressure in the case of a liquid, or only separated by a very light membrane for gas. This may not be convenient for achieving high pressure in some devices, but that is an engineering issue that has nothing to do with Pascal's law. This is even true for gas. After all, the law is originally based on a study of Earth atmosphere which can hardly be considered as enclosed. Of couse, the fluid is considered only in those parts of space where it is present before and after the pressure change. To conclude, my understanding is that the confinement may be needed to actually achieve a change of pressure somewhere in the fluid, in engineering applications of the law but **confinement has nothing to do with Pascal's law itself.** # Why then ? Why this agreement on requiring an irrelevant condition for the applicability of Pascal's law. The question should possibly be another one. **What is meant by requiring that the fluid be confined or enclosed ?** Maybe the answer is given by the sciencefair site which (if I did not miss anything) is the only one to actually define what it means: > contained in a flexible yet leak-proof enclosure so that it can't flow out I will not dispute this disputable definition, but the intent seem clearly to prevent dynamic flow, to have a static system. Whatever the actual intent, that is the only explanation I found. Hyperphysics is very professional and to make the point absolutely sure uses both belt and suspenders: " _an enclosed static fluid_ ". The University of Illinois has the same worry about decency: " _an enclosed fluid at rest_ ". As I understand the problem, it would be wiser to only use the correct qualifier, and mention " **static fluid** " or " **fluid at rest** ", rather than inappropriate qualifiers that create much confusion and misunderstanding, particularly in an educational context, as shown by the example that initially motivated this question. **Is this analysis correct or did I miss a point ?** If I err, can you tell me where ? In a widely ignored question (I am very good at that) that only managed to gather one downvote, I was trying get reactions or opinions on the issue of precision in science. I did not mean quantitative but rather qualitative precision, precision in concepts and hypothesis rather than mathematical formulae. I guess this is just another example, and I did not have to look for it: it found me. All contributions to understanding this are answers.


title: What is the importance of Vacua in Field Theory?

text: I understand that defining the Vacuum is important in Field Theory, why? Is this because it is the 'ground' state, before particles are added, so defines the 'background'? I assume its not important in Quantum Mechanics, is that right?


title: Iodine-131 half-life and reality

text: Iodine is a chemical element with symbol I and atomic number 53. There is currently a lot of discussions regarding radioactivity in Japan, and iodine-131. Iodine-131 has a half-life of 9 days. Does it mean that people drinking radioactive water (with iodine-131) will lose half of it within 9 days?   And thus the health risk would be lower and lower over time?


title: If the universe were a fractal

text: Inflation seems to solve many of the problems of cosmology like horizon problem, flatness problem etc. Now suppose, I am a devil's advocate and tries to find holes in this beautiful theory. I argue that the early universe were having a fractal geometry. For any generic initial conditions suppose it was indeed a fractal. Then obviously no amount of stretching can make it smooth and flat locally. How would one reconcile this picture with inflation?


title: Collision of light waves & matter

text: When light or electromagnetic wave hits an obstacle, what happens? Are the reactions times always negligible? By reaction I mean all that happens after the hit like reflection for example.


title: Did "big bang" radiate light?

text: According to present day physics nothing existed before the "big bang", even space and time. But often in documentaries, the "big bang" is shown as a ball of light that exploded at some point. If this were so, then photons should have been the first particles that flowed in the new universe. If we placed an imaginary observer at some visible distance from the "big bang" would they have been able to observe it?


title: How to define a convex surface in case of refraction?

text: In an exam at high school level, it was said, "ray goes from optically denser to rarer medium through a convex surface. It forms a real image...." this was a part of the question. Now I thought that a convex surface can be defined as the surface that bulges out towards the incident ray. But my teacher made the opposite diagram, what is the convention in play here? How would you define a convex surface?


title: Finding Constant Angular Acceleration

text: The question is, "A centrifuge in a medical laboratory rotates at an angular speed of 3500 rev/min. When switched off, it rotates 46.0 times before coming to rest. Find the constant angular acceleration of the centrifuge." So, I said that the centrifuge makes 58.3 revolutions every second $(58.3~rev./s)$, and one revolution takes 0.0172 s $(0.0172~s/rev.)$ $\omega_i=\Large\frac{58.3~rev.}{s} \cdot \frac{2\pi}{1~rev.}\small=366~rad/s$ $\Large\frac{0.0172~s}{1~rev.}\cdot\frac{46.0~rev.}{1}\small=0.7912$ This is how long it continues to rotate after the centrifuge stops applying a force. $\omega_f=0$ $\alpha=-463~rad/s^2$ However, the answer $-223~rad/s^2$ What did I do incorrectly? Is any of my analysis erroneous?


I have complications to do the following problem: A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$. Find its velocity and acceleration vectors. My first idea was to parameterize the curve given, however did not know how to introduce speed $v$. Therefore I derived with respect to time, the equation of the curve, obtaining: $$2y\frac{\partial y}{\partial t}=-4a\frac{\partial x}{\partial t}$$ Also, I know that $$\left( \frac{\partial y}{\partial t}\right)^2 +\left( \frac{\partial x}{\partial t}\right)^2=v^2$$ Thus have two equations relating the $x$ and $y$ components of the velocity, but I have not been able to resolve. Is my method OK? Is there another way? Is it easier to do so using the parametric equations, but then as I enter the speed $v$?


title: What really is Planck's constant and what are its origins?

text: In the physics texts I have read and other info online, they says Planck's constant is the quantum of action or that it is a constant of the ratio of the energy of a particle to its frequency. Im still not understanding exactly what it is? From what I have read as well, Planck did a "fit" of data concerning others experiments and came up with this value, what data exactly did he fit to come up with this really small value, or maybe he did it some other way? Perhaps an answer concerning its origins will help me better understand my first question.


title: Magnetic Induction

text: ![enter image description here](http://i.stack.imgur.com/bLVBf.jpg) Consider the figure above in which there is an electric current (constant) in R1 (consider it to be made of a conductor). Obviously there will be a magnetic field induced in R2 (consider it to be made of a ferromagnetic material) due to the electric current in R1. (http://hyperphysics.phy- astr.gsu.edu/hbase/magnetic/curloo.html) R3 (consider it to be made of a conductor) is an open loop as shown in the figure. Will there be any induced voltage across AB in R3 due to the magnetic field in R2?


title: What is the energy in eV between atoms in a typical solid state material?

text: Comps 2 question: What is the energy in eV between atoms in a typical solid state material ? Just rough estimate ? How is that related to the thermal energy that needs to be supplied in order to melt it ? For example a typical bond has 1eV but we need much smaller energy to break it, why is that ? For NaCl the latice energy is 800kJ/mol which is 7eV per atom. Where is the mistake here ? 1eV = 6.10^18 eV, 1eV = 11000K Thanks a lot!


title: Is there a time delay during tunnelling?

text: A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process? ![Image from the wikipedia article](http://i.stack.imgur.com/zccBI.gif)


title: Confused about time dilation/length contraction

text: I have a following problem: A meson is generated $h$ meters above the earth's surface and begins to move towards the earth with velocity $v$. Its (proper) lifetime is $t_m$.   1. What is $v$ if the meson is to reach the surface of the earth?   2. How long did the meson live, according to a clock on the surface of the earth?   3. According to the meson, how far away from the surface of the earth was it created? I familiarized myself with formulas for time dilation and length contraction. If we attach a primed frame of reference to the meson, then $$\Delta t = \gamma \Delta t'$$ $$\Delta x = \frac{1}{\gamma} \Delta x'$$ But then, what is $v$? Is it $\frac{\Delta x}{\Delta t}$ or $\frac{\Delta x'}{\Delta t'}$? Clearly the two aren't the same, but I thought the velocity is 'set in stone' so to speak, regardless of the frame of reference? So what is the meaning of each of those two quantities?


title: How does a spacecraft's orientation get determined

text: What method are employed to determine a spacecraft orientation with respect to a _known_ orientation or plane? Are gyroscopes reliable enough to make this determination, for example in Voyager spacecraft.


title: Why do diamonds shine?

text: I have always wondered why diamonds shine. Can anyone tell me why?![An image for a diamond shining!](http://i.stack.imgur.com/p2Uep.jpg)


title: Where does Computer Science background students fit in Theoretical Physics

text: I am basically an Electronics student - background in computer science (that's where I want to work). I applied for an internship in USA in a research institute where the group is focused in Theoretical Condensed Matter Physics, Chemical Physics, Physical Chemistry, Materials Science. I mentioned my areas of interests as: Computational Science, Machine Learning, Web development My skills as: Python, C, Django, Java, etc.. I got selected. Now, I would like to know where could possibly a CS background guy would actually work on? I am looking for a detailed answer


title: When playing the flute, does lip-hole aperture size affect air pressure in the mouth?

text: I apologize if this is too basic of a question for this forum, but when having arm-chair discussions about the fluid dynamics of flute playing, a friend has said: > The lip-hole area together with the lung pressure is the cause of the > pressure built in the mouth. > > When measuring the mouth pressure you are already taking into account the > lip-hole area and the lungs pressure. My intuition is that this is incorrect--mouth pressure is caused by the "upstream" pressure in the lungs, and not any "downstream" container/flow size changes. But intuition is often wrong in these situations--can anyone clarify the situation for us?


title: Quantum Mechanics Operator Hermiticity

text: > _If $A$ and $B$ are Hermitian operators, show that $$C~:=~i[A,B]$$ is > Hermitian too._ My work: $$\begin{gather} C=i(AB-BA) \\\ \langle\psi\rvert C\lvert\phi\rangle = i\langle\psi\rvert AB\lvert\phi\rangle-i\langle\psi\rvert BA\lvert\phi\rangle \end{gather}$$ I guess I need to split up the operators somehow to use: $$\begin{align} \langle\psi\rvert A\lvert\phi\rangle &= \langle\phi\rvert A\lvert\psi\rangle^* \\\ \langle\psi\rvert B\lvert\phi\rangle &= \langle\phi\rvert B\lvert\psi\rangle^* \end{align}$$ I know a little about the identy operator, which I've seen used to do a similar trick, but I'm not that clear on its exact meaning hmm... $$1=\sum_n\lvert n\rangle\langle n\rvert$$ The definition of Hermiticity I learnt from lectures is the one I stated above for A, can you prove it in this way for C?


title: What is the correct form of the NHEK metric?

text: I've noticed that in different articles people are writing the near horizon extreme Kerr metric (NHEK) in different forms. Original Kerr/CFT correspondence article by Guica et. al. follows Bardeen- Horowitz 'Extreme Kerr Throat' article, in which NHEK metric (line element) is given by $$ds^2=2GJ\Omega^2\left[-(1+r^2)dt^2+\frac{dr^2}{1+r^2}+d\theta^2+\lambda^2(d\phi+rdt)^2\right]$$ Compere, and some other authors say that the NHEK line element is $$ds^2=2GJ\Omega^2\left[-r^2dt^2+\frac{dr^2}{r^2}+d\theta^2+\lambda^2(d\phi+rdt)^2\right]$$ I am confused. I followed Bardeen and Horowitz derivation of the NHEK metric, and got the same result. Second metric is simplified considerably (especially when solving Lie derivative). Why the difference, and can I use which ever I want? EDIT: Links to articles: Kerr/CFT (Guica et. al.): http://arxiv.org/abs/0809.4266 (eq 3.7) Kerr Throat (Bardeen-Horowitz): http://arxiv.org/abs/hep-th/9905099 (eq 2.9) The Kerr/CFT Correspondence and its Extensions (Compere): http://relativity.livingreviews.org/Articles/lrr-2012-11/ (eq 25 with parameters from eq 37) Yet Another Realization of Kerr/CFT Correspondence (Matsuo et. al.): http://arxiv.org/abs/0907.4272 (eq 5)


title: Relation between a Quasistatic and a reversible process

text: Why is it that if a process is reversible, it is quasi-static? Does it mean that then the process is also non-dissipative if it is quasistatic?


title: Is there any role of steering in turning?

text: ![enter image description here](http://i.stack.imgur.com/jqmeF.png) I am aware of the practical requirement of turning the steering wheel to turn a car while going on a straight and even curved road. But in the proofs of turning of car on leveled or banked curves, we see the tyres **straight**. Assuming a road where a car enters tangentially to a circle with some velocity satisfying the conditions for turning (no skidding), is there no reason in an ideal case to steer the car ? What all reasons in practical life make it necessary to steer ?


title: Quantum Field Theory and antiparticles vs particles

text: Does a particle and its antiparticle share the same field in QFT? If an electron is an energized spot in the electron field, is a positron a less energized spot or even a spot of negative energy (if there is such a thing) in the electron field? From the basic knowledge I posses, it would make sense that two particles that are identical except for their charge, would come from the same field. Thanks for helping me out and sorry for how naive this question is. I have been poking around on the internet trying to figure this out and have only become more confused.


title: Simple examples for exchange and correlation

text: Is there an easy, in the best case intuitive, explanation of the difference of exchange and correlation? Is there a simple way to distinguish whether a certain contribution is due to exchange or correlation?


title: Expansion of space and gravity

text: In my previous question I asked how gravity can be represented as dents in space. It seems that it's a metaphor. But I wondered with spac expanding does the effect of gravity get bigger as well, I know from other questions that mass doesn't expand like the gaps between mass do although I have no idea why. So using the metaphor from before does the expansion of space cause the "dents"(gravity) to increase?


title: Ideally speaking, will a rolling disk with no slipping come to a stop because of friction from the ground?

text: Consider a rotating disk on a horizontal plane with static friction. The contact point of the disk with the plane has null instantaneous velocity. Assuming the center of the disk has fixed $v_0$ velocity at a time $t_0$, is it right to conclude that the disk will stop in a time $t_1 > t_0$ by effect of the momentum of friction force? (By the Euler second law we get a negative angular acceleration)


title: What is the boundary condition of graphene flake with zigzag edges?

text: It is a question about free carrier behavior in graphene flakes. (or may be called charge confinement) Say if we have a perfect hexagonal free standing graphene flake terminated with zigzag edges. Since there are two subatoms (let's call them A,B) in every unit cell. Edges will be terminated, let say, ABABAB (as shown in the figure). ![figure of graphene flake with zigzag edge](http://i.stack.imgur.com/gt1tJ.png) My question is how to calculate (understand) electron wavefunction in this system (only considering relative low energy case, charge carrier can be seen as massless fermions). Another way to ask it what type of **boundary condition** one shall use for those two types of edges? According to this paper(pdf), scattering at the zigzag boundary dosen't couple the two valleys. I think we can only consider one valley picture(is this true?), which means the most simple Dirac equation $-i\hbar \nu_F\nabla \Psi_i=E\Psi_i$, where $i=A,B$ (or Klein-Gordon eq). For simplicity, spin effect here can also be ignored(no magnetic field). I am not only asking about the edge states, also for higher energy states. What confusing me is how to distinguish this from the particle in a box case (relativistic particle, here I mean). Intuitively, I think electron will behave as billiard in side of the flake. But there could be two cases, either electrons bouncing between A,B edges, or they do it only in one type of edge, such as only bouncing at edges terminated with subatom A. Can it be understood this way? If yes, which of the two picture is the real one? Hope it is clear. Thanks.


title: What do we consider "Perpetual Motion"

text: I know this is a bad question to most serious Physics but I have a question about what is considered “Perpetual motion.” The Foucault pendulum in the UN consists of sphere that passes directly over a raised metal ring at the centre that contains an electromagnet, which induces a current in the copper inside the ball. This supplies the necessary energy to overcome friction and air resistance and keeps it swinging uniformly. Now the swing of the pendulum is induced but the 36h 45m clockwise shift generated bay the earths rotation is perpetual or as long as the earth rotates. Is this assumption correct? Does a generator that works on tidal movements not fall in to the same assumption?


title: a question on Lagrange's equation when the time derivative of the generalized co-ordinates is constant

text: Consider a system whose generalized co-ordinates are $q_i$ and is under the constraints $\dot{q_i} = K_i \forall i = 1,2,3,...$ where $K_i$ are constants. I have a problem in writing the Lagrange's equation for this system as $\dot{q_i}$ is a constant. What would be $\frac{\partial L}{\partial \dot{q_i}}$ ?


title: Why does a tire produce more traction when sliding slightly?

text: It is well known in racing that driving the car on the ideal "slip angle" of the tire where it is crabbing slightly from the pointed direction produces more cornering speed than a lower slip angle or a higher one. (More explanation as requested) I'm considering two main effects on the tire when in a turn:   1. The tread of the tire is twisted from the angle of the wheel it is mounted to. There is more force as speed increases, and generally, more twisting.    2. The tire slides somewhat at an angle on the road surface rather than rolling.  At low speeds, the angle between the pointed direction of the wheel (90 degrees to the axis of rotation) and the direction of travel is nearly 0. When the speed increases to the point the angle reaches about 10 degrees, the tire generate more grip and the car goes faster around the turn. (Higher angles produce lower grip) So the grip is higher at 10 degrees of slip than at 0 or 20 degrees. What is the physical effect that causes this increase in grip?


title: Doubts about the definition of mass

text: I'm having some problems understanding what are the possible definitons of mass and how they are related to each other. In Classical Mechanics, we can distinguish between inertial and gravitational mass (although they are supposed to be the same $m_i=m_g$): $$F=m_ia$$ $$F=G\frac{Mm_g}{r^2}$$ On the other hand, in Special Relativity, mass is: $$p^\mu p_\mu=m^2$$ But in Quantum Mechanics, I think none of these definitions should be valid (Newton's second law doesn't hold, gravity can't be described in QM and QM isn't relativistic). So, what mass should we use in Schrödinger's equation, when we state that: $T=\frac{p^2}{2m}$? In QFT, the correct mass is $p^\mu p_\mu=m^2$, isn't it? Finally, are there more possible definitions of mass, besides the description in String Theory (maybe in General Relativity, I've read that there are problems defining energy in a localised point, that we can only evaluate the total energy)? Are some definitons more fundamental than the rest? EDIT: What about this definition I've found in QM $m=\hbar (\frac{d^2E}{dk^2})-1$?


title: Maxwell-Boltzmann distribution for transport equations

text: I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use. As far as I know it should not be the MB distribution for $v$-space (Velocity) or $E$-axis (Energy), since that will get me the wrong dimensions in the end. I have to use the distribution per state. But I'm not sure how this looks. The integral I have to solve, for me getting the electrical conductivity (1st transport coefficient) I need, is given by: ${{\mathcal{L}}^{\,\left( 0 \right)}}={{\left( \frac{2m}{{{\hbar }^{2}}} \right)}^{3/2}}\frac{{{e}^{2}}\tau }{{{\pi }^{2}}m}\int{\left( -\frac{\partial {{f}_{MB}}}{\partial \varepsilon } \right)}\,{{\varepsilon }^{3/2}}d\varepsilon,$ at least, again, when trying to calculate the electrical conductivity, which in the end should end up being Drudes formula $\sigma =\frac{n{{e}^{2}}\tau }{m}$. So basically, not hard. But I have to get the distribution function right. As far as I know the MB-distribution is given by: ${{f}_{MB}}\left( \varepsilon \right)=C{{e}^{-\varepsilon /{{k}_{B}}T}},$ where $C$ is what I need to figure out, since that will determine the dimensions of my coefficients. According to my book the normalized MB distribution function is: $\bar{n}=\frac{{\bar{N}}}{{{Z}_{1}}\left( T,V \right)}{{e}^{-\varepsilon /{{k}_{B}}T}},$ where: $\frac{{{Z}_{1}}\left( T,V \right)}{{\bar{N}}}=\frac{V}{{\bar{N}}}\left( \frac{2\pi m{{k}_{B}}T}{{{h}^{2}}} \right){{Z}_{\operatorname{int}}}\left( T \right),$ and ${{Z}_{\operatorname{int}}}\left( T \right) = 1$ in my case. But I'm not quite sure how to about this? As far as I can see, it's not just inserting the reversed term of this in $C$ - at least not from what I can see. Maybe it's the $V/N$ I'm not sure about. Well, anyone who can give me a clue?


title: Why do both plates of a capacitor have the same charge?

text: How do we know that both plates of a capacitor have the same charge? You could argue conservation of charge, but I don't see how conservation of charge implies the charge on both plates is the same. Say you have a charge of +q on one plate and -m on the other. +q doesn't equal -m. How do we know that the difference of charge doesn't end up on the terminals? Isn't that possible? Wouldn't conservation of charge not be violated if the charges on both plates are not equal, but the difference in charges ends up as surface charge in the wire or some other place in the circuit?


title: Nanorobots. What stops us from producing them yet?

text: If we can already predicts accuratelly motion on molecular levels, what stops us from developing small robots to, for instance, navigate through our blood vessels looking for cancerous cells and destroying them? What are the predictions for when we will able to do this? If someone is very interested on this goal and wants to participate on research, what should exactly he study? Programming, chemistry, physics, quantum mechanics? What could help at all? Books/resources welcome.


title: Field outside a solenoid?

text: Say you have a solenoid with diameter $d$ and length $L$. How can I show that as $d/L$ approaches 0, the field outside the solenoid is zero? I'm looking for a formal proof involving integration. This isn't homework, I'm just curious. I don't have any work to show because the math required for this is too far past my skill level. I wouldn't have a problem following along however. Thank you.


title: Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?

text: Suppose we have an integral $$\int \mathrm{d}^4k \,\ f(k)$$ we want to evaluate and that we're in Minkowski space with some metric $(+,-,-,-)$. Is it true that: $$\mathrm{d}^4k = \mathrm{d}k^0\ \mathrm{d}^3\mathbf{k} = \mathrm{d}k^0 \,\,\,\,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$$ just like in ordinary space? If not, what are the differences between this and an Euclidean integral in (say) 4 dimensions?


title: How to calculate a firing location from point of impact data?

text: I would like to know how to calculate the point at which a bullet is fired from a gun given information from the scene where the bullet falls. The scene would contain the point of impact (GPS location data), the angle at which the bullet decended (taken from the ceiling to the actual point of impact), and the height of the point of impact. As you can see, I am trying to determine weather a person who fires a bullet into the air and it impacts someone, can be located via some physics and mathematical formulas. From the crime scene we would also have the specific bullet type and its dimensions and manufacturers ballistics trajectory information. I've checked some sites for ballistics and there are many tables calculating the ranges of specific bullets and guns. I hope to use this data somehow. If someone has already done this, please let me know.


title: How do I find the tension in additional strings in this problem?

text: > A mass of 5.00 kg hangs attached to three strings as shown in the figure > (see image below). Find the tension in each string. Hint: Consider the > equilibrium of the point where the strings join. ![](http://s19.postimage.org/j7rqan5df/Photo_on_12_01_01_at_8_18_PM.jpg) So finding $T_3$ was relative quick, knowing $W = mg$, $m = 5.00\text{ kg}$, $g = 10\ \mathrm{ms^{-2}}$ $$W = 50\text{ N} = T_3$$ It is the other two ($T_1$ and $T_2$) I'm not sure. In fact I'm at lost with what I learned in class and applying. I noticed the problem states a hint (equilibrium where strings join) but I'm not seeing how this information can be used.


title: Kinetic energy of Electron

text: I had to find the kinetic energy of electron with wavelength $2$ pm. I used the formula $$ KE = \frac{p^2}{2m} = \frac{h^2}{\lambda^2 2m}$$ which gave me result, $KE = 376.9$ KeV. But the answer given in the book is $292$ KeV. Am I making a mistake in calculating it?


title: Comparing Static Frictions

text: In this figure, which of the static frictional forces will be more? ![enter image description here](http://i.stack.imgur.com/L9tHZ.png) _My aim isn't to solve this particular problem_ but to learn how is static friction distributed . Since each of the rough-surfaces are perfectly capable of providing the $-1N$ horizontal frictional force but why don't they ? This is kind of ambiguity that who will provide a bigger share in total static friction. And as the surface have different $\mu$, so we can't even invoke symmetry.


title: What needs to be integrated to solve this problem?

text: > An object is placed on a frictionless table with its one end attached to a > cord which is connected to a pulley and the tension is maintained constant > at 25 N. what is the change in kinetic energy of the object from its > position 3m away to 1m away from the raised platform? ![poorly drawn, so not at all to scale...just shows the setup.](http://i.stack.imgur.com/EDPcw.jpg) I think that we should integrate work with respect to theta here, over the interval $\tan^{-1}(1.2/3)$ to $\tan^{-1}(1.2/1)$. But for that, we need to differentiate work with respect to $\theta$, right? So doesn't it end up the same if I differentiate it and then integrate it? Or do I integrate the expression $F s \cos(\theta)$ with $\mathrm{d}\theta$ without differentiating it first?


title: Non-SHM oscillatory motion

text: ![enter image description here](http://i.stack.imgur.com/muwVu.png) How to solve these kind of questions , where $|F| \propto x^2$? How to find time period and velocity type related things to the oscillatory motion? $$m\dfrac{d^2x}{dt^2}=F=-\dfrac{dU}{dx}=-3kx|x|.$$ But after this $$m\dfrac{d^2x}{dt^2}=-3kx|x|.$$ What is general solution of this ODE? I think it would give the $x$ in terms of $t$ and I would be able to get time period from it.


title: how laser interact with atoms?

text: I am reading a book introducing basic concept of laser. It is pretty shocking to me that people can generate beam with almost all photons in the same state. In the book, it said that a two-level atoms (with energy level is $\hbar\omega_0$) can absorb a photon from the laser so to excite the atom. The laser with wavevector $k$ and frequency $\omega$. Here is what confusing me. The laser not necessarily have the same frequency as the atom (i.e. $\omega_0 \neq\omega$), so how come the atom absorb a photon which is not of the frequency $\omega_0$? Can it still absorb photon from laser? If so, where is the extra energy ($\hbar\omega - \hbar\omega_0$)gone? Also, if this is possible, so how does the momentum of the atom changed if it absorb the photon from the laser? I know that if the atom absorb photon of wavevector $k$, then the momentum change on the atom will be $\hbar k$, does it make sense? It seems someone wrong to me because I think the atom can only absorb photon of frequency $\omega_0$ such that the momentum change should be $\hbar k_0$. In addition, the book introduce a concept of lifetime of the atomic upper state $\tau$. I am trying to understand the force exert on the atom by absorbing one photon. I know that the force is $\Delta p/\Delta t$. Can I say $\tau$ is just how long it takes to make a momentum change if absorb an photon of wavevector $k_0$ so the force the atom experience is $F = \hbar k_0/\tau$ ?


title: velocity required when rounding a flat curve and banked track

text: When rounding a flat curve, the centripetal force is provided by the frictional force. I learned that when a car rounds a flat curve with a fixed radius $R$, it can be able to make a turn as long it is moving with a velocity equal to or less than $v_{max}$ $$v_{max}=\mu mg$$ However, in the case of a frictionless banked track with a fixed radius R, a car can only make the turn if it has a particular velocity... could someone please explain why that is the case


title: The motion of a spring

text: ![Single Spring](http://i.stack.imgur.com/qYxFE.gif) I have a question about the force set by this spring, I saw many times that $\overrightarrow{F}=-Kx\overrightarrow{i}$. I'm asking why not using $\overrightarrow{F}=Kx\overrightarrow{i}$ without the minus. And supposing that $\overrightarrow{F}$ is changing during the motion of the solid object as well as the form of the spring. Here $K$=the Hooke's constant, $K>0$. **P.S:I need a detailed explanation of this phenomenon.**


title: Uncertainty on a single observable measurement

text: Heisenberg Uncertainty Principle states (in the form of the Robertson- Schroedinger Formula) that measurement of two non-commuting observables has a limiting precision, even for flawless measurement devices. Okay, no problem with this. But what about a measurement on a single observable, does Quantum Mechanics imposes some fundamental limit? p.s.: Googling around I found this paper which states "that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations", talking mainly about bipartite systems.


title: Vibrational noise for scientific apparatus on a satellite

text: Say we're running an experiment on a satellite in _some_ earth orbit. For example, maybe we're imaging something with transmission electron microscope or we're catching atoms in ion traps --- really anything. In practice, and otherwise keeping things very simple on the satellite to avoid mechanical / etc. noises, what kind of vibrational noise profile will we have relative to what's possible on earth? What would be the primary cause of the main noise source (e.g. on earth this might be the building's ventilation system followed by geological sources, etc.)?


title: Why does the point of intersection of two shadows look brighter?

text: When I sit in my garden during the day I always keep looking at the two intersecting shadows of two rods. It looks something like this: ![enter image description here](http://i.stack.imgur.com/2RYfK.png) What I find weird about it is that at the point of intersection of the shadows, instead of becoming darker, they become bright. Can anybody explain why this happens?


title: How to calculate concentration of vapor at the surface of a water drop

text: I'm reading a paper that examines the evaporation rates of water. In the final formula, it has the following constant: $c_s - c_\infty $ where $c_s$ is the concentration of the vapor at the sphere surface and $c_\infty$ is the concentration of the vapor at infinity. I'm fairly confident in how to derive $c_\infty$: 1) Calculate water vapor pressure $p_s = 610.78 e^{\frac{17.2694 T}{T+238.3}}$ 2) Actual vapor pressure is then: $ p=(Relative Humidity)p_s$ 3) Using ideal gas law gives concentration at infinity: $c_\infty = \frac{(Molar Mass of Water)p}{RT}$ This generally looks like it gives me answers consistent with the paper's values. But, if I screwed up, please let me know. My problem is with $c_s$. It's weird, because I recognize how easy it should be to get this, but just can't. I've asked some of the other grad students here and they basically all are befuddled. I think this is the physicist's version of a "tip of my tongue" experience. So, can anyone give me a link or method by which I can get this? Thanks.


title: Show that the electric field E in the system at rest is $E=\frac{Q}{4 \pi \epsilon_0 \sqrt{(x^2+y^2+z^2)^3}} (x,y,z)$

text: A body point charge $Q$ moves in relation to the reference system $\Sigma$ according to the law of motion $x(t)=v_0 t$, $y(t)=0$, $z(t)=0$.


title: how does a helicopter get forward thrust?

text: Just passed a helicopter on my way to work. We have read in some detail how an airplane gets forward thrust and lift by deflecting air. How does a helicopter with horizontal fans achieve that ?


title: Estimating the number of atom/nuclei in a single quantum dot

text: I often read in introductions about quantum dots that depending on the fabrication method, a single dot contains about 100 - 100000 atoms. Assuming a self-assembled dot of lens or pyramid (cone) shape, I did some rough estimation by considering the volume (or the area) of a dot divided by the volume (or area of a cell) of a single atom, taken to be $10^{-3}$$m^{-3}$. The estimation falls within the range of $100-100000$, which is not surprising given how wide this range is. Is there a typical and vigorous method that people use to estimate the number of atoms in a single dot?


title: Lorentz Transformations

text: I am trying to understand Lorentz Transformations in SR. I have some doubts. 1) In the derivation for Lorentz Transformations, why do we assume that Galilean Transformations hold true when an observer isn't in motion? i.e. when you say $x'=\gamma (x-ut)$. You assume that an observer at rest, measures $x'=(x-ht)$. 2) Why do we think of multiplying only by a factor $\gamma$ and not adding or differentiating or some other linear operator to act on the measurements ? 3) Does the Second Postulate of SR, ultimately comes from the first one only i.e. all inertial observers are equal, hence there is no special inertial ether frame, thus speed of light must be same for all inertial observers. ( We already know the laws of electrodynamics are true)


title: Can a theory be proven by an experiment (or series of) that sustains it?

text: This is a question that I've always had but it wasn't until the recent news regarding the BICEP2 experiment that I really gave thought about it (please note that the question is general and not particular to the theories involved in that experiment). I think a series of experiments or experimental data that conforms to a theory increases the odds that the theory is accurate, that through the theory things can be explained or the outcome of future things (e.g. experiment results) predicted given certain properties or conditions. Kind of like in statistics and the concept of degree of confidence, that when more experiments sustain a theory the degree of confidence which holds the theory true is raised. So... is it impossible to ultimately prove a theory? Is it eventually accepted as accurate or _proven_ if the degree of confidence is high enough or is it actually possible to prove a theory by several different repeatable experiments that conform to it?


title: What is the wave length of the entire universe?

text: In quantum physics, particles are also waves. Larger particles have shorter wave lengths, and macroscopic objects have extremely short wave lengths so that the wave aspect can be ignored, and classical physics works fine at those levels. The bigger the object, the shorter the wave length. So: What is the wave length of the biggest "object" of all: the universe? Has this ever been calculated? Does it have any meaning to talk about wave lengths at those levels?


title: How can particles travel in a straight line?

text: A particle can be set off in a certain direction by giving them momentum. Momentum is a vector, so the particle heads off in a specific direction. But the wave function of the particle allows it to obtain other momentum values, which would steer the particle on a different path. How then can we "shoot" electrons and other particles in straight lines? How can they maintain their momentum in the face of quantum uncertainty?


title: Origin of Ladder Operator methods

text: Ladder operators are found in various contexts (such as calculating the spectra of the harmonic oscillator and angular momentum) in almost all introductory Quantum Mechanics textbooks. And every book I have consulted starts by defining the ladder operators. This makes me wonder why do these operators have their respective forms? I.e. why is the ladder operator for the harmonic oscillator $$\hat{a}=\sqrt{\frac{m\omega}{2\hbar}} \left( \hat{x} + \frac{i}{m\omega}\hat{p} \right) $$ and not something else? On a similar note, does anyone know the physicist/paper who/which proposed this method? Wikipedia mentions Dirac, but I have been unable to find any leads.


title: Magnetic B Field of Point Charge Not at Constant Velocity

text: I'm working on an N-body simulator for charged particles. I know that moving charged particles generate a magnetic field, and another moving charged particle could be effected by this magnetic field. Using the Maxwell's Equations we can derive the magnetic field of a point charge moving at a constant velocity, which is roughly approximated by Biot- Savart's Law if we ignore relativistic effects. Here's the magnetic field of B at a point due to the motion of a charged particle (ignoring relativity): \begin{equation} \vec{B} = \frac{\mu_0 q \vec{v}}{4 \pi} \times \frac{\hat{r}}{|\vec{r}|^2} \end{equation} My question is what happens if we stop assuming that the velocity of particle A is constant (for example, two charged particles A and B orbiting and interacting with each other)? Can I accurately assume for a certain time step in my simulation that the velocity is constant and use that to calculate the magnetic field due to that particle's motion? Or are their other terms which would arise/change in the derivation from Maxwell's Equations if velocity is not constant?


title: Does the existence of Higgs imply the existence of Magnetic Monopoles?

text: I am aware that in theories with spontaneous symmetry breaking, Magnetic Monopoles can exist as topological solitons. Can the same be done with the Standard Model gauge group. I am familiar with the contents of 't Hooft's paper Magnetic Monopoles in Unified Gauge theories. But the analysis in that paper is done for the $\operatorname{SO}(3)$ gauge group. Is there a similar analysis for the standard model gauge group? Does the discovery of Higgs particle imply the existence of magnetic monopoles as topological solitons, and magnetic charge being treated as a topological charge?


title: What happens when a ferromagnetic object encounters a field too strong for it?

text: Just thinking aloud ... It is possible for a star to grow so large it collapses under it's own gravity. Along a parallel path (so to speak) when a conductor carries a current too large for it to sustain, it burns out. Can a ferromagnetic object be imparted a field too strong for it? What happens then? I would begin to guess the dipoles within the magnet can only be magnetized so far; a stronger field wouldn't have an effect. But surely the same argument could have applied to a wire conductor?


title: Do laws of thermodynamics have a place in Theory of Everything?

text: I am having a difficulty understanding why second law of thermodynamics is still a valid universally accepted concept. I understand it works on paper for describing isolated heat systems. However, I do not understand how can it hold place as a valid concept on our path towards a theory of everything. I would like to generate a discussion around some ideas I have that brought me to this conclusion. Maybe there is someone out there who's also thinking about this. Maybe you've got time to point out errors in my logic or suggest reading. Physicists assume matter and energy is conserved and also tell us "entropy increases!". According to information theory, entropy is related to information. The relationship is "when entropy increases information decreases". (Very short summary) Now if entropy increases then at some point in the past there was less entropy. So if you go all the way back to Big Bang entropy was at minimum and the amount of information was at maximum. Well, there seems to be something contradictory here! In the present day picture, information is more abundant than ever, we have galaxies, particles, planets, life and all the other stuff, and at Big Bang or slightly after we just had some radiation. From this, I can't understand why people state that entropy is increasing. Any useful insight?


title: An explanation for the Landauer's principle

text: Has anyone understood the Landauer's principle? What is the current status? In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's engine) How does one account for thermodynamic concepts applicable to situations involving measurement? What does it mean to reset the state of the apparatus why is free energy expended in the process?


title: What makes thrust reversers different from fans on a sailboat?

text: Why do thrust reversers on jet planes work? By Newton's third law, it seems like the force exerted by pushing air through the nozzle should cancel the force from redirecting the air forwards. The problem seems identical to the case of a fan on a sailboat, with "fan" replaced by "jet engine" and "sail" replaced by "thrust reverser."


title: How do we calculate the speed of an air bubble rising in water?

text: We all know that an gas bubble expands as it rises through a liquid due to decreasing pressure.But at what speed does it rise? if we make a bubble of unit volume filled with a gas of given density at the bottom of one meter deep liquid container (liquid's density is also known), then how much time will the bubble take to rise? We also have to incorporate the continuously increasing volume of the bubble.


title: A quantum particle which is almost at rest but whose position is random!

text: Assume a particle is given by a quantum state which is constructed in such a way that it is equally probable to find it anywhere in an fixed interval $(0,L)$ but has arbitrarily low velocity. The particle is almost at rest but its position is still random! I will give a construction for such a quantum state. Let $$\psi(x) = B(x)e^{ikx},$$ where $B(x)$ is a function with smooth cut off which is almost like a square function which is $1$ in $(0,L)$ and zero everywhere else. ( I have introduced $B(x)$ over square function to eliminate arguments about continuity of $\psi(x)$). The most probable momentum of this particle is $k$ with a manageble uncertainty. If we fix $L$ to be at certain high value, then the uncertainty in momentum is fixed at a low value. Now the question is, in the above set up we can choose $k$ to be arbitrarily small and with almost same low uncertainty and still have its position equally distributed in an entire interval $(0,L)$. In essence we have a valid quantum state in which a particle is almost at rest, but whose position is totally random in an interval. Although I am new to quantum mechanics, I find this very intriguing and almost hard to imagine such a real world situation. Is this a possible flaw with in QM? I'd appreciate your comments and explanation of any pitfalls in this argument.


title: Why does taking a long step increase the chance of slipping?

text: Me and my friend were walking and it was raining. He didn't have any grip on the slippers so he took smaller steps to avoid slipping. We both were wondering why does taking a long step increase the chance of slipping on the slippers and not on a short step?


title: twin paradox question

text: I'm trying to wrap my mind around the twin paradox, but I can't figure out this one problem from my textbook. It uses the relativistic Doppler effect to demonstrate how the paradox works. The first part of the problem is as follows: Amelia and Casper are twins. Amelia is going on a trip to a distant planet while Casper remains on Earth. The planet is about $12$ light-years from Earth, traveling at $0.6c$. Therefore from Casper's perspective his sister's trip lasts 40 years (20 years outbound and 20 years returning). From Amelia's perspective the trip only lasts 32 years (16 years outbound and 16 years returning). Casper sends a message to Amelia once a year on his birthday. The frequency of these messages will be Doppler shifted as follows: $$\text{outbound trip:} \\\ 0.5yr^{-1}=1yr^{-1}\sqrt{\frac{1-u/c}{1+u/c}}$$ $$\text{return trip:} \\\ 2yr^{-1}=1yr^{-1}\sqrt{\frac{1+u/c}{1-u/c}}$$ So Amelia will receive 8 messages on her outgoing trip ($0.5yr^{-1}*16yr)$ and 32 messages on her return trip ($2yr^{-1}*16yr$), totalling to the 40 messages that were sent by Casper. Now the question asks me to calculate how many messages Casper would receive if Amelia sent a message to him on each of her birthdays. And my calculations are as follows: on the outgoing trip, Casper will receive $10$ messages on Amelia's outgoing trip($0.5yr^{-1}*20yr$), and $40$ messages on her return trip ($2yr^{-1}*20yr$). But that totals to $50$ messages, which is more than what Amelia sent out. Why are my calculations coming out this way?


title: Can I make a rod in the vertical plane move with its one end on the ground in a slanting position?

text: Consider a rod kept vertically on the ground. I keeps the rod in a slanting position making some angle with the horizontal. Can I now move this rod along the horizontal plane by applying a force at its bottom? The torque due to my force at the bottom will act against that due to gravity keeping the rod at equilibrium in that slanting position and I could move it. I tried it experimentally using one of my books instead of rod and it kind of worked. But, when I thought about the situation in different ways I get opposite answers. Consider the rod at rest at that slanting position. If I leave it it will fall by rotating about the point of contact. When I'm moving the rod I'm applying force on the bottom point. As my force passes through the axis of rotation torque due to it would be zero and I cannot move it the way I want. Another way of my thinking-my force at the bottom of the rod would actually provide a torque along the center of mass of the rod which will act against the torque due to gravity and in this way my experiment would work the way I thought. Why am I getting different results if I think in different ways? Please help.


title: Calculate the latitude / longitude coordinates of the location where the Sun is at the zenith

text: There are plenty of resources showing how to calculate zenith and azimuth of the Sun when the time and the location are given. However, I need to calculate the location where the sun is at the zenith for a given time and date, not the other way around. Is there a more or less easy way to do this calculation?


title: PN Junction Depletion Region

text: So it took me a little bit to understand this, but I want to make sure I have a few things right. First of all, when a Crystal Structure with One side N-Doped, One Side P-Doped are in the same crystal lattice, the Electrons from the N-side are going to jump over to the P-side at the Junction where they meet. When they jump, this creates a Positive charge on the N-Side (Since electrons are leaving) and a Negative Charge on the P-Side (Since Electrons are being added) And these 2 sides were "Neutral" before. My few questions is in regards to this. (Lets pretend no voltage is applied)   1. The Depletion region makes sense, but the "equilibrium" with the depletion region: is that because the Negative charge over on the P-Side near the junction is opposing any more electrons from coming over? If so....how come more "holes" aren't moving into the negatively created region on the P-side...like I guess how come the negatively created region isn't jumping all over the place on the P-side, or for that matter, why aren't more extra electrons just jumping into the positive side created on the N-doped part near the junction. ![enter image description here](http://i.stack.imgur.com/8RsQj.png) Like Look at the + Side in the "Space charged region".....why aren't the electrons jumping from the N-doped neutral region? Seems like the Free electrons should want to be attracted to the + side of the space charged region. Or is it just because the electric field from the negative side near the P-doped region near the junction is pushing them away?   1. Since the concept of "holes" just confuses me more, and I like to just think of it as electron movement (Which is what it is anyways right?).....what exactly happens when the depletion region expands due to reverse bias? I understand Forward Bias....the Electrons are being "FORCED" over the Opposing Electric field created by the Depletion region. But when it's reverse bias what is "really" happening? Obviously "holes" aren't getting pulled out since that makes no sense(or is it that actually electrons are getting "shoved" to the other side by the + terminal), Is the depletion region "basically" expanding one way sorta, like towards the P-doped side. Since the electrons are getting pulled out of the P-doped side it's just going to create bigger gap....but why aren't electrons from the other side just jumping right back into the gap? Or is it because the Negative charged region is getting filled up more and more towards the P-doped side, which opposes any more electrons from coming over? Sorry for the long questions, just "Holes" moving really whacks it up for me since the way I imagine it is just electrons flowing, and that makes the most sense to me!


title: How is the hierarchy problem consistent with the decoupling theorem?

text: One the one hand we have the hierarchy problem in it's various forms, in my understanding in it's most serious form one could state it as the observation that if there is a heavy mass scale M in addition to the weak scale m, then when we run the higgs mass (say) mh in the wilsonian renormalization group from some large scale Lambda down to the physical weak scale we will generically find that mh is of order M unless the initial conditions of the renormalization group were very finely tuned such that mh(Lambda) and M cancel very precisely. On the other hand we have the decoupling theorem, which also can be stated in various ways but most practically for here we can say that the beta function computed at low energies should be independent of high energy scales. Naively, I would think that you could only have one or the other of these statements. On the one hand the hierarchy problem tells us the Higgs mass computed at low energies is sensitive to high energy physics, on the other hand the decoupling theorem tells us that no low energy observable should be sensitive to high energy physics. How do we reconcile these? Does the decoupling theorem not apply to the higgs?


title: Is it possible to calculate specific velocities from acceleration?

text: I'm trying to understand a sample problem from a current (published 2011) high school physics textbook, but I really think the question is flawed. The task is to convert an acceleration-time graph (AT-graph) into a velocity-time graph (VT-graph). The AC-graph is given as: ![enter image description here](http://i.stack.imgur.com/tTSbF.jpg) Then the book gives the following instructions for finding velocities from accelerations: ![enter image description here](http://i.stack.imgur.com/kztRH.jpg) Here's my first problem. Where did they get the formula $v=(\Delta a)(\Delta t)$? Isn't $\Delta a$ a more advanced concept called "jerk"? (a concept that this textbook never introduces, by the way). Shouldn't it be $\Delta v = a\Delta t$? And if so, we're not finding $v$ (which, correct me if I'm wrong, is impossible from the data given), but merely $\Delta v$. Then they show the following calculations: ![enter image description here](http://i.stack.imgur.com/ZzrCh.jpg) This chart is confusing to me. Is the time column an instant of time or a time interval? (I think it's a time interval). It seems to me that they're calculating $\Delta v$, not $v$, in which case it's impossible to draw a VT graph. But that's what they do next anyway: ![enter image description here](http://i.stack.imgur.com/TMsNF.jpg) Any feedback is appreciated.


title: Planet's Moon attrated by sun

text: I'm currently writing a code to generate solar system and $N$ number of planets / moons. I use real data to test (earth / sun / moon data). I succeeded in placing the earth and make it orbit around the sun using the correct mass and velocity. But when I place the moon around the earth and launch the simulation, the moon is a kind of _ignoring_ Earth. At start $(x,y)$:   Sun : 0,0   Earth : 1.4959826e8   Moon : 1.4959826e8-384400 using $F = (G \times a.mass \times b.mass) / (dist \times dist)$ At start $F$:   Sun & Earth: 3.5855635298968626E22   Earth & moon : 1.9817101152925866E20   Moon & Sun: 4.379973928784021E20 Since I placed them on $y=0$, moon has an $f_y$ of $0$ and $f_x$ of -2.39826381349143456E17 (because she's placed between sun and earth At start, the moon has a velocity of 0.001022 km/sec After velocity update ($v = v + dt \times F / mass$) $v =$ 0.28200845732138924   $v_x =$ -0.28200660544886147   $v_y =$ 0.001022 So regarding the result, it make sense that the moon is attracted more by the sun than the earth (since vx is negative), but why? Where in my formulas I make a mistake ? I tested also to start the simulation with the velocity of moon = 29.783 + 0.001022 , (earth velocity) but then the moon just turn around the sun like the earth (I surely forgot to put some info, don't hesitate to tell me to add things , I'm not really used to ask physics questions) (Here's a video if you want an idea of what happen)


title: Projectile motion in two and three dimensions question?

text: So I bought this book in the library and physics fascinates me and I found this quote in the book " Galileo has proved that when any effects due to air resistance are ignored, the ranges for projectiles (on a level field) whose angles of projection exceed or fall short of 45° by the same amount are equal.This can be easily proved" I don't understand it at all? And I don't think it is that easy to prove, but I want to know it so much :/ Can you explain this to me?


title: What type of substances allows the use of the Ideal Gas Law?

text: I know that I can use the ideal gas law with pure gases or pure liquids. But can I also use the ideal gas law at saturated gases and saturated liquids as long as they aren't two phase substances?


title: Glass and isotropy

text: Glasses are amorphous materials. Nevertheless, as far as I know, in some areas of Condensed Matter, they consider that the glass is isotropic. Under what restrictions they can do this assumption? Mathematically, the assumption that glasses are isotropic make the calculations, in my imagination, dramatically simpler. In what they are simplied? And, finally, there are some good references in this subject?


title: Can a very small portion of an ellipse be a parabola?

text: We consider that when a body is projected from any height from the earth surface with a speed lesser than the orbital speed ( tangentially to the earth surface at that point.) it follows an elliptical path with earth as a focus. This condition when derived mathematically does not contain any lower boundary of the speed of projection. But we consider here that Earth is not intersecting its path at any point. Now when we consider such a height with the same speed and direction of velocity of projection so that the earth surface intersect its path then by approximations we can show that if height is sufficiently lower the path will be a parabola. In none of the cases we have assumed the earth to be a point or a flat surface. So is it true that a very small portion of an ellipse is parabola even if both are entirely different conics by definition?


title: Special conformal transformations and locality

text: In the conformal symmetry, used in some QFT theories, the infinitesimal generators, applying to space-time, are all linear (translations, rotations, boosts, dilatation), except the special conformal transformations, which are not linear. I feel that this non - linearity could cause a conflict with locality, in the following sense:   * Let us consider two wave packets 1 and 2, separated by a space-like interval, corresponding to impulsions P1 and P2. If we make a linear transformation, for example a Lorentz transformation, we obtain impulsions P'1 and P'2. Now let us consider the total system 1 + 2; it has an impulsion P, which is equal to P1 + P2 because both systems are not causally related. By this same Lorentz transformation, the total impulsion P becomes P', but because the Lorentz transformation is linear, we have P' = P'1 + P'2, and P' is linear in P'1 and P'2, and is linear in P1 and P2. This is coherent with the fact that there is still no interaction between the systems 1 and 2.   * On the other hand, imagine we had taken, for example, a pseudo-Lorentz transformation , which would be, for example, quadratic, then, in the expression of P', we would have had cross-terms of type P1.P2, what would mean an interaction between systems not causally connected, which is incoherent. So, I need a detailed argumentation, to infirm or confirm my feeling : non- linear special conformal transformations could cause a conflict with locality.


title: Schrödinger's cat; why was it necessary?

text: Could someone please explain to me the idea that Schrödinger was trying to illustrate by the cat in his box? I understand that he was trying to introduce the notion of the cat being both alive and dead at the same time. But why was it necessary to introduce this thought experiment and what did it achieve?


title: Any interesting physics theroies/equations to be used in a video game?

text: I am designing a little game based on Newtons Graviational Law. Are there any theories that I can use to create games? thanks


title: How are stellar and galactic ages determined?

text: Being a 4th year undergraduate physicist, you'd think I'd know this! But it's never really taught in any detail, just vague mentions of metallicities and, in galactic case, redshift. So how exactly do we measure the ages of stars and galaxies. There doesn't seem to be much of an introduction to the methods online, so can anyone enlighten me? A long and detailed answer would be brilliant but a reference to an accessible paper would be appreciated!


title: Help with Cutkosky cutting rules for fermions

text: I know that a cut boson propagator is replaced with the mass shell delta function. But what happens when you cut a fermion propagator? Do you just replace the denominator with a mass shell delta function, and do nothing to the numerator? Why? If so, it's a bit peculiar because the numerator actually reduce the degree of singularity and might alter the behavior of the poles in the complex plane.


title: Conservation of angular momentum for a nonrigid body

text: Question: > The sun is not a rigid body but a hot ball of gas. The period of rotation > varies from 37 days at the pole to 26 days at the equator. The mean radius > of the sun is $7\times 10^8\text{ m}$. Suppose the sun collapses into a > neutron star of radius approximately $10^4\text{ m}$. Assume that the > neutron star is a spherical ball. Estimate the final period of rotation of > the neutron star. You may assume it is a rigid sphere for this approximate > calculation. So I understand how this is a conservation of angular momentum problem and the neutron star side is just $I\omega$ where $I$ is for a solid sphere, but I don't know what to do about the sun side. It seems like it would be an integral of all the disks of the sphere for $I\omega$, but it doesn't say anywhere about whether or not density is uniform throughout the sun and how $\omega$ varies (linearly, by curve of the sphere?). It seems like density should be uniform, so I could probably figure out the I using that. Then I thought I could use the average value of $\omega$ and just multiply it with the integral for $I$, but I can't do this since I don't know the function for $\omega$ so I wouldn't be able to integrate it along the interval and then divide by the interval. Can anyone help me with this? Thanks!


title: A rod of charge?

text: Say you have a _finite_ rod of conducting charge. The field from one side of the rod looks like Figure 1: ![enter image description here](http://i.stack.imgur.com/2L7X3.jpg) At the centre of the sheet, the field lines are straight because of symmetry. (for an infinitesimal length of of the rod) (See Figure 2). Therefore no matter how far you move away at the rod, the field lines at the centre never diverge. Therefore the field is always constant at the centre of the rod. (Kind of how the field is always constant for an infinite rod everywhere, since everywhere is the centre) However, if you place a point charge _at the centre_ and use Coloumb's Law to calculate the force acting on it, the further away you move it from the rod, the weaker the force gets. Why? ## **Note that I'm talking about placing the point charge _at the centre._ I understand why the force becomes weaker for points other than the centre (since the lines diverge). I'm specifically talking bout the center.** Thanks a lot! Edit: Sorry, I just realized my diagram of the field lines are wrong (Figure 1). The field lines should have positive concavity, not negative. The question is till valid though.


title: What are the final particles emitted from an evaporating black hole?

text: Hawking radiation predicts that black holes can slowly evaporate through the effective emission of a particle. This particle is a real particle, as in, it is not a black hole itself. I'll write this (a bit tongue-in-cheek) as follows, with $A$ being the emitted particle, and black hole prime being the black hole with slightly reduced mass. $$\mbox{black hole} \rightarrow A + \mbox{black hole}' $$ There is every reason to think this continues until the black hole stops being a black hole. So we are left with a radiated particle and something else. We don't know much about this process, but _I think_ we can still limit it to a 2-product decay. $$\mbox{black hole} \rightarrow A + B$$ What could the something else, $B$, be? I don't know much about it, but I know that it is:   1. Not a black hole   2. A physically plausible particle It might be more realistic to ask _what other conditions should we impose on B_? I realize this is probably an unsolved problem. Also, won't $A$ be really highly energetic? How energetic? Actually, what is $A$ to begin with?


title: Experimental limits on anisotropies in the $e/m_{e}$ ratio

text: Currently the charge-to-mass ratio of the electron is known to 10 orders of magnitude. However, i'm curious if:   1. Are there any experiments trying to bound the anisotropy of this ratio for different directions of space? Over what time does the data needs to be averaged to get to our current ten-figure precision? Less than a day? Less than a second? Less than a month?   2. Does an spatial anisotropy (or an spatial inhomogeneity) of this ratio break Poincare symmetry, or can that be restored with replacing the mass scalar with a tensor object? Also, what theoretical ideas explicitly disallow a non-scalar fundamental mass? What about a non-scalar electromagnetic charge?   3. Does mass spectroscopic experimental data bound any anisotropic variations? Do we have any measurements of this ratio on small cavities where van der waals forces are dominant?


title: Second quantization Hamiltonian Matrix for an aggregate

text: I am working on the matrix form of the Hamiltonian in the second quantization. I haven't taken any course on second quantization and I'm learning it on my own. I'm a little bit confused about the actual form of a system-bath Hamiltonian. Can anyone please introduce some references with numerical examples on this topic? like how the Hamiltonian looks like for a system-bath with given values of frequency of the modes. I'm talking about a simple aggregate Hamiltonian in the one-exciton basis. The total Hamiltonian is the summation of three terms: the electronic part, the vibrational part and the coupling term that describes the interaction between the electronic excitation and the vibrational modes. Like the one in this paper: http://www.pks.mpg.de/~eisfeld/wwww/pdf/Roden_PTCDA_Hendi_Absorption.pdf The Hamiltonian is in the form of equation (A5) in the paper (page 10). The Hamiltonian should take the matrix form and that is where I'm not quite sure how to get it right. In particular the vibrational term which is ${H_{vib}} = \sum\limits_{n = 1}^N {\sum\limits_{j = 1}^M {{\omega _{nj}}} } a_{nj}^\dagger {a_{nj}}$. I understand that for this term the Hamiltonian is diagonal, but I'm not quite sure what values the number operator takes. I already have the values of frequency (omega) in table 1 (page 5). I think the number operator is one for all the non-zero(the diagonal)terms of ${H_{vib}}$ . Another thing that confuses me is the two summations, where N is the number of monomers and M the number of modes. This makes it kind of confusing for me to write down the H matrix for example for a dimer(N=2) and trimer(N=3), while I have some arbitrary number of modes,let's say M=6 or 4. ${H_{vib}}$ has to take a square form, but with these numbers I'm not quite sure how to write it down.


title: Questions about Van de Graaff generator

text: Only asking those questions because I can't afford to get a real generator.   1. If the voltage on the sphere was 50 kV, then I used a metal rod to discharge it and I connected a voltmeter to wire grounding the rod, will it read 50 kV?   2. Does the formula $V=kq/r$ apply for the generator? (According to some sites, it does.) If it does, which radius is meant? The hollow part radius? Will the thickness of the wall matter? ![enter image description here](http://i.stack.imgur.com/VoEmy.png)


title: Why does special relativity talk about the speed of light in a vacuum?

text: What's the importance of the speed of light being in a vacuum? Does not being in a vacuum cause a difference?


title: Black Holes and Energy Conservation

text: A supernova's Ni/Fe core remnant with mass exceeding about three solar masses would result in a black hole. Although the core's temperature was in the ~1E10K range, the black hole temperature based on predicted Hawking radiation would be very near absolute zero, well below CMB temperature. It seems implausible that a very high temperature supernova remnant can instantly evolve to a near-zero K temperature black hole. How is this consistent with conservation of energy?


title: Can ice thickness be different on two nearby lakes?

text: In winter, is it possible for two distinct bodies of water, which are a few kilometers apart (so they are exposed to roughly same temperature), to have different thickness of ice? Does the area of the surface, total volume, or depth have any significant effect on the ice thickness?


title: Find the lowest excitation of a given Hamiltonian

text: Is there a standard way to find the lowest excitation energy of given Hamiltonian without knowing the eigenstates? In particular I have the find the lowest excitations of an 1D Ising Hamiltonian in 1D with nearest neighbor interaction: $$H = \frac{J}{2\hbar^2} \sum_{<i,j>} \bf{s}_i \cdot \bf{s}_j$$ I am pretty confident I want to find spin waves and it is most likely easy to show they are eigenstates but how do I proof that they yield the lowest excitation of the system (without arguing with intuition)?


title: Do cosmological and Doppler redshift produce different patterns?

text: For a given black body radiation curve, would the changes to the spectrum resulting from cosmological expansion and those from Doppler effects be distinguishable on the basis of the shapes of the resulting curves alone? Or, put another way, starting from the same spectrum, can both processes produce the same observation (for suitably chosen magnitudes of expansion or velocity)?


title: Would a metal enclosure (such as a shipping container) protect its contents from the effects an electromagnetic pulse?

text: I was watching a program about disaster preparedness, and it was suggested that the metal enclosure of a common shipping container (of the intermodal variety) would be sufficient to protect its contents from a large electromagnetic pulse (the kind that could affect an entire region or continent). I have my doubts that this is true, as it seems like a misunderstanding of how electromagnetic pulses work—but I can't find any reliable resources on the subject. What does physics have to say about this? **Would a metal enclosure (such as a shipping container) protect its contents from the effects an electromagnetic pulse large enough to affect a large geographic region?**


title: Speed of a dynamic hydraulic system

text: We all have noticed that changing the temperature of the water in the shower is not instantaneous, rather the result is felt when the water that was in the tap works its way up to the showerhead. However, changing the pressure does feel instantaneous. I wonder at what speed the change in pressure propagates in the direction of flow in a flowing fluid. My guess would be at the speed of sound in the medium, based on the fact that it is faster than the speed of the flow of the water (like the temperature is), yet obviously at or below C. I am obviously missing the correct keywords to google for as I cannot find any references to this phenomenon. What is the answer to the query, or better yet, how could I have found this information (short of empirically)? Thanks.


title: How to apply an algebraic operator expression to a ket found in Dirac's QM book?

text: I've been trying to learn quantum mechanics from a formal point of view, so I picked up Dirac's book. In the fourth edition, 33rd page, starting from this:$$\xi|\xi'\rangle=\xi'|\xi'\rangle$$ (Where $\xi$ is a linear operator and all the other $\xi'$'s are eigen-(value|ket)s.) ,and this:$$\phi(\xi)=a_1\xi^n+a_2\xi^{n-1}\cdots a_n=0$$ (where $\phi$ is an algebraic expression) He has deduced $$\phi(\xi)|\xi'\rangle=\phi(\xi')|\xi'\rangle$$ I understand that the LHS is a linear operator acting on a ket, while the RHS is a ket multiplied by a number. What I don't get is how the step is justified. He seems to have applied $\phi$ to both sides. But shouldn't that give $$\phi(\xi|\xi'\rangle)=\phi(\xi'|\xi'\rangle)$$? This expression makes no sense as it is, as I doubt that you can apply an algebraic expression on a ket (I'm not sure of this, but to me, $|A\rangle^2$ &c makes no sense, as I don't think that you can multiply a ket with a ket and get another ket) So how did he deduce the expression? The context: Dirac is proving that an eigenvalue $\xi'$ of $\xi$ must satisfy $\phi(\xi')=0$ if $\phi(\xi)=0$. Oh (no need to answer this if you don't want), and is there any reason for Dirac introducing the confusing notation that eigen-whatevers of an operator should be denoted by the same symbol? Usually, different types of variables (eg matrices, vectors, numbers) use different classes of symbols (capital letters, letters with overbars, and lowercase letters respectively).


title: Why is pseudorapidity defined as $-\log \tan \theta/2$

text: Why the log? Is it there to make the growth of the function slower? As this is a common experimental observable, it doesn't seem reasonable to take the range from $[0,\infty)$ to $(-\infty,\infty)$ (For a particle emitted along the beam axis after collision $\theta = 0$ wouldn't be better to have a number that says how close it is to zero rather than one that says how large a number it is. I hope that makes the question clear.)


title: The fine structure non-constant

text: If the fine structure constant is different in different parts of the universe, then what would happen if we travelled to those regions? (I realise this is completely impossible as they are impossibly distant, so this is just a thought experiment). If we hop in our spaceship and travel to a region where the fine structure constant has a greater magnitude, then will we be subject to those physical effects? Or will we, as beings composed of matter from our current region, still be subject to our original value of the fine structure constant?


title: AdS space - Poincare Patch

text: How can I work out in detail the explicit coordinate transformation formulas needed to go from the "canonical" coordinates to the "Poincare patch"? I'm reading about AdS but the text takes the validity of the Poincare patch for granted, which troubles me. It only has a drawing showing the Poincare patch covering half the whole space, which doesn't help.


title: What happens when two strings collide?

text: I have a question, that perhaps someone with a much better understanding of physics can help me answer. Please correct me if I'm wrong. From what I understand, a string in string theory is basically a strand of energy that vibrates. The string can vibrate in a variety of different ways. It is thought that things such as quarks consist of a string vibrating in a very specific way. The question is, if two of these vibrating strings collide, would not there vibration patterns change? Is it possible for a string vibrating with one pattern to collide with a string vibrating in the exact opposite pattern in such a way that the two strings are essentially cancelled out?


title: Occurrence of turbulences in Fluid Dynamics from the equations of motion?

text: How can it be shown that turbulences occur in Fluid Dynamics? I think poeple imply that they develope because of the $\text{rot}$ terms in the equations of motion, i.e. the Navier-Stokes equations, but I don't see how. Of course, these cross-derivations are big for a curled up vector fields, but why do these expressions force the fluid on an inward spiraly trajectory, and then even multiple of these? Is there maybe an illustrative explicit calculation in two dimensions?


How do I express the Kepler general orbit $r(\phi)$ in rectangular coordinates? I use the identities $x=r\cos\phi$, $y=r\sin\phi$, and $r^2 = x^2 + y^2$, but I block at some point.


title: Polarization in Nicol prism

text: My book reads "When unpolarized light is incident on nicol prism (made of 2 crystals joined by Canada balsam a type of glue) it divides into 2 rays, both rays are plane polarized and electric field vectors of one of the rays are perpendicular to plane. These ray is Ordinary Ray. And electric field vector of another ray have oscillatios parallel to the plane. These ray is Extra ordinary ray. For these refractive index are 1.658 &1.486 respectively.The refractive index of Canada Balsam is 1.55. so, ordinary ray experiencs TIR at the surface of the glue Canada Balsam and comes out from one side of the prism while extra ordinary ray comes out as plane polarized light" My question is "Is it possible for a medium (here calcite) to have two refractive indices?"


title: Information and Black holes

text: From Youtube: A Thin Sheet of Reality: The Universe as a Hologram (Full) I have a few questions:   1. Why there are not layers of information on a black hole?   2. If the information is stored in the surface, can it be projected inside the blackhole?


title: Resultant wave in the Michelson-Morley experiment

text: I was wondering when the two waves in the experiment, don't they lead to constructive interference? Consider the first case in the image. The two combining waves should lead to constructive interference. ![Wikipedia](http://i.stack.imgur.com/u6zXO.gif) Source: Wikipedia. **Edit** Sorry for the confusion. What I wanted to ask is what John replied. But John how will they have half the intensity. The wavelength will be the same and so the frequency even if the wave splits. But after recombination the frequency should increase. Shouldn't it?


title: How to apply the WKB approximation in this case?

text: I'm trying to learn how to apply the WKB approximation. Given the following problem: > _An electron, say, in the nuclear potential_ $$U(r)=\begin{cases} & -U_{0} > \;\;\;\;\;\;\text{ if } r < r_{0} \\\ & k/r \;\;\;\;\;\;\;\;\text{ if } r > > r_{0} \end{cases}$$ _1\. What is the radial Schrödinger equation for the > $\ell=0$ state?_ > > _2\. Assuming the energy of the barrier (i.e. $k/r_{0}$) to be high, how do > you use the WKB approximation to estimate the bound state energies inside > the well?_ * * * For the first question, I thought the radial part of the equation of motion was the following $$\left \\{ - {\hbar^2 \over 2m r^2} {d\over dr}\left(r^2{d\over dr}\right) +{\hbar^2 \ell(\ell+1)\over 2mr^2}+V(r) \right \\} R(r)=ER(r)$$ Do I simply just let $\ell=0$ and obtain the following? Which potential do I use? $$\left \\{ - {\hbar^2 \over 2m r^2} {d\over dr}\left(r^2{d\over dr}\right) +V(r) \right \\} R(r)=ER(r)$$ For the other question, do I use $\int \sqrt{2m(E-V(r))}=(n+1/2)\hbar π$, where $n=0,1,2,...$ ? If so, what are the turning points? And again, which of the two potentials do I use?


title: Transmit DC power with one cord?

text: My DC devices have two wires connecting them to the power source, but what would be needed to transfer DC power using just one? I depict it as a kind of headphone, which can work with just one wire.


title: Tubelights+power lines pictures?

text: I've come across many pictures like these, sometimes in chain emails reporting the dangers of power lines. Another claim is that they run on "wasted" energy. The explanations given are that the wires set up a field, and thus a potential difference. This p.d. gives current in the wires. Now, I can't help but feeling skeptical. I can't see how the tubes would stay lit for the time it takes to set up the whole grid. Here's my logic: If current flows through the tubelight, there will be a net charge distribution on the caps. At one point, the charge distribution will be such that it creates its own potential, halting the flow of light. This works even if one end is grounded. An easier way to analyse this is a capacitor (GP: G for ground, P for power lines), with a bulb inside it. Each terminal of the bulb is connected to a plate (A and B). There's an optional grounding wire W. In this situation, it's obvious that eventually the plates AB will get enough charge (same charge density as PG incidentally) to create zero p.d. Current should be there for a brief moment in time. ![diagram](http://i.stack.imgur.com/eJGEf.png) I understand that this is a DC situation, but for power lines, I think that something similar should happen. Or maybe not. I'm clear that the potential difference across the live and neutral switches polarities, but I'm not sure how the potential field is outside the wire. In fact, I feel that there shouldn't be a V/E field, only a magnetic field. If it's true that the tubelights stay lit, then how is the energy "wasted energy"? I feel that even if the tubelight can stay lit, the energy is being drawn from the power lines. This looks just like how one can naively say that there is energy wasted in an open socket; when in reality plugging something in draws more energy from the system (and can dim other appliances). **Update** : So my questions are thus:   1. I'd like a clearer explanation of the potential and E field outside an AC power line.   2. Is the energy "wasted energy"?


title: How much energy Maxwell's demon will earn?

text: Suppose we have one mole of one-atom ideal gas at temperature $T$. Suppose Maxwell's daemon has separated molecules into two sections, one with speed below mean and another with speed above mean. How much energy will the daemon gain? **UPDATE** Yes probably this is the same question as how much energy real daemon should spend or how much energy it would be possible to get from the two subvolumes later, with heat machine. If these values are different, then please explain.


title: Can one compute the vibrational spectrum of a bond by the Fourier transform of the dipole moment vector autocorrelation function $C_{\mu\mu}(t)$?

text: Is it true that one can calculate the vibrational spectrum of a bond by the Fourier transform of the dipole moment vector autocorrelation function $C_{\mu \mu}(t)$? For example, suppose that I have a diatomic molecule $\text{A-B}$, containing atoms $\text{A}$ and $\text{B}$. $\text{A}$ and $\text{B}$ have partial charges $q_A$ and $q_B$ that sum to zero: $q_A + q_B = 0$. I can find the dipole moment vector $\vec{\mu}$ of this diatomic molecule: $$\vec{\mu}(t) = \sum_i q_i \vec{r}_i^{\prime} = q_A \vec{r}_A^{\prime} + q_B \vec{r}_B^{\prime}$$ where $\vec{r}_A^{\prime}(t)$ and $\vec{r}_B^{\prime}(t)$ are the position vectors of the charges (atoms). These position vectors depend on time $t$ because the charges (atoms) move -- the bond vibrates. Thus the dipole moment vector $\vec{\mu}(t)$ also depends on time $t$. I think that the autocorrelation function $C_{\mu\mu}(t)$ can be written $$C_{\mu\mu}(t) = \langle \vec{\mu}(t) \cdot \vec{\mu}(0) \rangle$$ where $\langle ... \rangle$ denotes an ensemble average. Now, $C_{\mu\mu}(t)$ is in the time domain. It has dimensions of $\text{(dipole moment)}^2$ (typically, $\text{Debye}^2$ in chemistry). But I would like to compute the vibrational spectrum (a plot of intensity, arbitrary units, etc. versus frequency). Is it true that the vibrational spectrum is the Fourier transform of $C_{\mu\mu}(t)$?


title: Could we run an electric car on electric eels?

text: Could we run an electric car on a tank full of electric eels? I've heard electric eels are around 400 to 500 volts and can keep shocking for up to an hour. They also have a 10 volt system to sense with, which might be good for the headlights and cd player.


title: Properties to select suitable materials for making permanent magnets

text: I have read that soft iron is suitable for making a permanent magnet. Because it is required for permanent magnet to have high coercivity and high retentivity. Same text also said earlier that soft iron has low coercivity and low retentivity and is very useful in making solenoids cores. What is the actual answer and also the reason?


title: Sum of acceleration vectors

text: If a point mass has some accelerations $\mathbf{a_1} $ and $\mathbf{a_2} $, why is mathematically true that the "total" acceleration is $\mathbf{a}= \mathbf {a_1}+\mathbf {a_2}$?


title: How many bits are needed to simulate the universe?

text: This is not the same as: How many bytes can the observable universe store? The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the number of unique states this space can be in. Imagine now, we are to simulate this space by enumerating each state along with which states it can transition to with a probability for each transition. How much information is needed to encode the number of legal transitions and the probabilities? Does this question even make sense? If so, is there any indication that any of these probabilities are or are not Computable numbers? **Edit**   Here's a thought experiment.   1. Select your piece of space and start recording all the different states you see.    2. If the Bekenstein bound tells us we can store n bits in our space, wait until you see 2^n different states. Now we've seen all the states our space can be in (otherwise we can violate the Bekenstein bound).    3. For any state, record any other state that the space can legally transition to without violating any physical laws. To simulate this portion of space, take it's state and transition it to a legal state. Repeat. We have only used a finite number of bits and we have modeled a section of space.


title: How does centrifugal force work?

text: I know what centrifugal force is, but how does it work? Why are things forced to the outside?


title: How do you justify neglecting electron-electron interaction in the Drude model?

text: I'm sure there's some way to justify it. Maybe a screening effect?


title: The notion called aether

text: I am trying to learn relativity theory and going through an introductory text on special relativity. I stumbled on the Michelson-Morley experiment. The book claims (accounts) that the result of this experiments banished away the concept of Aether. In order to understand how exactly the results of this historical experiment refuted the long standing idea I think I need to know what exactly was the idea of aether. Can anyone describe the concept of aether, what were the evidences that propelled this idea?


title: Thorium radioactivty vs Uranium radioactivty nuclear power

text: May i please open this question by asking that if you intended to answer this please could you provide links based on your answer. I have read ( and posted one ) on thorium and a lot of the answers are contradictory to what i have read with no scientific papers of links to back up what is being said. I am sure some of you are extremely intelligent but i do not know you. I am very interested in this topic and just want to learn more. **why am i asking this** I am very curious as to why ( and this not being the question, is somewhat political in nature ) the governments has not given more research time or scale development to using thorium as an alternative to are current energy crisis, not so much in that we do not have enough energy but how energy production is having a very negative effect on the environment. So this question is just to understand one side of the larger question, not meant for this board.               Traditional nuclear power radioactivity      Neptunium-237 Plutonium-239 (tried to provide links but i do not have enough point yet) Those 2 elements being the largest factors in organic destruction > The amount of HLW worldwide is currently increasing by about 12,000 metric > tons every year, which is the equivalent to about 100 double-decker buses or > a two-story structure with a footprint the size of a basketball court. > **marathonresources.com.au/nuclearwaste.asp** > > A 1000-MW nuclear power plant produces about 27 tonnes of spent nuclear fuel > (unreprocessed) every year. **world-nuclear.org/info/inf04.html** I don't think i need to outline the physics of why this is a very serious problem. Yeah maybe not for us, in our life time (besides the event of meltdown , in the case of Japan having +22 nuclear plants in a region of the earth that has 3 highly active tectonic plates), but for humanity this is really grim. If anyone is interested in a very good documentary on the matter please see http://en.wikipedia.org/wiki/Into_Eternity_%28film%29 note:This is not your run of the mill documentaries. I don't want to get into the whole nuclear weapon debate, what i am asking has nothing to do this that. This is primarily the radioactive waste produced by these two different forms of electrical generation and the physics with the long term effect on nature. Can we be certain that with traditional means we are not creating a pandora's box for future generations to come. One that could alter life on this planet to the point of complete destruction?               Thorium radiation       http://imgur.com/a8TDT <\-- poster outline of Thorium "Thorium produces 10 to 10,000 times less long-lived radioactive waste;" **wikipedia.org/wiki/Thorium#Benefits_and_challenges** yet in the same post it states "potential problems in recycling thorium due to highly radioactive " ( under thorium energy fuel cycle ) due to Th-228 So yes there is still radioactivity in its production but the radioactivity ratio between the two technologies, from what i have read , makes thorium a cleaner waste disposal process with less harmful effect in every area of concern from production, meltdown and disposal. With Thorium harmful decay is gone in 10 years for 83% of materials and 300 years for 17% compared to 10 000 years with conventional nuclear energy. With what little research has been done, it can also prevent a complete core meltdown. I cannot even imagine how amazing this technology can become with more funding and research into production development and disposal.               In conclusion:       Am i missing something in the research that i have done that does not make thorium an cleaner alternative to nuclear energy by a factor of a lot? And if i have not missed anything, why is this single difference not driving the research and development into this energy system ( Please i do not want to get political in this answer, if it is political please keep the answer very short, although i am interested i do not want to side line the main topic of this question )


title: Alcubierre warp bubble effect on gravity and space

text: I read the question _Faster-than-light communication using Alcubierre warp drive metric around a single qubit?_ , and these questions came to mind:   1. What kind of impact would an Alcubierre warp bubble have on a local star's or planet's gravitational field?    2. Could an Alcubierre warp buble be used inside a solar system without altering the orbits of planets or the orientation of stars?   3. What would the effects be of a warp bubble in a planets atmosphere?


title: How does this Stirling engine work?

text: I'm looking at this Stirling engine, which I believe is a variation of an alpha type. It was developed by Nasa back in the 1980's. The thing is, I can't figure out how the hydrogen cycles through the pistons. Could someone help me? This is another link that might help you understand what it looks like if you scroll down about 3 quarters. There are several pictures on this page. I've tried making sense of it but I don't understand how the heated hydrogen cycles.