Does the rotation of the earth dramatically affect airplane flight time?

Say I'm flying from Sydney, to Los Angeles (S2LA), back to Sydney (LA2S). During S2LA, travelling with the rotation of the earth, would the flight time be longer than LA2S on account of Los Angeles turning/moving away from our position? Or, in the opposite direction, would the flight to Sydney be faster since the Earth turns underneath us and moves Sydney closer? ===   * Please ignore jet stream effects and all other variables; this is a control case in an ideal environment.   * By "dramatically" I suppose I mean a delay of 1 hour or more.


Flight time Toronto to Moscow the same

I have a question. How come that the flight from Toronto to Moscow takes the same time as the flight from Moscow to Toronto. Should it take much longer because of the earth rotation? One direction we travel in direction or an orbit and traveling back we are going against the Earth orbit... From Toronto 9hours From Moscow 9:45 hours. If flying from Moscow we are traveling against the Earth rotation so we should add half of the travel to our current travel. It means that the travel from Moscow should take about 13 hours... Thanks,


Can a hovering helicopter travel half the globe in 12 hours?

Suppose we have a helicopter that is able to stay stationary in flight for extended periods of time. If such a helicopter stayed at point A in the sky for 12 hours straight, would it reach the other side of the globe?


Relation between Earth's rotation-gravity and moving object on Earth

This might be silly question. It's about the rotation of the Earth and the objects moving on it. If I jump into the air, why did I also move with the Earth though I am in the air? I am supposed to be land in backward/forward location, as it keeps rotating. But this doesn't happen. What is this phenomenon called?


How come the atmosphere moves with Earth?

now, I have read a lot of explanations on that but still can't really understand why it would happen so if you can give some examples for a such a thing happening. I mean lets say gravity attracts the air and due to air viscosity all of the air gets carried with the Earth but why will the speed be same ?


If I jump will I land in the same spot?

If I were to jump one meter in the air and hang for one second, would I fall back down in the same spot or would the earth rotate ever so slightly under me, causing me to land a short distance away from my original point of departure? I am conflicted on this. If I look at the equation for angular velocity, I see that $w = v/r$ where $w$ is the angular velocity, $v$ is the linear velocity, and $r$ is the radius of the object I am on (in this case the Earth). There is another version of this stating that $w$ = $2\pi/t_{rev}$ where $t_{rev}$ is the time it takes to complete one revolution. Being on the Earth, I have a certain linear velocity, $v_{G}$. When I jump in the air 1 meter, I am not applying any force except for vertically so I do not believe my linear velocity would change. However, I am increasing the distance I am from the center of the earth so now my angular velocity would be $w_{A} = v_{G}/(r+1)$. Therefore, it seems that my angular velocity in the air ($w_{A})$ would be slightly less than my angular velocity on the ground ($w_{G}$). If I were to recalculate the linear velocity given this discrepancy in $w$, I would get $v_{G}=w_{G}r$ and $v_{A}=w_{A}r$. This shows I get a small difference unless the radius in $v_{A}$ must account for the jump ($r+1$), in which case I end up with $v_{A} = v_{G}$. I've gone around in circles trying to decide if one would actually move. This top answer seems to think you would: Earth moves how much under my feet when I jump? Any insight would be appreciated. Thank you!


Earth moves how much under my feet when I jump?

If I'm standing at the equator, jump, and land 1 second later, the Earth does NOT move 1000mph (or .28 miles per second) relative to me, since my velocity while jumping is also 1000mph. However, the Earth is moving in a circle (albeit a very large one), while I, while jumping, am moving in a straight line. How much do I move relative to my starting point because of this? I realize it will be a miniscule amount, and not noticeable in practise, but I'd be interested in the theoretical answer.


Earth is rotating

> **Possible Duplicate:**   >  Why does the atmosphere rotate along with the earth? If i take off from land on a helicopter straight above the earth surface to a certain height and stay there for few mins/hours and come down. Why am i coming down to the same place where i took off? If the earth is rotating i should land on a different place right because i have not moved i am just coming down straight.I moved only vertically. I got this thought because i was thinking why are we spending so many hours on flights to reach a country on west if i started from a eastern country. May be there are a lot of scientific reasons behind this which i am not aware excuse me if it sounds silly.I thought this would be the best place to ask.


Sideways motion between a vertical launch from a planet and landing

I saw a video some days ago (Hello Kitty in Space) of a schoolgirl successfully launching a balloon into space which later popped and landed ~47 km from launch site. If I vertically launch an object (say via balloon or rotors) from the surface of a spinning planet with an atmosphere like ours, then as it rises, will the planet's surface move away below it, or will the object rotate with the earth? (Assume that there are no local strong winds relative to the atmosphere, and it is completely calm.) The latter would mean the atmosphere, being itself a collection of such objects (air molecules), also spins with the planet. Related SE question: Why does the atmosphere rotate along with the earth? It seems from common sense that since at launch the object shares the motion of the surface it would keep rotating with the planet, and hence would later land at the launch site. However, as it ascends, the lateral speed required to maintain the same angular velocity with the planet rises linearly. Where would it get this extra momentum/energy from? From the rotating atmosphere? How did the atmosphere get moving in the first place then? It might seem a lot of questions for a single SE post, but they're all connected, so a single explanatory answer should suffice.


Does the ground beneath a levitating object change due to the rotation of the earth?

I don't know whether this question pertains to physics. But anyways, here goes... If I were to hover 1m above the ground in a helicopter, would the ground below me change after 1 hr due to the rotation of the earth?


Would Oscars made of pure gold bend?

Since gold is often considered "soft": If the Oscars were made of pure gold (instead of gold-plated britannium), would they bend (deform) over time?


Stacking gold Bars

I once heard that because gold is so malleable, while also being very heavy; that if one were to stack several layers of bars on top of on another (like is so familiarly depicted in movies & TV), the shape of the ones on the bottom would be smushed down because of the weight of the ones on top and gold's high malleability. Is there any truth to this?


How can I estimate the power between the guide and the sky diver?

I would like to estimate the Maximum power/ tension that can be, between the sky diving guider and the "tourist". In this picture what the max tenstion will be, I think it is maximum when the parachute is opened.


Tension in parallel springs

> _A block of mass $200$kg is connected to a horizontal ceiling by four > identical light elastic ropes, each having natural length $7$m and stiffness > $180$N/m. It is also connected to the floor by a single light elastic rope > having stiffness $80$N/m. All five ropes are stretched and vertical, and air > resistance is neglected._ > > _Find the tension in one of the upper ropes._ I know it's just $kx$, but I don't understand why it is not $\frac{kx}{4}$ because tension is shared between four ropes.


Magnitude of force to keep stick in equilibrium

**Problem statement** A straight and homogenous stick with mass m is pressed against a wall with the force F. The stick is horizontal perpendicular against the wall. Given that the friction between the wall and the stick is μ, determine the horizontal component of F in order for the stick to not fall down. **My thoughts** Forces involved: We have: The gravitational force **mg** in the negative y-direction. The normal force from the wall, **N** (negative x-dreiction). The friction force in the positive y-direction which is **f=μN** and the force **F** which acts in the positive x-direction. Thus: $$\sum F_{x}: F-N=0 \Rightarrow F=N \\\ \sum F_{y}: mg-f=mg-\mu N=0 \Rightarrow N=F=\frac{mg}{\mu }$$ $$\boxed{F=\frac{mg}{\mu}}$$ ![picture](http://i.imgur.com/QFJq7wT.png) * _Correct answer is $\boxed{F=\frac{mg}{2\mu}}$ *_


Is there an equation that tells you more about the amplitude of an object which is in resonance?

I'm a high school senior and I have to write a paper about resonance and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly explained. Could anyone explain whether there is an equation to describe the amplitude and if so, whether you could explain to me how you can obtain this formula?


Understanding the Seebeck effect

Thermoelectricity is, as I understand it, the difference in voltage between the hot and cold ends of two dissimilar materials. If two materials are connected at two different junctions, the hot junction will effectively liberate electrons which will flow to the cold junction, along with the heat. All the diagrams of this I could find showed exactly two materials, connected at both the hot and cold ends. In order to have the hot side remain hot, and the cold remain cold, while transmitting the electricity, ideally a substance is desired that conducts electricity well, but heat poorly. This is the measure of quality. A good overview paper is: New Directions for Low- Dimensional Thermoelectric Materials by Dresselhaus et al. "ZT= S2rT/j, where S, r, T, and j are, respectively, the Seebeck coefficient, electrical conductivity, temperature, and thermal conductivity" Maximizing efficiency of a thermocouple is, in fact, a matter of finding materials that conduct heat poorly, while conducting electricity well. In practice, that's difficult, so in constructing nanomaterials to do so, they are trying to scatter phonons while not scattering electrons. Questions:   1. How do you make a series circuit with lots of thermocouples? Surely this must be done, yet when I draw a diagram, I can't come up with a way that doesn't look like two identical thermocouples are simply operating in opposing directions. This is answered below (and thanks), but note the answerer is incorrect about the need for thermal conductivity. Ideally, you want to insulate these things, and have as little heat as possible produce as much electricity as possible.   2. In the diagram drawn by the answer, it shows a thermopile as a zig-zag connection of two materials between hot and cold. This makes perfect sense now that I see it, but then, does material A transport electrons from hot to cold, while material B transports them from cold to hot? I thought I intuitively understood the Seebeck effect as a liberation of electrons from the hot end, effectively by "shaking them loose" but it appears one material must be doing the reverse? I'm guessing this is similar to galvanic action, where one material wants an electron to complete a valence shell, and the other wants to give one away?   3. I have now drawn a diagram showing a single thermocouple, a thermopile per the answer below, and my question, which is whether you can introduce a third material connecting the other two. I'm guessing you can, and that whatever its electropotential, since it's symmetric it should have no effect on the voltage of the thermopile other than its resistance. ![diagrams of thermopiles](http://i.stack.imgur.com/W714r.png)


Adiabatic Expansion with expanding control volume

I have a tube with a length "L" and diameter "d" that is open on 1 side . At a certain point ( say "x" ) from the closed end of the tube, I have a gas with a high pressure. At this point, "x", there is also a weight of mass "m". It is also known what the velocity of the weight is at point "L". Initially : ![initial](http://i.imgur.com/DPXFndD.png) Finally : ![final](http://i.imgur.com/xu5Qmmr.png) Assuming that the tube is held stationary, what force is imparted on the closed section of tubing ( left side )? Basically, think of it as a rifle barrel with a bullet inside. I wish to find a expression for the force on the closed end of the tube as it varies with time. What I propose : Determine the Work by the gas. And since work is defined as $W = Fx $ and then $ \frac{dW}{dt} = \frac{d(Fx)}{dt}$ perhaps this could lead to an expression for force?


Size of an elementary particle

Do we have a well defined mathematical expression denoting the size of a fundamental particle with no internal structure (electron for example) ? If we do, how does it fit in with the uncertainty principle ? And if we don't then what exactly do the experiments reveal claiming radius of electron is of the order $10^{-18} m$ or something like that ? Also in this particular case, does this mean that the probability of the electron being within that radius is 1 and zero outside ? A proper clarification would be very helpful.


Is the Higgs a quantum field or a particle?

The Higgs is not detected in the asymptotic data, so it is possible that there is no particle interpretation for the Higgs quantum field. Indeed, the Higgs potential is only positive definite if the quartic term is included --- the quadratic term corresponds to a negative mass term. It would seem, therefore, that the Higgs field does not have an on-shell mass spectrum, so that there is no straightforward particle interpretation. One can say that there is an effective field theory in which there is a resonance near a given mass that we will call the Higgs _resonance_ , but in the absence of a pure mass shell spectrum (that is, if there is a continuous mass spectrum), it is generally taken in QFT that there is no particle interpretation. The resonance is clearly not a $\delta$-function, so is there some other precise way in which we can call the Higgs a particle? Of course this doesn't call into question the empirical effectiveness of the Standard Model of Particle Physics, it only asks about its interpretation and about how we put the Mathematics into words. I was somewhat struck by Rolf Heuer's observation (this morning) that this is the first observation of a scalar particle. Indeed, according to the SM, there are no quantum fields that have non-zero mass terms in the absence of interactions. In the absence of interactions, the Higgs field is a massless scalar field. Should we say that it is the Higgs _interaction_ that gives mass to the standard model? (EDIT: Is it better to say that every term that is not quadratic in the fields _contributes_ towards the effective masses of each of the asymptotically observed fields? Or what alternative phrasing is closer to the Mathematics of the interacting fields?) EDIT(2, $\scriptstyle\mathsf{see\ below\ for\ the\ comment\ that\ prompted\ this\ possible\ rephrasing}$): Is there any part of the definition of "particle" that is not a matter of convention? Does the Higgs cross that bar?


What is the difference between pole and running mass?

For example, when we meassure Higgs boson mass to be 125 GeV, do we think about renormalized or pole mass? Should the mass of the Higgs change if it is produced at higher energies?


Is the force carrier of the magnetism in a common household magnet a photon?

As I have understood it, the Standard Model includes particles that carry the different forces, e.g. the electromagnetic (EM) force, the gravitational (G) force. When talking about EM fields such as visible light or microwaves, the associated particle is said to be the photon. But what about a static EM field without any electricity, like a common household magnet? How does that magnet communicate its force? Via photons?


Why does frozen water burst a pipe?

When water freezes in a pipe it can crack the pipe open. I assume this takes quite a lot of energy as when I try to crack a pipe it can be hard work! I think water freezing is a result of energy (heat) being lost from the water and out of the pipe into the freezing environment around it. So what energy is cracking the pipe and how? When warm and not frozen there is more energy in the pipe than when frozen? My secondary question might be - is this a particular phenomenon of water or would other matter crack open a pipe when it freezes solid from liquid? Andrew


Loop-the-loop question

> Problem: The marble rolls down the track and around a loop-the-loop of > radius R. The marble has mass $m$ and radius $r$. What minimum height $h$ > must the track have for the marble to make it around the loop-the-loop > without falling off?   >  Express your answer in terms of the variables $R$ and $r$. I found this solution to be very reasonable: $$mg = m a_c = m \frac{V^2}R $$ which leads to $$V = \sqrt{g R} $$ The energy at the top of the loop KE = Delta PE $$\frac12 m V^2 + m g (2R) = m g h \\\ \frac12 (g R) + g (2R) = g h \\\ \left(\frac12+2\right) R = h $$ so $h = 5/2 R $ However the correct answer is actually $\frac52(R-r)$, I think it's because the radius of the loop is measured from the center of the ball rolling on it, so the they subtracted $R$ from $r$, but how would you derive that? I tried the same steps just using $R-r$ instead of $R$ but I got a different answer.


Practical example of stabilizer codes

Given the Steane code $$ \left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + \left|0001111\right\rangle + \left|1011010\right\rangle + \left|0111100\right\rangle + \left|1101001\right\rangle) $$ $$ \left|1\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|1111111\right\rangle + \left|0101010\right\rangle + \left|1001100\right\rangle + \left|0011001\right\rangle + \left|1110000\right\rangle + \left|0100101\right\rangle + \left|1000011\right\rangle + \left|0010110\right\rangle) $$ and its relative stabilizers: $$ K^1 = IIIXXXX $$ $$ K^2 = XIXIXIX $$ $$ K^3 = IXXIIXX $$ $$ K^4 = IIIZZZZ $$ $$ K^5 = ZIZIZIZ $$ $$ K^6 = IZZIIZZ $$ The stabilizer set establishes valid codewords for a state if the equation $$s\left|\psi\right\rangle=\left|\psi\right\rangle,\;\;\;\forall s \in S \;\;\;\;\; (1)$$ is satisfied. That means $\left|\psi\right\rangle$ is a +1 eigenstate of $s$. We then consider a practical example of the usage of these stabilizers ![enter image description here](http://i.stack.imgur.com/kg9F6.png) The state of the system is represented by: $$\left|\psi\right\rangle_F={1\over 2}(\left|\psi\right\rangle_I+U\left|\psi\right\rangle_I)\left|0\right\rangle + {1\over 2}(\left|\psi\right\rangle_I-U\left|\psi\right\rangle_I)\left|1\right\rangle$$ where $U \in \left\lbrace K^1,K^2,K^3\right\rbrace$. We apply $U$ to the input state and we measure the ancilla qubits (syndrome measurement) to verify the integrity of the input (if $\left|\psi\right\rangle_I$ is +1 eigenstate of $K^1,K^2,K^3$). If the equation $(1)$ is not satisfied, then the corrupted qubit is corrected with a $Z$ gate addressed by the syndrome measurement. This is how does the system work?


How long does it take for a black hole to form?

The well-known fable of an astronaut sending signals out to an external observer while falling toward an event horizon states that the time lapse between such signals becomes greater even if in the astronaut sends them out periodically (as judged in his inertial frame). When viewed from earth and weighing time-dilation due to the gravitational field of the collapsing star, how is it possible that a black hole can form in finite time (for any external observer) if it takes an infinite amount of time to "see" events occurring at the event horizon?


What is the direction of static friction?

**Note** : My question is duplicate of the following   1. Direction of friction when a car turns   2. Why does friction cause a car to turn? * * * I've gone through many related questions especially the first. As I understand the static friction is always opposite to the force applied on the object as shown:   ![image](http://www.school-for-champions.com/science/images/friction- slide_kinetic.gif)   But in the case when front wheels of a vehichal are turned the force of static friction is not opposite to the applied force. For example consider a car accelerating forward. The net force on the car is in forward direction which is provided from the rear tyres, if eventually break is pressed static friction(assuming tyres aren't skidding) comes into picture. This friction **should be and is** opposite in direction to the direction of force applied by the rear tyres. When the front tyres are turned the direction of static friction is changed(radially inward) means the direction of static friction is not opposite to the direction of applied force as shown:   ![image 2](http://img.gawkerassets.com/img/18zoykoy35nhfpng/ku-xlarge.png) **Question:** Is the force of static friction is always opposite to the applied force ? If not then what determines its direction?


Magnetic Shielding?

Can magnetic fields be "blocked"? For example, in the game, TitanFall, a robot stop bullets with ( presumably ) a magnetic shield. I wish to calculate the magnetic force required to stop a bullet within a few microseconds. But the problem I have is that my entire electronic system or the vehicle ( most likely even a building ) will be subjected to massive fields most likely destroying it as well. Does any know of a way to "block" or divert the field around my vehicle? Is it even possible? My knowledge in magnetic fields are quite limited at this time.


Can a light be bent by a magnetic field?

I'm struck with two competing ideas on the question in the title. Listing #1: http://van.physics.illinois.edu/qa/listing.php?id=2009 Q: "How far can a magnetic field bend light?" A: "Unfortunately, the path light takes is not affected by the presence of a magnetic field. Light itself is composed of an oscillating electric and magnetic field, and one very important property of electric and magnetic fields is what we call "linearity." That is, if you have two sources of electric and/or magnetic fields, you can predict what the combined field is just by adding the two source fields together. The two fields don’t change each other at all. " Listing #2(Answer #1): Does electric charge affect space time fabric? Q: "Does electric charge affect the space time fabric? If so, why?" A: [See link. Rather, see both links if you must.] I'm more inclined to consider the latter question and answer as the correct interpretation. Anyway, if anyone could help me out with this conceptualization that would be great, thanks.


Aharonov-Bohm Effect in Torus

I had a very brief introduction to the Aharonov-Bohm effect in class. The lecturer introduced the notion that $H(\Phi=\Phi_0)$ and $H(\Phi=0)$ gives identical energy spectrum and that the Hamiltonians are related by a the large gauge unitary transformation. I did a quick Google on the large gauge transformation, but I did not quite understand much about it aside from the fact that it is a topological related gauge transformation. Can someone explain a bit more about what that gauge is about and how it is performed? Also, in a many-body system with the following Hamiltonian (1), in a 3D Torus with flux, $\Phi$ piercing through the hole on the torus, how do show that the energy eigenvalues of $H(\Phi=\Phi_0)$ and $H(\Phi=0)$ are indeed identical? $\Phi_0 = \frac{h}{e}$ in this case. $$H(\Phi) = \Sigma_{j} \frac{1}{2M}\biggl(\vec{p_j}+e\frac{\Phi}{L}\hat{x}\biggr)^2 +\Sigma_j \ U(\vec{r_j}) + \Sigma_{j<k} \ V\Bigl(\vec{r_j}-\vec{r_k}\Bigr)\tag{1}$$ The general idea of how I will go about solving this is by perhaps acting the hamiltonian on a wavefunction to determine the energy eigenvalue though I am not sure how to do it explicitly.


What telescope would I need to observe Mars's polar caps?

What telescope refractor aperture size would I need to observe Mars's polar caps? I have a Levenuhk Strike NG 80mm, and I can see red disk of planet but cannot see any details on the surface.


Can a wave propagate in any substance? Aren't there any prerequisites?

We see waves propagate in air, water, through the cristal of a metal and along a rope. Isn't a wave a wonder of Nature, or is it just a simple phenomenon? Are homogeneity and isotropy necessary properties for the correct propagation of waves? Update are a rope, water and space/EM field elastic in the same way?


Why don't FCC metals have a brittle-to-ductile temperature transition?

I initially thought that it had something to do with the number of slip systems in FCC vs. BCC, but they're both the same.


Is Brownian motion a deterministic system? I.e the motion of all particles are completely determined or is there an innate indeterminism like quantum systems?


Is the Sun-set and the Sun-rise Symmetrical for the Observer?

Is there the effect of sun rising and sun setting, in terms of Rayleigh scattering and visual spectrum and other factors completely similar and symmetric? I mean can one recognise them from a picture taken from the sky?


Differential equation for evolution of probability density in Quantum Mechanics?

I have come up with this differential equation for the evolution of $\vert \Psi \vert^2$, the probability density in quantum mechanics. Is there a name for this equation? Is the logic sound? So I start from the conservation of the total probability: $$ \frac{d}{dt} \int _{all space} \vert \Psi \vert^2 d^3\textbf{r} = 0$$ so that $$\int _{all space} \vert \Psi \vert^2 d^3\textbf{r} = {\rm const}$$ This means that $$\int _{all space} \vert \Psi (\textbf{r},t) \vert^2 d^3\textbf{r} = \int _{all space} \vert \Psi (\textbf{r}+d\textbf{r},t+dt) \vert^2 d^3\textbf{r}={\rm same\,const}$$ So since the integration is over the same volume I can equate the intergrands? This gives us: $$\vert \Psi (\textbf{r},t) \vert^2 = \vert \Psi (\textbf{r}+d\textbf{r},t+dt) \vert^2$$ or $$\Phi (\textbf{r},t) = \Phi (\textbf{r}+d\textbf{r},t+dt) $$ if we call $\vert \Psi (\textbf{r},t) \vert^2 = \Phi (\textbf{r},t)$. A Taylor expansion to first order gives us: $$ \Phi (\textbf{r}+d\textbf{r},t+dt) =\Phi (\textbf{r},t) + \nabla\Phi\cdot d\textbf{r}+\frac{\partial \Phi}{\partial t} dt$$ Plugging this into the previous equation gives us: $$\boxed{ \nabla\vert \Psi \vert^2\cdot \frac{d\textbf{r}}{dt} = -\frac{\partial \vert \Psi \vert^2}{\partial t} }$$ What is $\frac{d\textbf{r}}{dt} $ in the context of quantum mechanics? Is this equation correct? What is the physical meaning of this equation?


How does the gravity of a massive non-spherical object act on things around it?

Firstly, not sure if this question ought to be in the space SE site. Please let me know if it should. (Posted in both for now) Secondly, I don't know a whole lot about physics (I'm just inquisitive). So please try to keep answers simple (or at least dummed down to laymans terms). Inspired by "A Hitchhikers Guide to the Galaxy" movie (haven't read the book yet) My question is, for a non-spherical object (lets say a cube for now) of a size and mass like that of Earth, how would objects act in it's gravity? Aspects of this question lead to the following questions •Would something weigh more/less in certain areas over other areas? •I'm aware that it's possible to 'slingshot' around massive spherical objects to change their directory. Would it be possible to slingshot objects around something non-spherical to change their velocity? •If this massive object was orbiting our sun, would it's orbit be as uniform as ours? if not what would that look like and why?


Pipe in a flowing river problem

I'm working on a certain problem in fluid mechanics, which isn't really my strongest area. The problem is as follows: Curved pipe is partially submerged in a flowing river so that one end is pointing in the same direction as the velocity of river. Level of water inside of the pipe is 7cm higher than the level of river. Determine the speed of river. Basically what I argued is that this reduces to Torricelli's law: level of water in pipe is constant so the velocity of the surface is zero (or very nearly so, I assume it would oscillate in real life), therefore water should move on the other end with $v_{2}=\sqrt{2gH}$, but it isn't since $v_{2}=v_{river}$ counteracts the movement. I've tried to be more rigorous so I took pressures at the submerged end of pipe: $$p_{\text{water in pipe}}=p_{\text{atmosphere}}+\rho g h_{\text{depth}} + \rho g H_{\text{above water}}$$ $$p_{\text{river}}=p_{\text{atmosphere}}+\rho g h_{\text{depth}} + \frac{1}{2} \rho v^{2}$$ Since they have to be in equilibrium, pressures are equal and you get Torricelli's expression above. Is my reasoning correct? It's somewhat counter-intuitive to me because the water is moving _away_ from the pipe.


Can the phrase "Terminal Velocity" be used to describe non-gravity situations?

According to Wikipedia: > [Terminal Velocity] is the velocity of the object when the sum of the drag > force (Fd) and buoyancy equals the downward force of gravity (FG) acting on > the object. Since the net force on the object is zero, the object has zero > acceleration. I was wondering if this can be more generalized. Assume that we replace the force of gravity with another type of force (for example, the force of a theoretical engine on a rocket whose fuel never loses mass). In this case, the force is not one of gravity (along the y-axis) but of the engine (along the x-axis). However, drag would still play a part in causing the acceleration due to the rocket's engine to reach 0. As far as I'm concerned, these concepts are the same, but whenever one talks about "Terminal Velocity" they always discuss it in context of gravity. Can the term "Terminal Velocity" be used in the "rocket" case as described above, where the force is NOT that of gravity?


Measuring position and momentum at the same time?

In a non-relativistic quantum mechanical system in an infinite potential well. I try to measure the energy and the position of the system simultaneously. Since, the respective operators do commute according to Heisenberg's uncertainty relation I should be able to measure them both with infinite precision. Now, since I know that there is no potential energy in the well I can use $ E=\frac{p^2}{2m} $ since the potential energy is 0 and determine it's momentum provided I know it's mass. But I shouldn't be able know the momentum and position simultaneously with infinite precision! So where am I going wrong?


Exhaustive list of assumptions for the Clauser-Horne-Shimony-Holt inequality

I am trying to create an exhaustive list of all assumptions which work as the base of the CHSH inequality.   1. Locality - this means an object can be influenced only by its surroundings. So, the events taken place at Alice and Bob's ends cannot influence each other.   2. Realism - the value of the observed quantity is independent of observation.   3. The quantity being observed is a discrete random variable.   4. Repeated rounds of experiments are independent of each other and evenly distributed.   5. A measurement will always produce a result (a photon will always be detected).   6. No enhancement assumption - it means when a measuring setup is placed between the source of the entangled particle and a detector the probability of measurement doesn't increase. Am I missing anything?


Loss of kinetic energy in inelastic collision

I know that momentum and energy are always conserved in collisions, but if we have a perfectly inelastic collision in which an object sticks to another object $m_1 v_1 + m_2 v_2 = (m_1+m_2)v_{12}$, the kinetic energy is not conserved. I know that kinetic energy converts into thermal or sound energy, but I don't see how this would account for the whole of the lost kinetic energy. Does the kinetic energy transform into some sort of potential energy between the bonding of the two objects? For example, if the two objects stick together with a small magnet (assuming the initial attraction between the objects is negligible) does the kinetic energy transfer to some sort of magnetic potential?


Detailed balance formulation in solar cells?

Hello I wanted to know where does the integral of following picture come from and what are the alternatives in it? How and where can i find information i need to know to understand this text?   thank you in advance! ![Detailed balance formulation](http://i.stack.imgur.com/LBBlE.png)


How to show $ \epsilon_{iab}\epsilon_{jcd}(x_ap_d\lbrace x_c,p_b \rbrace+x_cp_b\lbrace x_a,p_d \rbrace) = x_ip_j-x_jp_i$

If $ \lbrace f,g \rbrace $ is Poisson bracket and $\epsilon_{ijk}$ is Levi- Civita symbol, how to show that $$ \epsilon_{iab}\epsilon_{jcd}(x_ap_d\lbrace x_c,p_b \rbrace+x_cp_b\lbrace x_a,p_d \rbrace) = x_ip_j-x_jp_i$$ where $x_i$ are generalized coordinates and $p_i$ are momentums ?


Introduction and overview of Condensed Matter Physics

Is there any book that provides an overview of Condensed Matter Physics? I have had a course in QM and statistical physics and some. I dont know anything about this field, so is there a readable introduction to this large field? One that provides an overview, instead of too much detail? Edit: I am looking for something of a lower level than this Phys.SE question. Can we reopen?


Supplements for Kittel's Solid State Physics?

I think by supplement I really mean replace. I spent a lot of time agonizing over the first chapter of Kittel as he introduces a bunch of concepts such as Bravais lattice and he doesn't clearly define them. It's frustrating and infuriating considering that I have no background in crystallography nor solid state physics, and as an introduction to the subject I haven't found the book to be very helpful.


> **Possible Duplicate:**   >  Books for Condensed Matter Physics Could someone introduce books or reviews on electron-electron interaction to me? Especially its effects on screening and transport?


Doesn't the use of a thermometer alter the temperature of the system?

If I place a mercury thermometer in hot water, heat energy will transfer from the water to the mercury inside the thermometer. Will this continue until thermal equilibrium is reached and thus the mercury will show the temperature of the water? However, if this is so, will the thermometer show the right temperature as some of the heat energy is transferred to the thermometer and this in turn will cause original temperature of water to fall? Please correct me if I am wrong.


Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles?

As Weinberg exposited in his QFT Vol1, there are two equivalent ways of arriving at the same quantum field theories: **(1).** Start with single-particle representations of Poincare group, and then make a multiparticle theory out of it, while preserving principles of causality etc. I would call this approach the second quantization of particles, since second quantization is usually used to emphasize the many- body nature of a theory. **(2).** Start with field representations of Poincare group, canonically quantize it, while preserving principles of causality, positive definiteness of energies etc. I would call this approach the quantization of fields, just as everyone else would call it. Weinberg showed the proof of the equivalence between the above two approaches using some, though not hard, but let's say nontrivial, mathematics. The equivalence seems like a sheer miracle to me, or a complete coincidence. I do not feel that I understand the equivalence with the current state of mind. Is there a way to trivialize the equivalence? Or putting it another way, is there an a priori reasoning to argue, given the two sets of starting points of (1)(2), we have to get the same theory in the end? Just as a side remark, many have suggested the term "second quantization" should be totally dumped, because it is really just the first quantization of fields. To me however, it still serves some purposes since the equivalence is not transparent.


Horizontal magnetic attraction?

I came across and interesting effect today, I have a dozen of Neodymium magnets around my house. And, they are very strong. Anyhow, one of them got attracted to my large steel plate table(use for cutting and building). It was almost impossible to take it apart, till I contacted the manufactured of those magnets and they proposed to slid it off. Amazingly, it worked. But what shocked me is the level of huge force decrease. It's like I'm going against friction alone... Only at the edge of the plate I felt a force that is strong, but half way through... The magnet as almost "off" only the edge of the magnet was attracted strongly to the edge of the plate, what explains this?


Did the universe always have 4 space time dimensions?

Is the dimensionality of spacetime in all usual models constant?


What is the universality class of transition in one-dimensional XXZ Heisenberg at $\Delta$ = -1?

In the one-dimensional spin-$\frac12$ XXZ Heisenberg model, $$H=J\sum_i{S_i^x S_{i+1}^x + S_i^y S_{i+1}^y+\Delta S_i^z S_{i+1}^z},$$ with $J>0$. There are two transition points:   * $\Delta=1$   * $\Delta=-1$ The transition at $\Delta=1$ is of BKT type. What about the transition at $\Delta=-1$? Could anyone provide some reference?


How are the angles equal?

At the back of my mind I know they should be equal, but mathematically, how are the two $\Delta \phi$ angles equal? ![Angles Image](http://i.stack.imgur.com/qIxBs.png) The only explanation present in the text is that, "both velocities are perpendicular to the radii vectors," but I don't see how that makes them equal. Also how will you make those two triangles in the 2 diagrams similar? Any images to support the explanation would be appreciated.


The lab have a constant electric field and a constant magnetic field, what is the electric and magnetic field inside a conductor and far from it

The following is an old question from an exam in a Physics $2$ course I am taking, I have tried to solve the question and after I thought I got the answer I looked at the solution and saw it isn't correct. The solution explains what the answer is, but doesn't really explains the facts used. > In the lab frame there is an electric field $E=E_{y}$ and a magnetic field > $B_{z}=\beta E$. > > We place a cube made of a conducting material, point $a$ is at the center of > the cube while point $b$ is far from it. > > Calculate the following: $$ E_{y}(a),E_{y}(b),B_{z}(a),B_{z}(b) $$ and $$ > E'_{y}(a),E'_{y}(b),B'_{z}(a),B'_{z}(b) $$ as they are seen in a frame of > reference moving at a speed $c\beta\hat{x}$. **My efforts:** I wrote that $$ E_{y}(a)=E_{y}(b)=E_{y}=E $$ because the electric field is constant (in the lab frame). Similarly, I wrote that $$ B_{y}(a)=B_{y}(b)=B_{z}=B $$ because the magnetic field is constant (in the lab frame). Then I used field transformation $$ E'_{\perp}=\gamma(E_{\perp}+\beta\times B) $$ $$ B'_{\perp}=\gamma(B_{\perp}+-\beta\times E) $$ to calculate the other four values requested. I then looked at the solution, the solution claims that $$ E_{y}(a)=0,\, E_{y}(b)=E $$ $$ B_{z}(a)=\beta E,\, B_{z}(b)=\beta E $$ and the other field were calculated using the above transformations. I then remembered that in a conductor the electric field is $0$, this explains why $E_{y}(a)=0$. I don't understand this situation completely, Please help me understand it by answering the following questions (that goes a bit beyond the question, but I find interesting and am having difficulties answering myself): > 1) Why does $b$ have to be far from the conductor so we can say that the > electric is $E$ there ? what happens near the conductor ? (I wonder if we > can say something about the charge distribution on it boundary, $\sigma$) > > 2) Why does the magnetic field does not change in space, inside or outside > the conductor ? (I know that the electric field does change, at least inside > the conductor, why shouldn't the magnetic field change as well ?) > > 3) What can we say about the work done while moving the conductor in the lab > ?


Can human hand move at a speed rate like this baseball pitch or is it just the speed of ball?

Fastest baseball pitch ever recorded was in 1974 at a speed of 100.9 miles per hour. Does this mean that the pitcher's hand was also traveling at that speed or just the ball? Is it physically possible to move hand/leg at that speed? I'm asking this because basically pitcher's hand was moving 17.7 inches per 10 millisecond which is really a super(unbelievable) speed for human.


Will Randall-Sundrum extra dimension scenario become defunct if not supported by LHC?

The Randall-Sundrum extra dimension scenario had been one of the most extensively studied class of theories. This offered a solution to the hierarchy problem. However, if this picture is not supported by the LHC, will it become completely defunct? What about theories like little higgs, composite higgs, technicolor, higgsless models (perhaps already practically abandoned?)?


On motivation for the definition of ADM mass

The **ADM mass** is expressed in terms of the initial data as a surface integral over a surface $S$ at spatial infinity: $$M:=-\frac{1}{8\pi}\lim_{r\to \infty}\int_S(k-k_0)\sqrt{\sigma}dS$$ where $\sigma_{ij}$ is the induced metric on $S$, $k=\sigma^{ij}k_{ij}$ is the trace of the extrinsic curvature of $S$ embedded in $\Sigma$ ($\Sigma$ is a hypersurface in spacetime containing $S$). and $k_0$ is the trace of extrinsic curvature of $S$ embedded in flat space. Can someone explain to me why ADM mass is defined so. Why is integral of difference of traces of extrinsic curvatures important?


Conservation law of energy and Big Bang?

Did the law of conservation of energy apply to the earliest moments of the Big Bang? If so, what theoretical physics supports this? I hear that Einstein's theory of relativity disputes the law of conservation of energy- so does that mean the law is false, or only some aspect of it?


Dark energy and conservation of energy

With accelerated expansion of universe which is same in all direction we know that dark energy increase with time because space between any two point in space time increases with time. So after some finite time we can not see nearby galaxy cluster which we can see now. So doesn't that violate conservation of energy which says energy neither can created nor can destroyed. Because with expanding universe energy in the form of dark energy increases with time so if we consider whole universe (visible + invisible) as isolated system then energy of whole universe increase means energy is created from nothing. Am I missing something over here?


Is false vacuum bubble nucleation possible in our universe?

Is it possible that a false vacuum bubble to nucleate into our universe rather than a true vacuum one ? If yes,it will expand at speed of light within our spacetime or what ?


Ampere's law on a long wire with varying current density

On a question from my book: > A long straight wire with a circular cross section of radius $R$ carries a > current $I$. Assume the current density is not constant over the cross > section of the wire, but rather varies as $J=\alpha r$ where $\alpha$ is a > constant. Given $I, R$ > > Find $\alpha$ > > Find the magnetic field as a function of r both inside and outside the wire I think it's just the calculus parts confuses me. My attempt: $$J=\alpha r' = \frac{dI}{dA}$$ $$dI = 2 \pi r'^2 dr' \alpha$$ $$I = 2 \pi \alpha \int_0^R r'^2 dr'$$ $$I = 2 \pi R^3 \alpha /3$$ $$\alpha = \frac{3I}{2 \pi R^3}$$ from here you just use ampere's and I believe there's no variance issues? $$\oint \vec{B} \cdot \vec{dl} = \mu_0 I_{in}$$ apply J=I/A $$B 2 \pi r = \mu_0 \alpha r A$$ $$B = \frac{\mu_0 \alpha A}{2 \pi}$$] $$B = \frac{3 \mu_0 I r^2}{2 R^3}$$ Is this right? The units seem to line up so I'm hopeful. Outside the wire is treated as the general uniform wire case I assume and am not too worried about that.


How can you calculate how fast a spinning ring/cylinder will accelerate a mass via gravitomagnetism?

Lets say you have a cylinder of length L, radius R, and mass M. How fast will it accelerate a mass of mass M2 that is entering the "throat" of the cylinder, considering the effects of gravitoelectromagnetism? By Gravitoelectromagnetism, I'm specifically talking about the effect where a spinning body will pull an object through the "throat" of its spin. Also, I'm wondering what the practical limit of this is: considering the strongest known materials, how fast could a cylinder be spun?


Discretization of Hamiltonian using finite difference always justified?

I have this continuum version $$ H_{R}=\int dx\psi^{\dagger}(x)(\frac{p^{2}}{2}+V)\psi(x) $$ with $V$ as constant potential. Is it always justified to go from this to $$ \sum_{i}c_{i}^{ \dagger }\left[c_{i+1}+c_{i-1}-2c_{i}\right] +V \sum_{i}c_{i}^{ \dagger }c_{i} $$ using the finite difference form of the one-dimensional second derivative? Ignore the factor $-1/2 $ and assume lattice constant $a= 1 $ and $\hbar =1 $. Actually I am thinking whether it is justified to use this even when the derivative of eigenfunction is discontinuous at some of the points in real space like for the delta-function barrier. Will that affect the second derivative of the field operators ?


Can relativistic energy transformation be explained by time dilation and E=h f?

Can one explain the relativistic energy transformation formula: $$E = \gamma\ E',$$ where the primed frame has a velocity $v$ relative to the unprimed frame, in terms of relativistic time dilation and the quantum relation $E=h\nu$? I imagine a pair of observers, A and B, initially at rest, each with an identical quantum system with oscillation period $T$. Now A stays at rest whereas B is boosted to velocity $v$. Just as in the "twin paradox" the two observers are no longer identical: B has experienced a boost whereas A has not. Both observers should agree on the fact that B has more energy than A. From A's perspective B has extra kinetic energy by virtue of his velocity $v$. Relativistically A should use the energy transformation formula above. But we should also be able to argue that B has more energy from B's perspective as well. From B's perspective he is stationary and A has velocity $-v$. Therefore, due to relativistic time dilation, B sees A's oscillation period $T$ increased to $\gamma\ T$. Thus B finds that his quantum oscillator will perform a factor of $\gamma\ T/T=\gamma$ more oscillations in the same period as A's quantum system. Thus B sees that the frequency of his quantum system has increased by a factor of $\gamma$ over the frequency of A's system. As we have the quantum relation, $E=h\nu$, this implies that B observes that the energy of his quantum system is a factor of $\gamma$ larger than the energy of A's stationary system. Thus observer B too, using his frame of reference, can confirm that his system has more energy than observer A's system. Is this reasoning correct?


Intuitively Re-Deriving Equations of Mathematical Physics

Using the intuitive interpretation of the Laplacian $\vec{\nabla}^2$ as the difference between the average value of a field in the neighbourhood of a point & the value of the field at that point, one can pretty easily & quickly derive the form of the heat equation, Poisson's equation & the wave equation (as is done in that link if anyone's interested: Davis - Fourier Series & Orthogonal Functions P196). I quite honestly cannot remember those equations, I re-derive them using the intuition that the Laplacian affords me mixed with physical reasoning drawn from the situation (drawn from the field we're using whether it's temperature, concentration, electric potential or displacement). I'm wondering if similar intuition can be used to derive the form of the Helmholtz equation, the Schrodinger equation, the Dirac equation, & really any other nice equation from mathematical physics that people have nice intuition for in their head & wouldn't mind sharing. It doesn't have to be in any way rigorous or even necessarily completely logical so long as you get the right result, though it should really be quick & to the point, thanks.


What exactly are super WIMPs?

I recently got confused (and slightly annoyed by the lack of technical details) when reading a popular article (authored by Jonathan Feng and Mark Trodden) introducing the concept of super WIMPs. The article characterized super WIMPs (without giving more detailed explanations) as follows:   * WIMPs could probably decay to so-called super WIMPs, which would only gravitationally interact with visible matter    * different kinds of super WIMP particles could interact via additional newly postulated weak "dark forces" ( = gauge bosons ?) with each other   * this kind of dark matter particles can probably interact with dark energy ( how? What is dark energy in this particular scenarios suposed to be? )   * the authors vaguely stated the super WIMP models are some kind of extensions of supersymmetric models that lead to the "ordinary" WIMPs From this characterization I really dont get what super WIMPs are suposed to be so my question is: What are the underlying theoretical ideas behind these phenomenological models? Are they derived in some "top down" approach from high energy theories or is some "buttom up" extension of something like the MSSM for example applied ? And I would appreciate a technically more accurate description of the super WIMP particles and their interactions.


Are there books on Regularization and Renormalization in QFT at an Introductory level?

Are there books on Regularization and Renormalization, in the context of quantum field theory at an Introductory level? Could you suggest one? _Added_ : I posted at math.SE the question _Reference request: Introduction to mathematical theory of Regularization_ and accepted this answer by Willie Wong.


Schrödinger evolution for a Klein-Gordon equation

I have a problem with the transition from quantum relativistic wave equations (specifically Klein-Gordon equation) to QFT, since a lot of assumptions seem implicit. For example I have a problem with the time evolution operator, which is crucial on deriving the perturbative expansion $-$ the main tool in QFT I believe. c So here's what I have a problem with: when we make the leap from Schrödinger equation to a Klein-Gordon equation, we get a second order time derivative, and hence loose the simple concepts from nonrelativistic QM like: the Hamiltonian, time evolution operator etc. But for a scalar quantum field we can make a Lagrangian density: $$ \mathcal{L}(x) = \hbar^2 c^2 g^{\mu \nu} \partial_\mu \phi \partial_\nu \phi^* - m^2c^4 \phi \phi^* $$ and perform the "second quantization", from which we get a Hamiltonian, canonical commutation relations and the ability to use pictures (Schrödinger's, Heisenberg's...). So how does this work? Before there was no Hamiltonian in principle, and now there is. Is this the Hamiltonian we pluck into the perturbative expansions' formulas? What changed, when compared to the single solution wave equation in the beginning?


What are the most important discoveries/breakthroughs in physics recently?

Can you provide a list of the most important discoveries/breakthroughs in physics recently? By recent, I mean the past decade or so. All branches of physics are welcome. Basically, I am interested in major physics breakthroughs/discoveries which haven't become well-known yet outside their narrow specialties. Most breakthroughs in the 90s like string dualities and the accelerating universe have already become common knowledge.


Seeing one's back on the event horizon

If we would hypothetically be exactly on the event horizon, we should see our own back, because of the circular motion of photons on the event horizon, right? But what would be the image size, or $-$ asking differently $-$ how far away, would our back seem to be? Would it be magnified or minified, when compared to the image of a person $2 \pi R_{Schwarzschild}$ away?


Magnetic field of a wire with over 1000 amperes?

Does a large thick wire that has over 1000 amperes of current flowing through it generate powerful magnetic fields? What formula is best here to predict $B$?


Calculating the power of a lightbulb

How do I calculate the power of a lightbulb? I have values but I don't know the equation to use.


$p\ dq$ is the "tautological" one-form?

The one-form $$\theta=\sum_i p_i\, \text dq^i$$ is a central object in hamiltonian mechanics. It has a bunch of applications: $\omega=\text d\theta$ is the symplectic structure on phase space, $S=\int\theta$ is the classical action, and so on and so forth. It is associated with the names Liouville one- form, Poincaré one-form, canonical one-form, and symplectic potential, none of which surprises me, but its Wikipedia entry informs me that the preferred[by whom?] name for it is actually "tautological" one-form, on the grounds that 'canonical' (which would be my natural choice) is 'already heavily loaded', and because of the risk of confusion with some algebraic thingammy. This name completely mystifies me. **Why was the name "tautological" chosen for this object?** When, where, and by whom? Or was this name chosen because that's its name?


Velocity after inelastic collision between bullet and block

The following is the problem that I am working on. > A bullet of $.01\: \mathrm{kg}$ is shot into a block of mass $.89\: > \mathrm{kg}$ that is hanging from the ceiling. After the bullet has been > caught in the block, it swings and rises $.40\: \mathrm{m}$ from its initial > height. Find the initial velocity of the bullet. I though that $\frac{1}{2}m{v_0}^2 = (m+M)gh$ would give me the solution $25.6\: \mathrm{m/s}$, but the answer is supposedly $2.5 \times 10^2\: \mathrm{m/s}$. What am I missing ?


Why does light of high frequency appear violet?

When people are asked to match monchromatic violet light with an additive mix of basic colours, they (paradoxically) mix in red. In fact, the CIE 1931 color space chromaticity diagram shows this effect begins at about 510nm (greenish- cyan), where people mix in no red. From that point on, the higher the frequency of the light source, the more red they mix in. This effect is reflected by the red curve of the CIE standard observer color matching functions, which has an additional bump in the area of blue light. However, that curve does not match the actual spectral sensitivity of red cones. So where does this additional perception of red at higher frequencies come from?


Is the color wheel just an optical illusion?

As a kid, I was taught that that blue and yellow make green, yellow and red make orange, and red and blue make purple - forming the subtractive color wheel. As an adolescent I was taught that blue and green make cyan, green and red make yellow, and red and blue make magenta - forming the additive color wheel. Somewhere in that time I was also taught that the colors of the rainbow are ROY G. BIV. That last one is the only one that makes _much_ sense to me in physics because perceivable light is not somehow a cycle, but rather a tiny segment of the EM spectrum. Why do the colors at the top and bottom of the spectrum seem to be mixable? Is there anything in nature that indicates this should be the case? Is this just a psychological or physiological phenomenon?


Why does the visible light spectrum appear to be circular

I'm not sure if this is an acceptable place to ask this question, as it may have more to do with the biological workings of human eyes than with the physical properties of light, but I'd rather hear a physical explanation than a biological one (if one exists). Essentially, we often describe the visible spectrum with a color wheel. In this wheel, Red appears next to Purple (violet), but Red and Violet are at opposite ends of the visible light spectrum. What accounts for this? That is, why do we perceive the Visible Light Spectrum as circular, instead of linear?


Quantum Fourier Transform and Entropy

QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of entanglement can be witnessed via an increase in the entropy of the subsystems. Since all the subsystems witness a positive entropy change ,does the entropy of the complete system also increase (it seems to increase since entropy is additive) ? Now if it does increase , It seems to violate reversible nature of Quantum algorithms. I am very confused.


If light rays obey to the wave equation, why can they be thought as straight lines?

I'm a newbie with physics but I'm wondering how a ray of light can essentially be represented. I have always known that a ray of light proceeds in a straight line until it encounters another object (or material) that refracts/reflects it. But a light ray should be part of an electro-magnetic wave, is this correct? If it is so, it should obey to the wave equation and this doesn't seem to me to describe a straight line ray. I'm having problems visualizing how light is emitted and how it relates with the wave equation. Can someone with a clear understanding of the problem explain it to me in simple terms?


Why and how maximum force is $\frac{dF}{dx}=0$

In an certain question my teacher asked to find the maximum force. She said that the maximum force in electrostatics means $\frac{dF}{dx}=0$. Why is it like that?


Difference between the increase in optical path due to refraction and that due to reflection

If we place two glass plates of refractive index n and each having thickness t,on the way of a light ray the increase in optical path becomes ![enter image description here](http://i.stack.imgur.com/7p0h5.jpg) (S2P-S1P)=2(n-1)t due to refraction through them,and the path difference(or extra path traversed by light) due to reflection at the second surface of one glass plate is ![enter image description here](http://i.stack.imgur.com/NNxzf.gif) 2ntcos(alpha).Without seeing the expression if we look at the phenomenon directly,aren't they basically same? as both are going through a glass media of same length!!


Is spacetime discrete or continuous?

Is the spacetime continuous or discrete? Or better, is the 4-dimensional spacetime of general-relativity discrete or continuous? What if we consider additional dimensions like string theory hypothesizes? Are those compact additional dimensions discrete or continuous? Are there experimental evidences of continuity/discreteness? When particles move inside space do they occupy spacetime by little chunks? What would imply if spacetime is discrete on continuous theories? I've found little information on the web and books. Probably my question is ill-posed and I apologize for this.


The 6-j symbol and intersecting Wilson loops, redux

This is a quite specific question continuing the problems I have with computing the expectation value of intersecting Wilson loops I laid out here. Using the tools from the answer there, I quite quickly arrive at the following expression for the local factor associated to a vertex, where two Wilson loops with reps $\alpha_1$ and $\alpha_2$ meet, and where the four surrounding regions have reps $\beta_1$ to $\beta_4$: $$ G(\alpha_1,\alpha_2,\beta_{1,2,3,4})_{\mu\nu}^{\sigma\rho} := \epsilon_\mu^{ijk}(\alpha_1,\beta_1,\beta_4)\epsilon_\nu^{lmn}(\alpha_2,\beta_1,\beta_2){\epsilon^*}^\sigma_{ijk}(\alpha_1,\beta_2,\beta_3){\epsilon^*}^\rho_{lmn}(\alpha_2,\beta_3,\beta_4)$$ The Greek indices are the indices incurred from decomposing tensor products as $a^i \otimes b^j \otimes b^k = \epsilon_\mu^{ijk}e^\mu$, leading to integral results like $$\int \alpha_i(V_b)^i_{i'} \beta_c(V_b)^j_{j'} \beta_{c'}(V_b)^k_{k'} \mathrm{d} V_b = {\epsilon^*}^\mu_{i'j'k'}\epsilon^{ijk}_\mu$$ (see previous answer). Since the $\epsilon^*$ that has the $\mu$ this is summed with lives on the opposite end of the (part of) the Wilson line, the Greek indices must necessarily remain open at the vertices. I am totally fine with this being the result of the computation, but I am still puzzled why the relation to the 6j symbol is so casually tossed about. Let me first remark that the above equation is already suspiciously similar to the very first equation in the definition of $6j$ symbols, but the free indices are irritating me. If $\epsilon_\mu^{ijk}(\alpha_l,\beta_m,\beta_n)$ is the $3jm$ symbol (with $i,j,k$ playing the role of the $m$ and the reps corresponding to the $j$), what is the additional index $\mu$ doing here? If it is not the $3jm$ symbol (which I am currently thinking), then why would the $G$ defined above be the $6j$ symbol (and why has it free indices)? (If these are neither $3jm$ nor $6j$ symbols, then why do Witten, Ramgoolam, Moore, etc. insist they are?) Note that the $6j$ symbol cannot arise after summing the Greek indices, since the $G$s the second index belongs to are, in general, at other vertices, and so have not exactly the same 6 reps as arguments. Furthermore, the $3jm$ symbols are, if I understand them correctly, essentially the Clebsch-Gordan coefficients for expanding a tensor product of _two_ irreducible reps in a third, and the $\epsilon$ above expand the tensor product of _three_ irreducible reps in all possible fourths (which are then summed over in form of the Greek indices). Something does not add up here, and I heavily suspect it is only in my understanding of the symbols, so I would really appreciate someone clearing up my confusion. **EDIT** : Ok, I think I have found something, but I am still a far shot from solving this riddle, and it requires to think more carefully about the coefficients $\epsilon^{ijk}_\mu$: Let $\alpha,\beta,\gamma$ be reps with basis elements $a^i,b^j,c^k$as before. Then, we can decompose the tensor product stepwise instead of at once as: $$ a^i \otimes b^j \otimes c^k = \sum_{\rho \subset \alpha \otimes \beta} C(\alpha,\beta,\rho)^{ij}_\zeta e(\rho)^\zeta \otimes c^k = \sum_{\rho \subset \alpha \otimes \beta} \sum_{\sigma \subset \rho \otimes \gamma} C(\alpha,\beta,\rho)^{ij}_\zeta C(\rho,\gamma,\sigma)^{\zeta k}_\mu e(\sigma)^\mu$$ (I apologize for the abundance of symbols, but it really becomes clearer what's happening that way.) Here, the $C(j_1,j_2,j_3)$ are now manifestly Clebsch-Gordan coefficients for $j_1,j_2$ in $j_3$, and thus essentially $3jm$ symbols, and the notation $\rho \subset \alpha \otimes \beta$ means that the irreducible rep $\rho$ occurs as a subrep in $\alpha \otimes \beta$. Since Clebsch-Gordan coefficients for reps not appearing in a given tensor product are zero, we can drop the constraint on the sums and sum over all irreducible reps. Thus, $\epsilon^{ijk}_\mu = \sum_\rho C(\alpha,\beta,\rho)^{ij}_\zeta C(\rho,\gamma,\sigma)^{\zeta k}_\mu$. Now, in the integral result above, by the Peter-Weyl theorem (see also previous answer), the $\epsilon$ are only summed over the $\mu$ belonging to trivial subreps of $\alpha \otimes \beta \otimes \gamma$, i.e $\sigma = 0$, if we denote the trivial rep by $0$ in analogy to $j = 0$ in the spin case. Therefore, we have that the result of the integral is $$I := \int \alpha(g)^i_{i'}\beta(g)^j_{j'}\gamma(g)^k_{k'} = \left(\sum_\rho C(\alpha,\beta,\rho)^{ij}_\zeta C(\rho,\gamma,0)^{\zeta k}_\mu C^*(\alpha,\beta,\rho)_{i'j'}^\eta C^*(\rho,\gamma,0)_{\eta k'}^\mu\right) $$ But the trivial irreducible rep has only one dimension, so the sum over the $\mu$ is just the multiplicity $n(\rho,\gamma,0)$ of $0$ in $\rho \otimes \gamma = \bigoplus_\sigma n(\rho,\gamma,\sigma)\sigma$, i.e. $$ I = \sum_\rho n(\rho,\gamma,0)C(\alpha,\beta,\rho)^{ij}_\zeta C(\rho,\gamma,0)^{\zeta k} C^*(\alpha,\beta,\rho)_{i'j'}^\eta C^*(\rho,\gamma,0)_{\eta k'}$$ This gets rid of the annoying $\mu$, would lead to the $G$ from the beginning of the question to be comprised of the sum over a product of 8 $3jm$ symbols (the $C(\alpha,\beta,\gamma)$), of which 4 each are summed over their $m$ indices, yielding the product of two $6j$ symbols summed over one of their $j$s (the $\rho$). Also, the index structure in $e^{ijk}e^*_{ijk}$ in $G$ would translate to an index structure of the $C$ exactly matching that of the $3jm$ in a $6j$ symbol. But before I work that out, can anybody tell me if this is the right track or if I butchered something along the way (I am not comfortable enough with my skills yet to fully trust my reasoning when it leads me to an answer whose shape I already know)? Or should I perhaps take this to the mathematicians, since the answer seems to be purely group theoretic so far?


How does electricity propagate in a conductor?

On a systems level, I understand that as electrons are pushed into a wire, there is a net field and a net electron velocity. And I've read that the net electron drift is slow. But electricity travels through the wire, essentially at c, and I want to understand that mechanism. My apologies if my question is poorly stated, I know bare bones undergraduate quantum theory circa 1990s but it doesn't explain the motion of electricity in detail. Here's my conception, I'm hoping someone will fill in the holes, ha ha. An electron moves into the wire. It's got a kinetic energy. After travelling a short distance, it spontaneously emits a photon, which hits another electron in a valence shell. That electron then presumably does the same. If this conception is simply wrong, please enlighten me. The questions that arise:   1. Presumably at this level, electrons are acting more like waves and less like particles, but is there any classical component in the picture, ie are electrons coming in imparting other electrons with kinetic energy through repulsion, or does it not work that way?   2. If electrons momentarily have energy, then pass it on by a photon, what determines when that photon is emitted, and what frequency it will be? I assume that electrons in this cloud are not limited by any kind of exclusion principal, and that any frequencies are possible?   3. Why should a photon emitted by an electron be in the direction of travel? Conservation of momentum tells me that if an electron is moving, the photon should be emitted in that direction, slowing the electron, but could an electron emit a photon in the opposite direction? If it did, I assume it would somehow have had to absorb energy from elsewhere? That sounds possible by analogy with quantum tunneling.   4. What is the mechanism by which electrons propagating increase the temperature of the material? Are they transmitting energy to the electrons in the valence shell, which tug at the nucleus, do some photons hit the nuclei directly, or is there some other way?    5. Presumably, electricity travels slower than light, because there is some time in each exchange, and some time when electrons are moving at sublight speeds before emitting a photon. By how much is this slower than light, and what is the speed of each interaction?


Conduction and propagation

What is the difference between conduction of electric wave in conductor and propagation of electromagnetic wave in dielectric? Why propagation term is used for dielectric and conduction for conductor?. Somehow why propagation of electromagnetic wave (is it energy wave) is not possible in conductor, but in dielectrics, and conduction (power signal) not possible in dielectric.


what exactly do electric waves transfer from one point of the wire to other..?

> **Possible Duplicate:**   >  how does electricity propagate in a conductor? so basically i was considering the speed of the charges inside wire defined by the drift velocity and speed of electric waves that's equal to speed of light..so my point is if electric waves don't carry any charge (as mostly light that we encounter from sun's radiation is em and since they don't carry any charge we don't get shock)so what do they actually carry..i was trying to figure out its resemblance to mechanical waves ..as mechanical wave don't itself carry any matter with it they only transfer energy..then so do the electric waves they can't carry charge but they must transfer energy in the form of you know electric waves..or could i say now that these electric waves are source of electric field..then thing that's confusing me is that if electric field propagates at speed of light(speed of electric waves)..then do the voltage that we define as eL or voltage or potential at a point is=electric field intensity * L(distance) then should the voltage drop or potential also varies accordingly or i could say that the potential also following the electric field intensity at the speed of light..but this is contradictory to our general observation in which we define particular time period and phasors which define variation of voltage that..so not at the speed of light..


Does the average momentum vanish for an eigenstate of the simple harmonic oscillator?

Suppose we have a simple harmonic oscillator, let's consider the ground state, $|0\rangle$ and the first excited state $|1\rangle$. $\langle 0|\hat p|0 \rangle$ is zero right? Since the particle can either be travelling to the left or right, where $\hat p$ is the momentum operator. Similarly, I think $\langle 1|\hat p|1 \rangle = 0$ But, $\langle 0 | \hat p | 1 \rangle$ is non-zero, right? Since they are different states. Also, since $\hat p$ is Hermitian, $\langle 0 | \hat p | 1 \rangle = \langle 1 | \hat p | 0 \rangle $, right?


Surface Tension - Lung Alveoli

So, the way I understand this is as follows : The alveoli (pretend they're bubbles) have diameters of the order of microns implying a massive pressure required to inflate them by the Young-Laplace equation. $p_{in}-p_{out}=\frac{2\gamma}{r}$ However, the presence of pulmonary surfactant molecules (lets just pretend they're like detergents molecules in washing liquid) can effectively reduce the surface tension at the unexpanded alveoli and hence allow easy inflation. Now this bit I don't understand : As the alveoli expand the **distance between the individual surfactant molecules on the alveoli increases and hence the surface tension rises again** therefore decreasing the rate of expansion. What is the mathematical connection between surface tension and separation between surfactant molecules ? How can I rationalise the statement in bold ?


Why are the bounds to the permittivity $\epsilon$ a circular arc in the complex plane?

I'm reading this paper which is essentially about connecting the complex permittivity $\epsilon$ with the microstructure of a thin film. They talk about how you can place limits on the possible values of $\epsilon$ depending on how much information you have on the microstructure, and say: > We use the fact that all bounds are circular arcs in the complex $\epsilon$ > plane to give... Why is this the case? My intuition tells me it has something to do with the Kramers-Kronig relations or energy conservation, but I don't know why.


Justification of ignoring large set of entanglements

If we can think about the universe as a wave function then many particles should be entangled with many other particles in the universe. The obvious question arises why we don't see those entanglements in everyday circumstances. One standard explanation given is those entanglements average out and cancel so we can ignore those. However, hardly any mathematical justification is given for them to cancel. My question is how much trust one should have on that particular assertion? Is there any mathematical arguments already put forward by anyone?


Is holomorphy the real reason for nonrenormalization in supersymmetry?

Seiberg traced the nonrenormalization of supersymmetric theories to holomorphy of the superpotential in chiral superspace. However, this overlooks the fact that with a different number of supersymmetric generators, supersymmetry can be real or symplectic, instead of complex. But yet, even for those cases, we still have nonrenormalization. If holomorphy isn't the reason, what is? If the reason for nonrenormalizability is totally different for different dimensions and number of supersymmetry generators and choice of superfields, is it then _ad hoc_ that nonrenormalizability always holds in each case?


If light was able to pass through a wall, would the wall be invisible to the human eye?

In addition, to get light to other side of the wall, could it be converted to radio waves and then back to light waves? Edit: My idea was if there was a special material that was painted on both sides of a wall that converted radio waves to light waves and light waves to radio waves would the wall appear invisible? (My thought being that the electromagnetic radiation would travel through the wall since radio waves can travel through walls) Also, thanks for all the responses!


Currents and the Speed of Light

Why is it that currents don't flow at the speed of light, but rather significant ratios of the speed of light. I don't have any formal reasoning as to why they would flow at the speed of light-I just feel as if it would make sense. That being said, the fact that they do move at near the speed of light is also peculiar to me. Lastly, if you have current and area determined, can you figure out the velocity of the charges? I suppose you would also need to know how big the charges are. I just have no intuition as to how to go about analyzing the speed of current in some given wire.


Windflow in a car

When driving on a highway, if the front two windows of a car are open , how does the air flow in and out of the windows? Clearly, air cannot keep accumulating inside the car, so how/where does the air flow out?


How large of a solar sail would be needed to travel to mars in under a year?

I'm attempting to approach this using the identity $$F/A = I/c$$ I can solve for Area easily enough $$A = F(c/I)$$ and I know the distance $d$ is $$d=1/2(at^2)$$ But I'm having difficulty trying to relate this to the time it would take to reach mars. Any ideas where to go from here?


what is an inverse femto barn?

I came across the use of the unit barn and inverse barn while reading about the operation of LHC. What is an inverse femtobarn ? What does it tell about the experiment being described ?


Relatively how much energy do fluorescent light tubes take to turn on?

Fluorescent lights are already efficient when they’re running but I’ve heard that it takes a lot of energy to turn a fluorescent light tube on. So is it more efficient to turn off a fluorescent tube immediately when you’ve finished using it or is it better to leave it on and then wait until you’re more likely to not use it again for a while?


Why does angular momentum shorten the Schwarzschild Radius of a black hole?

Angular momentum causes the event horizon of a black hole to recede. At maximum angular momentum, $J=GM^2/c$, the Schwarzschild radius is half of what it would be if the black hole wasn't spinning. Can someone explain why angular momentum reduces the Schwarzschild radius?


Confused about Newton's 3rd law

I am confused about Newton's 3rd Law. If a person jumps off the ground a force is applied both to the person and to the ground. However, as $F=ma$ acceleration experienced by the Earth is much less than that experienced by the person. But: I press with gravitation force on the ground so it should press with the same force on me, so if my mass is less than earth mass my acceleration should be greater as well but I am not moving (flying)? Second: If small rocket(with small mass) pressure against bigger rock with greater mass the rocket should have greater acceleration towards direction opposite to its flying path so how the rocket can actually move the rock(towards left at picture where rock acceleration is small) and not the opposite(rocket acceleration at picture towards right is bigger)?   _Edited_   If a rocket with mass $m_{rocket}$ pushes against a rock with mass $m_{rock}$ with force $F_{thrust}$ the rock will push back with equal force (Newton's 3rd Law). The rocket will experience an acceleration $a_{rocket}$ in the opposite direction of $F_{thrust}$ and the rock will experience $a_{rock}$ in the _same_ direction as the thrust. However, in this example $m_{rocket} < m_{rock} \therefore a_{rocket} < a_{rock}$   Why doesn't the rocket move in the opposite direction of $F_{thrust}$ since the rock has a greater mass? ![enter image description here](http://i.stack.imgur.com/9kKKg.jpg) Not sure if it helps but added picture to second question Edit:To put second question simple how a small(low mass) object can push big(great mass) object if according to newton 3rd law a big mass object causes greater acceleration on small mass object


Ideal gas law problems

I got really confused about real gases volume and ideal gas volume. Ideal gas molecules take up no space, if we put gas into a 2.4L water bottle, we know that all the gas will expand all over the bottle and we say at this moment the gas has volume of 2.4L. So what is this volume?


How to justify matter-field interaction for non-gauge-invariant Hamiltonian?

I'm wondering how can one formally justify the electromagnetic response of a system which does not verify local U(1) gauge invariance. A good example of what I would like to consider is given by the two-body interaction term discussed in relation with superconductivity as I'll elaborate below, but many examples can be found and the question is rather general. Most of the people starts with a BCS Hamiltonian having generically the following form   $$H_{\text{BCS}}=\sum_{k,k'}\hat{c}_{k\alpha}^{\dagger}\left(\mathbf{i}\sigma_{y}\right)_{\alpha\beta}^{\dagger}\hat{c}_{-k\beta}^{\dagger}U\left(k,k'\right)\hat{c}_{k'\alpha}\left(\mathbf{i}\sigma_{y}\right)_{\alpha\beta}\hat{c}_{-k'\beta}$$ _i.e._ describing singlet Cooper pairing of electron with fermionic operators $\hat{c}_{k}$ in mode $k$, the greek indices being the spin ones. I think this Hamiltonian is manifestly not U$(1)$ local gauge invariant, due to the $k$ and $k'$ on different operators. **I'm wondering** whether it makes sense to talk about the electrodynamic response of a superconductor when one starts with a non gauge invariant Hamiltonian. More generally, **does it makes sense to discuss non-gauge invariant Hamiltonian in the context of condensed matter ?** How should we understand such non-gauge-invariant Hamiltonians, $H_{\text{BCS}}$ being a simple example ? More details:   * The original BCS Hamiltonian has $k=k'$ and $U\left(k,k'\right) \rightarrow -g$ a constant, and so the $s$-wave interaction _is_ both local and global U(1) invariant. $H_{\text{BCS}}$ is only U(1) symmetry global invariant, as far as I can see.   * The Hamiltonian $H_{\text{BCS}}$ given above is particularly useful to describe some non-conventional effects ($d$-wave pairing for instance) and can be further generalise. I have not doubt about the validity of the results obtained using this Hamiltonian (some of them are even justified experimentally).   * _I'm wondering about the possibility to formally define an electromagnetic response in a non-U(1) gauge invariant theory._ It is for instance clear that one can add some gauge invariant part of the above Hamiltonian, such that the constitutive Maxwell equations are preserved (no magnetic monopole and Faraday's law). But it seems also clear for me that one intrinsically imposes from the beginning some different matter-field interaction, isn't it ? Or at least that the covariant substitution is no more a correct prescription...


projectile that splits into two fragments of equal mass

I am studying for an exam, and this is part of a problem in my book. A projectile is launch from level ground and is intended to hit a target 100m away. Instead, it explodes into two fragments of equal mass, one of which lands 100m beyond the target. If the fragments don't take the same amount of time to land, must the second one land 100m short of the target? The back of the book tells me that this isn't true, but I'm having a hard time figuring out why. I know that the trajectory of the center of mass for the system is going to follow the trajectory of the projectile before it exploded. Thus, the CM of the system is at a distance of 100m from the origin. However, the equation for the center of mass would be $100 = mx_{cm} = \frac{1}{2}mx_1 + \frac{1}{2}mx_2$. Now $x_1 = 200$ by the conditions of the problem, so $ \implies x_2 = 0$. So clearly there must be some reason why this doesn't hold, but I can't figure it out. Could anyone explain to me why this won't work?


Triple points for other substances

Can substances other than H2O have a triple point, where the three usual phases of matter (solid/liquid/gas) can exist?


Rough, easy DIY method of measuring magnetic field strength

How to easily, using standard DIY equipment measure the strength of magnetic field generated by a permanent magnet? Narrowing down the "loose language" of the above: strength of magnetic field: either flux density **B** at given point relative to the magnet or magnetic flux ΦB over area enclosed by a loop made of wire - whichever will be easier to measure, either of those is fine. standard DIY equipment: commonly found household items, rudimentary tinkering tools. Soldering tools, multimeter, simple electronic parts, or maybe an easy to make spring-based dynamometer - anything of this class of complexity. The distance of measurement is such that the field is easily noticeable through simplest methods e.g. another magnet held in hand exerts perceptible force - distance of maybe 5cm away at most. The measurement doesn't need to be very accurate - error of order of 50% is quite acceptable. Simplicity is preferred over accuracy. Rationale: trying to estimate what coil I need to generate sufficient amount of power to light a LED with a frictionless generator based on that magnet (knowing speed of movement of the magnet and location of the coil relative to the path of the magnet). If you know other simple methods of doing that (without need for measuring the field), they are most welcome them too.


Do protons exchange photons with electrons?

I'm sorry for this question but, I just don't get it. According to the electromagnetic field theory, electrons repel each other by exchanging photons. How do protons attract electrons, by photon exchange?


Buoyancy: helium vs hydrogen balloons

Given I have two identical balloons on earth, how will the buoyancy compare between the one filled with helium and another filled with hydrogen? How can I calculate the ratio of buoyancy given two different substances and identical balloons? I am also interested in the equations relating to this problem.


What is meant by positive and negative gravity/energy/spactimecurvature?

I have recently come across some cosmological assertions (based on empirical data) about the universe being self contained in the sense that it is entirely capable of coming into existence from a zero-energy initial state . This is based on the observation that at grand scale the positive and negative gravity/energy etc. cancel out each other. What do the terms positive and negative actually mean in this context ?


How to determine a reaction force?

An object sits on an inclined plane. The weight of the object will have a normal and parallel component. I always thought that the reaction of the plane was simply the negative of the normal component of the weight. Similarly, an object swings on a pendulum. The weight of the object can be decomposed into a radial and tangential component. I assumed that the reaction (tension) of the string must be the negative of the radial component. But several examples have made me doubt my assumptions. One exercice in my textbook involves determining the reaction on a mass as it slides down a parabolic surface, as a function of $\theta$, the angle the vertical makes with the surface at any given point. Under my assumptions about reaction force, the answer is so trivial as to make the exerice pointless (since they give you $\theta$), but instead the exerice launches into a lot of complicated reasoning involving the Frenet-Serret base and comes out with a very different answer to just $-mg\ sin(\theta)$. Also, consider the second example I gave. If the object is swinging in a circle (to make it even simpler, say it has uniform circular motion), then it must have radial acceleration (centripetal, specifically). But that's impossible if the reaction is exactly the negative of the radial weight. But then... how can I determine a reaction force? In the absence of the simple rule I gave in the first paragraph, what else is there? Can it be done without making assumptions about the motion (eg. if you suppose the motion of an object is uniform circular, you have a formula all ready for the centripetal force and may thus be able to deduce the reaction force).


Double slit experiment from first principles of QM

I have read many descriptions of electron double slit experiment but I could not find the description from the first principles of quantum mechanics. Most of the descriptions makes comparison with light waves or water waves and after some arguments from optics explain why the interference happens. Light waves and water wave description are not fundamental, they are phenomenological models. Could somebody explain the electron double slit interference only from the first principles of quantum mechanics? I know the answer from the Feynman path integral approach but I would like to understand it from the pre-Feynman Integral approach.


Lagrangian definition of stress energy tensor

Can anyone explain why $T_{\mu \nu} = \frac{2}{\sqrt{-g}} \frac{\delta \mathcal{L}_M}{\delta g^{\mu \nu}} $, other than justifying it from the Einstein field equations?


Error calculation with linear regression

I am trying to determine the boltzmann constant by using a bipolar junction transistor. In my circuit (apparently I don't have enough point to join a image sorry), the Ebers and Moll model gives the relation $ i_c = I_s\exp\left(\frac{V_{BE}}{V_T}\right)$ where $ V_T= \frac{k_b\cdot T}{q}$ and $V_{BE}$ is the difference of potential between the emiter and the base. I'm plotting the $\log(i_c)$ as a function of $V_{BE}$ and use the slope of the line ($\alpha$) to deduce boltzmann constant. So $ log(i_c)= \alpha\cdot V_{BE} + b $ from which I deduce $k_b = \frac{q}{\alpha\cdot T\cdot \ln(10)}$ I have done that for 4 different temperatures. I average the different values of $k_b$ to find $k_b = 1.57\cdot 10^{-23}$ How can I calculate the error margin for each of the $\alpha$ coefficient and how do I calculate the error for the mean coefficient $\bar\alpha$?


What is the importance of the Higgs-strahlung process in the Higgs search?

I would particularly like to know why this process is considered the main search mode for Tevatron but useless for search at LHC.


average speed and velocity

A distance on a straight line from point $a$ to $b$ is $2 km$. A student walks from this line with a speed of 4km/h and another student walks with a speed of 6km/hour. what is the average velocity and average speed of student?


Is there a "Size" Cutoff to Quantum Behaviour?

We all know that subatomic particles exhibit quantum behavior. I was wondering if there's a cutoff in size where we stop exhibiting such behavior. From what I have read, it seems to me that we still see quantum effects up to the nanometer level.


Quantum perpetual motion

> Perpetual motion describes hypothetical machines that operate or produce > useful work indefinitely and, more generally, hypothetical machines that > produce more work or energy than they consume, whether they might operate > indefinitely or not. (Source:Wikipedia) With this definition in mind, particularly the "operates indefinitely" (I don't care about producing work), won't quantum mechanics allow perpetual motion due to energy quantization? For example, an electron in hydrogen can be thought of as perpetual motion. It's indefinite(I think so); unlike gravitational orbits (which slowly release energy). This is due to the quantization of energy. Without it, the electron would have fallen into the nucleus. More generally, if we energy is quantized in a system, dissipative forces of lesser magnitude cannot act on it, due to quantization. For example, if a block can have only an integer value of energy in Joules, then frictional forces of power $P<\frac{1 J}{\text{planck time}}$ cannot act. Or something like that. So does quantum mechanics permit an infinitely advanced civilization to build a machine which operated indefinitely without doing work? I'm not well versed in quantum mechanics, so I may be making a mistake here, or I may just be confused. Refer to equations if you want, but try not to use them too heavily unless the answer depends on it. It's OK if they're explained a bit.


Why do same/opposite electric charges repel/attract each other, respectively?

I know plus pushes another plus away, but why, really, do they do that? On the other hand, molecules of the same type are attracted to each other. I find that weird. I do know some stuff about four universal forces. But why in general the general "rule" is that opposite charges pull each other? Yes, I do realize this could be connected to very basic stuff that science is still trying to figure out, and can be traced to the Higgs, but still, there must be something to tell. Please don't answer like my chemistry teacher: "The reason this is not a metal because it's is non metallic element", or similar explanations.


Attraction and repulsion of charge?

Why do like charges on identical bodies cause a repulsion and unlike charges cause an attraction?


Why does proton and electron attract each other?

Not that their charges are opposite! "+" & "-" are the signs we named them. By nature Why do they attract each other? And Why do they repel each other?


Comprehensive book on group theory for physicists?

I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc. Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated?


Lie theory and particle physics

I have recently been reading _Intro to Lie algebras and representation theory_ by Humphreys, and when I am finished I am interested in reading about Lie groups and Lie algebras and their applications to particle physics. > Is there a book that assumes basic knowledge of Lie algebras, and no > knowledge of lie groups and particle physics/quantum mechanics? I have seen Howard Georgi's book, but it assumes good knowledge of particle physics. In addition, I do not know differential geometry.


Would anyone suggest me usefull web resources on lie groups and lie algebra and a good book to start with?

Would anyone suggest me useful web resources on lie groups and lie algebra and a good book to start with?


The formula of the force exerted on an electric dipole by non-uniform electric field

When an electric dipole of moment $\mathbf{P}$ is located in a non-uniform electric field $\mathbf{E}$, there is an net force exerted on it. However, the formula of the force in some books is read $\mathbf{F}=\nabla(\mathbf{P}·\mathbf{E})$, while in other books, it is $\mathbf{F}=(\mathbf{P}·\nabla)\mathbf{E}$. Obviously, the two formula are not the same. So, which one is true?


What is the conserved canonical momentum for a relativistically moving charge in a static Coulomb electric field?

The canonical momentum is a fundamental conserved quantity from Noether's theorem for translational invariance of the Lagrangian. Yet I'm finding it very difficult to see its derivation, or even a statement of what it is for something as fundamental as a relativistically moving charge in a static Coulomb electric field. Can anyone state what it is, or even give a derivation if it's not too much trouble?


Liouville-von Neumann equation can be directly derived from Heisenberg picture?

The Liouville-von Neumann equation for the density matrix is: $$ i\hbar\frac{\partial\rho}{\partial t}=[H,\rho],$$ while in the Heisenberg picture: $$ \frac{d}{dt}A(t)=\frac{i}{\hbar}[H,A(t)] +\frac{\partial A(t)}{\partial t}$$ if we adopt some kind of conservation law (like in classical theory), i.e. $$\frac{d}{dt}A(t)=0. $$ Then we have $$\frac{i}{\hbar}[H,A(t)] +\frac{\partial A(t)}{\partial t}=0 $$ by replacing $\rho=A(t)$, we can directly reach the von Neumann equation. Is this derivation correct? if it is, what is the physical meaning behind $\frac{d}{dt}A(t)=0$ then?


Can a vacuum cleaner be used to purify the air in a small room?

A hepa vacuum cleaner will pick up fine dust from the floor, filter it and send the clean air out through the exhaust. However with movement in the room fine dust will also be goinng up in the air and so the vacuum will not take it in and this fine dust will settle hours later. As far as i can see, a vacuum cleaner is very similar to an air scrubber, takes air in, filters it and sends it out. 1) is it not possible to close windows and leave the vacuum on in the middle of the room and expect it to filter fine dust in the air/room?   2) what if i maneuvered around and tried to vacuum the air aswell as the floor for several hours, would this do the job? 3)is a air scrubber/filter necessary? The room in question is about $18\,\mathrm{m}^2$ and the vacuum cleaner i intend to use is a sealed hepa unit which is about 500 air watts and says it can do $58\,\mathrm{L/s}$ which i think is litres per second. Please give general answers to the questions I have asked aswell as specific to the vacuum and room in question. Thanks.


What can be the lightest possible moon launch vehicle?

I tried calculating this, but it gets too complicated. Assume, we have a Moon orbit station and ISS on Earth orbit. We have a Moon base. We want to send a tourist for a week on the Moon and back. We need to launch only the oxygen/fuel cells and the fuel for trans-lunar and trans-earth injection. The lunar lander lands and takes off in one piece (we don't need a pile of used stages on the lunar base). It can be lighter than 10 metric tons of Apollo LEM. Fuel cells (200 kg each) may go, because now we have solar panels. So, how low can we get with newer technologies? And the main question, how small can the launch weight be? Is this doable with conventional Soyuz or Proton rocket? Assume, we might have a coilgun to do trans-Earth injection right from the lunar surface. Delta-v of 2.7 km/s means 90 km of rail and accelerating @ 5g, if I remember my calculations correctly. Some data from Wikipedia:   * Apollo Lunar Module      * Ascent stage 4,547 kg of which 2,353 kg is propellant     * Descent stage: 10,149 kg (8,200 kg of propellant for 2,500 m/s delta-v)   * Command and Service module      * command module 5,809 kg     * service module 24,523 kg all together 46,980 kg   * Saturn V      * 1st stage with fuel: 2,300,000 kg     * 2nd stage: 480,000 kg     * 3rd stage: 120,800 kg The third stage fired only partially (165 + 335 seconds) to get to LEO, and then was used for TLI. So, 120 tons were sent to LEO, and only 47 tons left after TLI. How low can the latter get? The lunar module will be orbiting the Moon and reused. This means several tonnes less for TLI and Lunar orbit injection. But the fuel for it has to fly from Earth. If CM gets smaller, this can also make the vehicle lighter. Service module can be reduced by using inflatable materials, and it can be reused and stored at ISS. So we save 25 tons x 9 km/s (launch from Earth), but add 3km/s of delta-v to park it after the way back. So, all together, we need to launch   * the Earth landing module (CM analog)   * fuel for      * TLI     * LOI     * lunar landing and takeoff     * TEI     * fuel to park SM in LEO If coilgun is used, we don't need takeoff and TEI fuel. (Hm... we need to launch the SM back too :) How much does this weigh?


Integration of 3-momentum

During a lecture that I missed, I was trapped when the lecturer uses the relation $$dp_x~ dp_y ~dp_z ~=~d^3\mathbf{p} ~=~ 4\pi p^2 dp.$$ Can I know how is this relation derived please?


S-Matrix, String theory, Matrix mechanics and Quantum Mechanics

I'm trying to learn theoretical physics up to string theory. I know linear algebra, calculus 1+2, complex analysis. I know the basics of homology, homotopy, group theory and differential geometry. Now I'm starting to read a first introduction to QM, which is this PDF: http://arxiv.org/abs/1007.4184 . And I read a lot on physics exchange on these topics. My main goal is to get a good sense of string theory and maybe that I can solve some basic problems. Now I did read that the historical background of string theory is the S-Matrix(which I guess has to do with the matrix formulation of QM). Should I first learn this approach to QM and then switch to S-Matrix and finally string theory? Or just completely skip these topics(S-Matrix and Matrix Mechanics) and learn string theory in an ordinary style?(like in the usual literature, which I assume is not taught with the S-Matrix model). Edit/ I know usual mechanics, theoretical mechanics(Lagrangian and Hamiltonian too) and a bit electromagnetism, but didn't do much problems on these topics, but I know the concepts.


Negative emf in AC generator

At a certain instant in AC generator, when the normal of the plane (rectangular coil) makes an angle of 270 degrees with with the magnetic induction B, the value of emf is: $E = -NAB\omega$ My teachers would usually say that this is the minimum value of emf that a generator produces. Does it really mean that? Or does the negative sign only mean that emf is at its peak value but the current is flowing in opposite direction?


Punching - Force or Momentum?

If I want to punch a person inflicting maximum damage, what do I need to care about? My force of punching, i.e, do I need more acceleration? Or do I need momentum, i.e my velocity for punching?


Calculate amount of energy based on height of object

How can you calculate the amount of energy an object produces that falls from a particular height? Or water. In an eg i would like to know how can you calculate the amount of electricity water can produce at a certain height?


Why does your car lurch toward an oncoming truck as it passes you?

I notice that the larger the truck the greater the magnitude of the lurch. Can anyone give a physical explanation to this?