Is there really no meaning in potential energy and potential?

I have been told all my physics life that potential energy between two mass/charge has no meaning and only their difference has meaning. The same goes for electric potential, only the difference matter. Perhaps I am not understanding it correctly, but before I talk about masses, let's talk about potential energy/potential associated with two charges. I am not sure where had I seen it, but a long time ago I was presented with a problem like this. Let's say I have a +Q and a -Q. What is the potential energy between them? The change in potential energy is the negative work done by the conservative force namely (vector sign and dot product got rid of, since the cosine 1) $\Delta U = -\int_{a}^{b} k(Q)(-Q) \frac{1}{r^2} = -k(Q)(-Q) \left. \frac{-1}{r} \right |_{a}^{b} = -k(Q)(-Q) \left (\frac{1}{b} - \frac{1}{a} \right) $ Now I assume that I brought it from infinitely far, so that 1/a = 0 In that case I am left with $\delta U = \frac{kQQ}{b}$ Here are my questions 1) A long time ago, I saw a formula looking EXACTLY like what I just did there, but it doesn't concern with the _change_ , it's just gives me the potential energy. Now the formula I remember was $U = -\frac{kQq}{r}$ where there is a negative. I thought this formula already takes care of the signs? Or am I wrong? 2) Kinda the same concept. If I tell you some charge (not telling you the sign) has a electric field and you have another charge (which is the test particle, not telling you the sign again even though it is conventional to use + charge ) somewhere in that field. I tell you that the electric potential at that point (not the difference) is K (where K is positive number). What can you conclude, if anything? What if it were negative? Suppose I tell you suddenly that the charges are the same signs, and I give you a location in which the electric potential is positive (I think it has to be). What does it mean? EDIT: Let me also just clarify a bit that I was taught that electric potential (not difference, I stress again) is the work that someone does to bring a charge from infinity to some point whereever. In my book however, it's defined as $V = \int_{R}^{\infty} \vec{E} \cdot \vec{ds}$


What is the intuition behind the direction of torque?

I've seen the other posts on this question, but unfortunately I'm still having difficulty understanding the meaning of the direction of the torque vector. It makes intuitive sense that the magnitude of the torque exerted on an object is dependent on the length of the lever arm and the angle between the lever arm and the applied force. What I don't understand is what the direction of the torque vector is describing. How can I relate the direction of the torque vector to a real world example (that is not an example involving a wrench + screw and the screw "unscrewing" in the direction of the torque...which doesn't give me any more of an intuition on what torque means). Thanks!


Can a photon be made to orbit a known (or undiscovered theoretical) body?

Can a photon through some process be made to orbit a celestial or any other object? Two follow-up questions.   1. Can this orbit be described as the photon crossing its own path.   2. Will this wave-function be effected by positive interference. To the effect of increasing frequency?


What force particle mediates electric fields and magnetic fields?

The force carrier for magnetic fields and electric fields are supposedly photons. I don't get it: 1) Wouldn't that mean that a charged particle (e.g. an electron or even a polarized H2O molecule) would constantly be losing endergy from sending out photons? 2) Wouldn't that mean that an electric field is inseparable from a magnetic field, as photons have both - and that one can't have one without the other? 3) Would it be possible, then, to determine the wavelength of magnetic-field- mediating photons? If so, what is the wavelength - is it random or constant? 4) How can a photon (which has momentum) from one electrically charged particle to an oppositely charged particle cause these particles to _be pulled toward each other_ \- or how can a magnetic field cause an electrically charged moving particle to experience a force _perpendicular to_ the source of the magnetic field if a particle with a non-zero mass moving between the two is the mediator of that force? If "virtual photons" are involved, please explain why they work differently from regular photons.


How does charge flowing between emf terminals reduce voltage difference?

I'm currently learning what electromotive force is and while reading my book's description of an ideal source of emf, I had difficulty understanding what these sentences mean: > The nonelectrostatic force maintains the potential difference between the > terminals. If it were not present, charge would flow between the terminals > until the potential difference was zero. I don't quite get what it means by this. How does the nonelectrostatic force "maintain" the potential difference between the terminals? If it wasn't present and only the electric force remained, why would the potential difference decrease to zero? The only thing I could think of was that the electric force from the E field inside the source of emf would still be exerting forces on charges from high potential to low potential, turning its electric potential energy into kinetic energy by doing work on the charges. I still don't know how that would reduce the voltage difference across both of its terminals to zero though. Regarding the ideal source of emf, the book assumes there is a positive and a negative terminal with the positive terminal at a higher potential and the nonelectrostatic force going from low to high potential while the electric force goes from high to low, just in case that helps clear any ambiguity.


Did relativity make Newtonian mechanics obsolete?

Did Einstein completely prove Newton wrong? If so, why we apply Newtonian mechanics even today? Because Newton said that time is absolute and Einstein suggested it relative? So, if fundamentals are conflicting, how can both of them be true at a time?


Relative velocities of boats and a stone thrown by the boat

> **Question:** A police boat is chasing a boat with criminals along a > straight river by moving against the stream. The speed of the river stream > is 3 miles per hour, the speed of the boat with criminals relative to the > river is 30 miles per hour, and the police boat is 4 miles per hour faster > than the boat with criminals. > > Currently the criminals are ahead of the police, and horizontally throw a > stone at the police boat at a speed 16 miles per hour relative to their boat > (i.e. relative to the boat of criminals). > > What is the horizontal velocity of the stone relative to the police boat and > to the river bank? You need to state what the origin and the positive > direction of motion are. Choose the direction of the river stream to be the positive direction and choose the origin to be in front of criminals' boat. Denote the velocity of the river stream by $\dot{x}_R$ Denote the velocity of the police boat by $\dot{x}_P$ Denote the velocity of the criminal boat by $\dot{x}_C$. Denote the velocity of the stone thrown by $\dot{x}_S$. From the question we have that $\dot{x}_R = 3$, and we also have that the velocity of the criminal boat relative to the river stream is \begin{align*} \dot{x}_C - \dot{x}_R &= -30 \\\ \implies \dot{x}_C - 3 &= -30 \\\ \implies \dot{x}_C &= -27 \end{align*} Note that the minus 30 is because from the point of view of the river, the criminal boat is travelling in the negative direction. Now from $\dot{x}_C$ I can calculate $\dot{x}_P$, since \begin{align*} \dot{x}_P &= \dot{x}_C + (-4) \\\ &= -27 - 4 \\\ &= -31 \end{align*} Note that the minus 4 is because the police boat is 4 mph faster, but in the negative direction. Also from $\dot{x}_C$ I can calculate $\dot{x}_S$. From the question we have that \begin{align*} \dot{x}_S - \dot{x}_C &= 16 \\\ \implies \dot{x}_S - (-27) &= 16 \\\ \implies \dot{x}_S &= -11 \end{align*} I was wondering if my solution was right, even though $\dot{x}_S = -11$ is negative, even though it moves in the positive direction.


Birds inside of a closed box

Suppose there's a closed box with birds inside, on top of a scale. If the birds started flying inside, would the box get lighter?


Weighing a flying bird

Let thing of a bird standing still in a box on top of a weighing machine that shows a mass $m_0$. Now, imagine that the bird is flying, still in the same box and the same weighing machine shows a mass $m_1$. As the bird when flying, is applying a force towards the weighing machine, could we deduce that $m_0 = m_1$? I'm asking this question because saying that these masses are equal makes me as uncomfortable as saying that they are not equal and can't figure the right answer. So does $m_0 = m_1$ and why?


Bird flying in a cage

Assume that you are holding a cage containing a bird. Do you have to make less effort if the bird flies from its position in the cage and manages to stay in the middle without touching the walls of the cage?   Does it make a difference whether the cage is completely closed or it has rods to let air pass?


Why is a nucleus isotropic?

I believe in Neutron Scattering the neutrons after hitting a nucleus can bounce in any of 360*3 dimensions -> 1080 degrees? Why is this so? Shouldn't it only bounce "off" the neutron in approximately the same "direction" that it came in such as when a particle bounces off a mirror -> because of the cross-section ...


Proof that QCD is the theory describing strong interactions?

I would like to ask what are the experimental evidences that led to the conclusion that QCD is the right theory to describe strong interactions. I know that some of the key point are the decay of $\pi_{0}$ and the measurement of Jets but I'd love to see a full answer to this question. Is there a still a chance to Regge theory nowadays?


Electric Potential of a Cube Made of Point Charges

I'm trying to find the potential energy of multiple geometric shapes made entirely out of point charges. This particular shape is a cube made out of two different point charges, A and B, each separated by a constant distance. I'm not entirely sure how to go about this problem but I'm pretty sure that the equations V=Ed and E=kQ/r^2. I'm pretty sure you just add up the charges but I have no idea how to do this in a cube form..


Why does lightning cause sound?

If I understand correctly, lightning is the discharge of electricity from the atmosphere into the planet. However, if I switch on a lamp, the wires are not causing thunder (or any audible sound). I've also heard that the thunder comes from lightning breaking the sound barrier. This sounds weird to me since I would assume that lightning would be traveling at, well, light speed, so I'm not sure how the threshold could be crossed. How does lightning cause thunder?


The gauge-invariance of the probability current

It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\\ \phi\to\phi-\frac{\partial \chi}{\partial t}\\\ \psi\to \psi \exp\left(\frac{iq\chi}{\hbar}\right)\end{cases}$$ The Schrodinger equation $$\left[-\frac{\hbar^2}{2m}\left(\nabla-\frac{iq\vec A}{\hbar}\right)^2+q\phi \right]\psi=i\hbar\frac{\partial}{\partial t}\psi$$ gives back the same equation. How does it follow that the probability current is gauge invariant?


How sound intensity (dB) and sound pressure level (dB) are related?

Source: http://www.engineeringtoolbox.com/sound-power-intensity-pressure- d_57.html Both sound intesity and pressure level are measured in dB. Given a specific sound, are these two dB values the same?


Duality and Fourier Transforms

I read that $(FF(f))(x)=2\pi f(-x)$, where $F$ is the Fourier transform _and_ $F(f(x-a))(k)=\exp(-ika) X(k)$ where $X(k)=F(f(x))$ _implies_ $F(\exp(iax)f(x))(k)=X(k-a)$. But I don't see how that is done... I am quite happy with getting $F^{-1}X(k-a)=\exp(iax)f(x)$ by brute force calculation. I would like to see how to use duality though.


What's the definition of the time ordering operator for more than two particles?

For two particles, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) \rangle = \langle a(t_1) a^\dagger (t_2)\rangle \theta (t_1-t_2) + \xi \langle a^\dagger (t_2)a(t_1) \rangle \theta (t_2-t_1)$ with $\xi$ is a plus sign for bosons and a minus sign for fermions. How would I write, for example, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) a(t_3) a^\dagger (t_4) \rangle$ ?


Velocity field induced by vortex points along ellipse

I'm investigating the velocity field induced by a continuous distribution of 2D vortex points distributed along an ellipse $\\{a\cos\theta,b\sin\theta\\}$. I'm interested in the field inside the ellipse, and I need some help to prove whether this field is zero or not. The intensity of each vortex point is proportional to $d\theta$ and not to the length along the ellipse. A vortex point located at a point $\boldsymbol{x'}$ induces a velocity field $\boldsymbol{u}(\boldsymbol{x})=\frac{d\theta}{2\pi |\boldsymbol{x}-\boldsymbol{x'}|} \boldsymbol{e}_\perp$ where ${e}_\perp$ is the unitary vector orthogonal to $(\boldsymbol{x}-\boldsymbol{x'})$ which is in 2D: $\boldsymbol{e}_z\times(\boldsymbol{x}-\boldsymbol{x'})/|\boldsymbol{x}-\boldsymbol{x'}|$. The total velocity field at a point $(x,y)$ inside the ellipse is obtained by integration over $\theta$. Numerical experiments seem to show that the field is zero inside the ellipse, but I cannot prove it. Dropping the factor $2\pi$, the field is in cartesian coordinates: $$\boldsymbol{u}=\int_0^{2\pi} \left\\{\frac{-y + b \sin\theta}{(x - a \cos\theta)^2 + (y - b \sin\theta)^2}, \frac{x - a \cos\theta}{(x - a \cos\theta)^2 + (y - b \sin\theta)^2}\right\\} d\theta \stackrel{?}{=}\\{0,0\\}$$ Is the field really zero? Maybe there is no need for the integrals to prove it. Maybe complex analysis is of help? I should mention that the following property is true in this problem: For any closed contour inside the ellipse the circulation is zero: $$\oint \boldsymbol{u}\cdot\boldsymbol{dl} =0$$ Since we are in a simply connected region, the velocity is the gradient of a potential which is single valued. But then is this potential constant?... I'm able to prove that the velocity is zero on both the $x$ and the $y$ axis. Also $u_x$ is an even function of $x$ and an odd function of $y$. The opposite applies for $u_y$. I'm able to prove the result for a circle $a=b$. Can somebody help me for the ellipse? Any idea?


Why was PACER abandoned?

The PACER project is described in this question: How much of the energy from 1 megaton H Bomb explosion could we capture to do useful work? Why was it abandoned? It seems that it is the only readily economical and engineeringwise useful path to fusion power, and it seems that its breeder possibilities can easily let it pay for itself for generating fissile elements and helium (which is getting to be rare too nowadays!) Was it political or technical limitations that killed it? Is there hope for a renewed interest in this in todays energy conscious politics?


Dielectric in Parallel Plate Capacitor

Given a parallel plate capacitor of width $w$, length $l$, with a dielectric moving along the length $l$. Let the dielectric be from $x$ onwards. The capacitance will be $\frac{w \epsilon_0}{d} (\epsilon_r l - \chi_e x)$. Griffiths (p. 195) says that the total charge $Q$ in the $C=\frac{Q}{V}$ expression is constant as the dielectric moves. But $Q$ here refers to the free charge, and the free charge definitely increases as you move the dielectric in increasing $x$. What am I misunderstanding?


Classical car collision

I have a very confusing discussion with a friend of mine. 2 cars ($car_a$ and $car_b$) of the same mass $m$ are on a collision course. Both cars travel at $50_\frac{km}{h}$ towards each other. They collide. Ignoring any shreds and collateral damage, what is the speed of collision that the driver of $car_a$ felt? What I mean is, if $car_a$ were to be driven into an infinite mass wall, what would the velocity be to replicate the damage caused by the initial collision?


Is a collision with an immovable object equal to a head-on collision?

**Scenario 1** Two identical and bilaterally symmetrical cars, driven by identical drivers in the exact center of the car and in the same body position, each traveling the same speed, collide exactly head on. (Essentially, eliminate all variables that would cause rotation or interpenetration during the collision). **Scenario 2** One of the above cars hits an immovable wall instead of an oncoming car. **Question** Will each car in these scenarios experience the same forces? For clarity, the cars in scenario 1 have twice the closing speed of the car and wall in scenario 2.


Is two cars colliding at 50mph the same as one car colliding into a wall at 100 mph?

I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, while he said that they are different, and he said he supplied a proof showing otherwise. He didn't say whether or not the cars are the same mass, but I assumed they were. To state it more clearly, in the first instance each car is traveling at 50mph in the opposite direction and they collide with each other. In the second scenario, a car travels at 100 mph and crashes into a brick wall. Which one is "worse"? When I first heard it, I thought, "of course they're the same!" But then I took a step back and thought about it again. It seems like in the first scenario the total energy of the system is the KE of the two cars, or $\frac{1}{2}mv^2 + \frac{1}{2}mv^2 = mv^2$. In the second scenario, it's the KE of the car plus wall, which is $\frac{1}{2}m(2v)^2 + 0 = 2mv^2$. So the car crashing into the wall has to absorb (and dissipate via heat) twice as much energy, so crashing into the wall is in fact worse. Is this correct? To clarify, I'm not concerned with the difference between a wall and a car, and I don't think that's what the question is getting at. Imagine instead that in the second scenario, a car is crashing at 100mph into the same car sitting there at 0mph (with it's brakes on of course). First scenario is the same, two of the same cars going 50mph in opposite directions collide. Are those two situations identical?


If two objects collide, will the collision force be twice as big as the original force?

Say, if we have two trucks travelling towards eachother at 60m/s, and those two trucks carry the same payload, and are the same model (aka they're exactly the same), will the collision force be as if just one truck crashed into a wall at 120m/s? Theoretically the forces will balance each other out, but it won't always be this way.


Where does the loss in gravitational energy of the load go when a spring is pulled?

A mass spring system is in equilibrium. If I pull on the load by $x$ meters, the energy stored in the spring is (this is what is given in my book): $$E=\frac12kx^2 $$ However, doesn't the load lose gravitational potential energy as it moves down? Where would this energy go? By conservation law, shouldn't the energy equation be: $$E_{stored}= \frac12kx^2 + mgx$$ In short, where does the loss of gravitational potential energy (mgx) of the load get transferred to if it is not stored in the spring? (Referring to a vertical mass spring system) The picture in my mind: ![enter image description here](http://i.stack.imgur.com/OdVee.png)


How to know the time a disc takes to stop from rotating and the numbers of revolutions

Assuming I rotate a disk, I want to know how long it takes to completely stop, and the number of revolutions it made since I removed my fingers off the disk. Lets say a DVD I rotate with my fingers. I only know the radians per second (velocity) of the last moment I touched the disc. Can you guys tell me where to start? Im trying to implement this on an iPhone app. So it would be nice if you mention **equations**. It should not be exact.


Simulation of physics of chains/ropes in force fields resources?

I'm thinking about a project to tackle, and I'd like to make a simulation that allows the user to define a rope or chain of length L, pin it at arbitrary points r1, r2.... etc. and draw the resulting curve in real time. Also, I'd like the user to be able to alter the field that the rope exists in, for example more complex vector fields than just a straight gravitational field. This is a bonus, however, and I'd like to get the basic example working. Could you recommend some resources, preferably free/online, for me to learn the physics involved (I'm not exactly sure what to CALL this area of classical mechanics)? I learn through concepts and then math so a resource that is concept-heavy would be nice. Thanks!


how apparent weight varies due to the rotational motion of earth

I learned that as the earth rotates about its axis, the bodies on the earth also follow a circular path. In most books I read, they give the example of a person standing on a weight balance at the equator... and I did understand that. However, by doing the following calculation, I am seeing that the apparent weight at other points on the earth (apart from the poles) is the same This is the picture on my mind: ![enter image description here](http://i.stack.imgur.com/4C73k.png) At B, $$W-N=m{\omega}^2 R$$ At A, a component of weight will provides the centripetal force to rotate around the circle with the radius $r$, $$Wcos{\theta} - Ncos\theta =m{\omega}^2r $$ as $r=Rcos\theta$, $$Wcos{\theta} - Ncos\theta =m{\omega}^2R\cos\theta$$ The equation eventually ends up as... $$W - N =m{\omega}^2R $$ So from this, I think that the normal reaction force which is the apparent weight remains the same as to the apparent weight at the equator. However the book states that the apparent weight varies along $A$ and $B$ Also, we assume that the earth is spherical. I am really sorry for making the question so long. Could someone please tell me which part of my concept is wrong.


Calculating lagrangian density from first principle

In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle.


Can a bullet leave a gun and tumble to the ground?

This question seems to have been asked a few times in different configurations, but none of them answer my variation. I've struggled to understand this for nearly 15 years and had conflicting answers from my school physics teachers and more recently friends who are physicists. So a round leaves my gun barrel at $40$ m/s. Its initial Airspeed is $40$ m/s. In another question they asked about firing down the length of a train traveling the same speed. I understand that firing toward the front of the train would result in a ground speed of $80$ m/s and an airspeed of $40$ m/s. Also, firing toward the back of the train results in a ground speed of $0$ m/s and an airspeed of $40$ m/s. My question... if you were to walk to the back of the train, open the door and fire directly out the back, would you end up with a ground **and** airspeed of $0$ m/s? Meaning the projectile would literally just tumble in a straight trajectory down to the ground? Plenty of people have thrown spanners into this one over the years - like talking about the way an explosive force will 'hang' in a certain space if not pushed, pushing the projectile away from itself as well as the firing pin of the gun, giving it extra forward momentum in that instance. (unlike firing from the front of the train would always equal $80$ m/s for air and ground. The explosion cannot be 'left behind'). I personally don't buy this one... But i don't know enough to judge.


Momentum of light in medium

Maybe this has been asked before, but I didn't find anything about it. I am wondering about the momentum of light in media with refractive index n>1 (so to say, not in vacuum). There are two approaches to this problem I think, but they lead to different results. First, one can take the equation $p = \frac{h}{\lambda}$ Because it holds $\lambda = \frac{\lambda_0}{n}$, one gets $ p = n \frac{h}{\lambda_0} = n\cdot p_0$. So momentum is larger than in vacuum. Second, one can take the eqation $p = m \cdot v$. Because $v= c$ for phonons and in medium it holds $c=\frac{c_0}{n}$, one arrives at $p = \frac{m c_0}{n} = \frac{p_0}{n}$, which is clearly smaller than $p_0$. These two results dont fit together. So which result is right and why?


A statics problem to find minimal friction

consider the following: ![enter image description here](http://i.stack.imgur.com/tpCcw.jpg) I need to find the minimal coeeficient of friction $\mu _{min}$ so that both recatngle boxes would remain static. The lower angle in the triangle is $2\alpha$ as indicated. I ended up with this expression: $$\mu _{min}=\frac{m_2}{2\cdot m_1 \cdot \tan \alpha}$$ but the answer in the book is rather this one: $$\frac{m_2}{(2m_1+m_2)\tan\alpha}$$ Who is correct?I know that the normal force that that the triangle is exerting on both is like this: ![enter image description here](http://i.stack.imgur.com/qYGQr.jpg) (on both sides of course) so with geometry and soome FBD that's what I came out with. Would like to hear your thoughts!


top quark and Z,W bosons?

The masses of the Z and W particle sum almost exactly to the mass of the Top quark,within the errors: Z + W = 80.385±0.015 + 91.1876±0.0021 = 171.57 ±0.0171 GeV Top quark 172.9± 1.5 GeV A: Is this one of those simple coincidences? B: The Z,W particles are decays of the T? C: Someone has a not too cranky idea connecting them? EDIT: After consideration of dmckee and Lubos posts. How about instead of a decay from a t quark, collide a $W^\pm$ and a $Z$ to produce a red top and anti-red bottom. $$W^+ + Z^0 \to t(r) + \bar{b}(\bar{r})$$ this conserves charge, spin, color, confinement and energy - provided the excess energy of the bottom quark comes from the kinetic term of the collision. It immediately decays as lubos and dmckee pointed out in an early question EDIT 2: Also note decay time of t-quark is $4.2\ 10^{-25} s$, nearly matching the W,Z decays times of $3.0\ 10^{-25} s$ , although I'm yet to find an uncertainty for these. And with incredible hubris I'm calling this the Metzgeer Momentary Meson $t\bar{b} $   :) joke


Can entanglement swapping be performed on already-entangled photons, and if so, can it preserve this entanglement over the swap?

Consider 2 uncorrelated photon pairs (a1,a2), (b1,b2) such that (a1,a2) are entangled, and separately (b1,b2) are entangled. We wish to entangle-swap so as to end up with a new entanglement (a1,b1) by using the ancillary photon pair (a3,b3), such that (a1,a3) are entangled and (b1,b3) are entangled. This suggests that we do a multipartite (3-way in this case) entanglement preparation prior to the swap, such that (a1,a2,a3) are entangled, and separately (b1,b2,b3) are entangled. The swap proceeds in the usual way by Bell state measurement on a3 and b3, and we end up having entangled (a1,b1). The question is whether, after this operation, the entanglements (a1,a2) and (b1,b2) remain intact? If not, can we modify the procedure to guarantee this? If yes, will (a2,b2) now be entangled as a result of the swap? (they were uncorrelated before it). If not, how can we arrange that they are entangled, by only manipulating the other 4 photons?


Why does dust stick so well to fan blades?

After reading and understanding the reasons why dust stick to rotating fan propeller, I am interested to find out why the dust particles stick so well. Spraying powerful jets of water does not effectively remove the dirt. Some scrubbing is still required, whether it is metallic blades or plastic ones. Why is that so?


Application of non maximally entangled state

In quantum information and quantum computation, we generally use Bell type states which are maximally entangled. I find that the set of entangled states as interesting objects from a mathematical point of view and one can ask many questions regarding their structure and so on. But my question is, what are the practical uses of such states and why are they physically interesting. The only case I can find out is, when due to some environmental interaction such states are created. However I can only see the use of maximally entangled states in literature. Caveat: In multipartite cases, maximal entanglement can be tricky. I am not sure, whether I have have phrased the question correctly. Feel free to ask and edit. Advanced thanks for any help, suggestion etc.


Is the resistance 0 in the ballistic regime?

Given that in the ballistic regime a particle (electron) can move freely without scattering (there are no impurities ), is the resistance through a ballistic sample zero?


Perfectly focusing refractive surface

On reading Feynman's lecture on physics, in the geometrical optics section he said that a curve which focuses all the rays coming from a point to another fixed point beyond the refracting surface perfectly is a complicated fourth degree curve which is actually the locus of all point with its distance $Op$ from one point, $O$ plus the distance $O_1p$, from another point $o_1$ times a number $n$ (refractive index of the material beyond the refractive surface) is a constant independent of point $p$ on the curve. But I don't know how to derive this curve, or as a matter of fact, how to even begin to. Any derivation would be greatly appreciated (simple preferred).given below is the excerpt from feynman's lectures which is what i reffered to in my question.![enter image description here](http://i.stack.imgur.com/QnY7n.png) ![enter image description here](http://i.stack.imgur.com/1pFTy.png)


Have the Rowan University "hydrino" findings been replicated elsewhere?

In 2009, Rowan University released a paper claiming to replicate Blacklight Power's results on energy generation using hydrino states of the hydrogen atom. The paper appears to describe the procedure in every detail as far as my untrained eye can tell. Has anyone else attempted to replicate these results and did they succeed?


Quantum entanglement: does it necessarily imply superluminal information transfer?

From what I understand, information is communicated _instantly_ between two quantum-entangled particles regardless of the spatial distance between them. However, does this necessarily imply superluminal data transfer? If the "distance" between the particles is simply assumed to be measured in our common 3D euclidean space then that would seem to imply superluminal communication. However, could there be other paths between the two particles that lie beyond our observable 3D euclidean space, other paths that involve additional dimensions in which the particles remain very close or some sort of folding of space on other dimensions that provide an information pathway? Anybody aware of any such research/findings? Thnx.


Why can't classical information be transmitted through quantum entanglement by measuring time between change events?

If the effect of measurement in quantum entanglement occurs instantaneously why can't it be used to transmit classical information faster than light? I'm based my question off this seemingly well cited Wikipedia article: http://en.wikipedia.org/wiki/Quantum_entanglement#cite_note-10 Edit: It would seem that my question should be more focused on why we can't use change as a method of data transmission.


Why do we think that quantum entanglement implies action at a distance?

> **Possible Duplicate:**   >  Why quantum entanglement is considered to be active link between particles? I am a layman trying to read into quantum mechanics. As I understand it quantum entanglement is an experimentally proven mechanism by which the quantum state of two particles become 100% correlated, that is, measuring the quantum state of one object causes you to know the quantum state of its entangled particle with 100% certainty (they're opposite). Where I don't understand is why this is used to imply that information is "traveling", faster than light or not. Where is the intuition coming from that the correlation between two separated particles has anything to do with one particle effecting the other? For me, a much stronger explanation for why these two particles are correlated is that the entanglement itself effects the particles, that is, upon becoming entangled their quantum states are individually governed by some formula (as a function of time alone) where those formulas produce exact opposite results for each particle. Separating the particles doesn't have to change the formula, so if you measure one you know the other just because they must be opposite. Yet from what I've read it's taken for granted that quantum entanglement = information is traveling from one to the other. Do we have a reason for thinking that? Have we shown that we can definitely modify the quantum state of one particle and therefore change the quantum state of its entangled partner, or anything else to show that information is traveling? It's the old question of "causation vs. correlation." In principle, the concept of measurement itself modifying the Universe itself (beyond any observer effects) strikes me as somewhat silly.


Why quantum entanglement is considered to be active link between particles?

From everything I've read about quantum mechanics and quantum entanglement phenomena it's unobvious for me, why quantum entanglement is considered to be active link. I.e. it's stated every time that measurement of one particle _affects_ another. While in my head there is less magic explanation: the entangling measurement affect both particles in the way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without magic _instant_ modification of remote entangled particle. Obviously, I'm not the only one who had this idea. What are the problems associated with this view and why _magic_ view is preferred?


Suggest why electrical power input P1 differs from power used P2

We have done an experiment heating water with a wire element and have determined it takes 21.5964 watts to heat 200ml of water to a specific temperature in 10 minutes. However the power of the electrical input is 29.9859 watts. It asks for an explaination of why they are different but I'm a bit lost


How does $p_x$ commute with $p_y$, i.e. $[p_x,p_y]=0$?

I know it's a simple and basic question but would someone show me how to evaluate $[\hat{p}_x,\hat{p}_y]$?


What is a general definition of the spin of a particle?

In quantum field theory, one defines a particle as a unitary irreducible representations of the Poincaré group. The study of these representations allows to define the mass and the spin of the particle. However, the spin is not defined the same way for massive particles (where the eigenvalue of the Pauli-Lubanski vector squared are $-m^2 s(s+1)$ where $$s = -S, -S +1, \cdots, S,$$ and $S$ is the spin of the particle (and $m$ the mass)) and massless particles (where the helicity has eigenvalues $\pm \lambda$ and $S=\left|\lambda\right|$ - not to mention continuous spin representations). With this definition, the "spin" $S$ that appears in both cases doesn't seem to be exactly the same thing. The eigenvalue that labels the irreducible representations are not from the same operator in the massive and the massless case ... however, it's tempting (for me) to see the maximum value of these eigenvalues as the same physical quantity if both cases. So I wonder if there is a more general definition that would embrace both massive and massless particles (even less practicable)?


What would the universe look like if it started out without any irregularities?

_(Warning! Newbie question coming up!)_ ## Background As seen on this picture of the cosmic microwave background (take from the Wikipedia entry on the very same topic) there exists irregularities in the distribution of matter: ![Cosmic microwave background. Boom baby!](http://i.stack.imgur.com/KjAdE.png) To my knowledge, this is because the Universe wasn't formed with all the matter (or whatever you should call whatever existed right after the big bang) in a completely regular pattern (or if it was the case that anti-matter had this big fight with ordinary matter after the Big Bang, it's really not that important I guess), and I guess this is the reason why we have a highly diverse universe today, inhabited by galaxies, black holes, and Justin Bieber. ## Question What would the Universe look like if there were no irregularities in it from the get-go? Would we have a big massive black hole in the middle (if one even can talk about a middle), would the Big Bang never happen, or have I just misunderstood the whole thing, making my question completely nonsensical?


How do I adjust the kinematic equations to avoid reaching speeds faster than light?

I like some 'science' in my 'science fiction', so I started crunching out the kinematic equations for some of the scenarios my characters are getting involved in, and ran smack dab into an issue. (Please excuse my formatting, I can't figure out sub/superscript notations) $v_f = \sqrt{2ad}$, with $v_i$ assumed to be 'close enough' to zero. That's easy enough to crunch the math on. Except... With sufficiently high values for $a$ or $d$, you start crowding, or even violating, the light speed limit. And I can't find the equations to help handle relativistic distortion! I know they exist because I remember working with relativity when I took my physics class, years and years ago.


A question about spontaneous symmetry breaking at macroscopic limit

The question relates to this post. Spontaneous symmetry breaking is somehow a volume effect, that in-principle only happens at infinity large system. Weinberg in the second volume of his QFT used a chair demostrated the lost of rotational symmetry due to large scale of the chair. p. 163 > We do not have to look far for examples of spontaneous symmetry breaking. > Consider a chair. The equations governing the atoms of the chair are > rotationally symmetric, but a solution of these equations, the actual chair, > has a definite orientation in space. Here we will be concerned not so much > with the breaking of symmetries by objects like chairs, but rather with the > symmetry breaking in the ground state of any realistic quantum field theory, > the vacuum. p.164-165 > Spontaneous symmetry breaking actually occurs only for idealized systems > that are infinitely large. The appearance of broken symmetry for a chair > arises because it has a macroscopic moment of inertia $I$, so that its > ground state is part of a tower of rotationally excited states whose > energies are separated by only tiny amounts, of order $\frac{{\hbar}^2}{I}$. > This gives the state vector of the chair an exquisite sensitivity to > external perturbations; even very weak external fields will shift the energy > by much more than the energy difference of these rotational levels. In > consequence, any rotationally asymmetric external field will cause the > ground state or any other state of the chair with definite angular momentum > numbers rapidly to develop components with other angular momentum quantum > numbers. The states of the chair that are relatively stable with respect to > small external perturbations are not those with definite angular momentum > quantum numbers, but rather those with a definite orientation, in which the > rotational symmetry of the underlying theory is broken. For the vacuum also, To a very good approximation, the chair is described by quantum electrodynamics $$L= -\frac{1}{4} F_{\mu\nu}F^{\mu\nu} + i \bar{\psi}(\gamma^{\mu}D_{\mu}-m) \psi $$ The rotation of chair corresponds to $SO(3)$ group as a subgroup of the Lorentz group $SO(1,3)$. If vacuum is similar with the chair, the rotational symmetry could also break together with global rigid $O(N)$ symmetry. The standard argument that Higgs boson being a scalar, is to keep Lorentz invariance. If the $SO(3)$ rotational symmetry is lost, then this argument is not necessarily valid. Is there any other rationalization for the Higgs boson being scalar? If vacuum is _not_ similar with the chair, why only global rigid $O(N)$ symmetry is broken but not $SO(3)$? Is that a pure guess then confirmed experimentally?


1. If the universe is expanding, what is it expanding into?   2. When the big bang happened where did it occur?    3. When the big bang happened how did it occur?    4. Where did the energy come from? Energy can not be created or destroyed does that mean, energy has existed before the universe was here?


Is the universe infinite?

Is the universe infinite? Or is it finite? If it is infinite,it's very difficult to imagine an endless space(though not impossible). But if it's finite, the idea that we can't go beyond a certain space just creeps me out. So, what is it actually?


Can we prove that the universe is finite or infinite?

If I say that the universe is finite, how can you say with certain that I am wrong?


What is the universe expanding into?

Due to curiosity, it made me wonder what is outside of the universe, is it a new chemical or just empty space? But empty space have protons appearing and disappearing in it, it basically still has something in it. (It might have something to do with string theory.)


Is the universe finite or infinite?

I thought the universe was finite, but then I read this: How can something finite become infinite? And they seem to assume it is infinite. So which is it?


If the Big Bang theory suggests that the Universe is "expanding" then what is it expanding INTO?

I am a software engineer and not an astrophysicist but I want to know if anyone is working on sorting out what exists outside the universe? So what about outside spacetime? what is there? or shall I assume there are infinite galaxies? and even that is not a satisfying answer. I know this question might get closed soon ... but guys please tell me what is there outside the space as we know it? since childhood I have wondered about this. Its really a simple question. If we say that we live "inside" a Universe ... then we are objectively saying that there IS something "outside" the universe as well? Am I crazy? What exists there? Is it just empty space? Or what?


Space and the size of infinity

If you could build a spaceship and keep travelling in one direction, what would finally happen? One answer is that you would never ever reach the end. But this sounds purely platonic space and comes into conflict with the big bang theory (or the very first big bang, if you claim there have been many big bangs). That is, space was created in the big bang and is expanding and there is no space outside that realm. So what happens if the spaceship doesn't continue travelling forever? This brings us to the second possible answer: the spaceship would eventually stop travelling farther, change its direction and may return. To me, both of these answers are equally scary and unconvincing and contradicting. What would be the ultimate fate of the spaceship considering the big bang as the origin of space? UPDATE: The attempt here is to also make a _distinction_ between the space produced by the big bang and the dimensions outside the universe or whatever existed before the big bang, and come up with an answer as less contradictory as possible. Let us, only for the sake of discussion, imagine a virtual spaceship that can overtake the accelerating expansion of the universe and let it travel in a particular direction. When it reaches the edges of the universe, if that is not very inconvenient, it would surpass the universe itself, in case it doesn't go in circle. Even though this particular thought experiment wouldn't be fundamentally different than the expansion of the universe itself, it may help understand a bit about beyond the universe. Now if the spaceship continues travelling alone outwards, would it be _extending_ the space itself in that particular direction?


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

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


Capacitor with dielectric between the plates

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


Frames, Tetrads and GR

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


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

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


Normal reaction - force without acceleration

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


Can entropy of Universe be constant?

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


Do some half-lives change over time?

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


How does a thermal temperature gun work?

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


Applying Ehrenfest's theorem to Hamiltonian

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


Anharmonic oscillator solution function

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


Sun revolves around the Earth

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


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

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


Relative Motion and orbiting planets

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


What made us think that Earth moves around the Sun?

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


Why was Galilei "right"?

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


heliocentricity and the theory of relativity

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


Revolution of Earth

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


Does the earth really move round the sun?

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


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

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


Heliocentric Worldview

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


motion of an electron near a conducting wire

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


Sterile Neutrinos as Dark Matter

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


cm^3/g as a unit of adsorption

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


Geodesic devation on a two sphere

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


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


Quantization of electrostatic $\vec E$ field?

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


What would cause a spinning fluid to stop spinning?

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


What keeps mass from turning into energy?

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


Can matter be created from energy?

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


Application of $E = mc^2$

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


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

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


velocity in inertial and nontial frames

![enter image description here](http://i.stack.imgur.com/Pik0X.jpg)![enter image description here](http://i.stack.imgur.com/LL2TD.jpg) I got confused about the difference between the last term of both pictures. In the first one, we have w x r, but in the second we have w x r underlined. Does anyone have a better explanation? They should be the same.


Relativistic object impacts the earth

A familiar trope within science-fiction is that of a large relativistic object hitting a planet such as the earth. This is normally an interstellar spacecraft or a kinetic weapon with a mass in the range 103 \- 106 kg. But what would actually happen? The two scenarios seem to be: (a) the object creates a kind of conical tunnel through the earth with most of the material exiting on the far side; (b) the object dumps all of its kinetic energy within a few tens or hundreds of kilometres of the impact point and we have the equivalent of a conventional asteroid impact. Light transit time through an earth diameter of 12,800 km is just over 40 milliseconds. There’s not much time for lateral effects as the object barrels in. So what would happen if a 1 tonne object hit the earth, square on, at 0.99995c (γ = 100)?


The velocity of sound in terms of Fermi velocity

Assume this question: In a simple model of a monovalent metal consisting of point positive ion cores embedded in a uniform jellium of electrons, a value for the average energy for electron is: $$E = \frac{9}{10} \frac{e^{2}}{r} + \frac{3\hbar^{2}}{10mr^{2}}\left(\frac{9}{4\pi}\right)^{2/3}$$ where r is the radius of a sphere containing one electron. Find the velocity of sound in terms of Fermi velocity. I'm attempting to solve this question, but I only can find the equilibrium vaule of $r$. I cannot understand the relation between the velocity of sound and this question.


Euler's buckling formula applicable for impact calculations?

$$F = \frac{\pi^2 EI}{(KL)^2}$$ Is Euler's buckling formula applicable for impact calculations, considering speeds relevant for a car or aircraft crash? If there is a level where the formula becomes inapplicable or inappropriate in impact calculations, what determines this, and what behavior (and hence other formula) will then be relevant?


States of matter in physics are the distinct forms that different phases of matter take on. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. What is physics behind States of matter? **For Example:** I found a Trick to freeze water in about half a second, in this trick, When I open caps of a plastic bottle of cold water, cold Water freezes in a chain process, You can see the freezing process. What is physics of The process of freezing water?


What sense can be made of the natural logarithm in physics?

What sense can be made of the natural logarithm, When appearing in a physical process? For example, This integral in the thermodynamic $\int_i^f \frac {dV}{V}=Ln\frac {V_f}{V_i}$ when $V$ denotes Volume. in general $Ln\frac {Q_f}{Q_i}$ when the $Q$ denotes Physical quantities. or this one $S=k_BLn\Omega$ Why sometimes natural logarithm can be interpreted as a physical process? What are the odds of that happening?


Compact manifold taken as an Einstein Manifold

In Kaluza-Klein theories I often see that the compact space is assumed to be an Einstein manifold, that is, its Ricci tensor is proportional to its metric. So, why is this done?


What kind of invariants are proper time and proper length?

Under the Lorentz transformations, quantities are classed as four-vectors, Lorentz scalars etc depending upon how their measurement in one coordinate system transforms as a measurement in another coordinate system. The proper length and proper time measured in one coordinate system will be a calculated, but not measured, invariant for all other coordinate systems. So what kind of invariants are proper time and proper length?


R-symmetry commutator

I've seen the claim made several placed; Terning's "Modern Supersymmetry" p. 5 on N=1 SUSY algebra states it as well as anyone: > The SUSY algebra is invariant under a multiplication of $Q_\alpha$ by a > phase, so in general there is one linear combination of $U(1)$ charges, > called the $R$-charge, that does not commute with $Q$ and $Q^\dagger$: > >> $[Q_\alpha,R] = Q_\alpha, \;\;\;[Q^\dagger_\dot{\alpha},R]=-Q^\dagger_\dot{\alpha}$ The first statement is straightforward to see. But (1) Why is there is one linear combination of charges that does not commute? (2) How do we arrive at these commutators? (I imagine that the generators can be rescaled to give the coefficient $\pm1$, but I would like a clearer explanation.) I spoke to a peer who said that the commutation relations could be found in a very general, mathematically heavy treatment of the most general possible SUSY algebra. Is there some easier way to understand?


Slowing down light in an opaque crystal for a whole minute

I just read about a team of physicists at the University of Darmstadt, Germany, that managed to completely slow down a beam of light that traveled through an opaque crystal (article here). How is it possible for a beam of light come to a complete stop? In the article they mentioned that they fired a laser at the crystal causing the atoms to go into a quantum superposition. How does this affect the stopping of the light? Also if the uncertainty principle applies to photons (which I do not know if it does), how does this not violate the uncertainty principle if the photons aren't moving?


What is the difference between baryonic and gravitational mass?

I was reading a webpage on neutron stars, and it mentioned that a neutron star's gravitational mass is about 20% lower than its baryonic mass due to gravitational redshift. I understand the basics of what the terms mean, but I do not see why gravitational redshifting would cause the gravitational mass to be reduced.


Will this achieve linear movement of a closed container?

Can I create a device that moves in one direction with a design like Figure 1? I suspect that the forces cancel each other by the recirculation. It is a simple exercise of action and reaction, but I can not figure out the math to explain. Maybe my problem is of type XY problem. My intention is to create a device that produces movement from a **closed container** , something like a black box. (which would be added energy) Figure 1. ![enter image description here](http://i.stack.imgur.com/dt1NI.png)


Asymmetry in magnetic field direction of an electric wire

The simplest magnetic field is that of an infinitely long wire with uniform current. It does enjoy radial symmetry about the wire and has the variation as 1/r. To find the direction of the resulting magnetic field you use the right hand grip rule (for conventional current). This rule repeats the experimental fact. But it is a asymmetry. We get a bit less asymmetry calculating the magnetic field for a "anti"wire with positrons. Now we have to use the left hand grip rule. Where this asymmetry comes from?


Proof that total derivative is the only function that can be added to Lagrangian without changing the eom

So I was reading this: Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time and while the answers for the first question are good, nobody gave much attention to the second one. In fact, people only said that it can be proved without giving any proof or any. So, if I have a Lagrangian and ADD an arbitrary function of q', q and t in such a way that the equations of motion are the same, does this extra function MUST be a total time derivative? **EDIT** Ok, I feel really dumb now. I guess the most voted answer of the question I posted was kinda wrong. So, I changed my question a little bit: If I have a function that obeys the Euler-Lagrange equation off-shell, this implies that my function is a time derivative? This was used in the most voted answer of this other question: Deriving the Lagrangian for a free particle , equation 7. Also, why people only talk about things that change the lagrangian only by a total derivative? If this is not always the case that keeps the equation of motion the same, so why is it so important? And why in the two questions I posted about the same statement on Landau's mechanics book only consider this kind of change in the lagrangian?


What's the difference between running up a hill and running up an inclined treadmill?

Clearly there will be differences like air resistance; I'm not interested in that. It seems like you're working against gravity when you're actually running in a way that you're not if you're on a treadmill, but on the other hand it seems like one should be able to take a piece of the treadmill's belt as an inertial reference point. What's going on here?


kitaev-honeycomb : can't get wilson loop squared to yield +1

I'm new here, loving this website and I'm having some difficulty with the wilson-loop operator in kitaev's honeycomb model. **problem statement** The Kitaev model (Kitaev, 2006 is the original paper) consists of spins residing at the lattice sites of a honeycomb lattice with separate nn couplings for the three directions that are identified for the bonds. The wilson-loop operator is $w_p=\sigma^x_1 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6$, where the indices $i \in\\{1,...,6\\} $ indicate the $6$ lattice sites involved in the hexagonal loop (see picture). ![Kitaev honeycomb loop](http://i.stack.imgur.com/aiT0X.png) In Jiannis K. Pachos' book (Introduction to topological quantum computation, 2012) the author states that $(w_p)^2=1$, which I'm trying to find myself. Actually this should be not at all hard, but I'm stuck unfortunately. **attempt at solution** I've tried the following $$ (w_p)^2 = \sigma^x_1 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^x_1 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \\\ = -\sigma^x_1 \sigma^x_1 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \\\ = -\sigma^y_2 \sigma^y_2 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \\\ = + \sigma^z_3 \sigma^z_3 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^x_4 \sigma^y_5 \sigma^z_6 \\\ = + \sigma^x_4 \sigma^x_4 \sigma^y_5 \sigma^z_6 \sigma^y_5 \sigma^z_6 \\\ = - \sigma^y_5 \sigma^y_5 \sigma^z_6 \sigma^z_6 \\\ =-1 $$ Where I've pulled $\sigma_1$ through first, next the $\sigma_2$, etc. And I've used $\\{\sigma^\alpha_i , \sigma^\beta_j \\}= 2 \delta_{i,j}\delta_{\alpha,\beta} I_2 $ (so that every swapping of unequal $\sigma$'s gives a minus sign and $\sigma^\alpha_i\sigma^\alpha_i =I_2$ ). So I get $(w_p)^2=-1$, which is not what I wanted to find. All text on the subject state that $w_p$ acting on a lattice configuration yield $w_p=\pm1 $ which can be easily concluded from $(w_p)^2=1$ (the expression I didn't get). My guess is that my commutation relations are not correct, but I'm unsure. Who can help me out? A big thanks in advance! Best, L


Symmetries of a Uniform Magnetic Field

Simple question. A system with a uniform electric field everywhere in space has translational invariance in the directions perpendicular to the electric field but no translational invariance parallel to it. This system also has rotational invariance in the plane perpendicular to the electric field. What about a uniform magnetic field? Judging from the Hamiltonian $(\vec{p}-q\vec{A})^2/2m$, it would seem that the symmetries depend on our choice of gauge. Choosing a different $\vec{A}$ breaks different symmetries. Is there a most symmetric choice for $\vec{A}$?


'Hole in the clouds' in the Sarychev Peak eruption

One of my favourite ever pictures taken from space is a picture of the 2009 eruption of Sarychev Peak (Ostrov Matua island, Japan) taken by an ISS astronaut during a lucky fly-over. ![enter image description here](http://i.stack.imgur.com/O1FfD.jpg) Image Source: Earth Observatory Image of the Day. I heartily recommend clicking through and seeing the animation. I always assumed that the hole in the cloud cover around the island was caused by some sort of shockwave originating in the eruption plume, most probably as a result of increased temperatures evaporating the cloud, or some such. However, upon revisiting the IOTD page, I was surprised to learn that this is not necessarily the case and that the origin of this hole is a matter of some controversy: > **Editor’s note: Following the publication of this photograph, the > atmospheric and volcanic features it captured generated debate among > meteorologists, geoscientists, and volcanologists who viewed it. Post- > publication, scientists have proposed—and disagreed about—three possible > explanations for the hole in the cloud deck above the volcano. > > One explanation is that the hole in the clouds has nothing to do with the > eruption at all. In places where islands are surrounded by oceans with cool > surface temperatures, it is common for a sheet of clouds to form and drift > with the low-level winds. When the cloud layer encounters an island, the > moist air closer to the surface is forced upward. Because the air above the > marine layer is dry, the clouds evaporate, leaving a hole in the cloud deck. > These openings, or wakes, in the clouds can extend far downwind of the > island, sometimes wrapping into swirling eddies called von Karman vortices. > > The other two possibilities that scientists have offered appeared in the > original caption. One is that the shockwave from the eruption shoved up the > overlying atmosphere and disturbed the cloud deck, either making a hole or > widening an existing opening. The final possibility is that as the plume > rises, air flows down around the sides like water flowing off the back of a > surfacing dolphin. As air sinks, it tends to warm; clouds in the air > evaporate. **Has this controversy been settled?** Is there a convincing, accepted explanation for the origin of the hole in the cloud cover?


The equivalent electric field of a magnetic field

I know that Lorentz force for a charge $q$, with velocity $\vec{v}$ in magnetic field $\vec{B}$ is given by $$\vec{F} =q \vec{v} \times \vec{B}$$ but there will exist a frame of reference where observer move at same velocity with that of charge $q$, so according to him $v=0$. hence he will see no magnetic force is exerted on charge $q$. I have work on this problem for a while and found that the special relativity predicts equivalent electric force will acting upon charge instead. I want to know the relationship between this equivalent electric force and magnetic force. Thanks in advance


How does beta+ decay actually occur?

I'm having difficulty in understanding beta plus decay. How can a proton which has slightly less mass than neutron transform into a neutron, positron and neutrino? Form where does the extra mass for neutron,electron and neutrino come? Is it that during the decay some of the binding energy gets converted into mass?


Why is a new moon not the same as a solar eclipse?

Forgive the elementary nature of this question: Because a new moon occurs when the moon is positioned between the earth and sun, doesn't this also mean that somewhere on the Earth, a solar eclipse (or partial eclipse) is happening? What, then, is the difference between a solar eclipse and a new moon?


Why does a dielectric have a frequency dependent resistivity?

This question has come about because of my discussion with Steve B in the link below. Related: Why is glass much more transparent than water? For conductors, I can clearly see how resistivity $\rho\,\,(=1/\sigma)$ can depend on frequency from Ohm’s law, $\mathbf{J}=\sigma\mathbf{E}$. So if the E-field is an electromagnetic wave impinging on a conductor, clearly the resistivity is frequency dependent. In a similar fashion, the frequency dependence of the electric permittivity $\epsilon=\epsilon_0n^2(\omega)$ can be derived through the frequency dependence of the electric polarization and impinging electromagnetic wave (see How Does $\epsilon$ Relate to the Dampened Harmonic Motion of Electrons?).   1. What does it mean physically for a dielectric to have a frequency dependent resistivity from (i) classical and (ii) quantum viewpoints? I am especially interested in the optical frequency range.   2. Can a simple mathematical relationship be derived similar to the frequency dependent resistivity (for conductors) and electric permittivity (for dielectrics)? Thank you in advance for any help on this question


Would connecting p-type and n-type semiconductors work as a diode?

If we placed `p-type` and `n-type` semiconductors close enough to be touching (see fig. 1), would this arrangement work as a diode? Please explain. ![connecting p-type and n-type semiconductors](http://i.stack.imgur.com/n5UzB.jpg) Fig. 1 - Connecting p-type and n-type semiconductors


Off-diagonal terms of the Husimi $Q$ function?

The Husimi $Q$ function of a quantum state $\rho $ is defined as $ Q (\alpha)=\langle \alpha \vert \rho \vert \alpha \rangle $, where $\alpha = (x, p) $ is a phase space coordinate and $\vert \alpha \rangle$ is a coherent state. Is the off-diagonal generalization $ Q (\alpha, \beta)=\langle \alpha \vert \rho \vert \beta \rangle $ used for anything? Does it have a name? This is an interesting object because it essentially measures coherence (or decoherence) in the overcomplete basis of wavepackets .


Do image charges radiate?

Suppose I have a charge moving back and forth above an infinite, grounded, conducting plane. Can I calculate the total radiated power by using image charges? That is, are the scalar and vector potentials the same in the upper- half space for all time for both the image charge "picture" and the standard picture?


A nonintegrable quantum system whose classical limit is integrable?

In this discussion: http://chat.stackexchange.com/rooms/4243/discussion- between-arnold-neumaier-and-ron-maimon Arnold Neumaier suggested that there might be a close link between classical and quantum integrability, while I think there are many more classically integrable systems than quantum integrable ones. The reason is that classically integrable systems are easy to make up--- you make up an infinite number of action and angle variables, and change canonical coordinates in some complicated way to x,p pairs, and say this x-p version is your system of interest. But quantum systems don't admit the same canonical transformation structure as classical systems, so there might be systems which have an integrable classical limit, but no real sign of integrability outside of the classical limit. But I don't know any examples! Most of the 1+1d integrable stuff is for cases where the classical and quantum integrability are linked up, for the obvious reason that people are interested in finding integrable systems, not examples where they are not. The reason I think finding an example is not trivial is because the classical integrability guarantees that the motion is not classically chaotic, and that the asymptotic quantum energy states are pretty regular. So I don't think one can look for a counterexample in finite dimensions, where all high enough energy states are permanently semi- classical. But consider a field theory on a lattice in 2+1 dimensions (continuous time). The lattice is so that the dynamics can be arbitrary, no continuum limit, no renormalization. Even if you have an integrable classical dynamics for the field theory, the energy can still dissipate over larger volumes (this isn't 1+1 d), and eventually the classical field will be weak enough that the classical limit is no longer valid, and you see the quanta. This allows the possibility that every finite energy state to eventually leave the semi- classical domain, and turns quantum, and then the integrability is lost. So is there a 2+1 (or 3+1) dimensional lattice scalar field theory where the classical dynamics is integrable, but the quantum mechanical system is not? By saying that the quantum system is not integrable, I mean:   * the many particle S-matrix doesn't factorize or simplify in any significant way (aside from the weak asymptotic relations implied by having a classical integrable limit)   * there are only a finite number of quantum conserved currents (but an infinite number of conserved currents in the classical limit).


Is there any significance to the negative sign on this speed?

A girl is riding a bicycle along a straight road at constant speed, and passes a friend standing at a bus stop (event #$1$). At a time of $60$ s later the friend catches a bus (event #$2$) If the distance separating the events is 126 m in the frame of the girl on the bicycle, what is the bicycle's speed? $$u = u' + v$$ can be written as: $$Δx/t = Δx'/t + v$$ $$v = Δx/t - Δx'/t$$ $$v = 0m/60s - 126m /60s$$ $$v = -126 m/ 60s$$ $$v = -2.1 m/s$$ Just wondering if the negative holds any significance? I know we're talking about speed which is scalar but how come the calculation gives a negative? Sorry I am just beginning to learn about relativity.


How can you test what color different people perceive?

If I would show someone a yellow object and ask them, "is this object yellow?"   That person would say "yes". But I could never know if my perception of the color yellow is the same as that other person's.   Because he or she could actually be seeing, what I know to be the color green.   But then tells me that its the color yellow because that has been taught to him or her from young age. So how can you test if people are really seeing the same color? Question closed and can now be found @ http://biology.stackexchange.com/questions/5728/how-can-you-test-what-color- different-people-perceive


M-Theory and computer simulation

I have a question. Is it possible to perform computer simulations based on the M-Theory? I was looking for such simulators or source codes but I have not found anything. However, M-theory must have a mathematical model that can be saved as a code to be executed by the computer. Something like this might work? Leaving aside the problem of computational complexity.


Calculate work done in an inclined plane

How can you calculate the work done by a force (of unknown quantity) exerted on a 10kg block on an inclined plane. The force is pointing upwards and parallel to the incline (which is inclined 30 degrees with respect to the horizontal). a. frctionless plane b. coefficient of friction = 0.12 So the forces acting the block are the normal force, its weight, the friction force (for letter (b)), and the force exerted upwards the incline. All are given or can be solved almost instantly except for the force upwards denoted by F. How do I solve this problem? I am not sure what value of acceleration to use in the axis of the incline for F=ma. Sorry I could not provide a diagram for this.


Physical significance of negative temperature

I read some answers regarding negative temperatures but I think my question is new. I want to know that what is the physical significance of negative temperature. Suppose I say a body has temperature -2 K. Can I interpret it physically?


How does a fixed amount of transmitted radio energy supply an unknown number of destinations?

I did some maths and physics up to the age of 18, and hold an amateur radio licence. This thing has puzzled me for a while - does reception of an electromagnetic wave imply an interaction with the transmitter? Does it drain some of the transmitter's energy?


Heisenberg's uncertainty principle - Planck's (reduced) constant divided by two or not?

The most common form of Heisenberg's uncertainty principle I've seen online is $$ \Delta x \Delta p ~\geq~ \dfrac{\hbar}{2}.$$ However, I also regularly see $$\Delta x \Delta p ~\geq~ \hbar. $$ Sadly, I used the latter one in a project recently and I'm afraid it's incorrect. Obviously the upper one one is true if the latter one is, but why are these two versions used instead of only one of them?


Proof of Gauss' Law

How would you prove Gauss' law for an asymmetrical closed surface? I can find it for symmetrical surface but couldn't for Asymmetrical surfaces.


Understanding a paper: What is the meaning of $b_0$?

I am looking at this paper (Multicoated gratings, J. Opt. Soc. Am., 1981) and I am getting confused around equation 22. I do not completely understand where he comes up with the equation $$\xi^j_q=b_q^j(R^{-1}V_q^j)\qquad \text{(22)}$$ And then what is the meaning of the $b^{j+1}$. I initially thought they were the eigenvalues of the T matrix he defines, but all he says is that it is a vector of components $b^q_j$. This includes the $\bf b^0$ and $\bf b^{Q+1}$ which I do not see how they are vectors?


band gaps in tight binding model

What happens at the zone boundaries of the brillouin zones in the tight binding model? How does the band gap originate in the TB model?


What is an observer in quantum mechanics?

My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts. **What is an observer?** What are the conditions required to be qualified of **observer** , both mathematically and experimentally?


What is an "observer" really?

> **Possible Duplicate:**   >  What is an observer in quantum mechanics? I'm sick of quantum physics explanations which term experiments where the outcome depends on "if you observe it or not". For example, the two-slit photon experiment. I figure that something physical happens, irrespective of if a "being" of some kind is there to consciously watch it. Is it really to do with absorption and emission? Like the only way to know for sure where a photon is, you need to have it absorbed and re-emitted by an atom/electrons so that you can detect it (on one level, seeing with your eyes is about absorbing photons on the atoms in your eye and having that create a potential on your nerves which can travel through your brain). So in a sense, if a tree fell in the forest and nobody heard, it still would have fallen because the atoms in the tree would have absorbed thermal energy, and the atoms of the tree would have caused a vibration in the tree and the ground, which vibrated the air, and so this energy would have dissipated into the environment, and that counts as observation without a human ever getting involved? Do I understand things or am I very wrong?


Quantum observation in the double slit experiment?

As far as quantum observation, when a human observes electrons going through the double whole experiment, have scientist tried having a blind person observe the experiment to see if the electrons actually can tell if a person is able to view it or not? This will tell us a lot as far as how intelligent the electrons are and if a persons eyes gives off a certain radio signal to warn the electrons of its observation.. This may seem crazy but i had to ask.


What does it mean 'the observer' in Quantum Physics?

Is it only necessary a human consciousness? A measurement device? Can it be said that any of them cause the wave function collapse?


Some very basic questions on the Higgs Boson

What exactly is a boson? Is the Higgs boson the cause of gravity or a result of it? Does the collision of particles at the LHC create a gravity field or waves or somehow interact with the gravity field of the earth? The Higgs Boson is supposed to be quite massive and equivalent to a large number of protons. Were many particles needed to create it or only a few travelling at high speeds? Was the high energy converted into the large mass? Why is the particle so short lived and what does it decay into?


Space curvature based on net energy = 0

In Neil DeGrass Tyson's epic video, at 2:26:50 https://www.youtube.com/watch?v=AdHlVY8pEk0&list=PL1L9zQimONkUOxXJyM0xcJja9ItQu1P8l&src_vid=AdHlVY8pEk0&feature=iv&annotation_id=annotation_4179310099#t=12s He mentions how if net energy is negative, the spacetime curvature is spherical, and if it's net positive, saddle-shaped. He uses the terms "flat" and "saddle-shaped" which are 2d, but he's actually just using that as an analogy for 3d curvature, which we can't really visualize, correct? If so, what does it mean for 3d space to be "saddle- shaped" or "spherical"? 1) II'm guessing spherical implies that if we keep traveling in one direction in space, it would be possible to end up back where you started? (kind of like how you can end up in the same position traversing the surface of a planet if the 2d plane is curved? 2) If net energy is 0. But they also say there is far more dark energy and dark matter than energy and matter. So isn't this a contradiction? How does the accounting work out?


Does gravity act in the centre of the Earth?

If we we dig a hole from north pole to the south pole of the Earth and we throw a ball in this hole where would it stop? Will it come back on the surface or it will stop at the centre?


What did recombination look like?

I recently remembered that someone worked out what the big bang sounded like and that got me thinking... About 377,000 years after the Big Bang, electrons became bound to nuclei to form neutral atoms. Because of (?) this, the mean free path of photons became effectively infinite, i.e. the universe became transparent to radiation. **What would this have _looked_ like?** More precisely I could ask: did the sky suddenly become dark, or was the amount of radiation basically same after as before? What would the distribution and timescale have been like? In a perfectly homogeneous universe it would happen at the same rate everywhere. Did the universe have any structure at this point? Would you have been able to see blotches of lighter and darker patches of the sky (assuming you were within one of the more transparent patches), these being proto-shapes of galactic filaments perhaps, or the noisy grit of the CMB? Or would it just be a vague cloud at any scale, and in any part of the spectrum?


Comparing Energy Technologies in terms of: Cost per Power Capacity  and Research Spendings

### Cost per Power Capacity For a number of energy technologies I'd like to know what the minimum costs are to install a given power capacity. Are there any such comparisons available? ### Research Spendings Technologies often own much to publicly funded research efforts so I'm also interested in estimations regarding development cost of the technologies themselves. Of course foundations to a given technology may have been readily available, so let's limit this to spendings on larger research projects _dedicated_ to developing a technology and motivated by the need of energy. I'm aware it's unlikely any exhaustive comparison in full detail exists but maybe something related? (Maybe someone should tag this question 'energy-economics' -- I'm lacking the reputation)


Q factor of parallel RLC circuit in series with a capacitor and resistor

I know that for parallel RLC circuits, the $Q$ factor is given by: $$ Q = R \sqrt {\frac{L}{C}} $$ But now suppose it is connected in series to a resistor $R_2$ and capacitor $C_2$. Would the $Q$ factor be changed? ![enter image description here](http://i.stack.imgur.com/dpLzs.png)


why is mass of air bubble in material medium considered to be negative?

The mass of air bubble in any medium is considered as negative. Is the air bubble is massless. I m in confusion. can we not neglect the mass of air bubble in material medium. But i have found in many books the mass of air bubble in material medium as negative. please discuss.....


Are Newton's gravity waves detectable by a laser interferometer?

Newton's theory of gravity supports "gravity waves" in that moving objects cause changing gravitational fields. For example, two bodies rotating around their center of mass will have a stronger gravitational field when they are longitudinally oriented than when they are transverse oriented. Given two masses of mass $M$ orbiting on a circle of radius $r$, at a distance $d$ from an observer, the strength of the attraction is: $$\begin{matrix} F_{min} &=& \frac{2GM}{d^2},\\\ F_{max} &=& \frac{2GM}{d^2}\frac{1+r^2/d^2}{(1-r^2/d^2)^2} \end{matrix}$$ ![enter image description here](http://i.stack.imgur.com/dIjHy.jpg) This should be detectable at long distance. My question is this: With that sort of gravity, would the laser interferometer based gravity wave detectors be able to detect the gravity wave? An example is the LIGO, Laster Interferometer Gravitational-wave Observatory.


Is there a published upper limit on the electron's electric quadrupole moment?

I understand an electric quadrupole moment is forbidden in the standard electron theory. In this paper considering general relativistic corrections (Kerr-Newman metric around the electron), however, there is a claim that it could be on the order of $Q=-124 \, \mathrm{eb}$. That seems crazy large to me, but I can't find any published upper limits to refute it. Surely someone has tested this? Maybe it's hidden in some dipole moment data? If not, is anyone planning to measure it soon?


Electron Wave Interference

In the double slit interference pattern for the wave of an electron, what will happen if I make the slits to be smaller than the size of an electron ? Will I still observe an interference pattern on the opposite side of the screen or no electron will be able to cross the slit? If no, then how can a quantum prisoner escape ?


Why is everything colder nowadays?

I know that when the universe began it was incredibly hot. Ever since, it is been cooling, and nowadays the average temperature of the universe is quite close to 0 K. Is this a consequence of having the same energy spread in a wider space, or is there something else going on?


Exciting Surface Plasmon-Polaritons with Grating Coupling

I'm very new the topic of SPPs and have been trying to understand this particular method of exciting surface plasmons using a 1D periodic grating of grooves, with distance $a$ between each groove. If the light incident on the grating is at an angle $\theta$ from the normal and has wavevector ${\bf k}$, then apparently if this condition is met: $\beta = k \sin\theta \pm\nu g$ where $\beta$ is corresponding SPP wavevector, $g$ is the lattice constant $2 \pi/a$ and $\nu={1,2,3,...}$ then SPP excitation is possible. I haven't ever really had a formal course in optics, so my question is where this condition comes from. It seems like Fraunhofer diffraction, but only for the light being diffracted at a $90^\circ$ angle to the normal. Most books don't state how they get this result, they just say it's because of the grating "roughness" which really confuses me. Any help would be greatly appreciated.


Jumping sewer lid - WHY?

**Intro:** Few hours ago, there was a storm. We heard some constant banging which couldn't be explained by thundering. Then we found out, it was a sewer lid jumping. Maybe it's normal in other parts of the world, but for me it was like the first time in my life. I've captured the video. **The question** is what was causing this to happen. It's kind of clear that it was air pressure so strong that it was capable of lifting this metal lid. But where did this air pressure appear?   * Wind blowing into the sewer? If so, would it be so strong to lift the lid? And shouldn't be the sewers protected against wind somehow?   * Water filling the sewer so quickly, that it made the air pressure this strong? Would this really be the easiest way for the air to leave the sewer?   * Something else (such as bored sewer worked :) )?


Minimum size of an asteroid to actually impact earth

From what I understand, an object entering the atmosphere will start to burn up from the tremendous resistance of the atmosphere. Presumably, for asteroids under a certain size, they will burn up completely and never impact the surface of the earth. Do we have a way of determining the minimum size needed for actual impact? If so, roughly what is the size and how does it compare to the average size of asteroids that pass by us regularly?