Can PEPS explain the holographic principle in quantum gravity?

Condensed matter physicists have shown using quantum information that in many condensed matter systems, entanglement entropy only scales as the area of the boundary, and not the volume. This is the basis for the density matrix renormalization group and Projected Entangled Pair States (PEPS). Does this also explain the holographic principle in quantum gravity?


is the sun itself moving

I just thought of an interesting question.Is the sun actually moving? I have learnt that the way the lunar landers and the space ships of the Mercury and Apallo missions moved and controlled their positions through the use of thrusters.NoW apply that same concept to the sun are the constant explosions on the surface of the sun enough to move it?


What is the formula for the relativistic ellipse?

If an astronomer moves at relativistic speed, the stars and constellations are distorted. He sees the stars towards which he is moving blue shifted, while the ones he's moving away from are red shifted. In addition, the apparent direction of distant stars is modified. I think that the coolest way of representing this is the "relativistic ellipse". Think of a spherical shell with the inner surface reflective. Imagine a flashbulb going off at the center. The light is reflected and returns to the source. Now think of the same situation observed from a moving frame of reference. The light is still emitted and returns to the center at the same time, but that point has now moved. Since the speed of light is the same in all frames of reference, the distance traveled by each light ray has to be the same. So the paths of the light rays (and the boundary of the spherical shell) describes an ellipse, the "relativistic ellipse": ![RelativisticEllipse](http://i.stack.imgur.com/9PoOJ.png) The above drawing is from the book "Relativity in Curved Spacetime" which I highly recommend and can be purchased here or here. Perhaps when my copy arrives it will have the equation. Should be possible to work it out using Lorentz invariance or contraction or something similar. * * * Per the answer by Helder Velez, Chapter 4 of Hans de Vries's book has the following useful diagram:   ![HansEllipse](http://i.stack.imgur.com/gC4Gu.jpg)


What is the extent of Earth's gravitational pull?

1. Where the gravitational pull of Earth exist up to?    2. What distance from Earth it will be zero?   3. How do the skydivers fly at a same altitude?    4. Won't they feel gravitational pull?    5. What is the Earth's gravitational pull?


Dimensonal analysis of damping constant?

What are the units of the damping constant from the following equation by dimensional analysis? $$\zeta = \frac{c}{2\sqrt{mk}}$$ I'm assuming the units have to be s^-1, as the damping constant is present in the exponential equation which plots damping of y=Ae^kt (which plots amplitude vs time). Is that a correct assumption? If somebody could do a quick dimensional analysis to confirm it would be great.


Net acceleration felt by a body on Earth

For any body on earth will the only acceleration it has be gravity or should we take into consideration even centrifugal force due to rotation? Is there any precise formula to determine the net acceleration?


Kepler's third law doesn't give earth's orbital period! Why?

I tried to calculate earth's orbital period using Kepler's third law, but I found 365.2075 days for the orbital period instead of 365.256363004 which is the correct value. I checked everything, and I couldn't find what's the problem. I used these values for my calculation:   * Semi-major axis, a: 149,598,261 km   * Gravitational constant, G: 6.67*10-11 N·(m/kg)2   * Solar mass, M: 1.9891*1030 kg


How to calculate the energy freed in the reaction: $^{10}_5Be +\space ^2_1H \rightarrow \space^{11}_5B + \space ^1_1H$?

I have the following reaction: $^{10}_5\mathrm{Be} +\space ^2_1\mathrm{H} \rightarrow \space^{11}_5\mathrm{B} + \space ^1_1\mathrm{H}$ And I know that I have to use the formula: $E = \Delta m\cdot c^2 = \Delta m \cdot \frac{931,5MeV}{u}$. So I just need $\Delta m$ which is equal to: $\Delta m = m_b - m_a$ where $m_b$ represents the mass "before the reaction" and $m_a$ the mass "after the reaction" so we have:   $m_b = m(^{10}_5\mathrm{Be}) + m(^2_1\mathrm{H})$   $m_a = m(^{11}_5\mathrm{B}) + m(^1_1\mathrm{H})$ The book which contains this problem contains the following table: http://i.imgur.com/esoGDVf.png but from this table, I only know $ m(^1_1\mathrm{H})$ and $m(^2_1\mathrm{H})$ i.e.   $m_b = m(^{10}_5\mathrm{Be}) + 2.01410u$   $m_a = m(^{11}_5\mathrm{B}) + 1.00783u$ How do I calculate $m(^{10}_5\mathrm{Be})$ and $m(^{11}_5\mathrm{B})$ ? P.S. I don't know if the tag is correct. The chapter in the book where I found this exercise is called "Basics of nuclear physics".


About unitarity and R-charge in 2+1 superconformal field theory

* How does unitarity require that every scalar operator in a $2+1$ SCFT will have to have a scaling dimension $\geq \frac{1}{2}$ ?    * Why is an operator with scaling dimension exactly equal to $\frac{1}{2}$ said to be "free (i.e decoupled from the rest of the theory)" ?    * Let us say that we know in some such theory the R-charge is monotonically decreasing with increasing coupling constant (say $\lambda$). Then define $\lambda _n ^f$ to be that value of the coupling constant at which the R-charge of the operator $Tr[\phi ^n]$ becomes $= \frac{1}{2n}$. Let $\lambda _n ^m$ be that that value of the coupling at which the R-charge of the same operator becomes $= \frac{2}{n}$ (..marginal ?..) Then clearly $\lambda _n ^m < \lambda_n ^f$.  How does this imply that there has to exist a $\lambda _c \leq \lambda_2^f$ where the theory might undergo a phase transition?


Time dilation in a gravitational field and the equivalence principle

A clock near the surface of the earth will run slower than one on the top of the mountain. If the equivalence principal tells us that being at rest in a gravitational field is equivalent to being in an accelerated frame of reference in free space, shouldn't the clock near the earth run _increasingly_ slower than the other clock over time? If those two clocks are considered to be in two different frames of acceleration, the one near the earth will have a greater acceleration than the one on the mountain, and thus over time, their relative velocity will increase over time which will increase the time dilation. Or is this not a proper use of the equivalence principle?


Given that matter cannot escape a black hole, how did the big bang produce the universe we see today?

Extrapolation of the expansion of the Universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. If the matter contained within our galaxy were concentrated within a small radius wouldn't that lead to the entire universe being a black hole? If so how is it that all the matter of our observable universe could have originated from a region of infinite density?


Heat of vaporization of water - dependence on relative humidity?

Does the heat of vaporization of water depend strongly on the relative humidity of the gas into which it evaporates? Some context: If we want to calculate the dew point of water, we find the temperature at which the _partial pressure_ of the water lies on the liquid/vapor boundary of the water phase diagram. This is why water can evaporate from our bodies even though we do not heat it to anywhere near its boiling point. The heat of vaporization should be pressure dependent (in addition to temperature dependent). Yet, when specifying the heat of vaporization, most references only specify the _total_ ambient temperature, usually 1 atmosphere. Why is the total pressure used in this case instead of the partial pressure? And if the partial pressure is what matters after all, then wouldn't relative humidity be important when calculating heats of vaporization? Of course, relative humidity governs the rate and the total amount of evaporation, which is why we can't cool ourselves by sweating in humid weather, but that's not what my question is about.


Hydrogen ground state energy calculation?

We want to find the energy of a hydrogen atom ($Z=1$) in the ground state $$ \psi_{100} = \frac{1}{\sqrt{\pi}}e^{-r}\ \ \ \ \ \ (\mbox{atomic units}) $$ with Hamiltonian $$ H = -\frac{1}{2}\nabla^2-\frac{1}{r} $$ Then $$ \begin{align*} \langle \psi_{100}|H|\psi_{100}\rangle &=\int_0^\infty \int_0^{2\pi} \int_0^\pi r^2\sin\theta\frac{1}{\sqrt{\pi}}e^{-r}\left(-\frac{1}{2}\frac{d^2}{dr^2}-\frac{1}{r}\right)\frac{1}{\sqrt{\pi}}e^{-r} d\theta d\phi dr \\\ &=\int_0^\pi \sin\theta d\theta \int_0^{2\pi}d\phi \int_0^\infty \frac{r^2e^{-r}}{\sqrt{\pi}}\left(-\frac{1}{2\sqrt{\pi}}e^{-r}-\frac{1}{r\sqrt{\pi}}e^{-r}\right)dr \\\ &= 4\pi \cdot \frac{1}{\pi}\int_0^\infty \left(-\frac{r^2}{2}e^{-2r}-re^{-2r}\right)dr \\\ &= 4\left(-\frac{3}{8}\right) \\\ &= -\frac{3}{2} \end{align*} $$ However, I've read everywhere that $E = -\frac{Z^2}{2n^2}$, and so for a hydrogen atom in the ground state we should have $E=-\frac{1}{2}$. So why am I getting $-\frac{3}{2}$? I've double-checked with Mathematica.


Lever Counterweight of uneven weight distances

So, I have a camera crane that has a pivot leaving 2 distances, 0.5mts and 1.5mts respectively. Plus a small L-shaped piece of metal and the end of d2 (1.5) which holds a camera, which I suppose I have to add it to the force applied on that side. One additional variable is that there's a piece of metal attached to the fulcrum and then connected to the second distance (d2, 1.5) at the end, which leaves me the doubt of where to add that weight (which is 580grs, let's say d2*) to the force, or add it as another variable in the equation. The current equation that i'm using (which was without the second piece of weight on distance 2) is: $$ w = \dfrac{f * d2}{d1} $$ ![Lever example](http://i.stack.imgur.com/1P35v.png) So i'm dubious if this is the right equation taking in count the variables I have explained above. Thanks!


Noether's Theorem in Field Theory

This question is regarding Noether's Theorem in general, but also in the application to an example. The example is: > _Find the conserved current for the Lagrangian_ > $$L=\bar{\psi}(\frac{i}{2}\gamma^{\mu}\partial_{\mu}-m)\psi.$$ Is my first step to find a transformation that leaves the action invariant? But isn't there more than one symmetry meaning this question has several answers? From Peskin and Schroeder, it says we need to find $$\partial_{\mu}j^{\mu}(x)=0 \; \text{ for } \; j^{\mu}(x)=\frac{\partial L}{\partial (\partial_{\mu}\psi)}\Delta\psi-J^{\mu}.$$ So I think I'm right in saying this $J^{\mu}$ is dependent on the transformation we're making? e.g. if it's just $\psi \rightarrow \psi +a$ then $J^{\mu}=0$. The Lagrangian changes under the transformation of the field as $$L \rightarrow L+\alpha \partial_{\mu}J^{\mu}.$$ But this doesn't help me because plugging $\psi \rightarrow \psi +\alpha \Delta \psi$ (an arbitrary transformation of the field $\psi$) into the Lagrangian at the top gives me (after no more than one line) $$L \rightarrow L+\alpha \bar{\psi}(\frac{i}{2}\gamma^{\mu}\partial_{\mu}-m)\Delta \psi$$ and how do we use this to find $J^{\mu}$? (Something I've assumed throughout all of this is that $\psi$ and $\bar{\psi}$ are treated completely separate and here we're only considering $\psi$. I hope I am right in doing this.) I haven't really pin pointed a question here as my understanding breaks down at many points and when I think I finally understand it, I'm given a new Lagrangian and become stuck again. There must be some general procedure?


Simple units question (School)

A tank has 2000 litres of capacity (Ct). It fills at 5 l/s. It is filled with 800 l at time 0. a) How many seconds will it need to fill half the tank. So I did this: X = time.               5 l   *  X     2000L      ----       = -------   -  800L       s           2               X =   200L        ---------          5  L            ---             s               X =   200          -------             5         ---------             s      Eventually, I get to `X = 40 / s`, but I guess it should be `X = 40s`. However, I fail to see what I should do to get the seconds multiplying the 40. PS: Shouldnt I give the X a unit at the beggining, or is it ok to be just X?


Numerical Ising Model - Wolff algorithm and correlations

I'm doing some numerical Monte Carlo analysis on the 2 dimensional Ising model at the critical point. I was using the Metropolis 'single flip' evolution at first with success, though it suffers from critical slow down and makes studying large lattices unlikely possible. I'm now looking at cluster flip algorithms, specifically the Wolff algorithm. I managed to implement it, and it looks to be working as it should (flipping a unique spin at $T = +\infty$, the whole lattice at $T=0$, matches the right energy density in the thermodynamic limit...) but I don't get the right behaviour for the two point $<\sigma_i\sigma_j>$ correlation function. According to CFT it should behave like: $$<\sigma_i\sigma_j> \;\propto \;\frac{1}{|i-j|^{\frac{1}{4}}}$$ I'm more and more convinced that it has to do with boundary conditions, I use non periodic free boundaries. The literature on the subject doesn't say much on this point. Am I missing a subtlety (or an evidence) in this procedure, or in the use of this algorithm?


What does it mean to have infinite negative conformal time?

In the context of Inflationary Cosmology, it is postulated that there was a period of shrinking Hubble Sphere radius $(aH)^{-1}$. $$ \frac{d}{dt} (aH)^{-1} < 0 $$ Then the regions of the universe which appear to us to not be in causal contact can indeed have been in causal contact at some (conformal? physical? I'm not sure. My intuition would be physical) time in the past. This solves the Horizon Problem, namely that we observe a homogenous isotropic universe to one part in 10,000, yet it doesn't seem that all regions of the universe were in casual contact to achieve such a uniformity. $\\\$ Anyway, when this shrinking Hubble sphere radius $(aH)^{-1}$ is invoked, it has the result of pushing the Hot Big Bang singularity back to negative infinity conformal time. It is this statement that I am having trouble grasping. $\\\$ Explicitly $$ \chi_{PH}(\tau) = \tau - \tau_i = \int_{t_i}^{t} \frac{1}{a(t)} dt = \int_{a_i}^a (a H)^{-1} d\log(a) $$ where by Friedmann $$ (aH)^{-1} \propto a^{\frac{1+3w}{2}} $$ giving $$ \chi_{PH}(a(\tau)) = \tau - \tau_i \propto \frac{2}{1+3w} \left[ a(\tau)^{\frac{2}{1+3w}} - a_i^{\frac{2}{1+3w} } \right] $$ So for a strong energy violating fluid such that $$ 1 + 3w < 0 $$ this becomes $$ \tau_i \propto \frac{2}{1+3w} a_i^{\frac{2}{1+3w}} \rightarrow -\infty $$ $\\\$ I understand the maths behind it, and can't argue against that the initial conformal time goes to minus infitity, but I don't know how to think about that. In a standard Hot Big Bang the singularity occurs at $\tau_i = 0$ conformal time. This seems fine to me. I am aware that conformal time is unphysical, but unless the scale factor goes negative, then negative conformal time suggests to me negative physical time. And a negative scale factor would bring a whole other conceptual problem! Namely, they are directly related by $$ d\tau = \frac{1}{a(t)} dt $$ $\\\$ So my questions are; What does it mean to have negative conformal time? And what does it mean to have negative infinity conformal time? $\\\$ Thanks


Can low end hepa vaccums still clean near all of the air?

In the US HEPA filters will remove 99.97% of particles sized 0.3 microns. In Europe HEPA filters do not have to meet this exact figure and there are different classes of HEPA filters e.g. h10(removes 85% at .3 microns, h11 removes 95% at .3 microns etc, h14 removes 99.97% etc.). Suppose you have a vacuum cleaner that is h10(removes 85% of particles at .3 microns), when vacuuming 15% of .3 microns will pass through the filter. If we continue to vacuum the area these will go into the vacuum again and be filtered again. Therefore even though the filter performs less, is it correct to say eventually(with continued vacuuming) the filter will remove the remaining 15% so its not a big deal if you get one with 85% or 99.9% filtration so long as you are bothered to continue vacuuming? Thanks


The "replica trick" initial formula?

In Spin-glass theory for pedestrians by Castellani and Cavagna, the initial formula used to introduce the replica trick is written as: $$\overline{\log Z}=\lim_{n\rightarrow0}\frac{1}{n}\log\overline{Z^{n}}\qquad(1)$$ where the overbar denotes average over quenched disorder. I don't know how to prove this formula. In other treatments I have seen of the replica method (wiki, for example), one starts from: $$\log Z = \lim_{n\rightarrow 0} \frac{Z^n-1}{n}\qquad(2)$$ which I understand. How are (2) and (1) connected? What's the proof of (1)?


Why is the orbital resonance of the Galilean moons stable?

It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the 3:2 resonance, is "stable and self-correcting", but fail to explain why this is so. The textbook _Fundamental Astronomy_ says that this phenomenon is due to "tidal forces" but does not elaborate further. I presume it refers to the tidal deceleration which causes the orbits of the moons to evolve outwards, which, other sources say, caused the moons to eventually enter into resonance, but this also does not explain why the resonance is stable. I am aware of a similar question here but I'm more interested in stability rather than instability in this case. In short, why is the orbital resonance of the Galilean moons stable, and how is it different from other cases of orbital resonance that are unstable? I don't mind (and would prefer) if the answer is mathematical in nature.


Is it possible to use the parabolic shape of a rotating fluid to measure the angular frequency of the rotation of the Earth?

A fluid in a rotating bucket will take on a parabolic shape (for example of some simple derivations of this result see http://en.wikipedia.org/wiki/Bucket_argument). The assumptions that play into the derivations that I've seen do not take into consideration a Coriolis effect. Suppose one did not know that the earth was spinning. Is it possible to measure the angular frequency of the earth using a bucket of fluid by considering how the Coriolis effect modified the curvature of the paraboloid in question? Perhaps it's possible to optically measure the curvature of the paraboloid setup by the spinning process and from that determine the angular frequency of the planets rotation. I am concerned though that the effect of the rotation of the earth is so minuscule on the parabolic shape that it would be impossible to physically measure it.


What is lambda R in Richardson's Law?

I've got to calculate the thermionic emission through a diode, so I need to use Richardson's Law. However, one thing's got me confused - according to the Wikipedia page: $$J = A_GT^2e^\frac{-W}{kt}$$ I could live with that, but for $A_G$. Apparently, I'm not the only one; Wikipedia's a bit cryptic about what $A_G$ is, mentioning that physicists have struggled with it for decades, "but there is agreement that $A_G$ must be written in the form:" $$A_G = \lambda_RA_0$$ "Where $\lambda_R$ is a material-specific correction factor that is typically of order 0.5, and $A_0$ is a universal constant." That's the last real mention of $\lambda_R$, and the only reference for it is in French. So, what is $\lambda_R$, really? How can I figure out its numerical value so that I can actually use Richardson's Law?


Coupling constant is turned off adiabatically?

To me, adiabatic processes are idealisation. What do people mean with statements such as: "turning off the coupling constant (in QED say) adiabatically"?


Conservation of energy in a different frame of reference

Consider a rollercoaster that goes down a slope: ![rollercoaster](http://i.stack.imgur.com/94VBI.png) At the higher level it has speed $v_0$, then it goes down a slope and at the end it has speed $v_0 + \Delta v$. The carriage is not powered and has negligible friction. So by conservation of energy we should, after eliminating mass $m$ that appears in all terms, have $$ \frac{1}{2}v_0^2 + gh = \frac{1}{2}(v_0 + \Delta v)^2 \\\ \frac{1}{2}v_0^2 + gh = \frac{1}{2}v_0^2 + v_0\Delta v + \frac{1}{2}\Delta v^2 \\\ gh = \frac{1}{2}\Delta v^2 + v_0\Delta v $$ (left side is energy at the beginning, right side energy at the end). But what if we consider the same situation in a reference frame moving left with speed $v_0$. Then we should get just $$ gh = \frac{1}{2}\Delta v^2 $$ These differ by a $v_0\Delta v$ term, so solving for $\Delta v$ gives different result. But obviously the speeds should be the same. So where is the error?


Is uncertainty principle a technical difficulty in measurement?

I have searched for an answer to this question on physics SE but I have not seen a question in which it is addressed properly. Please let me know if there is an answer already. My question briefly is, is the uncertainty principle a technical difficulty in measurement OR is it an intrinsic concept in Quantum Mechanics irrelevant of any measurement?? Everyone knows the thought experiment of measuring the position of an electron. One can detect electron's position by hitting it with a photon, due to Compton scattering the collision of the photon with electron will change electron's momentum. This experiment is used to explain uncertainty principle to layman, but it is over simplified, isn't it? It also gives an impression that if there was a better suited experimental method the uncertainty principle becomes irrelevant. I personally think it is intrinsic as it arises from the non-zero commutator of position and momentum operators irrespective of the measurement process. Am I right? **EDIT:** My question is similar to certain extent to this question and this question. The answers there are nice but they focus on explaining basics of quantum mechanics more than they comment on the technical difficulty part. In the answers of question 2 there are statements like "So, it's not a knowledge limit" and "you're sort of correct when you say it's an observational limit" without further comments To summarize, assume hypothetically we managed to find a way in the future where we can have a look at an electron without disturbing it by measurement or causing its wave function to collapse, would the uncertainty principle still hold in such a case?? Why/Why not?


Probability of position in linear shm?

The problem that got me thinking goes like this:- > _Find $dp/dx$ where $p$ is the probability of finding a body at a random > instant of time undergoing linear shm according to $x=a\sin(\omega t)$. Plot > the probability versus displacement graph. $x$=Displacement from mean._ My work: $$v=dx/dt=\omega \sqrt{a^2-x^2}$$ Probability of finding within $x$ and $x+dx$ is $dt/T$ where dt is the time it spends there and T$$ is the total period.   Therefore $$dp=dt/T=\frac{dx}{\pi \sqrt{a^2-x^2}}$$ because $t=2\pi /\omega$ and the factor 2 is to account for the fact that it spends time twice in one oscillation. The answer matches the answer and also the condition that integration $-a$ to $a$ of $dp =1$. But when i try to find p as a function of x to plot the graph I get $$p=\frac{1}{\pi}\arcsin(x/a)+C.$$ But then I get stuck as there is no way to find $C$ (except the fact that for $C=0$ the probability at the mean position is $0$ and hence $C$ cannot equal 0) which I know of. So how can I get a restraint on $C$ to find its value and hence to properly graph it with the condition that the probability from $-a$ to $a$ be 1?


Why can't we accelerate to the speed of light? It's just a speed and nothing else. Universe also crossed the speed of light at the time of big bang. Is this is just a interpretation or there is any fact behind it? I am asking it as I don't know much about this theory.


What really allows airplanes to fly?

What aerodynamic effects actually contribute to producing the lift on an airplane? I know there's a common belief that lift comes from the Bernoulli effect, where air moving over the wings is at reduced pressure because it's forced to travel further than air flowing under the wings. But I also know that this is wrong, or at best a minor contribution to the actual lift. The thing is, none of the many sources I've seen that discredit the Bernoulli effect explain what's actually going on, so I'm left wondering. Why do airplanes actually fly? Is this something that can be explained or summarized at a level appropriate for someone who isn't trained in fluid dynamics? (Links to further reading for more detail would also be much appreciated)


Can the lift generated by a helicopter be justified using Bernoulli theorem?

When the shaft of the helicopter rotates, it creates a low pressure. Because of the low pressure, the helicopter lifts. Is my understanding that this is just an application of Bernoulli's theorem?


Equal Transit Time Fallacy

I learned, in grade school, that lift was generated via the particles on either side of the wing having to reach the other end at the same time. Looking back, that indeed has no physicality to it. So what is the real explanation of how lift is generated? I've found references to Navier Stokes, but I don't know what that is. What is the best way to learn, from the ground up, why some curved object would generate a definite change in pressure? I can see the results, and I know that there is a pressure difference, but **why** is that pressure difference, and the two different velocities generated?


how to explain the upright force for the plane?

I remember in the high school physics, my teacher told us that the design of the plane wing is because we want the air above the wing flowing faster than the air flowing below so the pressure above and below will be different so the net force is pointing upright. I am thinking if it is possible to explain this by bernoulli equation? But I soon stuck there because I don't know if bernoulli equation applicable to the case of the air flow in the open region? If so, what cross section we should choose?


Why air above airplane's wing moves faster?

One explanation I read: Because of the wing's geometry, the "upper" side of the wing is longer, so the air has to travel faster: ![enter image description here](http://i.stack.imgur.com/HDgVA.jpg) **My wondering** : Who said (and what was his/her explanation) that air must travel the distance above and under the wing in the _same_ time? I'll try to be clearer. Considering the below image, does **m1** and **m2** meets at the same point exactly at the same time on point **T**? ![enter image description here](http://i.stack.imgur.com/j7Icc.png)


How does this help an aeroplane to fly?

I read it somewhere on the internet that wings of an aeroplane are designed in such a way, that they increase the velocity of air above the wings and so pressure above the plane becomes less than the pressure below it and therefore the aeroplane flies well in air, but how is velocity increased above the wings of an aeroplane?


Moment of inertia of a cylinder about its base

I've tried to find the moment of inertia of a cylinder rotating about an axis parallel to its base (i.e about the 'End diameter') as one can see here . But when I checked my results with different references ,I've found that it's incorrect!.I need a help to figure out where I did it wrong. since $$I=\int\limits x^2.dm$$ $$dm = \rho.dv$$ where $$dv= r.d\theta . dr .dh$$ & $$\rho=\frac{M}{\pi R^2 H}$$ $M$:cylinder total mass. $H$:total height of cylinder. $R$:the radius of the cylinder. The distance of each infinitesimal element from the axis of rotation would be : $$\sqrt{r^2+h^2}$$ Therfore, $$I= \frac{2M}{ R^2 H}\int\limits_{0}^{R} \int\limits_{0}^{H}\, r(r^2+h^2)dh\,dr$$ and this gives a result of : $$\frac{M~H^2}{3}+\frac{M~R^2}{2}$$ Which is obviously wrong since the second term should be multiplied by a factor of $1/2$.


Star Surface Temperature Vs. Mass

I am hoping that someone can clarify this for me. With these equations. (Boltzmann Law) and radius of Radius of star how does surface temp scale with mass > $R _x \approx R_\bigodot (\frac{M_x}{M_\bigodot})^.5$ > > $L _x \approx L_\bigodot (\frac{M_x}{M_\bigodot})^3.5$ > > $\frac{L}{\pi R^2} = \sigma T^4$ > > $T_\bigodot = 5800 K$ = Surface Temp of Sun What I have done is that I have substituted $R_x$ and $L_x$ in the 3rd equation and simplified it in terms of $T$ where my final expression is > $T = (\frac{L_\bigodot M_x^2.5}{\pi\sigma M_\bigodot^2.5 R_\bigodot})^0.25$ Am i done? What am I suppose to do next? Thanks


Why don't we see solar and lunar eclipses often?

Since we see the new moon at least once in a month when the Moon gets in between of the Sun and the Moon at the night and as far as I know if this happens during the day, you'll get to see a solar eclipse. Why don't we get to see this often or in the day? Does it mean that in some part of world there's a solar eclipse when we are seeing a new moon? I'm looking for a diagram or interactive way to understand this if possible as I'm not a native English speaker, but I'll try my best to do so.


Strange things about new moon

I have some strange and infantile questions about new moon. I want to know how is it possible that the Moon is not visible at night and also at day it is not Sun eclipse? I will explain the problem in a few images. ![enter image description here](http://i.stack.imgur.com/PURQc.png) ![enter image description here](http://i.stack.imgur.com/g0pBC.jpg) ![enter image description here](http://i.stack.imgur.com/ZijhQ.png) With these images, how it is possible that there is not solar eclipse at every new moon? Or is there somewhere on Earth?


Diagonalization of a hamiltonian for a quantum wire with proximity-induced superconductivity

I'm trying to diagonalize the Hamiltonian for a 1D wire with proximity-induced superconductivity. In the case without a superconductor it's all fine. However, with a superconductor I don't get the correct result for the energy spectrum of the Hamiltonian in > Tudor D. Stanescu and Sumanta Tewari. “Majorana fermions in semiconductor > nanowires: fundamentals, modeling, and experiment.” Journal of Physics: > Condensed Matter **25** , no. 23 (2013): 233201. arXiv:1302.5433 [cond- > mat.supr-con]. given by $$ H = \eta_{k}\tau_{z} + B\sigma_{x} + \alpha k\sigma_{y}\tau_{z} + \Delta\tau_{x} $$ Here $\sigma$ and $\tau$ are the Pauli matrices for the spin and particle-hole space. Now the correct result is: $E^{2}_{k} = \Delta^{2} + \eta_{k}^{2} + B^{2} + \left(\alpha k\right)^{2} \pm 2\sqrt{B^{2}\Delta^{2} + \eta^{2}_{k}B^{2} + \eta^{2}_{k}\left(\alpha k\right)^{2}}$ Now, my problem is that I don't know how I can bring the Hamiltonian in the correct matrix form for the calculation of the eigenvalues. If I try it with the upper Hamiltonian I have completely wrong results for the energy spectrum. I believe my mistake is the interpretation of the Pauli matrices $\tau$ but I don't know how I can write the Hamiltonian in the form to get the correct eigenvalues.


Why is gas mileage typically better when traveling on the highway than on country roads or in the city?

The gas mileage of my vehicle tends to improve the more I have been driving on the interstate on that tank of gas - if I go through a tank of gas without at any point driving on the interstate, I will typically get 24-26 MPG, but when I have driven almost exclusively on the interstate, I will typically get 26-29 MPG. What confuses me is that, when traveling on the interstate, I am driving great distances at higher RPMs, which I would expect to correlate to more gas usage and thus worse gas mileage. Why does the inverse seem to be true?


Riemann curvature tensor notation in Wald

This question is entirely on tensorial notation in Wald's General Relativity. When specifying the properties of the Riemann tensor on pg39, he states: $R_{[abc]}^{\quad \ \ \ d} = 0$ and > For the derivative operator $\nabla_a$ naturally associated with the metric, > $\nabla_a g_{bc}=0$, we have $R_{abcd} = -R_{abdc}$. and > The Bianchi identity holds: $\nabla_{[a}R_{bc]d}^{\quad \ \ e} = 0$ Questions:   1. What do the square brackets around "abc" mean?   2. Why does $R_{abc}^{\quad d}$ become $R_{abcd}$? What is the relation between the two?   3. What does having $R$ in the square brackets mean? Thank you.


How much the probability wave acts like a wave?

A superposition of two probability wave creates standing wave. Well, that is convincing. Dose waves described by schrodinger's equation have other properties of wave? like reflection, refraction, polarization ect.


Intuitively, Why is Power Proportional to $I^2R$

As the resistance of a circuit goes down, the power increases because the current increases, assuming constant voltage. Why is this? I feel like resistance and current are inversely proportional, so lowering one should just raise the other, and power should stay relatively constant. What is it about power that makes it work like this? Edit: Again, namely I find it confusing that decreasing resistance actually has a net increase in power used. I feel like while the current will increase, it should be countered by the lowered resistance...


How far can one hear sound?

I was thinking how far can I hear sound coming from a concert. Today I was walking at night and I could hear sound from somewhere very far. I started following the sound but sound used to disappear momentarily and then reappear. I went atleast 2 miles but could not find where it was coming from. Now I am really confused because sound is energy and because of energy losses, as I understand sound cannot go as far as 20 miles. The nearest concert was atleast 20 miles away. I came back and read articles(I cannot proof the reliability) where sound had traveled 200 miles but it was mostly sounds from explosion or volcanoes. Maybe this makes sense because explosions or volcanoes have alot of energy but how can one explain sound being heard from a concert very far away(approx 20 miles).


Candidates for holographic QFT of 4D Einstein gravity

If we are to believe that holographic principle holds over a wide number of dimensions, and gravitational theories, but specially, those that are relevant to our universe, then there must be some 3D QFT that is the dual description of our current 4D General relativity, over what it seems to be asymptotically flat de-Sitter spacetime. > What QFT theories are candidates for being the holographic dual of > gravitational theory in _our_ universe?


> **Possible Duplicate:**   >  What experiment would disprove string theory? A hypothesis without hard evidence sounds very much like philosophy or religion to me. All of them tries to establish a functional model explaining how the world works. In my understanding, string theory is an unprovable theory. What differs string theory from philosophy or religion?


Why does time slow down the closer you are to a mass?

When ever i look this up all I get is sites saying how its because general relativity says "-" why does it do it though? it is because there is more motion near gravity than further away? Or is it something completely different?


Why is metallic hydrogen degenerate matter?

Why is metallic hydrogen considered a form of degenerate matter, akin to neutronium and electron-degenerate matter? I can understand that for the other two, degeneracy pressure is the only force countering inward gravity for very massive stars, but how does this concept also apply to super pressurised hydrogen? Furthermore, why would being supported by degeneracy pressure make the hydrogen metallic in nature?


What are magnetic field lines?

Does a magnetic field have concentrations of magnetic force lines as seen when putting iron filings over top a bar magnet or are these imaginary? I.e. are they just an artifact of the iron being a 'conductor' of the magnetic field lines making them look like they are concentrated along these path lines but are really continuum of strength around the bar magnet when there are no filings are present? Also I learned that field lines do not cross, yet there are magnet configurations who's forces are explained as the magnetic force vectors are indeed crossing and are additive such as a Halbach Magnet Array. So what is actually happening here?


Would a rocket burn more fuel to get from Earth's surface to LEO, or to get from LEO to GEO?

Would a rocket burn more fuel to get from Earth's surface to Low Earth Orbit, or to get from LEO to Geosynchronous Earth Orbit?


Elasticity of Space; How does the expansion of Space affect gravity?

Does space have an elastic quality? What I was thinking about was if space is expanding, is it being 'stretched', like a balloon being blown up, and if so, is this causing gravity to weaken? Imagine space as a 2 dimensional sheet (got this from one of Brian Greene's books) with planetary bodies resting on it and causing a depression in it, if you were pulling this sheet from all sides over a period of time, you would cause the depression of the planetary body to decrease and eventually become flat, which if we go back to reality, would mean that the gravitational 'constant' had changed to the point where the planetary body had no influence on those objects which were previously orbiting around it (or even residing on it's surface). Is this the case in reality? Or does space not have an elastic quality? If not, can you explain to me what exactly it means for space to be expanding? In case you didn't notice, I'm a layman (hence the Brian Greene books :p), so try to keep your answers/explanations conceptual if possible.


Do bullet/gun physics change if the gun is traveling very fast?

If I'm running at say $400\: \mathrm{m/s}$ and a bullet travels at $400\: \mathrm{m/s}$ and I fire the gun, will I see the bullet leave the barrel? I either see it stay in the barrel floating because we are moving at the same speed. \-- Or -- The bullet would move and have a speed of $800\: \mathrm{m/s}$. What is the correct answer?


Locality in Quantum Mechanics

We speak of locality or non-locality of an equation in QM, depending on whether it has no differential operators of order higher than two. My question is, how could one tell from looking at the concrete solutions of the equation whether the equ. was local or not...or, to put it another way, what would it mean to say that a concrete solution was non-local? edit: let me emphasise this grew from a problem in one-particle quantum mechanics. (Klein-Gordon eq.) Let me clarify that I am asking what is the _physical meaning_ of saying a solution, or space of solutions, is non-local. Answers that hinge on the _form_ of the equation are...better than nothing, but I am hoping for a more physical answer, since it is the solutions which are physical, not the way they are written down .... This question, which I had already read, is related but the relation is unclear. Why are higher order Lagrangians called 'non-local'?


What happened to the work done by friction here?

**Problem/Solution** ![](http://img832.imageshack.us/img832/1313/88791065.jpg)! **Question** What happened to the work done by friction BEFORE it touched the spring? Why was that neglected? Also they say there is no physical meaning behind the negative root, so what is the "unphysical" meaning behind the negative root? How are we supposed to know that the speed is constant before and just as it makes contact with the spring? **@atomSmasher** ![](http://img59.imageshack.us/img59/917/friclk.jpg)! I am referring to the green region. Shouldn't it be $E_i = \frac{1}{2}mv_A ^2 - f_k(x_b + x_{green distance})$ $E_f = \frac{1}{2}kx_B ^2$ I realize we would have two unknowns then.


Cosmological constant of standard model of cosmology and observational data

I am curious whether the current Lambda-CDM model of cosmology matches well with observational data, especially expansion of the universe. How well does Lambda-CDM defend its established status from other models, such as quintessence (quintessence can be said to extend Lambda-CDM, but there are some models against the standard model, I guess.)?


Is there a connection between the core of the earth and heaviest element produced by stars?

I was unable to answer this question from my daughter. Is it just a coincidence or is there a connection between the following two observations: (1) the core of the earth is made of an iron (-nickel alloy) as well as the existence of iron meteorites with the fact that (2) the heaviest element that can be produced by a star (prior to supernova) is iron? Related: Elements of a Planet reveals nearby supernova remnant?


Calculating angular momentum

A particle of mass $m$ is at a very large distance $p$ from origin $O$ and is moving with velocity $\vec{V}$ which is perpendicular to $\vec{OP}$. I have to calculate angular momentum $L$ of the particle. I know that $\vec{L}=\vec{r}\times m\vec{\dot r}$.   Since $|\vec{r}|=p$ and $|\dot r|=V$ and $\alpha=90^{\circ}$ is angle between $\vec{r}$ and $\vec{\dot r}$, I got that $L=|\vec{r}||m\vec{\dot r}|sin\alpha=pmV\cdot 1=pmV$. In the book, it's written that $L=pV$. What happened with mass?


Does the (relativistic) mass change? Why?

I learned recently that when an object moves with a velocity comparable to the velocity of light the (relativistic) mass changes. How does this alteration take place?


Why does an object with higher speed gain more (relativistic) mass?

Today, in my high school physics class, we had an introductory class on electromagnetism. My teacher explained at some point that an object with a very high speed (he said it started to get somewhat clearly noticable when travelling at 10% of the speed of light) will gain mass, and that that's the reason why you can't go faster than light. One of my classmates then asked, why is this so? Why does an object with higher speed gain more mass? This of course is a logical question, since it is not very intuitive that a higher speed leads to a higher mass. My teacher (to my surprise (responded saying that it is a meaningless question, we don't know why, in the same way we don't know why the universe was created and those kind of philosophical questions. I, being interested in physics, couldn't believe this, I was sure that what he said wasn't true. So after a while of thinking I responded saying: _Can't we describe it with Einstein's $E=mc^2?$ If an object gains speed, he gains more (kinetic) energy. With this equality we see that the more energy an object gets, to more massive it becomes._ He then replied saying that this formula is used for different cases, whereupon he gave a vague explanation as to when it is used. He gave me an example to show what I said was incorrect; when a car goes from $10 m/s$ to $40m/s$, according to what I said we would see a big increase in mass, and we don't (this sounded logical to me). So here I am, with the following questions:   * Why does an object with a higher speed have more mass (than the same object with a smaller speed)?   * When is $E=mc^2$ used and why is my argument incorrect in explaining this phenomenon?


Reduced graphs and pinch-singular surfaces

I am reading a book on perturbative QCD by John Collins. In Chapter 5, the terms **_reduced graph_** and **_pinch-singular surface_** are used for the analysis of mass singularities. However, their meanings are not explainded very clearly. It says (Sect 5.1.4, page 91) > The PSSs (for the physical region, which is all that concerns us) are where > the on-shell propagators and momenta correspond to classically allowed > scattering processes treated in coordinate space. I cannot get the key points from this _definition_. For reduced graphs, it provides some examples. But I still cannot understand why they are important and how they are related to the Feynman diagrams. Could someone help me to clarify these terminologies? Many thanks!


Are there formulae for calculating stellar luminosity and effective temperature as a function of age?

> **Possible Duplicate:**   >  Are there formulae for calculating stellar luminosity and effective > temperature as a function of age? Is there a manageable formula or set of formulas or simple algorithms that approximate stellar luminosity and effective temperature (or radius) as a function of stellar age? I'm aware that accurate modeling of these attributes is complex and is determined by many factors; what I'm looking for is something that serves as a decent approximation of the sort used in numerous illustrations or applets that show example "paths" taken by representative stars as they trace their evolution across the H-R diagram. (From this original question posted on Physics.)


Ball rolling down an inclined plane going in to a loop

I apologize if this question is not up to par. When I was doing exercises in basic mechanics I checked the answers and I can't seem to find what I'm doing wrong. Suppose we have a ball with mass $m$ and radius $r$ on an inclined plane with height $h$. At the end of the inclined plane is a loop with a radius of $R$ and we can assume that $r<<R$. We are asked what the minimum height is the inclined plane should have so as to let the ball complete the loop. Here is my reasoning: We have $U_1\geq K_{rot,2}+K_{trans,2}+U_2$. For the ball rotating we have $I=\frac{1}{2}mr^2$ and $\omega=\frac{v}{r}$. So $mgh\geq \frac{1}{2}I\omega^2+\frac{1}{2}mv^2+mg\cdot2R=\frac{3}{4} mv^2+mg\cdot 2R$. The minimal speed to complete the loop implies $F_{centripetal}=\frac{mv^2}{R}= mg$ So $v^2= Rg$ and we have $gh\geq \frac{3}{4}Rg+g\cdot 2R$ which means $h\geq 2\frac{3}{4}R$, while the book says that the answer should be $h\geq 2.70R$. Can you explain what I am doing wrong? Thank you **EDIT:** Moment of inertia corrected. For the ball rotating we have $I=\frac{2}{5}mr^2$ and $\omega=\frac{v}{r}$. So $mgh\geq \frac{1}{2}I\omega^2+\frac{1}{2}mv^2+mg\cdot2R=\frac{7}{10} mv^2+mg\cdot 2R$. After the edit with correction of the moment of inertia I am getting the right answer. We get $gh\geq\frac{7}{10}Rg+g\cdot 2R$ so $h\geq2\frac{7}{10}R$ in accordance with the book.


Information about fields and superfields

I want some explanation of fields and superfields (types and components), and what the relationship between them and representation of a group.


Virtual photon description of B and E fields

I continue to find it amazing that something as “bulky” and macroscopic as a static magnetic or electric field is actually a manifestation of virtual photons. So putting on your QFT spectacles, look closely at the space near the pole of a powerful magnet – virtual photons! Now look between the plates of a charged capacitor – virtual photons again! But if it’s all virtual photons, how do we get the difference between a magnetic and electric field? [This question needs the tag "magnetostatics" as well].


How long does it take for a metal to reach equilibrium?

I wonder if there is a measure of how long a piece of metal takes to reach electrostatic equilibrium. Does it depend on piece's size? Does it depend on the amount of imbalance? Lots of websites and textbooks report "after a very short time". But how much short? Thanks a lot


Centripetal force in frame of reference of body moving In a circle

Suppose a body is moving in a circle about a fixed point. In the frame of reference of the body, is the centripetal force felt or is only the centrifugal force felt? More generally, does a body only feel the effect of pseudo forces in an accelerated reference frame?


Is the sum of the amplitudes of an electromagnetic wave always 1?

It's been a while, and I'm trying to verify my understanding. I remember reasoning (but never being taught) that the sum of the (normalized) electric and magnetic waves in a single electromagnetic wave at any single point in time is always one. Like so:               Given A of em-wave is normalized (max = 1, min = -1)              abs(sum(A of m-wave, A of e-wave)) = 1      I haven't been able to find anywhere that says this specifically (I probably suck at searching, or am wrong). Am I correct in my understanding?


Is the total energy of earth changing with time?

Many years ego, Earth was hot. Over time, it has lost energy and has become colder. Is it now in equilibrium or is its total energy changing?


Quantizing the Dirac Field: which commutation relations are more fundamental?

When quantizing a system, what is the more (physically) fundamental commutation relation, $[q,p]$ or $[a,a^\dagger]$? (or are they completely equivalent?) For instance, in Peskin & Schroeder's QFT, section 3.5, when trying to quantize the Dirac field, they first say what commutation relation they _expect_ to get for $[\Psi(\vec{x}),\Psi^\dagger(\vec{y})]$ (where $i\Psi^\dagger$ is the conjugate momentum to $\Psi$), in analogy to the Klein- Gordon field, then they _postulate_ a commutation relation between $[a^r_{\vec{p}},a^{s\dagger}_{\vec{q}}]$ etc., and then verify that they indeed get what they expected for $[\Psi(\vec{x}),\Psi^\dagger(\vec{y})]$. Why did we need to postulate the value of $[a^r_{\vec{p}},a^{s\dagger}_{\vec{q}}]$? Couldn't we have just computed it off of $[\Psi(\vec{x}),\Psi^\dagger(\vec{y})]$? (which, by expecting to get it, we could have just as well already _postulated_ it). I suppose that would entail explicitly writing something like: $$ a_{\vec{p}}^r = \frac{1}{\sqrt{2E_{\vec{p}}}} u^{r\dagger}(\vec{p})\int_{\mathbb{R}^3}d^3\vec{x}\,e^{-i\vec{p}\cdot\vec{x}}\Psi(\vec{x})$$ and a similar expression for $b$.


When (Exactly) Does Bremsstrahlung Radiation Occur?

Regarding the Bremsstrahlung Radiation emitted when a charged particle curves inside a uniform magnetic field; Is there a way of calculating the angle through which the charged particle will precess before emitting the first quantum of radiation? Also, is there a way of determining the angle through which the charged particle will precess between the first and second emissions of radiation? My investigations revealed only what I think are the angles of emission relative to the tangent of the curve here.


calculating of g force in fun ride

we vistited yesterday a fun park and saw a ride which was a big centrifuge only in vertical. this one had a speed meter but it was broken and i also wanted to know how much g-force is on there... so my first thought was to calculate this with the centrifugal-accerleration. I have $\omega = \frac {0.5*2\pi} 1 [\frac {rad} s]$ and $r= 25[m]$, so the accerleration is $a_z = \omega^2r = \pi^2*25 = ~246$ then i can calculate the g force with $g_{force} = \frac {a_z} g$ which gives me about $24g$ that seems fairly too high! what am i missing?


Angle of deflection of an atomic nucleus

when firing a proton (for example) to an atomic nucleus, from a distance $D$, the deflection angle of the proton $\alpha $ to the type of changes atomic nuclei? or always constant?


Waves produced by a mass of water on the calm sea surface

Suppose we have a parallelepiped shaped box full of water on the surface of the sea. Suddenly the box disappears. What is the shape of the waves vs. time caused by the fall of the water contained in the box?


Mathematical derivation of interference pattern for electrons?

One of the most famous experiments in quantum mechanics in the context of wave-particle duality is certainly passing a beam of electrons through two slits, which results in an interference pattern being formed on a screen positioned after them. Now, **starting from the Schrödinger equation** (which we know is obeyed by electrons), how can we derive the formula describing the interference pattern? I am pretty sure we already know the answer, i.e. it is the same pattern generated by light going through two slits (so a sine squared modulated by a sinc envelope), but how do we get it **_from quantum mechanics_** ?


What's the relationship between the energy density of a black-body and its radiant exitance?

Through a bit calculation we can derive that in a cavity, the energy density $$u(f,T)=\overline{E(f)}\times G(f)=\frac{8\pi h}{c^3}\frac{f^3}{e^{h\nu /kT}-1}$$ If we take the integral over all frequency, we get $$U(T)=\frac{8πh}{c^3}\frac{(kT)^4}{h^3}{\frac{π^4}{15}}=C_{onst}T^4$$ And Stefan-Boltzmann Law claims that for a perfect black-body $$j^*=\sigma T^4$$ where $j^*$ is the radiant exitance, which is defined as the total energy radiated per unit surface area of a black body across all wavelengths per unit time. And it just so happens that $\frac{\sigma}{C_{onst}}=\frac{c}{4}$, why is that? P.S. The professor told me to refer to some thermodynamics book, where a more general case is discussed. But we don't have that book in our library and the professor's now out of town xD.


Ice skating, how does it really work?

Okay, some textbooks I came across, and a homework assignment I had to do several years ago, suggested that the reason we can skate on ice is the peculiar $p(T)$-curve of the ice-water boundary. The reasoning is that due to the high pressure the skates put on the ice, it will melt at temperaturs below $273 K$ and thus provide a thin film of liquid on which we can skate. It was then mentioned as fun fact that you could ice-skate on a planet with lakes of frozen dioxide because that gas has the $p(T)$-curve the other way round. My calculations at that time told me that this was, pardon my french, bollocks. The pressure wasn't nearly high enough to lower the melting point to even something like $-0.5$ degrees Celsius. I suppose it is some other mechanism, probably related to the crystal structure of ice, but I'd really appreciate if someone more knowledgeable could tell something about it.


Being in a solid state, why is ice slippery?

Saying that ice is slippery is like saying that water is wet -- it's something we've known for as long as we can be said to have known anything. Presumably, humans as a species knew ice was slippery before we knew fire was hot, or that it existed. But ask anyone why, and they won't be able to give you any better explanation than one of those cave people would have.


What exactly is the composition of radiation in interplanetary space?

The articles I found on radiation in the solar system mostly dealt with solar wind, I wonder about other types. Is there a breakdown that tells me, withhin an order of magnitude, at least what intensity I can expect for a the different spectra - hard gamma through to radio frequencies, and chargede particles - and how this varies depending on my position?


How to explain (pedagogically) why there is 4 spacetime dimensions while we see only the 3 spatial dimesions?

I have been asked this question by a student, but I was able and in the same time incapable to give a good answer for this without equations, so do you have ideas how one can explain this in a simple way? (Answers like we can take time as an imaginary, or our space is actually pseudo-Euclidean will be hard to grasp for new students.) Note that the problem is _not_ in visualizing the 4th dimension, that an easy thing to explain. The problem is more related to why we are in 3D that moving along 1D time dimension? In Differential geometry this interpreted by fiber bundles, but how to explain it to usual student.


Why is a hole in a ball?

I wanted to know why there is a hole in the ball (basketball, volleyball, handball) to fill the ball with air. Why can't the ball come with filled in air and fully sealed so that there is no loss of air?


Doppler effect and light

Approaching the speed of sound in an aircraft is relatively difficult, because the closer you get to Mach 1, the denser the pressure is around you (sound accumulates causing vibrations). Is there a similar effect as you approach the speed of light? Does the Doppler Effect apply for light as it does with sound? Will light accumulate around your aircraft causing heat? Speaking strictly hypothetical.


mixture of maximally mixed and maximally entangled state

Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the state $\rho_\lambda=\lambda \frac{\mathbb{I}_{d^2}}{d^2}+(1-\lambda)|\psi\rangle\langle\psi|.$ Now for some values of $\lambda$ this state is entangled (example $\lambda=0$ it is $|\psi\rangle\langle\psi|$) and hence its entanglement can be detected by partial transpose operation. Can $\rho(\lambda)$ be an entangled state which is positive under partial transpose (known in literature as PPT entangled state) for some values $\lambda$? My intuition tells me that this is the case. However, I was told (without reference) that this is not the case and for the values of $\lambda$ we get only separable states or not PPT entangled states. I could not find the corresponding paper. May be I am not giving the proper string for searching. Advanced thanks for any suggestion, reference or comment.


Quick question on degeneracy of harmonic oscillator states

I'm currently learning about symmetry between particles. For a simple case of two non-interacting particles at $x_1$ and $x_2$, we know that the wavefunction can be written as $\psi_{n_1, n_2} = \phi_{n_1}(x_1) \phi_{n_2}(x_2)$ Let's consider two cases in ground state and first excited state. (a) Two particles are not identical, and have spin zero (b) Two identical particles, each with spin zero We know that the energy is given by $E_n = (n_1 + n_2 + 1)\hbar \omega$. **For case (a)** Since they are not identical, the wavefunction at ground state would be $\phi_1(x_1) \phi_1 (x_2)$ right? Then the degeneracy would be 0 right? Since $n_1 = n_2 = 1$. For the first excited state, the wavefunction would be $\phi_2(x_1)\phi_1(x_2)$, assuming $E_2(x_1) < E_2(x_2)$, meaning we just take whatever is lower. The degeneracy would be 0, since they are distinguishable? **For case (b)** Now they are identical, ground state wavefunction would still be $\phi_1(x_1)\phi_1(x_2)$ right? Degeneracy of ground state would be 0, since $n_1=n_2=1$? But for the first excited state, the degeneracy would be 2, since either $n_1=2$ and $n_2=1$ or $n_1=1$ and $n_2=2$? Spin 0 particles are bosons, so the wavefunction must be symmetric right? So I'm thinking $\psi = \frac{1}{2} \left[ \phi_2(x_1)\phi_1(x_2) + \phi_1(x_1)\phi_2(x_2)\right]$ The concept of symmetry and exchange symmetry is still new to me, I'd appreciate any response!


Torque for rotation

The force for revolution of earth is provided by the gravitational force of attraction between earth and the sun. What provides the force(torque) for the rotation of earth?


Why is electron presented in books, pictures as a sphere?

Why is electron presented in books, pictures as a sphere, when in fact it's not?


What does it mean to find acceleration in terms of g?

I'm having trouble understanding what a problem I have is seeking. To simplify the problem: > A particle reaches a speed of 1.6 m/s in a 5.0 micrometer launch. The speed > is reduced to zero in 1.0 mm by the air. Assume constant acceleration and > find the acceleration in terms of g during a) the launch and b) the speed > reduction. The basic strategy to find acceleration I am using is to calculate two velocity equations: one between (0 m/s, 0 m) and (1.6 m/s, 5.0 micrometers); the second between (1.6 m/s, 5.0 micrometers) and (0 m/s, 1.0 mm). Then I will derive the acceleration value for each. Because acceleration is constant I can expect a linear velocity equation. What is confusing me is that we are to assume constant acceleration. Thus the acceleration equation will merely be some real number. So, what exactly is expected if it is to be in terms of g? Is my strategy to find acceleration incorrect?


Nonlinear absorption coefficient and the band gap

How does the nonlinear absorption coefficient depend on the band gap? How can that coefficient be calculated theoretically? (Preferably with an example)


Help me to understand this conversion (4-vectors)

$u^{\mu}$ - 4-velocity $b^{\mu}$ - 4-vector of magnetic field $ u_{\mu}u^{\mu}=-1, \qquad u_{\mu}b^{\mu}=0 $ $$ u_{\beta}u^{\alpha}\nabla_{\alpha}b^{\beta}-u_{\beta}b^{\alpha}\nabla_{\alpha}u^{\beta}+\nabla_{\alpha}b^{\alpha}=0 $$ I don't understand why this equation gives this $$ u^{\alpha}u^{\beta}\nabla_{\alpha}b^{\beta}+\nabla_{\alpha}b^{\alpha}=0 $$ Help me please!


How to prove that a motion is Simple Harmonic Motion (SHM)?

I would like to know how one could show and prove that a given motion is simple harmonic motion. Once given an answer, I'll apply that technique to an example I am trying to figure out. Thank you in advance! I believe a motion can be proved simple harmonic, if the relation between its is as such: $$ a_x = - \omega^2\cdot x $$ And as such the period time is: $$ T =\frac{2\pi}{\omega} $$ Question-so-far: How do you prove such for a given force $F = \frac{G\cdot m_e \cdot M}{R_E} \cdot r$ ? Or any force that has non-trivial constants?


Hydrostatic equilibrium of a star derivation

I've been told to revise the derivation that proves $\frac{\mathrm{d}P}{\mathrm{d}r} =\frac{GM(r)p(r)}{r^2}$ where brackets indicate a function of, P is pressure and p is density. Rather helpfully he hasn't given us it to revise, so if anyone knows it I'd be really grateful. Thanks.


How can one determine at which distance the Lennard-Jones potential reaches a given value?

My question is fairly simple, but I do need clarification on how to get the inverse of the Lennard-Jones potential V(x). I am working with the following expression: $$ V(x) = e\times[(R/x)^{12} -2\times(R/x)^6] $$ So given a value $V$, how can I find $x(V)$ ?


The unitary time-evolution in the interation picture

I'm currently consuming a course on QFT where we need to define the unitary time-evolution to get the time evolution of the wave function in the interaction picture: $\hat{U}(t_1,t_0) = \exp\left(\frac{i}{\hbar}\hat{H}_0t_1\right)\exp\left(-\frac{i}{\hbar}\hat{H}(t_1-t_0)\right)\exp\left(-\frac{i}{\hbar}\hat{H}_0t_0\right)$ . Now one can show that this operator follows a Schrödinger equation by simply taking the derivative to time: $i\hbar\frac{d}{dt}\hat{U}(t,t_0) = \hat{H}_1^I(t)\hat{U}(t,t_0)$ . Where $\hat{H}_1^I$ is the perturbation to our free-field Hamiltonian $\hat{H}_0$. Now I started wondering whether $\hat{U}(t_1,t_0)$ shouldn't also follow a Heisenberg equation since it's an operator. I believe it shouldn't since $\hat{U}(t_1,t_0)$ gives a unitairy time- evolution which is a transformation, while the Heisenberg equation applies to observables. I was woundering if someone could confirm my reasoning or disprove it?


Why should SUSY be expected naturally?

In the last 40 years (approximately) people have been "discovering", "rediscovering" and "studying" SUSY as a powerful tool and "symmetry principle". Question: What if SUSY is not realized in Nature at the end? Is SUSY the only path to "relate" fermions and bosons or what else? Remark: SUSY has not been discovered yet, so keep you totally conservative. What if there is no SUSY? Bonus: What are the merits of SUSY? What are its main issues? I do know some answers to this, but I think it could very enlightening if we "listed" pros and contras of current supersymmetric theories to see where we are NOW.


Irreversible process

I have this problem. I have an ideal gas that goes through an irreversible adiabatic decompression. I have the initial state (P,T,V), and the final pressure, and I have to calculate the entropy difference of the proccess. So, what I know is that I can make up any reversible proces bewteen the initial and final state because entropy is a state function, and integrate the heat over that process, but I can't solve it. I'm aplying $P_1V_1^\lambda=P_2V_2^\lambda$ to get the final state, but as I am creating the final point of the adiabatic, I get entropy difference of $0$ for an invented reversible path. That way of getting the final state is not correct, right? I have $PV=nRT$ but I only have the final $P$ so I need another equation. EDIT: I have tried also to use $\Delta U=W\Rightarrow C_v\Delta T=P_{ext}\Delta V$, get $T_{final}$, and go on, but I don't get the correct result either. I thought this was general: $dU=C_vdT$, when can I apply that equation?


Why can't single LEDs produce white light directly?

Why does production of white light using a LED require combining a short wavelength LED such as blue or UV, and a yellow phosphor coating? Why can't a single LED produce pure white light?


The end of theoretical physics?

About the meta questions 1193 and 2609, I've heard parallelly, that the complete branch theoretical physics is already done and that there isn't any thing else to do in this field, how true is it?


Complex coordinates in CFT

**The Setup** : Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric $ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$. It seems to me that in the usual discussion (e.g. di Francesco, Ginsparg, Polchinski), one proceeds to consider an analytic continuation of the CFT to $\mathbb C^2$ with coordinates $z^1, z^2$ and complex metric $ds^2 = (dz^1)^2+(dz^2)^2$ and then, one performs the coordinate transformation $z = z^1+iz^2$ and $\bar z = z^1-iz^2$. In this way the coordinates $z$ and $\bar z$ can be considered "independent" because they are coordinates on a complex two-dimensional manifold. Also, in these coordinates the metric becomes $ds^2 = dz\,d\bar z$ and it becomes clear that conformal mappings consist of mappings: $(z, \bar z)\to (f(z), g(\bar z))$. **My confusion is this** : Since our original theory was on $\mathbb R^2$, books say that when we do calculations, we should consider the physical theory as living on the copy of $\mathbb R^2$ embedded in $\mathbb C^2$ given by the condition $\bar z = z^*$. But consider the mapping $(z, \bar z)\to (z^2, \bar z)$. This is a conformal mapping on $\mathbb C^2$, but it does not map the surface $\bar z = z^*$ to itself; for example the point $(z, \bar z)=(2,2)$ gets mapped to the point $(z^2, \bar z) =(4,2)$ and $2$ is clearly not equal to $4^*$. In particular, it seems to me that analytic continuation to a CFT on $\mathbb C^2$ enlarges the set of mappings one can have, so what relevance does it really have to the original CFT on $\mathbb R^2$? (my apologies for the long post)


The Physical Meaning behind a Commutator

I've just been introduced to the idea of commutators and I'm aware that it's not a trivial thing if two operators $A$ and $B$ commute, i.e. if two Hermitian operators commute then the eigenvalues of the two operators can be measured with certainty simultaneously. But what is the physical significance when two operators do not commute such as to give a certain value? For example the position and momentum operator do not commute and give a value of $i\hbar$. What is the significance of the $i\hbar$?


Momentum of Light Question

Since light beams carry momentum, why would a person holding a flashlight not feel a recoil similar to that of a rifle being fired?


What's the difference between dim and bright light?

When comparing two light sources, for example, a light bulb at 20W and a light bulb at 100W, what is it about the incoming light that makes the latter look brighter than the former? Are there different reasons why different light sources looks different in brightness (High five for cramming three instances of "different" in the same sentence)? For example, in this thread, it is stated that the human eye is most sensitive around 555nm, something that I guess translates to meaning that given a light of the same intensity (whatever that means, hence my question), it is going to be perceived as most bright when hitting 555nm. Does this question have different answers depending on if you're seeing light as a particle vs a wave?


If a car appears in horison and within 2 seconds passes you by, whats the speed it's doing?

While watching the first 4 seconds of driving at 745 km/h is ludicrous from any angle wondered 1)If we knew the curvature of the earth in a "flat" desert, what would be the speed of the car? 2)Assuming we don't know the curvature of the earth, how long would it take for the car to go around the earth ( assuming a "flat" desert all the way travelling on a great arc)? Using my ninja pause skills it seemed it took 2 seconds from the time the car appeared ( as a dot ) in horizon to the time it passed by the camera, although 2 second window of observation seems to lead to a great error in overall estimates, using the 745 as the value for 1 and 2 the error of human observation could be calculated (?)


How come an anti-reflective coating makes glass *more* transparent?

The book I'm reading about optics says that an anti-reflective film applied on glass* makes the glass _more_ transparent, because the air→film and film→glass reflected waves (originated from a paraxial incoming wave) interfere destructively with each other, resulting on virtually no reflected light; therefore the "extra" light that would normally get reflected, gets transmitted instead (to honor the principle of conservation of energy, I suppose?). However, this answer states that _"Superposition is the principle that the amplitudes due to two waves incident on the same point in space at the same time can be naively added together, but the waves do not affect each other."_ So, how does this fit into this picture? If the reflected waves actually continue happily travelling back, where does the extra transmitted light come from? * the film is described as (1) having an intermediate index of refraction between those of air and glass, so that both the air-film and film-glass reflections are "hard", i.e., produce a 180º inversion in the phase of the incoming wave, and (2) having a depth of 1/4 of the wavelength of the wave in the film, so that the film-glass reflection travels half its wavelength back and meets the air-film reflection in the opposite phase, thus cancelling it.


Total power consumption of electric device

For some electric devices, like a fan or air conditioner, I read about their power consumption in watts on their specification guide. Does it tell about the power at normal or full speed? or Does the speed even affect the power consumption? Can I find the consumption at different speeds?


How do I determine $\phi$ in a hollow circular cross section using torsion equivalence?

I know that the maximum shear stress $$\tau = \frac{T}{J}\rho$$ where $\rho$ is the radial distance from the center of the cross section. I have also determined the torsional constant $J$, which is equal to $\frac{\pi}{2}(R_o^4-R_i^4)$ for this particular cross section. The following boundary condition applies: $$\nabla^2\phi = F$$ I know that $\phi$ would be zero for a solid cross section, but I do not understand how I should calculate it with torsion equivalence. Any help is appreciated.


Photon propagator in terms of creation/annihilation?

As far as I understand it the photon propagator, $P(A\rightarrow B)$, described in Feynman's QED book, gives the amplitude that a photon moves from spacetime point A to spacetime point B. I was wondering if in quantum field theory terms $P(A\rightarrow B)$ is made up of the product of the following two amplitudes:   1. the amplitude that a photon is created at $B$ given that there is a photon at $A$.   2. the amplitude that a photon is annihilated at $A$ given that there is a photon at $B$. Is this the correct approach to describing a photon moving from $A$ to $B$ using creation and annihilation operators?


What are the strings in string theory made of?

This is a follow-up to an intriguing question last year about tension in string theory. What are the strings in string theory composed of? I am serious. Strings made of matter are complex objects that require a highly specific form of long-chain inter-atomic bonding (mostly carbon based) that would be difficult to implement if the physics parameters of our universe were tweaked even a tiny bit. That bonding gets even more complicated when you add in elasticity. The vibration modes of a real string are the non-obvious emergent outcome of a complex interplay of mass, angular momentum, various conservation laws, and convenient linearities inherent in of our form of spacetime. In short, a matter-based vibrating real string is the _outcome_ of the interplay of most of the more important physics rules of our universe. Its composition -- what is is made of -- is particularly complex. Real strings are composed out of a statistically unlikely form of long-chain bonding, which in turn depend on the rather unlikely properties that emerge from highly complex multiparticle entities called atoms. So how does string theory handle all of this? What are the strings in string theory made of, and what is it about this substance that makes string-theories simple in comparison to the emergent and non-obvious complexities required to produce string-like vibrations in real, matter-based strings? * * * **Addendum 2012-12-28 (all new as of 2012-12-29):** OK, I'm trying to go back to my original question after some apt complaints that my addendum yesterday had morphed it into an entirely new question. But I don't want to trash the great responses that addendum produced, so I'm trying to walk the razor's edge by creating an entirely new addendum that I hope expands on the intent of my question without changing it in any fundamental way. Here goes: The simplest answer to my question is that strings are pure mathematical abstractions, and so need no further explanation. All of the initial answers were variants of that answer. I truly did not expect that to happen! While such answers are sincere and certainly well-intended, I suspect that most people reading my original question will find them a bit disappointing and almost certainly not terribly insightful. They will be hoping for more, and here's why. While most of modern mathematical physics arguably is derived from materials analogies, early wave analogies tended towards placing waves within homogeneous and isotropic "water like" or "air like" media, e.g. the aether of the late 1800s. Over time and with no small amount of insight, these early analogies were transformed into sets of equations that increasingly removed the need for physical media analogies. The history of Maxwell's equations and then SR is a gorgeous example. That one nicely demonstrates the remarkable progress of the associated physics theories _away_ from using physical media, and _towards_ more universal mathematical constructs. In those cases I understand immediately why the outcomes are considered "fundamental." After all, they started out with clunky material-science analogies, and then managed over time to strip away the encumbering analogies, leaving for us shiny little nuggets of pure math that to this day are gorgeous to behold. Now in the more recent case of string theory, here's where I think the rub is for most of us who are not immersed in it on a daily basis: The very word "string" invokes the image of a vibrating entity that is a good deal more complicated and specific than some isotropic wave medium. For one thing the word string invokes (perhaps incorrectly) an image of an object localized in space. That is, the vibrations are taking place not within some isotropic field located throughout space, but within some _entity_ located in some very specific region of space. Strings in string theory also seem to possess a rather complicated and certainly non-trivial suite materials-like properties such as length, rigidity, tension, and I'm sure others (e.g. some analog of angular momentum?). So, again trying to keep to my original question: Can someone explain what a string in string theory is made of in a way that provides some insight into why such an unusually object-like "medium of vibration" was selected as the basis for building all of the surrounding mathematics of string theory? From one excellent comment (you know who you are!), I can even give an example of the kind of answer I was hoping for. Paraphrasing, the comment was this: > "Strings vibrate in ways that are immediately reminiscent of the harmonic > oscillators that have proven so useful analytically in wave and quantum > theory." Now I like that style of answer a lot! For one thing, anyone who has read Feynman's section on such oscillators in his lectures will immediately get the idea. Based on that, my own understanding of the origins of strings has now shifted to something far more specific and "connectable" to historical physics, which is this: > Making tuning forks smaller and smaller has been been shown repeatedly in > the history of physics to provide an exceptionally powerful analytical > method for analyzing how various types of vibrations propagate and interact. > So, why not take this idea to the logical limit and make space itself into > what amounts to a huge field of very small, tuning-fork-like harmonic > oscillators? Now _that_ I can at least understand as an argument for why strings "resonated" well with a lot of physicists as an interesting approach to unifying physics.


How to determine if an emergent gauge theory is deconfined or not?

2+1D lattice gauge theory can emerge in a spin system through fractionalization. Usually if the gauge structure is broken down to $\mathbb{Z}_N$, it is believed that the fractionalized spinons are deconfined. However in general, $\mathbb{Z}_N$ gauge theory also have a confined phase. The question is how to determine if the discrete emergent gauge theory is really deconfined or not? For example, I am considering a $\mathbb{Z}_3$ gauge-Higgs model defined on the Kagome lattice with the Hamiltonian $H=J\sum_{\langle i j\rangle}\cos(\theta_i-\theta_j-A_{ij})$, where $\theta_i=0,\pm2\pi/3$ is the matter field and $A_{ij}=0,\pm2\pi/3$ is the gauge field. If the matter field is in a ferromagnetic phase, then I can understand that the gauge field will be Higgs out. But the matter field here is a Kagome antiferromagnet, which is strongly frustrated and may not order at low temperature. So in this case, I would suspect that the effective $\mathbb{Z}_3$ gauge theory will be driven into a confined phase. Is my conjecture right? How to prove or disprove that? Thanks in advance.


Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$

I know how to derive below equations found on wikipedia and have done it myselt too: \begin{align} \hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\\ \hat{H} &= \hbar \omega \left(\hat{a}\hat{a}^\dagger - \frac{1}{2}\right)\\\ \end{align} where $\hat{a}=\tfrac{1}{\sqrt{2}} \left(\hat{P} - i \hat{X}\right)$ is a annihilation operator and $\hat{a}^\dagger=\tfrac{1}{\sqrt{2}} \left(\hat{P} + i \hat{X}\right)$ a creation operator. Let me write also that: \begin{align} \hat{P}&= \frac{1}{p_0}\hat{p} = -\frac{i\hbar}{\sqrt{\hbar m \omega}} \frac{d}{dx}\\\ \hat{X}&=\frac{1}{x_0} \hat{x}=\sqrt{\frac{m\omega}{\hbar}}x \end{align} In order to continue i need a proof that operators $\hat{a}$ and $\hat{a}^\dagger$ give a following commutator with hamiltonian $\hat{H}$: \begin{align} \left[\hat{H},\hat{a} \right] &= -\hbar\omega \, \hat{a}\\\ \left[\hat{H},\hat{a}^\dagger \right] &= +\hbar\omega \, \hat{a}^\dagger \end{align} These statements can be found on wikipedia as well as here, but nowhere it is proven that the above relations for commutator really hold. I tried to derive $\left[\hat{H},\hat{a} \right]$ and my result was: $$ \left[\hat{H},\hat{a} \right] \psi = -i \sqrt{\frac{\omega \hbar^3}{4m}}\psi $$ You should know that this this is 3rd commutator that i have ever calculated so it probably is wrong, but here is a photo of my attempt on paper. I would appreciate if anyone has any link to a proof of the commutator relations (one will do) or could post a proof here.


How is antenna gain correlated to beam width?

Let's say you have two dipole type antennas. Antenna A has a gain of 2.15 dBi, a horizontal beam width of 360 deg and a vertical beam width of 45 deg. Antenna B is similar to antenna A, but has a horizontal beam width of 360 deg and a vertical beam width of 42 deg. Can you use the ratio of the vertical beam widths to predict the gain of antenna B? Note: In the application I'm asking about I'm not sure what method they used to calculate the beam widths. Maybe someone else knows which methods are most commonly used for dipole antennas.


What is the information content of a human being?

How much memory would we need to represent a human? How would each atom be stored as? Bytes? Something more complex?


Feynman Lectures on Physics

I want to develop a good intuition of concepts in Physics, and I've heard that the Feynman Lectures on Physics are very good for this. However, I've also heard that the Mathematics is very complicated. I was just wondering, just how much Math do I need to know? I love Physics, and I'm willing to put in the work. How much time do you guys reckon this will take? Thank you :)


Colder surface radiates to warmer surface

When radiation from a colder source arrives at a warmer surface there is some debate about what happens next. To make the question more concrete lets say that the colder source is at temperature 288K. The warmer surface is at 888K and has emissivity of 1. 3 possibilities   1. We ignore such radiation because it cannot happen.   2. The radiation is subtracted from the much larger radiation of every wavelength leaving the hotter surface.   3. The radiation is fully absorbed and its effect is to be re radiated at characteristic temperature of 888K (plus infinitesimally small T increase due to radiation absorption). I would have thought that 2. and 3 are more plausible than 1. Both 2 and 3 satisfy the Stephan Boltzmann equation. 3 however seems to imply that the radiation from colder object is transformed into much higher quality radiation and a possible second law of thermodynamics infringement.


How does the grid on the microwave oven window prevent microwave radiation from coming out?

If I look through the microwave window I can see through, which means visible radiation can get out. We know also that there is a mesh on the microwave window which prevents microwave from coming out. My question is how does this work? how come making stripes or mesh of metals can attenuate microwave radiation yet allow visible radiation? Looks like an electrodynamics problem to me with periodic boundary conditions (because of the partitions on the microwave oven window). Is it discussed in any textbook?


Why is the free energy minimized by the Boltzmann distribution?

Can someone show me, without glossing over anything, why $F = E - TS$ is minimized when $p_i = e^{-U_i/k_bT}/\sum_ie^{-U_i/k_bT}$? I understand it conceptually, but am having difficulty showing it formally.


Strict general mathematical definition of drag

Is there a formal definition of drag, say, as some surface integral of normal and shear forces? There seem to be a lot of formulas for specific cases, but is there a general one? I need to accurately calculate the drag of three cylinders placed between two plates.


How much of the energy from 1 megaton H Bomb explosion could we capture to do useful work?

The world is full of nuclear warheads being stockpiled. Controlled fusion power seems a long way away. Could we put these warheads to better use by exploding them in a controlled way and capturing the energy they produce? By useful work I mean the power is then available for the national grid to boil kettles or have a shower! Extra points for looking at the practicalities of building a facility to do this (although I guess that would get the question closed :-(... )


Space expansion looking like time dilation

Space looks like time depending on the motion of the observer so I was going to ask if space expansion was the same as the unfolding of time, but this was asked on physics.stackexchange before and the answer was that in GR time does not flow - there is no more a flow of time than there is a flow of space. So instead I'll ask: is space expansion the same as time dilation ?


3-point correlation function for a massive scalar field

I am a little bit perplexed as to how to compute the three-point correlation function for a massive scalar field, I know that it should be equal to zero. I need to show that: $\lim_{T\rightarrow \infty (1-i\epsilon)} \int D\phi \phi(x_1) \phi(x_2) \phi(x_3) = 0$ How to show this? Edit: I forgot to mention without using the generating founction, $Z[J]$.


Could the universe be a series of Big Bangs?

Imagine an eruption of energy/mass $E$ from a singularity $O$, as in a Big Bang. After the energy/mass $E$ is all at more than a distance $d$ from $O$, is it for some value of $d$ possible that there could be a new eruption of energy/mass from $O$, i.e. a new Big Bang? If yes, is there an upper limit to the number of succeeding Big Bangs?


2D - Kinematics - Linkage System using Vector Algebra

I have this question that I dont know how to solve correctly : ![enter image description here](http://i.stack.imgur.com/HsYdc.jpg) My question is, how do I find $V_B$ ? I will find the angular velocities myself, but I want to know the method to get $V_B$ ? I know I can start by using $V_C=V_B+V_{C/B}$, but then I'm not sure what to do next...is the direction of $V_B$ and $V_{C/B}$ the same ? I'm using vector algebra (cross product with i and j etc). More specifically : $$\vec{V}_C=\vec{V}_B+\vec{V}_{C/B}$$ $$\vec{V}_C = -1 \hat{j}$$ $$\vec{V}_B= ?$$ $$\vec{V}_{C/B}= \omega_{CB} \hat{k} \times \vec{r}_{CB}$$ Shouldn't $\vec{V}_B = \omega_{CB} \hat{k} \times \vec{r}_CB$ ??? If not, then what should it be ? If you need more info please let me know.


What are the values of effective mass approximation

For my research work i am trying to calculate band gap of zinc oxide theoratically and found this paper (Determination of the Particle Size Distribution of Quantum Nanocrystals from Absorbance Spectr). What i am doing is I am making a small matlab programm which will reporduce the results using the same values from the above paper. I used the values given in the paper to make the program ![enter image description here](http://i.stack.imgur.com/v8Fbp.jpg) **Absorbtion onset** $\lambda ^{onset}=\frac{c*h}{E^{*}}$                  Values used for calculating Band gap     8.85418782 ×  10^-12          permittivity of free space     1.60217657 ×  10^-19          charge of an electron     9.11 ×  10^-31                free electron mass     1.05457173 × 10^-34               hcut     0.59                      effective mass of holes     0.26                     effective mass of electrons     8.5                      relative permittivity     3.2                     zno bandgap     c                       velocity of light      But after running the programm i got these results               Size    Absorbtion Onset     1   6.21E-26     1.5 6.21E-26     2   6.21E-26     2.5 6.21E-26     3   6.21E-26     3.5 6.21E-26     4   6.21E-26     4.5 6.21E-26     5   6.21E-26     5.5 6.21E-26     6   6.21E-26     6.5 6.21E-26     7   6.21E-26     7.5 6.21E-26     8   6.21E-26     8.5 6.21E-26     9   6.21E-26     9.5 6.21E-26     10  6.21E-26      The results i got doesnt match with tha paper and I belive that my coding in matlab is correct but i am doubtful about the values i have taken for calculating band gap. Can you help me with this


Is it physically meaningful to talk about the 'total temperature' of an object?

If I had a semi infinite, 1-D object and a finite 1-D object, both heated at the same constant rate at one end each for the same time period and both begin at the same initial temperature, is it physically meaningful for me to integrate along the length of the object and consider this integral as a function of time and a measure of the 'amount' of heat on the object?


Does classical physics predict the effects of shining a laser at a hair?

The discussion on this webpage mentions that shining a laser beam at a hair produces an effect like that of the double-slit experiment. Does classical physics predict the effect you observe when you do this (since light is a wave)?


Is it true that the sun will cause very high temperatures on Earth long before the red-giant-phase?

I heard at least three claims about the development of the heat of the sun. In an old book, I read, that nothing dramatically will happen in the next few billion years. Wikipedia states, that the average temperature will hit 30° in a billion years, 100° a billion years later, and in an internet forum, someone claimed that in 500 million years, the oceans would cook. Which of this claims is true? How reliable are the claims about events in such far future?


Does Light Experience Length Contraction?

Lorentz length contractions states that the length of any moving object gets divided by the Lorentz factor equal to the Lorentz factor for that object (always $\geq 1$), equal to $$ \gamma=\frac{1}{\sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } } $$ However, in massless particles $v=c$, so the Lorentz factor becomes $\infty$, meaning that an object traveling at $c$ will have $0$ length. However, photons and obviously all forms of electromagnetic waves move at c when traveling through a vacuum, such as from a space shuttle to a space station or back to Earth. Does this mean that photons have no length? How does this affect wavelength?


Aharonov-Bohm vs de Witt

dewitt claimed in his paper > Bryce S. DeWitt. Quantum theory without electromagnetic potentials, _Phys. > Rev._ **125** no. 6 (1962), pp. 2189-2191, DOI: 10.1103/PhysRev.125.2189, that the discovery of the Aharonov and Bohm that electromagnetic potentials play primary role in quantum mechanical theory is false. Who won? What are the errors in the argument of the losing side in this battle?


Help on unit conversion problem

This is a problem from school. I will show my attempt. The question: "The gas constant for dry air R is 287 $\frac{m^2}{s^2*K}$. Assuming the temperature is 330 K and the pressure is 1050 hPa, what is the atmospheric density." The professor said DO NOT produce an answer by finding a formula, but to use the magic of unit conversion to try to solve things. I know density is measured in kg/m^3 or thereabouts so I tried the following: 1050 hPA = 105, 000 Pa 1 Pa = 1 kg/m*s^2 105,000 $\frac{kg}{m*s^2}$ * 330 K * 287 $\frac{m^2}{s^2*K}$. This cancels some units... but not enough...in fact it cancels just K, so far as I understand, far from what I need for my density unit. Any ideas on what Im doing foolishly here?


What makes Poynting's theorem consistent for a charge moving in a static electric field?

Poynting's theorem is given by $$\frac{\partial}{\partial t}\int_{v}Udv \+ \oint_{A}\vec S\cdot \vec {dA} +\int_{v}\vec E\cdot\vec J dv =0 $$ Where,   * the total electromagnetic energy inside the volume v is $U = \frac 1 2 (\vec E\cdot\vec D+\vec B\cdot\vec H)$   * the Poynting vector $\vec S=\vec E\times \vec H$ This equation is interpreted as the conservation of electromagnetic and mechanical energy for a volume of space with each term representing respectively the rate at which   1. electromagnetic energy changes inside the volume   2. electromagnetic energy crosses the boundary of the enclosing surface   3. mechanical work is done on charges inside the volume  Now take the case of a charge accelerating from rest by a static electric field, and initially at the centre of a spherical volume fixed in space with radius cT where c is the speed of light and T the time taken for electromagnetic fields to propagate from the center to the spherical boundary. For 0 < t < T both the magnetic and mechanical energy inside the volume increases without electromagnetic energy crossing the boundary. So during this time, where does the negative term come from to maintain the RHS = 0 in Poynting's theorem?


Physics of batteries (volts vs charge)

Car batteries are usually 12 V. What is the difference between buying a car battery and hooking up a bunch of cheap household batteries in series? Both would register at 12 V. I assume that cars need much more current to start an engine then regular household things like lamps and toys. Does that mean that a car battery holds more charge within it? If we think of a simple cell battery, where there are two electrodes and an electrolyte. One electrode eventually, through chemical reaction, becomes positive and the other becomes negative. Thus in a car battery, does that mean the electrodes (if we can reduce a car battery to a primitive cell), have more charge separated on each electrode? But if that was the case, wouldn't a greater charge separation mean that the voltage would be greater between the terminals as well? In general, what is the relation between charge and voltage? I know the equation V = U/q, just like E = F/q (similar form, in the limit that the test charge is small as to not effect the PE or electric field. V = U/q is sorta useless too, since differences matter, but nevertheless that is how we defined it). If charges are separated further, does that mean greater voltage? If more charge is separated, does that mean greater voltage? Lastly, what is the difference b/w the charge in a 12 V car battery, and the charge in a 12 V makeshift, series strung battery from home?


Total energy of the Universe

In popular science books and articles, I keep running into the claim that the total energy of the Universe is zero, "because the positive energy of matter is cancelled out by the negative energy of the gravitational field". But I can't find anything concrete to substantiate this claim. As a first check, I did a calculation to compute the gravitational potential energy of a sphere of uniform density of radius $R$ using Newton's Laws and threw in $E=mc^2$ for energy of the sphere, and it was by no means obvious that the answer is zero! So, my questions:   1. What is the basis for the claim - does one require General Relativity, or can one get it from Newtonian gravity?   2. What conditions do you require in the model, in order for this to work?   3. Could someone please refer me to a good paper about this?


Why is gravitational potential energy negative? How is it different from other forms of energy? I recently saw a video by Dr. Michio Kaku, he said that the total energy content of the universe is zero, since gravitational potential energy is negative, thus balancing all the positive energy. Can anyone help me out here?


Total Energy of the Universe?

I've heard the total energy is zero, but I've also heard it cannot be said to be zero since there's so much unknown stuff in the universe. Is that true?


The Univere's mass-energy and uncertainty

A virtual creation with total mass-energy = $E$ is allowed as long as that virtual creation doesn’t last longer than $E/h$. Can the uncertainty principle also be used to estimate the mass-energy in the spontaneous creation of a universe - a spontaneous creation that has now lasted $13.6$ billion years? If so, the principle would require that universe to have a mass-energy less than $1.54\times 10^{-51}$ Joules. Is there a flaw in this?


Why is gravitational potential energy negative, and what does that mean?

I usually think of gravitational potential energy as representing just what it sounds like: the energy that we could potentially gain, using gravity. However, the equation for it (derived by integrating Newton's law of gravitational force)... $PE_1 = -\frac{GMm}{r}$ ..has me thrown for a loop, especially after this answer.   * If potential energy really meant what I thought it did, then it would always have to be non-negative... but this equation is _always_ negative. So what does "negative potential energy" mean!?   * If $KE + PE$ is always a constant, but PE is not only negative but becomes **more** negative as the particles attract, doesn't that mean the kinetic energy will become arbitrarily large? Shouldn't this mean all particles increase to infinite KE before a collision?   * If we are near the surface of the earth, we can estimate PE as $PE_2 = mgh$ by treating Earth as a flat gravitational plane. However, `h` in this equation plays exactly the same role as `r` in the first equation, doesn't it?      * So why is $PE_1$ negative while $PE_2$ is positive? Why does one increase with `h` while the other increases inversely with `r`?     * Do they both represent the same "form" of energy? Since $PE_2$ is just an approximation of $PE_1$, we should get nearly the same answer using either equation, if we were near Earth's surface and knew our distance to its center-of-mass. However, the two equations give _completely_ different answers! What gives!? Can anyone help clear up my confusion?


What is the total observational energy of the universe?

Based on what is measurable, how much energy is in the universe if the initial time is the big bang and the final time is the present?


Is the total mass of the universe constant in time?


total amount of energy in the universe

What is the total amount of energy in the universe? is there the same amount of energy as negative energy, cancelling each other out? Or is it something different?


Why does Coulomb's constant have units?

I think of Coulomb's constant as a conversion factor (not sure if this is correct). Kind of like how you would do calculations in kg and then times it by the conversion constant to convert your answer to pounds. The conversion factor would be $2.2\: \mathrm{lbs/kg}$. Since the units for Coulomb's constant is $\mathrm{N \cdot m^2/C^2}$, would it make sense to define the Newton as: $1\:\text{Newton} = \frac{1}{1/1\: \mathrm{meter^2} \cdot 1\: \mathrm{Coulomb^2}}$ Would the above definition be valid? **EDIT:** So if $k$ is not a conversion factor since the above definition for a Newton is invalid and $k$ is not just a scaling factor, since it has units, then what is it? If its just a proportionality constant to adjust the magnitude then why does it have units? Shouldn't it be a unit less constant? **EDIT:** So $k$ is not just a scaling factor (since it has units) and its not a conversion factor since a Newton can't be expressed as the other units. So if its unit just exists so that things cancel out "nicely" doesn't this make dimensional analysis useless since you can add in random constants and units to cancel out whatever you want? **My question is not about the meaning of $k$. Its about its units.**