Repulsive gravity

IANAP, so feel free to berate me for thinking apocryphal thoughts! Just as magnetism has two charges, in which particles of like-charge repulse and particles of dissimilar charge attract, might gravity have two charges in which particles of like-charge attract and particles of dissimilar charge repulse? In practice, the state of magnetism means that there is no system composed of many particles in which all particles attract. Rather, there is a net 0 charge if there are equal numbers of each particle type. My silly theory regarding gravity would mean in practice that there would be two (or more) "clumps" (or universes) in existence, which are racing away from each other. So in our clump (universe) we see only attracting particles, because all the opposing particles have long since separated out and are racing away beyond the boundary of the observable universe. Just like the alien who lands in China and assumes that all humans have slanted eyes, we only observe the attracting particles (or "charge") and disregard the other, unobservable, "charge". Is there any way to disprove this idea, or like string theory can I go one believing it as it can never be disproved? Thanks.


Attractiveness of spin 2 gauge theories

> **Possible Duplicate:**   >  Why is gravitation force always attractive? I have heard that the attractiveness of gravitation is due to the fact that it is a spin 2 gauge theory. Why is this so? I find this very interesting and would love to understand this fact.


Gravitational Force (conceptual)

1. Why is gravitational force always an attractive force?    2. And is the Newtonian formula of gravitational force applicable for very small particles like electrons and protons etc.? From **Formula of Gravitational Force** , I'm referring to: $$F_G = \cfrac{GMm}{R^2}, $$ where $M$ and $m$ are the masses of objects. A logical explanation will be much appreciated.


Why gravity is an attractive force?

Why gravity is an attractive force? * * * One may say that it is because of space time curvature but General Relativity is built on this law: $\displaystyle G \frac{m_1 \times m_2}{r^2}$ (To be more precise, it is derived from it's potentiel form known as Gauss's law for gravity that can be written like this: $\nabla \cdot g = - 4\pi Gp $). So GR can't explain why gravity is attractive. General Relativity only explains how gravity occurs in terms of space time. * * * Another may stick with the Quantum theory stating that gravitons are responsible for the force of gravity, but why a massless particle with spin 2 will exchange positive momentum?


What happens when two smooth surfaces touch?

I am wondering what will be the physics to explain how two neutral, chemically nonreactive objects stick. I know that using van der Waals formalism, we can treat neutral body electrodynamic forces and arrive with attractive forces that pull the objects together. Now, once the objects touch (say a mechanical cantiliver in a MEMS sensor like the one used in an iPhone), what happens to the forces? A quantitative answer or some estimate on how strong the attractive force is for simple cases will be very appreciated. in response to anna's comment : Let us consider what happens in vacuum for ultra smooth surfaces, with no residual electrical charge and fully chemically stablized surfaces (example, silicon crystals with stabilised surface bonds).


vander waals and casimir forces

Does one need to invoke quantum mechanics to explain casimir force or vander waals force. I see that textbooks show derivation of vander waal force with no QM but casimir force is typically described with QM. Is there a difference between vanderwaal and casimir forces ? Are there distinct examples of these two forces in real life. Is there a way to prove a given force is vanderwaal and not casimir or vice versa.


$\lambda=\frac{2h}{p}$?

I am studying quantum physics and there is something I don't understand: I know that for any particle $E=hf$ (Einstein relation) and $v=\lambda f$ ($v$ is the speed of the particle). I also know that the kinetic energy is $E_k=\frac{mv^2}{2}$. Solving those 3 equations for $\lambda$: $$h\frac{v}{\lambda}=\frac{mv^2}{2}$$ I finally find $\lambda=\frac{2h}{mv}=\frac{2h}{p}$ which is not consistent with the De Broglie relation $\lambda=\frac{h}{p}$. Where am I wrong in my development ?


Wave Packets, Group velocity, and Phase velocity

Mathematically, you find that the wave function of a particle $\Psi (x,t)$ moves with the same velocity as the velocity of the particle ($v_{particle} = v_{group}$). Is there a reason why the particle velocity should not equal the phase velocity?


Group Velocity and Phase Velocity of Matter Wave?

In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?


Speed of a particle in quantum mechanics: phase velocity vs. group velocity

Given that one usually defines two different velocities for a wave, these being the phase velocity and the group velocity, I was asking their meaning for the associated particle in quantum mechanics. And is one of them more representative for a particle?


group and phase velocity of free particle

If Schrödinger wave equation is for matter waves then for a free particle Group velocity $V_g =2$ Phase velocity $V_p$ But matter waves satisfy the relation $V_g V_p = C^2$ where $V_p>C$ Does this contradiction tell free particle should not be dealt quantum mechanically?


Efficiency of the insulation of a house

I had an argument about the most cost-effective way to keep the energy bill low in the winter (here, temperature usually have an average of -20°C (-4°F)). He thinks that it's more effective to keep a temperature at a constant temperature at say 24°C (75.2°F), because It would cost as much or more to re- heat the house if you let the temperature drop. I simply think that the lower the temperature the better, because heat from the house will dissipate less and you need less energy to maintant the temperature. Am-I right? if so, which scientific theory could I look at to my make point?


Perfectly vertical spinning top

Consider a non-spinning top. If a top is perfectly vertical, and the interface between its base and the ground is perfectly flat, it should stay in (unstable) equilibrium. I.e. it does fall. What about if the top, in addition to being perfectly vertical, is also spinning? Does this situation differ from the previous one?


Loschmidt's paradox - really a paradox?

Is Loschmidt's paradox a paradox even today? In other words, is the paradox resolved or not?


Repulsion of the pieces of a  broken magnet

> **Possible Duplicate:**   >  Why does it seem like a broken magnet's poles flip? I have experienced that if we break a bar magnet into two pieces and try to bring those broken faces together it gets repelled each other. Why is it so? consider a bar magnet, $ NN--------SS $ $NN$ for north pole and $SS$ for south pole. I broke that into two pieces, So one piece would be $ NN--SS'$ and another piece would be $'NN--SS$ .( $'$ indicates the broken part). Now if I bring those two together, $SS'$ of first should attract the $'NN$ of the other. But in the reality it is getting repelled. or is there any pole exchange occuring? $$NN--------SS$$ gives either $$NN---SS'$$ and $$'SS---NN$$ **OR** $$SS---NN'$$ and $$NN'\---SS$$ so it will repel each other. Please explain why is this happening? Edit: The cut has been made perpendicular to the polar axis.


What happens to the bar magnet field when it breaks?

References says alignment of a magnetic field of a bar magnet remains same even if we cut it into two or more pieces. According to this cut edges should attract with each other. When I tried it was working in the opposite way. why is it so ?


Broken bar magnet repels?

**![Why a bar magnet broken from between repel on joining again even if the poles are opposite, i.e. North and South.](http://i.stack.imgur.com/bM4tl.png)** **Why a bar magnet broken from between repel on joining again even if the poles are opposite, i.e. North and South.**


In truth, only atoms and the void

I have a question about this motto used by Sean Carroll in his blog: > _In truth, only atoms and the void._ Can you explain what this sentence means? My interpretation is that the sentence does not makes sense because in physics, "atom" has multiple meanings, the same goes for "void". These words have so many meanings that, used without qualification, they mean nothing. The word truth is also a notoriously loaded and undefined word. Does he mean the absolute truth (which has no place in physics) or is he using it colloquially, we don't know. Let's assume that he is using "atom" to mean "absolutely indivisible unit" and "void" to mean "absolutely empty space that contains nothing but atoms". This view is absurd because defines "void" to be "empty" and "not-empty" at the same time. But besides that, if in truth, there is nothing but atoms and the void, does Sean Carroll deny the existence of fields? Here are a few meanings that physicists give to "void" (a search of titles in arxiv containing "void"): rigid void, relativistic void, magnetic fields in voids, empty voids, nano void, dynamics of void and so on. So, in physics void can mean anything but "void". Then, what does "In truth, only atoms and the void" mean? Does it really have such a deep meaning to included as a motto of a blog?


Diffraction/Bragg's law : how does $2\theta$ come about?

I'm trying to get my head around a problem (I should have checked whether I had the answer in class, the exams are coming up now and I don't know if I'll get a lecturer response over the holidays) I can't get figure out the relationship between $\theta$ and $2\theta$ in the diagrams supposedly making clear how a crystal lattice diffracts. From what I've read just now my understanding is that Bragg diffraction is actually transmission part-way into the crystal, then reflection off of an atom inside, hence the angle is twice the incident angle. The textbook we've been referred to for further reading makes no note of a $2\theta$ (it can be read here). The example used in the lecture is below ![enter image description here](http://i.stack.imgur.com/VmKym.png) I obtained an answer by using a right-angled triangle made by the X-ray detector at the middle arrow, as this is the only perpendicular angle I can see. I really don't get how this would give the angle at the crystal as $2\theta$ (and I'm not at all confident that I should halve this angle to use in calculation of $\theta$ Can someone explain why I need to do so (as despite my misgivings, this is clearly indicated as the correct procedure). I've obtained an answer and am confident with the theory, maths etc., I just don't see the derivation of the $2\theta$ as opposed to $\theta$.


Dynamics of circular motion

If there is a disc rotating about its centre, let the surface be frictionless and if a coin is placed anywhere on the disc (not at the center) why doesn't it fly off even though there is a centrifugal force acting on it with respect to the disc's frame?


Do we expect that the universe is simply-connected?

I heard recently that the universe is expected to be essentially flat. If this is true, I believe this means (by the 3d Poincare conjecture) that the universe _cannot_ be simply-connected, since the 3-sphere isn't flat (i.e. doesn't admit a flat metric). Is any/all of this true? If so (or even if not), what sorts of unexpected things might follow from the non-simply-connectedness of our universe?


Symmetrical twin paradox

Take the following gedankenexperiment in which two astronauts meet each other again and again in a perfectly symmetrical setting - a hyperspherical (3-manifold) universe in which the 3 dimensions are curved into the 4. dimension so that they can travel without acceleration in straight opposite directions and yet meet each other time after time. On the one hand this situation is perfectly symmetrical - even in terms of homotopy and winding number. On the other hand the Lorentz invariance should break down according to GRT, so that one frame is preferred - but which one? **So the question is: Who will be older? And why?** And even if there is one prefered inertial frame - the frame of the other astronaut should be identical with respect to all relevant parameters so that both get older at the same rate. Which again seems to be a violation of SRT in which the other twin seems to be getting older faster/slower... How should one find out what the preferred frame is when everything is symmetrical - even in terms of GRT? And if we are back to a situation with a preferred frame: what is the difference to the classical Galilean transform? Don't we get all the problems back that seemed to be solved by RT - e.g. the speed limit of light, because if there was a preferred frame you should be allowed to classically add velocities and therefore also get speeds bigger than c ?!? (I know SRT is only a local theory but I don't understand why the global preferred frame should not 'override' the local one). Could anyone please enlighten me (please in a not too technical way because otherwise I wouldn't understand!) **EDIT**   Because there are still things that are unclear to me I posted a follow-up question: Here


General relativity and global aspects

The theory of general relativity tells me something about the global structure of space-time, eg simply connected ?


Our Universe Can't be Looped?

With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and the actually travelling twin again reached earth after completing the loop, then no such information would have biased the actually travelling twin, and the paradox will still remain (?). And universe thus can't be a loop, it must have an end point?


What is known about the topological structure of spacetime?

General relativity says that spacetime is a Lorentzian 4-manifold $M$ whose metric satisfies Einstein's field equations. I have two questions:   1. What topological restrictions do Einstein's equations put on the manifold. For instance, the existence of a Lorentz metric implies some topological things, like the euler characteristic vanishing.   2. Are there any experiments being done or even any hypothetical experiments that can give information on the topology? E.g. is there a group of graduate students out there trying to contract loops to discover the fundamental group of the universe?


Is it possible for information to be transmitted faster than light by using a rigid pole?

Is it possible for information (like 1 and 0s) to be transmitted faster than light? For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on his/her end. The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey. Would this actually work?


light travels a maximum speed... /?

> **Possible Duplicate:**   >  Is it possible for information to be transmitted faster than light? we know that speed of light is an unconquerable term in physics..light takes about 1 year to travel 9500000000000000 metres that is light year....suppose i have a needle of length 95000000000000000 metres long....suppose that one end of needle is at my hand and other end is at distance 95000000000000000 metres apart. . now if i push gently the end of needle at my hand then at the same time the other end at a distance of 95000000000000000 metres will move forward.....now light has taken 1 year to travel a distance of 95000000000000000 metres..and i have made a mechanical disturbance to travel the same distance with in no time from one end of the needle to other end placed at a distance of 9500000000000000 metres apart. . in other words i have made a mechanical disturbance to travel faster than light.. . .


Send a signal from Earth to a planet billion light years away instantly

If light was infinitely fast, we could just send a light signal from Earth to the planet. But I was wondering, if we made a perfectly non-elastic rope as long as the distance between earth and the far-away planet. Could somebody pulling the rope from the earth send an instant signal to a person holding the end of the rope on the far-away planet? Will the rope side on the other planet move at the exact same moment as the rope side on the Earth? Of course, we should ignore the obvious factors making this means of communication impossible -_-


Gravitational Effect Versus the Speed of Light

If, for some reason, the sun were to suddenly disappear altogether, I would like to know the following:   * would we "feel" it first (i.e. being thrown into outer space due to no longer having anything to orbit);   * would we see the sun disappear at precisely the same moment that we "feel" it?; or   * would we see it before we feel it (shortly before inevitably being subsequently thrown into outer space)? For reference: light from the sun takes ~8.5 minutes to reach us here on Earth. I have read that gravitational waves travel at the speed of light, however I personally would imagine that we feel it first for this reason: how could we possibly "feel" something **8.5 minutes after it has happened** if it is something as major as planet Earth being thrown into outer space? Surely we wouldn't be hurtling through space for 8.5 minutes before noticing, would we? But then that would lead us into the realm of the Universal Speed Limit and how, in theory, nothing should be able to exceed it (except, perhaps, subatomic particles being able to communicate instantly (MUCH faster than the speed of light), but that is a whole other question and not for discussion here). Any help would be great. Mods: if you feel that this question belongs in a theoretical Stack site, then please kindly move it to the appropriate one. Many thanks.


Solar Catastrophe

Consider all of sudden the sun vanishes. What would happen to planetary motion. Will it continue to move in elliptical path or move in a tangential to the orbit immediately after sun vanishes or move in elliptical orbit for some time after the vanishing of sun or any other cases? If so, please explain...


'Push' in a rigid rod travel at speed of sound or speed of light

Two person, $A$ and $B$, each holding one end of a long solid rod. Now person $A$ pushes the rod on one end. **Question** : Is it correct that the information that the rod has been pushed will travel to the other end at the speed of light whereas the actual 'push' will travel at the speed of sound in the rod? i.e. If the rod has length $ ct $ , then will person $B$ feel the push in time $t$ or $ct/v$? ($c$ is speed at which EM waves propagates in this experiment, and $v$ is the speed of sound in the rod.)


How fast gravity force propagates?

> **Possible Duplicate:**   >  The speed of gravity Lets say for example that a pertubance occured on the Sun that changes its distance to the Earth. How fast we are going to notice the gravity changes? Is it immediately? Light speed?


Do the changes of gravity travel across distances instantly or limited to the speed of light?

> **Possible Duplicate:**   >  The speed of gravity It takes a long time for a radio signal to travel to the planet Mars. What if we made a special type of radio that could detect small changes in gravity from a fall away object. For example, a satellite in orbit around Earth. That satellite had a device that allowed it to make small changes in it's gravity field. The detector orbiting Mars could detect these changes, and convert it into a communications signal. Would these two devices be able to communicate with each other instantly using gravity? There by providing a real-time communications link between Earth and Mars?


If you make a steel rod from here to Alpha Centauri and move it, will the movement appear there instantly?

> **Possible Duplicate:**   >  Is it possible for information to be transmitted faster than light? imagine this theoretical situation:      You have make an extremely long piece of steel (or anything really) one end is placed on earth the other is all the way at Alpha Centauri, 4ly away.   Here on earth the end is hanging loosely, on Alpha Centauri there is a bell at the end of the rod. Now if you move our end straight in the direction of AC will the bell there ring instantly ? Or will it be slower/same as speed of light.      If I take make it small scale, for example moving a steel rod with a bell on the end, I can't imagine that there would be a delay, but of course the speed of light is the limit, so what could cause the delay ? Thanks for explanation.   My very sketch: http://imageshack.us/photo/my-images/221/steelrod.png/


Steel rod to Mars vs the speed of sound, how is supersonic travel possible?

I remember reading this passage in the "Feynman Lectures", where Dr. Feynman describes an experiment in which a theoretical metal rod of length equal to the distance between Mars and Earth is arranged between mars and earth. Then the "rod handler" on earth gives the rod a push upwards. So the question posed is, will the rod instantaneously move backwards on Mars? He then proceeds to say that actually the movement will be felt roughly after the time it would take for sound to propagate from Earth to Mars i.e. at the speed of sound. This is because the atoms in the rod actually propagate their position at the speed of sound. See also this Phys.SE post and links therein. **My question is:** If this were true, how is supersonic travel possible? Won't there be a scenario where the atoms in the components of the aircraft won't "catch up" because the propagation of the new positions is slower than the actual speed? Won't the aircraft disintegrate?


Does gravity spread instantly?

> **Possible Duplicate:**   >  The speed of gravity I am real noob in physics, so sorry if this question is really stupid. Today in a casual conversation I claimed that if the sun were to instantly disappear, we would have felt it in any way nos ooner than after about 8 minutes(which is the distance in light minutes from Earth to Sun). My friend said that light-wise I am right, but we would instantly have felt the gravitation change. I argued that gravitation doesn't spread faster than light. Am I right or is he right? Thanks in advance and sorry again for the noob Q :)


Does gravity act instantaneously?

some one states that the earth would travel in it path for 8 min if the sun vanished. The equations of gravity show the Moon would crash into the Earth and the Earth would head for Mars the instant the Sun is gone. Can someone show how there is a delta Time and the relaxing of the bend in space-time fields is finite?


Here's a way to transmit data faster than the speed of light

> **Possible Duplicate:**   >  Is it possible for information to be transmitted faster than light by using > a rigid pole? Assume there is a long rod or a string connecting two points separated by a distance of several light years. It will take light several years to travel, but by a simple pull or push of the string or rod we can transmit date in binary format, what do you think?


what is the speed of gravitational interactions?

Example. Two bodies with masses m1 and m2 distance between them one year of light. What happens to the force of attraction between the two bodies when one body suddenly disappears? Is the force disappears at the same time or the force will act on second body for one year?


How much time does it take to affect?

We know gravitational is continuously acting on us. But let us assume that we are hanging in the space alone away from anything to affect our position. And suddenly a giant planet appear's a few million km from us then we will feel it's gravitational force on our body. But I wanted to know will it work instantly or it will take some time to take effect just like light take some time to reach us ?


Can Information Travel Faster Than The Speed Of Light?

Many believe that nothing can travel faster than speed of light, not even information. Personally, i think theoretically information can. Consider this following imaginary experiment: Imagine we are living on a planet that is big enough for a, let's say, 10-light-seconds-tall tower to erect. We hang a pendulum near the planet's surface using a long thin wire at the top of the tower. If someone at top of the tower cut the wire then the pendulum will instantly falling to the ground. In this case we can say that the information "someone cuts the wire" travels 10-light-seconds distance in no time. Since someone on the surface can only see the act of cutting the wire 10 seconds later, can we infer that the information travels faster than light?


Speed/direction of gravity for a moving source

Consider the Earth, and a bowling ball held 186,000 miles (1 light second) above it. When the ball is released, it will start to fall vertically downwards towards the Earth. Now consider the case if the Earth is moving sideways at 1000 miles/second. The bowling ball is released just as the Earth passes directly underneath. Does the ball fall a) vertically again, or b) does it fall towards where the Earth was 1 second before? Gravity propagating at the speed of light, would suggest answer b) but as most of the matter in the universe is travelling at very high speed, and planetary orbits are circularish, I think the answer is a)


If I move a long solid stick can I send message fastest than light?

> **Possible Duplicate:**   >  Is it possible for information to be transmitted faster than light? I mean by using a perfect solid stick long enough and moving it forward and backward can I send information fastest than light ? Can you imagine a solid stick long enough to reach the moon and using it to comunicate with the lunar base. Will be information faster than light? What are the theoretical reason other than technical reason for rules this as impossible? We should rule that a perfect unelastic solid exist ?


Does gravity travel at the speed of light?

Whenever I did calculations in high school physics involving gravity, it was either "a ball falling to the earth" type scenario, or a basic measurement of the gravitational attraction between two planetoids. I think I read somewhere recently that gravitational changes "aren't reflected instantly across the universe but instead propagate at the speed of light" somewhat like the ripples in a pond expanding. Is this true? Is there experimental evidence to confirm or deny this? What is the theoretical basis for it?


Gravity Concept Question

Thought experiment: Imagine the sun suddenly disappeared; lets say it some how transported to the edge of the observable universe.What will be the effects on the space-time? (1) What does General Relativity (specifically) have to say about the disappearance of mass from the portion of space-time being analyzed? I predict that the space will oscillate ,like a spring; interacting with it self (assuming the mass was spherical, and did not cause a force to act upon space in any direction), until it dampens out due to the interference, and initial "springiness" of space.But I do not know, I am no GR specialist. (2) Can someone also tell about what will happen if the opposite happened, (a mass suddenly appeared)?


How faster is the effect of force exerted by gravity?

We all know that Earth revolves around the Sun due to Gravitational force of the Sun. Also we know that it takes just over 8 minutes for the Sun's light to reach Earth. Now let us say, hypothetically if the sun were to suddenly extinguish (or disappear), would the Earth still not experience any effect of it until just over 8 minutes later (equivalent to time taken by light to reach from Sun to Earth) ? That is, Would the earth still continue to revolve (due to the centripetal force) for next 8 minutes after Sun disappearance and then thrown out of its revolving orbit (due to centrifugal) OR will it be immediately thrown out on the moment the Sun disappeared (i.e., not after 8 minutes) ?


Transfer of energy faster than the speed of light

In a vacuum: On my left I have a rod that is 558000 miles long (3 light seconds). A button is secured to its end which activates a laser beam sent back to me once I've pushed the rod in the direction of the button. On my right I have a laser aimed at a reflector that is 558000 miles away pointing straight back toward me. I push the rod on my left and activate the laser on my right at exactly the same time. Which laser beam will reach me first, the one on the right, or the one on the left?


sending information over a wire--mechanically

> **Possible Duplicate:**   >  Is it possible for information to be transmitted faster than light? I've thought about this since I was a little kid. I know it isn't exactly feasible, but it still bothers me. I hand you a really long wire, and we agree that "a long tug means 1, two short tugs mean 0", then you move off into the galaxy, a few light-years away from me. I proceed to give you information by tugging on the wire. With a really tight wire, couldn't I talk to you faster than the speed of light?


can we break the speed of light

I know this is impossible but I just want to know where I went wrong. here's my proposal: Let us imagine that we have a source of light and a switch that are far one light year from us. so it would take light one year to get to us. If we had a very long rod that connects my hand to the switch. When I move the rod a little distance I will reach the swich. So the time needed for me to close the switch is less than that made by light.right? Would I break the speed of light this way?


Spinning theoretical object moving faster than the speed of light

Let's say you have the Earth, or any celestial body, spinning as it is. What if you build a tower from the surface, and extended it out into space. If it was built far enough, could the furthest end exceed the speed of light?


Time taken for gravity of a distant object to interact with a newly created particle?

> **Possible Duplicate:**   >  The speed of gravity   >  Does gravity travel at the speed of light? Imagine there is a large mass $m_1$ (e.g. a star) 1 light-year away from us. It is stable, stationary relative to us and has been in place for a long time, much more than a year. A small mass $m_2$ (e.g. a proton) has just been created locally, 1 light-year away from $m_1$. How much time does it take for $m_2$ to feel the gravitational pull of $m_1$, and how can this be explained with the virtual-graviton theory of gravity? Some possible answers I can imagine: a) Immediately $m_2$ interacts with virtual-gravitons sent by $m_1$, a year ago. b) 1 year. It takes this long for freshly launched virtual-gravitons from $m_1$ to reach $m_2$ and vice-versa before any effect is felt on either mass c) 2 years. There needs to be an exchange of information / virtual-gravitons between $m_1$ and $m_2$ and this is the minimum time it could take. d) None of the above


Will we feel the gravity of a star 10 light years away for the next 10 years if, somehow, it vanishes today from its position?

I was watching a relativity video, and although I am not sure, I felt that it was trying to tell that the effect of gravitation of a body is instantaneous, in the sense that a sudden change in the mass of a body will instantaneously be felt by any object at a distance, even before light can be exchanged between them. So I want to make sure if its true. You don’t have to explain me why this is so if you don’t wish to. Also, please tell me if this has been experimentally established, or it is just a theory.


Why doesn't pushing balls in a tube propagate the movement faster than the SoL?

> **Possible Duplicate:**   >  Is it possible for information to be transmitted faster than light by using > a rigid pole? On one episode of QI they asked the question, "How fast do electrons move travelling around an electric current." The answer is (more or less) "very slowly", with the explanation that it's not the electrons that move fast, it's the force (I think). They likened it to pushing on one end of a long tube of touching marbles and observing how quickly one fell out the other end. This made me think about the tube. I realise that this tube cannot allow a force to propagate through the tube instantaneously because that would be faster than the speed of light, so my question is, why not? * * * **TL;DR;** Why doesn't a marble exit a long tube filled with touching marbles immediately when a force is applied to the marble at the other end?


How the effect travel's?

Let us assume that we placed lot's of ball touching each other in a hollow cylindrical tube, now if we push one ball at the end the ball at the other end move's instantly. So how do the information from one side of the tube travel's to the other side of the tube instantly. and at what speed at it travel's. If it travels at the speed of light so if make a long tube of the length of about $3*10^8$m it would take 1 second to see the effect at the other end assuming that nothing will bend or compress all thing's are ideal? I have read other related question but it didn't contained what I actually wanted to know. So it is not a duplicate.


Can a pushed plank beat light and break the laws of physics?

Imagine you are one lightyear away from a photon sensitive (light sensitive) switch. So it is obvious that light would take one year to reach to the switch. Now I have a one lightyear long plank. I simply point the plank towards the switch and press it. Now I just did work which light would take 1 year to do in a matter of seconds. Now the question is, did I break the laws of physics? Please do not give an answer like " it is impossible to make a plank this long ". Just think about it. Even I am thinking about this question right now.


What happens when I move a very long bar?

> **Possible Duplicate:**   >  Faster than light information Hey there, I just want to make clear that I'm new here and I don't know whether this is the right place to ask such a hypothetical question. So if it's not, I'd be glad if someone could tell me where to ask. :) Imagine you and a friend of yours were very far away from each other, let's say the distance is 1 light-year. Now you're holding a bar which measures exactly 1 light-year and currently touches your friend's shoulder. What happens when you move that bar (in order to poke your friend)? Will there be a delay? And what magnitude will that delay have? A year? Several years? Looking forward to your answers. :)


speed of gravitational waves

Do gravitational waves have a certain speed? Is it the speed of light or infinite, or am I misunderstanding what a gravitational wave is? I think it is a ripple in spacetime caused by interactions between objects, but i could be wrong.


Faster than light communication

> **Possible Duplicate:**   >  Is it possible for information to be transmitted faster than light? Suppose you have a very long rod, both ends are in space and the rod is 100 light years long. If you were to push the rod forward at one end, how long would it take for this be registered at the other end?. Is there theoretically a material the rod could be made of that would allow this?. Is this a possibility for faster than light communication across astronomical distances?. Also is "intermolecular" actually a word?.


Information faster than light?

Imagine that you have two typewriters on the other side of the galaxy. Their typebars are connected by ropes (stretched to the maximum), so anything you type will instantly appear at the second typewriter. Are the sentences information? If so, why not send information faster than light? If not, I'd at least ask if such a transfer is actually immediate. ![enter image description here](http://i.stack.imgur.com/8ft0S.png) Thank you very much.


The scissor paradox: can we pass the information faster than light?

click to view the image   Before I start, I want to say that this is not a duplicate of "Is it possible for information to be transmitted faster than light by using a rigid pole?", Since point A is not a real object, it is possible for A to exceed the speed of light. **_Notice that I have already taken the bending effect into account and decided that if the widths of the bars are small enough, then it's safe to treat the scissor as if it weren't bending_**. In other words, when they are thin, then the motion will obey the equation in a small region around point O. Please read to the end and have a look on my analysis in the last part before you explain.    Suppose we have a "scissor", which is composed by two bars with a same width of length "l". Bring them closer to each other, during this process, we have the equation(#):$$v=-\frac l4\frac{cos\frac{\theta}2}{sin^2\frac{\theta}2}\omega$$, where v is the velocity of A, \theta is the angle between BC and BA as shown in the picture.It's also an arbitrary function of time t, or $\theta=\theta(t)$. $\omega$ is the angular velocity of $\theta$, thus $\omega=\frac d{dt}\theta(t)$.Here is the derivation:   1\. Draw a line vertical to L from A, intersecting with L at C.     1. Since $sin\theta=\frac{AC}{AB}$, $$AB=\frac{AC}{sin{\theta}}$$.   2. Since $cos\frac{\theta}2=\frac{AO}{AB}$, $$AO=AB*cos\frac{{{\theta}}}2$$   3. from 2 and 3 we have: $$AO=\frac{cos\frac{\theta}2}{sin{\theta}}*AC$$   4. Since $AC=l$, the equation in 4 becomes: $$AO=\frac{cos\frac{\theta}2}{sin\theta}*l$$or$$AO=\frac l{2sin\frac {\theta}2}$$   5. Differentiate each side with respect to t, and denote $\frac d{dt}AO$ as "v", getting the equation(#): $$v=-\frac l4\frac{cos\frac{\theta}2}{sin^2\frac{\theta}2}\omega$$    Again, we just look at a small area around point O where our equation is obeyed. Now, at any time $t_0$, $\theta$ and $\omega$ are independent of each other, thus $\omega$ is a free variable. At t= 0, let's set the value of $\omega$ really large and constant, so that the instantaneous speed of A is larger than even the speed of light. Later, since the factor $\frac{cos \frac{\theta}2}{sin^2 \frac {\theta}2}$ in equation(#) is quite large when $\theta$ is close to 0, and since large $\omega$ leads to small $\theta$ during a short period of time, the velocity of A will be increased by this factor. Thus overall, $\omega$ is set to be a large constant, l is a constant, the only changing factor is increasing. Therefore, the velocity of A will increase. Meanwhile, we emit a beam of light. A is in a superluminal motion. And A will arrive at a detector first, causing the bars to touch the detector, and sending the command to the machine. Then the light beam comes later, thus being detected later. Notice that here again, we place the detector close enough to point O, so that our equation is valid. Remark: Someone may argue that we are not sure if A could attain a speed higher to that of light. So suppose at t=0, the force has already affected the area around point O, and is now traveling further.Meanwhile, ${\theta}_0=\frac{\pi}3$ A is speeded up to 0.999c, then since our formula is valid at t=0 and later period of time, let's apply it and set $l=0.001m, c=3*10^8m/s,{\theta}_0=\frac{\pi}3$. Then plug them in, we get $$\omega=-3.461*10^{11}rad/s $$. Now we want to know its velocity at $t=1*10^{-12}s$, and we get $v=6.89062*10^8m/s$, faster than light.    According to relativity, this shall violate casualty, and therefore could never happen. With which kind of mechanism is this paradox solved? I have taken the bending effect into account, and decided that as long as the widths of the bars are small enough, then it's safe to treat the scissor as if it weren't bending.


The speed of gravity?

Sorry for the layman question, but it's not my field. Suppose this thought experiment is performed. Light takes 8 minutes to go from the surface of the Sun to Earth. Imagine the Sun is suddenly removed. Clearly, for the remaining 8 minutes, we won't see any difference. However, I am wondering about the gravitational effect of the Sun. If the propagation of the gravitational force travels with the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent. What is the state of the art of research for this thought experiment? I am pretty sure this is knowledge that can be inferred from observation.


Consequences of inverse square law with vast distances (Gravity); (in addition, is light speed broken)?

As is well known, the gravitational force between two masses is dependent on the spatial distance between them. Therefore, even at vast distances, the masses exert equal and opposite forces on one another. I know that our theories need for this to be the case (to derive things such as escape velocity, which calls the force at r = $\infty$ to be zero (by utilizing a limit where the distance approaches infinity)), yet the universe is so vast and complex (with an unimaginable number of masses). With so many masses in space, it seems as though this could make a huge difference (over a large distance, such as special relativity's involvement in magnetism) . Also, say there is a supernova 400 light years away from earth. The time independent theory states that we should immediately notice a difference in the net forces acting on us, yet that would mean information travelled faster than light, correct? My main point is this: Is it absolutely imperative that there is still a force infinitely far away? Would the universe still function if we were to cut it off at something like a light year? ***** (This is my main point) Does the infinite reach of the gravitational force have anything to do with the scaffolding of the universe as a whole ?


Relativistic canonical transformation

What is relativistic canonical transformation? I need every piece of information about it. Does anyone know a reference or an article about relativistic canonical transformation? For example, in classical mechanics, under one and only one condition, you can say that a transformation is canonical and that is: $J\cdot M\cdot J^T= M$   where $J$ and $M$ are two matrices which are represented in _Goldstein (3rd Edition) - Page 342_


is there a way to split a black hole?

Classically, black holes can merge, becoming a single black hole with an horizon area greater than the sum of both merged components. Is it thermodynamically / statistically possible to split a black hole in multiple black holes? If the sum of the areas of the product black holes would exceed the area of the original black hole, it seems to be a statistically favorable transition by the fact alone that would be a state with larger entropy than the initial state


Ashcroft Mermin Solid State Physics Eq. 2.60ff

I'm trying to follow the steps in Eq. 2.60 of said book. What I cant seem to figure out is how to change the integration variables from 'k' to 'E', as they state. The equation is $$\int \frac{d\textbf{k}}{4\pi^3} F(\epsilon(\textbf{k})) = \int_0^\infty \frac{k^2 dk}{\pi^2} F(\epsilon(k)) = \int_{-\infty}^\infty d\epsilon \, g(\epsilon) F(\epsilon)$$ I can follow the first transformation (why is $\textbf{k}$ suddendly $k$?), $$\int\frac{1}{4\pi^3} k^2 F(\epsilon(k)) \, dk \int_0^\pi \sin \theta \, d\theta \int_0^{2\pi} d\phi = \int_0^\infty \frac{k^2 dk}{\pi^2} F(\epsilon(k))$$ But what's happening in the second step is unclear to me. In the book it says, "one often exploits the fact that the integrand depends on $\textbf{k}$ only through the electronic energy $\epsilon = \hbar^2k^2/2m$,...", but I'm unsure how this is used. Could anybody point this out to me?


Gas Laws And Adiabatic Process

Air at 20 degrees Celsius is compressed adiabatically from 1 bar to 10 bar, what will its temperature be? With $$P_1 = 1,$$ $$P_2 = 10$$ $$T_1 = 293K,$$ $$T_2 = unknown$$ using $$\dfrac{P_1}{P_2}=\dfrac{T_1}{T_2}$$ my solution was $$\dfrac{1}{10}=\dfrac{293}{T_2}$$ giving $$T_2 = 2930$$ My physics tutor said this is wrong and I should use $P_1V_1^\lambda=P_2V_2^\lambda$ and then use $\dfrac{V_1}{V_2}=\dfrac{T_1}{T_2}$ to find the temperature. The only problem I now have is that $V_1 = V_2 = unknown$ which is making me think that he may have forgot to add that information to the question. I would like to know if there is anyway to solve this (I do not want the answer just a point in the right direction). thanks in advance!


Why are the third generation superpartners lighter than the other sfermions in MSUGRA

In the MSUGRA breaking scenario, the stop particle typically appears at energies reachable at the LHC. Other sfermions, notably the partners of up, down, strange and charm are assumed to be degenerate in mass, and also heavier than the stop. Something similar holds for the stau. Why is the third generation different in MSUGRA (not degenerate as the first two), and why is the mass hierarchy inverted wrt. the Standard Model sector (3rd generation sparticles lighter)? (I guess these features are not neccessarily specific to MSUGRA, but might apply to more general models as well.)


Time dilation when falling into black hole

I know that if one astronaut falls into a black hole, then a distant observer will see him take an infinite amount of time to reach the event horizon (provided the observer can see light of arbitrarily large wavelengths). But the falling astronaut will only take a finite amount of time to reach the horizon. My question is: What will the falling astronaut see if he "looks backwards" while falling. Will he see the distant observer growing old and all the stars dying by the time he reaches the horizon ?


EQUAL TIME commutation relations

Why is equal time commutation relation used in canonical quantization of free fields?


How much force is in a keystroke? (estimated, of course)?

I'm a software developer, and I need to calculate the estimated amount of force expended typing stored text. Preferrably in some interesting way. (i.e. the force exerted on keys thus far is enough to push a car 5 miles) (or: equivalent to 100 kg of TNT) Assumptions:   * We're not going to worry about deletes or moving the cursor or anything, I'm just counting characters of stored text.   * I don't really care if the space requires more force or not, this is more of a "fun fact" than anything.   * From what I've found online, **the mean force required for a keystroke is about 12.9N** (source).   * Hundreds of millions of characters have been typed. Questions   * What is a good way to make this something people can relate to?   * How can I calculate it? Thank you all in advance for your valuable time and input. EDIT: I thought my original post would make this pretty clear: I realize I only have the _force_ required to push each keystroke. I'm looking for a way to demonstrate that force _applied_ to something to help people quantify it, hypothetical energy in terms people can understand.


Has quantum entanglement been demonstrated to be able to take place over infinite distances?

In my poor understanding of quantum physics, quantum entanglement means that certain properties of one of two 'entangled' quantum particles can lead to change over infinitely large distances when the other particles' properties are changed. Disregarding this already mind-boggling event taking place over say 10 meters distance; how have physicists been able to demonstrate, beyond reasonable doubt, that this can take place over infinitely large distances? For instance: have they done some of these tests between ISS and Earth perhaps? How can they be so sure?


What is imaginary time?

I am not professional physicist; but I am curious about Stephen Hawking's "imaginary time". It would be better to elaborate exactly what it is. I am not confused because of the word "imaginary" but I find it confusing to imagine a two dimensional "plane time". If we express time in a plane instead of a one dimensional axis, then what does the movement of an observer along the imaginary axis signify physically?


Path to obtain the shortest traveling time

Asume we have a particle sitting at the point A(0,0) in a gravitational field. (g=9.81) It is going to move along some path to the point B(a,b) Where a>0 and b<0\. What is the curve the particle needs to be moving at to arrive at B in the least time possible? (Fastest curve between two points. ) ![Example image,, various possible paths.](http://i.stack.imgur.com/D9fRA.png)


Specify the Stress Energy Tensor and Calculate the Curvature

I have a simple question about general relativity and the Einstein field equations, I wonder if you can specify the stress energy tensor, i.e. specify some mass distribution in space and then calculate the curvature to later find equations of motions etc, instead of starting out with how the geomerty would look. I am quite new to general relativity and so I am bound to have misconceptions. **Edit: 2013 December 19th** I have found this article which at page 10, Chapter 5, section 5.2 does something simillar to what I meant, apperently there is a general from for the Stress energy tensor (for what is known as a perfect fluid(?)), and from it they derive something simillar to the second component in the normal schwarzschild metric i.e $$A(r)=(1-\frac{2U}{r})^{-1}$$ where $U$ is the energy. I do have one remaining question, the name of the general form of the stress energy tensor confuses me somewhat, "perfect fluid" is it just its name, and is it still fully capabable of describing the stress energy tensor in general relativity?


Spring problem?

I came across this problem in physics "Physics for Scientists and Engineers with Modern Physics by Serway" > _A block on the end of a spring is pulled to position $x = A$ and released > from rest. In one full cycle of its motion, through what total distance does > it travel?_ Why the answer is $4A$ instead of $2A$?


What is the reasoning behind the Hill Sphere?

According to Wikipedia, Hill Sphere is : the volume of space around an object where the gravity of that object dominates over the gravity of a more massive but distant object around which the first object orbits. True as this may be, it just mathematically supports a phenomenon that has been observed but it does not give reason or logic as to why does this happen in the first place. I mean why should the gravity of a less massive object dominate the gravity of a more massive one? I wasn't aware of the Hill Sphere until recently when I was trying to visualize the orbits of different celestial bodies. The Hill Sphere comes closest to explaining why the moon orbits the Earth, more than it orbits the Sun and why the Earth orbits the sun, more than it orbits the center of our galaxy. By this logic all celestial bodies within the Gravitational pull of the center of our galaxy should directly be orbiting the center. My argument is that if the Hill sphere of the Sun is as large as the solar system itself, any object within this sphere should be orbiting the sun. Why was the moon caught into the earth's gravitational pull in the first place when it had a much stronger pull from the sun? The answer to this would also eventually clarify why the earth orbits around the sun and not the center of the milky way.


Add air resistance to projectile motion

I am given an initial x and y position and initial velocity and I was asked to graph the trajectory in 1 second intervals. This is what I have so far: If $x_0 = 1, v_{0x} = 70, y_0 = 0, v_{0y} = 80, a_x = 0, a_y = -9.8$, and time will be 0,1,2,3... and so on. Using these equations on every second you can find the plot will be a bell shaped with the highest point being ~ 325 m at about 600 seconds: $$ x = x0 + (v_{0x})t + 1/2((a_x)t^2) $$ $$ y = y0 + (v_{0y})t + 1/2((a_y)t^2) $$ Usually in physics, we are taught in perfect condition with no air resistance. But what if there was air resistance? How would it affect this problem? How can i add it to my calculations and see what the difference is?


Can an object be deconstructed on an atomic Level?

Can a machine deconstruct objects on an atomic level. But is that possible? Not the machine per say but the simple (not that simple) act of what it does. Ex.Taking a broken computer and separating the different atoms so it would be just a group of atoms instead of a computer. If you have any suggested readings on the topic that would be greatly appreciated. Q: Can an object be broken up to be just separate atoms?


If I charge a battery using a much higher amperage, can it explode?

If I have a 12V 4Ah lead acid battery and use a battery charger that, let's say for example, can charge 10A, 50A, or 100A. If I theoretically turned it to 100A will the battery explode? I understand that when you use a higher amperage the battery will charge quickly but due to resistance and flow of ions a lot more heat will be generated, so will this heat cause an explosion..or perhaps just a bursting of that battery spewing boiling acid? And no I am not trying this in real life..I just recall seeing the scene in the Amazing Spider-Man 2 when Parker is trying to build his web shooters to be able to resist large amounts of electricity yet they keep exploding.


Intuitive explanation of why momentum is the Fourier transform variable of position?

Does anyone have a (semi-)intuitive explanation of why momentum is the Fourier transform variable of position? (By semi-intuitive I mean, I already have intuition on Fourier transform between time/frequency domains in general, but I don't see why momentum would be the Fourier transform variable of position. E.g. I'd expect it to be a derivative instead.)


If you were able to get rid of Hydrogen from a weather balloon as it were rising and expanding would the weather balloon rise further than usual?

I know that the weather balloon will eventually be stopped because of the atmosphere no longer being buoyant but would the balloon be able to go farther than it regularly would?


Is the earth expanding?

I recently saw this video on youtube: http://www.youtube.com/watch?v=oJfBSc6e7QQ and I don't know what to make of it. It seems as if the theory has enough evidence to be correct but where would all the water have appeared from? Would that much water have appeared over 60 million years? Also what would cause it to expand. The video suggests that since the time of dinosaurs the earths size has doubled in volume, how much of this is and can be true? [could someone please tag this, I don't know what category this should come under]


Solving electromagnetic vector field using the Lagrangian

Given an action of the form \begin{equation}S=-\frac{1}{4}\int d^4x\eta^{\mu\nu}\eta^{\lambda\rho}F_{\mu\lambda}F_{\nu\rho}\end{equation} where $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$, $\eta_{\mu\nu}=g_{\mu\nu}/a^2(\eta)$, where $g_{\mu\nu}$ is given by the line element: \begin{equation}ds^2=a^2(\eta)[d\eta^2-(dx^i)^2]\end{equation} I would like to solve for $A_{\mu}$, and standard solution is \begin{equation}A_{\mu}^{(\alpha)}=e_{\mu}^{(\alpha)}e^{ik_\nu x^\nu}.\end{equation} I am interested in knowing how to derive this result. My approach is first write the Lagrangian from action and use EL eq \begin{equation}\frac{\partial \mathcal{L}}{\partial A_{\mu}}-\frac{d}{d x^{\nu}}\frac{\partial \mathcal{L}}{\partial(\partial_{\nu}A_{\mu})}=0\end{equation} My main problem is mathematical difficulty in evaluating the EL eq. Can anyone please help me on this?


Scalar top quark (stop) pair production

A rather simple question: Starting from an electrically neutral state, pairs of top quarks are produced as top and anti-top, and denoted as $t\bar t$. Now the production of pairs of scalar top quarks, the supersymmetric partners of the top quarks, seems to be commonly denoted as $\tilde t \tilde t^*$ (e.g. 1, 2), rather than $\tilde t \bar{\tilde t}$. Why this notational difference? What is $\tilde t^*$?


Electron shell bombardment

If you bombard an electron shell with a photon below the critical level to promote the electron to a higher state, will the shell absorb nothing and the photon get deflected with the same amount of frequency/energy that it came with initially?


Normalising a wave function in parts?

If we have the wave function $\psi_{100}(r,\theta,\phi)=R_{10}(r)Y_{00}(\theta,\phi)$ when we are normalising it we do the following: $$1=\int| \psi_{100}(r,\theta,\phi)|^2sin(\theta) r^2drd\theta d\phi$$ but can we also normalise the individual parts separately i.e. $$1=\int r^2|R_{10}(r)|^2 dr $$ and $$1=\int |Y_{00}(\theta,\phi)|^2 sin(\theta)d\theta d\phi $$ I ask this as this is what my textbook is doing and knowing integration it seems wrong! Please if this is right can you explain it, thanks.


Resonance in a gravitational field?

Assume that there are only well behaved functions as mass distributions, and there are no other forces except gravitation. Is it than possible to create an arrangement where a variation of a certain quantity (could be mass density or gravitational field or momentum) has a resonance?


Computer game with quantum optics/ information

Is there a computer game using principles of quantum optics or quantum information? By game I don't mean just a simulation or an interactive course, but something that can be played in an enjoyable way. By 'principles' I mean actual rules, not just things bearing the same name or vaguely related. As a reference, let me use Chromatron \- it is a puzzle game using principles of geometrical optics and color mixing. (There are some non-physical or unrealistic elements, but most most of them - like mirrors, prisms, beamsplitters and filters - are based on real physics).


How can I describe an equation for multiple objects over time?

Lets say i have $n$ different objects that effects each other only by the classic gravity force. I have their initial locations, masses and velocity's: $$ x_1(0),\cdots,x_n(0) $$ $$ m_1,\cdots,m_n $$ $$ v_1(0),\cdots,v_n(0) $$ Is it possible to describe each object location with an equation? $$ x_i(t)= ? $$ I tried doing this : $$ x_i(t) = x_i(0)+\int_0^t v_i(t') dt' $$ $$ v_i(t')=v_i(0)+\int_0^{t'} \frac{1}{m_i} \sum\limits_{j=1}^n \frac{Gm_im_j}{r_{i,j}(t'')^2} dt'' $$ Now I'm stuck because the distance function $ r_{i,j} $ is depends on $ x_i $ and $ x_j $ which makes the whole thing circular...


Thought experiment regarding perpetual motion machines and paradoxes

A paradox (Ex.: if someone goes back in time to kill their own grandfather, then they won't exist, but then they wouldn't be able to go in time to kill their grandfather, but then they WOULD exist, but then they would go back in time...) is, really, the only "perpetual motion machine" (and I know I use that term loosely here) that works, since the conclusion of one argument causes the beginning of the argument to be false, which changes the conclusion, which changes the premises of the argument, ad infinitum. Could this mean that if a fully verifiable paradox were ever found in action within the physical world, the properties of said paradox might be able to power an actual, physical perpetual motion machine? Perhaps the wave/particle duality of light might be considered such a paradox, or possibly the properties of quantum particles. If we could somehow put their inherent paradoxical qualities to practical use, we might have a solution to problems that, up until that point, have seemed to us to be, well, paradoxes. DISCLAIMER: I am not an upper-level scientist; this was merely a thought experiment. In all honesty, I probably have a number of concepts flubbered around in my head, which why I'm asking here - the home of many more- capable/knowledgeable-than-me actual scientists.


How to numerically solve a complex equation?

I want to know that if you are given a very complex equation g(x)=A(T). How could you solve for x, which is a function of variable T. To be more specific, I encounter a polylogarithmic function I need to solve numerically..


Microsecond trading with neutrinos

The Spread Networks corporation recently laid down 825 miles of fiberoptic cable between New York and Chicago, stretching across Pennsylvania, for the sole purpose of reducing the latency of microsecond trades to less than 13.33 milliseconds (http://www.spreadnetworks.com/spread-networks/spread- solutions/dark-fiber-networks/overview). The lesson I would draw from this is that, in the near future, oil and natural gas extraction won't be the only lucrative use of ocean platforms. So here's my question - since trades are occurring on the scale of tens to hundreds of microseconds, and considering the amount of money involved, can one use neutrino beams to beat the limitation due to having to travel the great-circle/orthodromic distance between two trading hubs? I'm imagining something similar to the MINOS detector (http://en.wikipedia.org/wiki/MINOS), where a neutron beam was generated at Fermilab in Batavia, Illinois, and detected ~735 km away, ~700 meters under the ground in a Northern Minnesota mine. Is it possible to beat a signal traveling at the speed of light across the great-circle distance from, say, New York to Tokyo, using a neutron beam traveling the earth? Is it realistic to talk about generating these beams on a microsecond time-scale? Addendum - Over what distances can you reasonably detect a neutrino beam?


Did classical applications of density functional theory precede its use as an electronic structure method?

Density Functional Theory (DFT) is usually considered an electronic structure method, however a paper by Argaman and Makov highlights the applicability of the DFT formalism to classical systems, such as classical fluid density. This presentation by Roundy et al. calculates water properties using a classical approach, with an eye to combining it with KS DFT for calculating solvent effects. Not being too clear on the history of DFT, _was DFT invented for electronic structure problems first_ , and its applicability to classical problems incidental, or was it formulated for classical systems first and then adapted to the quantum many body problem?


Huge buildings affect Earth's rotation?

Does constructing huge buildings affect the rotation of the Earth, similar to skater whose angular rotation increases when her arms are closed comparatively than open?


Some questions on Conformal Field Theory, Current algebras and the Sugawara construction

Since I don't know how to add another question to an already existing topic, I'm opening a new thread. However I'm referring to: Beginners questions concerning Conformal Field Theory As noted, a few weeks ago I started reading about Conformal Field Theory. I'm actually from a more mathematical background, however I'm not very familiar with Quantum Field Theory. Though I'm quite familiar with Quantum Mechanics/Classical Mechanics. Now again some questions again turned up:   1. Think of a theory with an energy-momentum-tensor that is given on the plane. Let's assume the most general form $T(z)=\sum z^{-n-2} L_{n}$ and $L_{n} = \frac{1}{2 \pi i} \oint dz z^{n+1} T(z)$. Now some of my reference (such as David Tong in the reference question above) point out that $L_{0}$ generates scalings/rotations and $L_{1},L_{-1}$ generate translations. So let's consider the example of a rotation. The generator of a rotation is $z \frac{\partial}{\partial z}$. Now in order to show that $L_{0}$ actualyy generates this rotation one needs to show that $[L_{0},\phi]$ = $z \frac{\partial}{\partial z}$ \phi. I've shown this for the example of the free boson, however I'm not 100% sure how to prove it in the general case. Can someone help me? (Maybe it's related to Operator Product Expansions...)    2. The second question goes a bit deeper into the theory. It concern Current Algebras. I've read some articles on the Sugawara construction and there Mr Sugawara proposes and Energy-Momentum-Tensor of the form $T(z) = \gamma \sum_{a=1}^{dim g} : j^{a}(z) j^{a}(z):$ . However I don't really see how he comes up with it or why this seems to be a "natural choice" of an Energy-Momentum tensor. I've heard that it includes the Energy Momentum Tensor of the free boson (given by $T(z)=\partial_{z} \phi \partial_{z} \phi$) as a special case. For me this is not so obvious. Can someone please explain to me how he comes up that in an easy way. I don't think it's necessary to show me all the calculations. Just the basic idea would be useful to get some intuition.    3. I'm having some troubles on understanding the intuition behind current algebras. (I haven't read about WZW Models yet). The Virasoro algebra appeared to me in a kind of natural way in the example of the free boson. The generalization is then pretty much straight forward. However I don't have that kind of intuition for current algebras. I've read that they provide some "additional symmetry structure" which reduces the number of possible correlation functions. But I don't know any details. I'd be more than happy if someone could comment on that.


A question on lowering the total spin

Is there a way to lower the total spin of the state and fixing the $S_z$ rather than lowering the $S_z$ by spin ladder operator? Or in other words, how to connect the $S=1$ state with $S=2$ or $S=0$ state? Is there such an operation though it might be unphysical?


Do electrons have definite and single value of momentum and position?

Do electrons (individually) have definite and single value of momentum and position or do they simultaneously have multiple position (a spread) at a time? In other words, according to the uncertainty principle, is it just impossible to _measure_ the exact position and momentum or is it actually impossible for an electron to _have_ a single position and momentum? Consequently, assuming it's just impossible to measure the exact position and momentum, does this mean that in atomic orbitals the electrons actually do occupy single position at a certain time (instead of somehow having 'smeared out' multiple positions at a time). How does velocity apply to atomic orbitals? Do electrons just randomly teleport according to the probability distribution or do they actually travel in 'normal' trajectories (going step by step instead of teleporting, for example footballs travel in step by step and don't randomly teleport AFAIK) Edit: Also, does $\hbar$ in the uncertainty principle equation, $\Delta x \Delta p = \frac{\hbar}{2} $ arise from Planck length ( **From my understanding, the impossibility to measure the exact position and momentum arises from the quantization of length and time**. Is my understanding correct?)


Are the polarization field and electric field in LIH dielectric in dynamic equilibrium?

If we know that the Polarization P in LIH dielectrics is proportional to the net field inside the dielectric according to: P = ε0χeE.....(1) And we know that D = εE........(2) Does it not follow that we can ascertain the polarization directly from the applied (free charge) field, since we can relate D to E, and then E to P? The author of my electrodynamics text (Griffiths), says that we cannot. His explanation being that once we place dielectric in an external field E0, the material will polarize and create an opposing field to the applied field, which in turn modifies the polarization again, and this process repeats over and over. In actuality, are these two quantities (E and P) in some sort of dynamic equilibrium within the material? If so, how come (1) and (2) are valid?


What is the Riemann curvature tensor contracted with the metric tensor?

Can the Ricci curvature tensor be obtained by a 'double contraction' of the Riemann curvature tensor? For example $R_{\mu\nu}=g^{\sigma\rho}R_{\sigma\mu\rho\nu}$.


What's the validity of the thermodynamic definition of entropy?

Thermodynamic Entropy Variation is defined as $$\Delta S = \int_i^f \frac{dQ}{T},$$ where $i$ and $f$ are the initial and final states of the process. My question is: **does this equation apply to quasi-static irreversible processes, or only to reversible processes?** Obviously, it does not apply to processes that go through non-equilibrium states, since Temperature (or any state variable) is not even well defined in these states. But I'm unsure of whether it applies to irreversible processes that are quasi-static (and therefore don't go through non-equilibrium states).


How long would it take me to travel to a distant star?

Suppose I wanted to travel to one of the recently discovered potentially Earth-like planets such as Kepler 186f that is 490 light years away. Assuming I had a powerful rocket and enough fuel, how long would it take me?


Special relativity allows arbitrarily low travel times between two locations

I wish I had a good way of illustrating this, but anyway, doesn't the following travel strategy allow you to get anywhere in arbitrarily little time? You're at rest at the origin of space-time, and you'd like to meet up with an object some distance away in the positive x-axis - in other words, you'd like to reach the vertical world line of that object. You begin traveling towards the object at t = 0 in the following 3 phase trip: **I**. You accelerate nearly to the speed of light relative to the stationary frame of the origin and the object you're trying to reach. **II**. You level out your speed and coast. **III**. You decelerate right before you reach the object. As long as the observer travels on a space-time path that's always nearly lightlike, the proper time of his journey will be almost zero. Not that he sees a finite amount of distance go by him in zero time - the proper distance between the endpoints of his nearly lightlike journey is also nearly zero, so the speed of light is never exceeded by objects passed by the traveller. I realize that the travel time in the stationary reference frame is finite - it's the same as that of a light ray, and that during the acceleration phase ( **I**.), the traveller will see all of this finite time go by at his destination, but _he'll_ never experience that amount of time going by, right? If the above reasoning is correct, then there isn't really a limit on how far you can travel in a human lifetime, right? People seem to think that the finite maximum speed c is a death knell for, say, trips to Andromeda (and beyond). But if the above is correct, then the only limit on short travel times is the energy required to accelerate (a limit which exists in a Newtonian world as well). In short, isn't it possible (in principle) to go arbitrarily far in a human lifetime?


How much time passed for the passenger traveling with at speed-of-light spaceship?

Let's suppose we have a spaceship with the exact speed of light. If a traveller takes this spaceship to go to proxima centauri (approximately 4 years light away from Earth) and come back, we (as observers on Earth) will see the ship coming back after approximately 8 years. But how much time would have passed for the traveller on the ship? How can be this calculated with a formula?


Double slit experiment and indirect measurements

In the classic Young double slit experiment, with slits labeled as "A" and "B" and the detector screen "C", we put a detector with 100% accuracy (no particle can pass through the slit without the detector noticing) on slit B, leaving slit A unchecked. What kind of pattern should we expect on the detector C? Probably the right question is: knowing that a particle hasn't been through one of the slits makes the wavefunction collapse, precipitating in a state in which the particle passed through the other slit?


Does the universe have a center?

If the big bang was the birth of everything, and the big bang was an event in the sense that it had a location and a time (time 0), wouldn't that mean that our universe has a center? _Where_ was the big bang? _What_ is there now? Are we moving away from the center still? Are these even valid questions?


Size of the Observable Universe

I wanted to know what the observable universe is so I was thinking and I thought, it must be age of the universe times 2. Well I was wrong. I found on one website that it is 46B LY across in each direction. How does this make sense? I get how the universe has expanded since then, but we should only be able to see light that is 13.7 billion LY old. Does this mean that the Universe is expanding faster than the speed of light? Or light from other objects is travelling to us faster than speed of light?


How can a quasar be 29 billion light-years away from Earth if Big Bang happened only 13.8 billion years ago?

I was reading through the Wikipedia article on Quasars and came across the fact that the most distant Quasar is 29 Billion Light years. This is what the article exactly says > _The highest redshift quasar known (as of June 2011[update]) is > ULAS-J1120+0641, with a redshift of 7.085, which corresponds to a **proper > distance** of approximately 29 billion light-years from Earth._ Now I come to understand that the Big Bang singularity is believed to be around 13.8 Billion years ago. So how is this possible? Does the presence of such a quasar negate the Big Bang Theory? I'm not a student of Physics and was reading this out of (whimsical) curiosity. Is there something I'm missing here or the "proper distance" mentioned in the fact is a concept that explains this? Edit: My Bad! Here's how.. A simple google search led me to this article (sciencedaily.com/releases/2011/06/110629132527.htm) which says the farthest quasar found is 12.9 billion LYs and not 29 billion. So in the end we have just proven that wikipedia needs more moderation. Lol, what a waste of time! Although I did find out a lot of new stuff from the answers, so thanks for all your responses!


Diameter of the universe

**Should the diameter of our universe always be more than its age in light years?** As if the distance between any two points in the universe is equal to 13.5 billion light years then the light from the big bang could also reach there and certainly more length than its age in light yrs would violate the very basic laws of our universe.


Can the coordinate of the big bang point be calculated via observed universe or it is impossible?

We know all galaxies spread out after Big Bang theory.The key idea is that the universe is expanding after that theory. Can we play back the scenes via observable universe (galaxies) and can we calculate the coordinate of big bang point as a fixed reference point in the universe? Is there a such calculation in literature or claim? EDIT: After answers I have some questions: If the distribution of matter in the universe is homogeneous,how should we think the geometry of universe. Is it a sphere ? Does not a line go to endless as we imagine? Is there any idea of the border of observed universe? If the universe is homogeneous and like sphere geometry, can we see the beginning of our baby galaxy while observing in the sky? I really will appreciate if someone explains what the universe geometry structure is if we have a homogeneous universe after big bang. Thanks


If nothing can travel faster than the speed of light, how can there be parts of the universe we can't see?

Assuming we originated from a single infinitely dense point in space time in the big bang, how can there be parts of the universe that we can't see as the light has not reached us yet, if nothing can travel faster than the speed of light relative to our frame of reference? Is that because the universe can expand faster than the speed of light? Or am I missing something?


Does Fermi-Dirac Statistics explain anti-particles?

I wondered whether the Fermi-Dirac Statistics describes the anti-fermion particles. Does it include the anti-particles?


If we were to travel through space (sci-fi style), how close to the false-color images would the galaxies we see be?

I understand that the black-and-white images you see looking through a household telescope are only like that due to the intensity of the light that reaches us, and that most of the astronomy images we find online have some color modification. But if we were to eventually travel between galaxies, how would those galaxies appear to the naked eye? How close to the false color images would they be, and how accurately do we know this?


I am learning Quantum Mechanics and I have some questions about some basic concept

1. What does a "STATE" exactly mean in quantum mechanics?    2. What is the equivalence of "STATE" in classical mechanics?   3. If we have a wave function $\Psi$ , its absolute square $|\Psi|^2$ is the probability density of finding the particle somewhere in the space, and I know it can be written as $\langle \Psi |\Psi \rangle$. But what is the physical meaning of $\langle \Phi | \Psi \rangle$, where $\Phi$ and $\Psi$ are two different wave functions. Why we need to take inner product of two different wave functions.


Why is this not a realisable operation on a quantum system?

Let $\rho = \begin{bmatrix}\ 1&0 \\\ 0&0 \end{bmatrix}$, $\rho' = \begin{bmatrix}\ 0&0 \\\ 0&1 \end{bmatrix}$, $\rho'' = \dfrac{1}{2}\begin{bmatrix}\ 1&1 \\\ 1&1 \end{bmatrix}$ (all density operators). Consider a physical operation $\phi$ such that $\phi(\rho) = \rho$, $\phi(\rho') = \rho'$, $\phi(\rho'') = \dfrac{1}{5}\begin{bmatrix}\ 4&2 \\\ 2&1 \end{bmatrix}$. Why is $\phi$ not a realisable physical operation? It certainly preserves trace and positivity...


Leap from photon gas energy distribution to black body radiation?

I remember considering in class in college, the case of a photon gas trapped in a d-dimensional box as a subject of interest, whose energy distribution, heat capacity, etc. should be calculated. This momentum/energy distribution was then related to that emitted by a black body - that up to a constant factor, they are one in the same. I could understand the argument that making a small hole in such a box would constitute a "black body", as the hole can't reflect back light impinging on it, but I can't see how to make the conclusion that this is the exact same distribution. Shouldn't the atomic structure of matter be brought into account as well, or is it considered "hollow" on sufficiently large scales?


Kinetic energy of two charged balls at infinite distance between them

If I have two balls with masses and charges $m_1, q_1^{+}$, $m_2, q_2^{+}$, initially held at distance $d$, and then released, how can I know the kinetic energies of each of the balls at infinite distance between them? I'm quite stuck on that, because they both have the same potential energy at the beginning, and it decreases not in the same pattern, as if one of the balls was stationary. So it not only falls like $1/R$, because at the same time, the other ball that is causing this potential energy, is also being repelled. So how can I really find out the energies? I tried to apply the conservation of energy law, because I know that at infinite distance from each other they'll have zero potential energy, thus all the initial was transformed into kinetic form, however I'm stuck with the initial potential energy (they both have it, so should I put $2U_p$?), and even so, I can't find their kinetic energies separately, without having another equation.


antimatter moving back in time

This just blew my mind away! I was watching a video about imagining the fourth dimension and the narrator said that little line. Can some people elaborate on this. Also please keep it simple not too complicated. Thank you!


Do particles travel backward and forward in time?

> All these classical ideas are pointless and obsolete today, because in > quantum mechanics, the particles are completely different objects, defined > by quantum motion of fields, not by the location of classical points (at > least not in a causal field picture). The notion of a point particle was > replaced by the more subtle notion of a quantum point particle, which has a > probability amplitude to be at various places. This quantum point particle > can reproduce the quantum field if it is allowed to go backward and forward > in time. _Ron Maimon_ That was quoted by Ron Maimon. From this - Can I gather that in reality, particles travel backward and forward in time or, is this just a mathematical expression or model?


Partition function for a microcanonical ensemble

Is it possible to write down a partition function for a microcanonical ensemble?


Easy formula for ultrarelativistic bremsstrahlung?

I am very curious if an easy calculable formula for the bremstrahlung radiation of deeply relativistic, charged particles exists, if they are moving on circular orbit: $P(E,m_0,Q,r)=?$ ...where   * $P$ is the power of the Bremstrahlung radiation;   * $E$ is the total kinetic energy of the particles (we are in deeply relativistic case, thus $E\gg{m_0}c^2$);   * $m_0$ is the total rest mass of the particles;   * $Q$ is the total charge of the particles;   * and $r$ is the radius of the orbit. If a such clean, trivial formula doesn't exist, a link were also okay, where it can be found.


squeezed radiation astronomy

Squeezed electromagnetic vacuum does have a renormalized energy density smaller than the vacuum. So it makes it in my opinion a inconspicuous candidate for a dark energy carrier. Are there observatories at the moment attempting to detect squeezed radiation from astrophysical and cosmic background sources? If not, What sort of equipment do you need to measure squeezed vacuum radiation?


electromagnetic interference

If the atmosphere is filled with electromagnetic waves all oscillating at different wavelengths and speeds how is it that they don’t all interfere with each other? For example turning on your light seems to have no effect on the sound coming from your radio.


Space as a function of time?

So - a little bit of background. Obviously from Einstein's equations it's shown that energy can be converted to matter and vice versa; in essence, energy and matter are different manifestations of the same "stuff". Now, I've done a bit of reading about the interplay between space and time. Some of what I've read would seem to indicate that just like energy and matter, space and time are different manifestations of the same "stuff", though the majority of what I've read seems to indicate that this isn't the case. So I got to thinking...what if space and time aren't the same thing, but there's interplay between them? What if one is a function of the other? And so I come to my question: Could space be a function of time? Or vice versa? From what I've gathered, our universe is expanding at a faster and faster rate. If space is a (seemingly exponential) function of time, then it makes complete sense that as more and more time passes, the amount of space in existence would increase. In addition (also from what I gather), nothing can go faster than the speed of light. We know that the closer to the speed of light that something is going, the more time slows down for that something, until the speed of light is reached and time stops for whatever it is. Since we're outside observers, a light year is the distance _we perceive_ light to travel in one year. But since (for the light) time stops completely, "how far it travels in a year" becomes meaningless to the light itself. Because no time is passing for it, wherever light goes, it effectively goes that distance in a relative time frame of zero seconds. This phenomenon would also make sense if space is a function of time; if there is no time affecting that light, there would be no space affecting it either. If from the light's perspective time has stopped completely, then from its perspective there would be no distance between it and any destination in the universe; any journey the light made would be instantaneous. Again, that's from the perspective of the light itself, not the perspective of someone who's observing the light. So does that make any sense? Could space be a function of time? Note: I am not a physicist. I am a lay-scientist, in the very loosest definition of that term. I ask this question assuming there are glaring errors and inaccuracies, which is why I'm asking it here - so you can all point me in the right direction.


Do any good theories exist on why the weak interaction is so profoundly chiral?

I find the profound asymmetry in the sensitivity of left and right chiral particles to be one of the most remarkable analytical observations captured in the Standard Model. Yet for some, I've not found much in the way of discussions that worry about _why_ of such as truly remarkable fact is true. I can't help but be reminded a wee bit of views on the motions of planets before Newton... you know, "it be Angels that do push them around, ask ye not why!" Seriously, I know the Standard Model has a lot of givens in it... but surely _someone_ has mulled over why the universe might exhibit such a non-intuitive and thus _interesting_ asymmetry? And perhaps even developed some solid speculations or full theories on why such in-your-face chiral asymmetries exist in nature? Do such theories exist, or is this asymmetry truly just a "given" and nothing more?


where does the photon go after scattering?

My question is about `photo electric` but it could be applied to other daily routine phenomenon. As we know rest mass of photon is zero. When a photon strikes the metal surface it transfers its energy to the electrons. Whether electron will be emitted or not, it depends upon work function. But my question is about that photon which was hit on metal surface. Does that photon vanished? Does that photon turned into nothing? where does it go after scattering? When I study this I only find the story about the emitted electrons but not about photons after collision. Am i missing some basic concept?


Electron degeneracy pressure

Why is it that in stars undergoing gravitational collapse electron degeneracy kicks in? Why couldn't the electrons form energy bands like in semiconductors?


Yang Mills theory and SU(N) groups

Trying to get a better understanding of the relation between a SU(N) Yang Mill theory and its number of "color" space. Most of the description I've found so far are either way to complex/specific. Yiannis answer on this post is almost what I'm looking for, except I was hoping someone could provide addition sources and readings corresponding precisely to what he is describing.


Graduate Physics Problems Books

Need to brush up on my late-undergrad and early-grad physics and was wondering if anyone can recommend books or lecture notes (hard copy, or on-line) that also have solutions. Two that I have come across are: **Princeton Problems in Physics with Solutions** \- Nathan Newbury **University of Chicago Graduate Problems in Physics with Solutions** \- Jeremiah A. Cronin **Spacetime Physics** \- Taylor & Wheeler (favorite book on special relativity; has a lot of problems with solutions at the back; a lot of the problems really enforce the material and discuss paradoxes) If possible, please also provide a reason why you like the books as opposed to just listing them.


Guides for solving E&M problems

I am an undergraduate physics student in a university and I am looking for a good guide or a handbook with lots of questions and full answers in subjects such as Gauss' law and Maxwell equations to study for my test.


A set of problems for "The Theoretical Minimum" Stanford course

I'm really excited by an opportunity to watch Leonard Susskind's course "The Theoretical Minimum". However, I couldn't find any physics problems on the website, and I'm a little bit wary of just watching videos. I want to think on some problems during that. Maybe there's a good collection of Physics problems on related themes, so I could try them between the videos?


Please recommend a physics problems book similar to Demidovich

> **Possible Duplicate:**   >  Graduate Physics Problems Books Does anyone have recommendation for a physics problems collection book (series) that is similar to Demidovich's _A Collection of Problems and Exercises in Mathematical Analysis_? I am looking for the encyclopediac coverage and Russian editorial style, if you like. # Update: I'd like problems for 1) senior undergraduates major in physics and/or 2) Ph.D. candidates in physics


Where can some worked problems in classical mechanics (and more specifically the Lagrangian and Hamiltonian formalisms) be found?

I've been looking for a textbook in classical mechanics that's readily available (like can be found in the library of James Cook University of Townsville, Australia) and full of fully-answered questions in the Lagrangian/Hamiltonian formalisms yet I can't find any. My first port of call was the Schaum's Outlines and Demystified series but the only member of these series I could find that was relevant was Lagrangian Dynamics which is difficult for me to track-down in real-life. It would be particularly helpful if one could point me to a free eBook with this material.


Problem book in Quantum mechanics with emphasis on physical(ly relevant) problems

I am a second year undergraduate and studying quantum mechanics from sakurai's 'Modern Quantum Mechanics'. Is it a good idea to solve problems from sakurai, which are mostly mathematical in nature? I need a textbook that has physically relevant problems, maybe going even into condensed matter, or field theory in its exercises. This would probably help me to appreciate and understand qm better. Sorry if this question is too localised but I just had to post it.


Problem books like I.E. Irodov for advanced physics

I really enjoyed doing problems from Irodov while learning introductory physics. But I am not able to find a book like that for Graduate level physics. Can you suggest me a book which has good (and hard) problems from advanced topics like Quantum Theory, QFT, Relativity, etc?


Requesting some research study problems on Classical Mechanics

Someone please tell (advice) me some research study problems on Classical Mechanics that can be tackled with Undergraduate level knowledge.


Goldstein's Classical Mechanics exercises solutions

Does anyone know where I can find some (good) solution of Goldstein's book _Classical Mechanics_?


Translations and Noether's Theorem

I'm fine with $U(1)$ symmetry and Noether's Theorem, but struggling with the translations of the field; namely $$\phi'(x^{\mu})=\phi(x^{\mu}-a^{\mu}),$$ where $a^{\mu}$ constant four-vector $$x^{\mu}=x^{\mu}+a^{\mu},$$ and the Lagrangian density $${\cal L}=\frac{1}{2}\partial_{\mu}\phi^*\partial^{\mu}\phi-V(\phi^*\phi).$$ So a few questions:   1. I can't show the Lagrangian is invariant under this transformation. Is it just a case that as $a^{\mu}$ is constant then the first term in the Lagrangian will obviously stay the same? But what about $V$? How I can show that's invariant?   2. Infinitesimally, is the transformation $\phi'(x^{\mu})=\phi(x^{\mu})-a^{\mu}\partial_{\mu}\phi(x^{\mu})?$    3. If I'm right in point 2., how can I apply Noether's Theorem to this?


How to simulate a full-suspension bike?

As a fun project, I would like to roughly simulate the suspension operation of a full-suspension mountain bike. This is _not_ another one of those "How does a bicycle stay upright?" questions. Follow some metrics of interest.   * Pedal bob - the amount of movement in the rear triangle upon pedaling up an incline. An estimate of the lost energy due to this.   * Sharp obstacle transient response - for example how does the bike move, when hitting a curb at high speed.   * Large obstacle transient response - for example, how does the bike move when it falls (along with the rider) 1 meter. I am somewhat familiar with python, Mathematica, ScyLab, Matlab, Ansys. I guess an analytical solution would be too difficult. _Which approach will give quickly a parameterizable model and analyze it for the abovementioned information?_ Here several common frame variations are mentioned. EDIT: More concretely:   * What model to use? Is there a widespread "bicycle" model for dynamic analysis?   * What software to utilize, in order to help me solve the problem?


Gravitational distortion of an object's diameter, at a distance,

Does the curvature of space-time cause objects to look smaller than they really are? What is the relationship between the optical distortion and the mass of the objects?


what causes virtual particle pair production to not occur in the space occupied by matter?

Are virtual particles only popping in and out of existence where the local energy density is below a certain point? What I wonder is, does any kind of matter prevent the pairs from appearing? Is there a shell surrounding an atom or maybe I should call it a boundary beyond which particle pair production occurs, and within the boundary it does not, I have wondered if the different orbitals around an atom are affected (set)by the influence of the virtual particles.


Does the curvature of spacetime theory assume gravity?

Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form "gravity wells." Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in-order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing?


Is the space-time deformation only a way to say how gravity works?

Here we have the classical picture of the deformation of the space-time: https://blogs.stsci.edu/livio/files/2012/06/spacetime.jpg And I would to know if this representation is only a way to say how the gravity field of the earth is shaped, and how the gravity works in the area near it, or not.


Does Spacetime have a "This Side Up" arrow?

> **Possible Duplicate:**   >  Does the curvature of spacetime theory assume gravity? Forgive my naivete as I am not schooled in Physics or Mathematics. I was watching NOVA's "The Fabric of the Cosmos" last night. The subject was basically spacetime and how our conception of it moved from the Newtonian description to the Einsteinian. i.e. That spacetime is like a fabric stretched across the universe and that large objects like planets and stars create a depression in the spacetime fabric and the orbiting of satellites is really just the satellite getting caught in the "swirl" of the depression. The narrator used a pool table surface as an example of the fabric of spacetime and then with some CGI he dropped a bowling ball on it which caused a depression and then shot a pool ball near it which caused the pool ball to get caught in the swirl. I found myself pondering the following though:   1. I find it really hard to believe that there is a "This Side Up" arrow for spacetime. But if there is, what causes it? You can see a diagram of what I'm trying to describe in this Gravity Probe B article. I understand that spacetime can be twisted so I'm guessing reality is more like the depressions are at all orientations through the universe (sorry, I lack the language to describe this). But I still wonder: Why is the depression one orientation and not the other?   2. What is the effect of the other side of the depression? i.e. If the swirl on the other side pulls objects in, does the other side of the depression repulse objects? Warning: any answers that include mathematics will be lost on me. Any suggestions for further layperson reading on this fascinating subject welcome. Thanks!


Misused physics analogies

Have you noticed that many questions and misconceptions in physics arise due to misuse of analogies, which were invented to "explain in simple words" some physical phenomena? For example there is a "stretching rubber band" analogy for Hubble expansion of the Universe, which make people ask about the "tension" of this rubber band or speculating about "cutting a hole" in it. I'm pretty sure that there are a lot of such misuses. Do you have any remarkable examples of these (together with a proper treatment n of course)?


How does relativity explain gravity, without assuming gravity

I have seen the "objects pull down on space-time" explanations, but they assume a "pull down" force themselves. Could anyone explain the space-time explanation without assuming gravity in the first place? ![](http://i.stack.imgur.com/RVFrW.png)


Is the concept of space-time curvature a recursive one?

A way some people explain (or try to explain) how gravity works is using space-time curvature: an object with high mass distorts the surrounding space- time plane like a bowling ball distorts a sheet of plastic and the surrounding objects are always trying to roll down to that other object. However, this explanation to me seems flawed, because in order to work, it needs to be influenced by the very thing it tries to explain. The reason a bowling ball distorts a sheet is because Earth's gravity is affecting it. However, the space-time curvature which this distortion is an analogy to is trying to explain gravity. The implication of this space-time curvature is that something is pulling down on the space-time plane, but this pulling itself requires gravity from a perpendicular source, it seems to me. I'm having difficulty wrapping my head around this. The method we use to explain gravity itself uses gravity to work, sort of like some kind of recursive loop. it's comparable to "to get fuel, we need to drive, and to drive, we need fuel", and I don't know enough about gravity to figure this out myself. Am I understanding this analogy correctly, or are there deeper things at play?


Bowling ball on a rubber sheet analogy - what pulls the ball down

> **Possible Duplicate:**   >  Does the curvature of spacetime theory assume gravity? Since I read Cosmos long ago, I see the same analogy about the balls rolling on a rubber sheet used to explain how gravity works. But a ball rolls on a surface because gravity is pulling it down. In space it will follow a straight line and go over any hole on the surface. So, in the analogy we all know, where the curvature of the rubber sheet is gravity, what is pulling the ball down? If space is curved, what keeps an object attached to that "surface" of space?


If the universe is 3D, how is space-time like a "fabric"?

I have been taught that space-time should be viewed as a fabric and that objects with a large gravitational influence indent that fabric. My question is, if the singularity of a black-hole punctures space-time, how is this accomplished if the universe is 3D? Can an object move completely around the black-hole in all directions? Would you be able to travel "below" a black- hole?


Why is getting a tan in the evening less likely than getting a tan in the morning?

When I was young I read one book in which is written that you get more tan on the morning than on evening even light angle from Sun to Earth is the same. Don't remember exact reason, I think because ultraviolet is more absorbed on the evening because air is more humid or something like this. Is it true?