title: How much can a laser's position be fine-tuned?

text: Suppose you wanted to do a time-resolved experiment with a molecular beam traveling at, say, 300 m/s involving a mobile excitation (pump) laser that scans across the length of the molecular beam and a stationary detector. So the time-resolution of the experiment depends on how precisely the position of the excitation laser can be fine-tuned, e.g. if the laser can be tuned in the millimeter range, then the time resolution would be in the microsecond time scale. (Don't worry about the path length of the beam to the detector. It's reasonable to imagine that one would be interested in obtaining ns accuracy for a system in which nothing happens for several ms). Also suppose that the velocity distribution of the particles in the beam have a sharp velocity distribution, such that ∆v/v≈0.01. My question is, then, to what degree of accuracy can the excitation laser's position be fine-tuned using modern optics? Obviously the intensity, wavelength, and type of laser will have some effect on the answer, but I'm interested in a ballpark figure anyway. The obvious follow-up question is how, experimentally, does one tune the laser to that level of accuracy? Would relativistic effects start to be an issue at some point? And is the velocity distribution (or, for that matter, the measurement of the velocity) actually going to end up being the limiting factor on time resolution in the end? Thanks in advance for your answers.


title: Phonons, rotons, and maxons

text: What are phonons, rotons, and maxons, and what does their dispersion curve have to do with superfluidity? I understand that they are quasiparticles, but I'm not entirely sure what that implies. Are these concepts purely notational and/or mathematical? Or are these three quasiparticles fundamentally different from each other?


title: Why is Heisenberg picture used if Schrödinger picture is simpler?

text: In Heisenberg picture the operators evolve in time instead of states, which evolve in time in Schrödinger picture. But this also means that to solve the equations (at least numerically) one has to work with $N^2$ numbers instead of Schrödinger's $N$ (i.e. Hamiltonian matrix vs state vector). So, why, despite being dramatically more inefficient for calculations, is Heisenberg picture still used?


title: How does cold air move through a room

text: If you turn on a fan in a warm room, it feels as if cold air is being pushed from the fan out in the direction that it's facing, but what's actually happening on a molecular level? When an object is heated, its molecules are excited and they can in turn excite other molecules around them thereby passing on heat through the air (or another medium). But the opposite of this - molecules vibrating less and passing on a lack of vibration - doesn't seem to make as much sense, intuitively at least. So is the apparent effect of cold air being pushed out by a fan or air conditioner caused by molecules passing on their relative lack of movement to their neighbours or is there something else going on?


title: How can I calculate the speed at which water evaporates when held at 100 degrees Celsius?

text: If I have a mixture of some higher bp solvents and water, and I heat it to 100 degrees celcius so that the water in the mixture begins to boil, how can I calculate the rate at which water leaves the solution, assuming the temperature is held relatively constant. I did some reading into this and found out the humidity plays a role, so I suppose we can assume 10% humidity, though, I haven't been able to find any relevant formulas that are clear cut about this. The device is 500w, but it has a digital thermometer control, so the hotplate is always at a particular temperature. Not sure how this would interfer with calculating heat transfer based off wattage soley.


title: Chern-Simons Theory in 3D

text: For the CS theory on a three manifold $M$ with a gauge group $G$, it is said that the gauge field $A$ is a connection on the trivial bundle over $M$. Why the bundle should be trivial? I know that space of classical solutions is made of flat connections but why should we assume the bundle is trivial from the beginning? Another question: Can anyone explain the meaning of farming of a three manifold in simple terms? Thanks.


title: Charge density in concentric spheres

text: Question: > If there are two conducting spherical shells and the inner shell is > grounded, what will be >the charge density in the inner shell if there is a > charge Q placed on the outer shell? Yes, this is a HW problem, but I am not asking you guys to solve it for me... just show me the way :D If there is a charge on the outer shell with radius $a$, the charge density will be $\frac{Q}{4\pi a^2}$. That should induce, a charge density on the inner side of outer shell -- $\frac{Q}{4\pi (a-x)^2}$ where $x$ is thickness of the outer shell. Now, if the inner shell was never grounded, $\frac{Q}{4\pi b^2}$ ($b$ = radius of the inner shell) charge density would have been induced on the inner shell, now that it is grounded there would be no charge on it, right? There is no need for a charge to be induced for the electric field to be 0 inside the inner shell. This seems to be my conclusion, but I fear it is too simple for the question. There might be something I am missing. Edit: the hint of the problem says when a sphere is grounded, potential is infinity.


title: Is refraction sharp or smooth?

text: Refraction: light changes direction of propagation when entering a material with a different refractive index. ![enter image description here](http://i.stack.imgur.com/E0Xwq.jpg) Does the direction of propagation of light change **sharply** and almost instantaneously (as shown in the diagram) or smoothly?


title: Can an electron and a positron annihilate to form a Z_0 boson?

text: I guess that, since the Z boson is more massive than both the electrons, they need to go pretty fast (so that their kinetic energy is large enough), but **is annihilation a property of the electromagnetic force only**? Can the weak force also cause annihilation?


title: What is the difference between these two Feynman diagrams?

text: In which direction is time flowing and what reactions do they represent? ![enter image description here](http://i.stack.imgur.com/cIg12.gif) EDIT for Gigi (I could not add a comment to your answer): 1) Do Feynman diagrams by definition only show fundamental particles? 2) why does the second diagram show how _neutrons_ transform into _protons_? In which direction is time flowing?


title: How am I able to tell whether it is dark or not while eyes closed?

text: How am I able to tell whether there is a light on in front of me even with my eyes closed? The usual darkness whilst eyes closed transforms into a not so bright glow when my closed eyes are in front of a light source? How am I able to intercept light when my eyes are closed?


title: Infinite possibilities of you

text: "The question you are asking appears to be subjective, and is likely to be closed." Challenge . . . ACCEPTED. Okay, here it is. A friend prone to uplifting aphorisms posted on Facebook: "You Are An Infinite Possibility." I thought about that and it seems to me that, given the Bekenstein bound, one can calculate the maximal number of possible states, in principle, of the human brain (given an average volume). Lo and behold, Wikipedia revealed that someone's actually done the calculation and gives the number as less than approximately $10^{7.8\times 10^{41}}$ states. On the other hand, if you model the brain as a quantum system and calculate its evolution over time with the Schrödinger equation --well, the wavefunction is continuous, so doesn't it _in principle_ describe an infinite number of possible states?


title: Stick and slip motion: mass and spring inside a box model

text: I am trying to determine a set of differential equation which can describe the motion of a mechanical system as below. Here, at the bottom we have a plate, and a box on top of it. Inside the box, there is a ball supported by 2 springs. Then we try to oscillate the bottom plate. If needed, the assumptions are as below   1\. Suppose that only horizontal motion is permitted.   2\. The box's mass is negligible.   3\. The ball has mass m.   4\. There exist static and dynamic friction force between the box and the plate.   The coefficient of static and dynamic force are $\mu_{s}$ and $\mu_{k}$, respectively.   5\. The input oscillation for the bottom plate is $\gamma(t)$ This is not a homework, I am trying to make a mechanical model for droplet oscillation.   I understand that the box will move when the force on it is greater than the static force. But I am still confused on when the box move and and its velocity when it is moving. ![enter image description here](http://i.stack.imgur.com/3KVNO.png)


title: Isotropic harmonic oscillator in polar versus cartesian

text: I read another Phys.SE post here: 3D Quantum harmonic oscillator that I believe says the wave function in Cartesian coordinates for a 3D harmonic oscillator is the product of the 3 one dimensional wave functions. If so, are the angular and radial equations combined within it? Is it possible to separate the radial part from the angular part? The wavefunction for 1D in the ground state is $$\psi_{0}(x)=(\frac{m\omega}{\pi\hbar})^{\frac{1}{4}}e^{-\frac{m\omega x^{2}}{2\hbar}}.$$ I think this product would then be: $$\psi_{0}(r)=(\frac{m\omega}{\pi\hbar})^{\frac{3}{4}}e^{-\frac{m\omega r^{2}}{2\hbar}}.$$ Is this the radial equation for the ground state? Would I then need to multiply by the angular equation for the ground state to get the full wave equation?


title: Modeling Spacetime In A Corpuscular Or Statistical Way

text: When I first read about Newton's gravity, it really bothered me. I didn't understand how shaking a lighter at the other end of the universe would instantly influence the lighter that was in front of me. Quantum Mechanics bothers me in a similar way. I don't understand how a particle I measured an infinitesimal moment before has a non-vanishing likelihood of appearing on Mars. In the gravity case, it turns out that the two lighters are connected by a spacetime fabric. I can't help but wonder if something should be connecting the particle that I think is near me and that "impossible" particle that appeared on Mars. One idea I've toyed around with was what if spacetime was actually material or corpuscular and matter was something more like an emptiness between the rocks. Is there any theoretical work on modeling spacetime in a corpuscular manner, or attempts to explain gravitation from a statistical point of view (as in spacetime being made up of little 'things')? I feel a field is something like a model for the empty space between the rocks. Is there a concept of some kind of co-field?


title: Has the photon both gravitational and inertial mass?

text: The theory of relativity shows that the inertial mass of a body increases with the energy it contains; if the increase of energy amounts to $E$, the increase in inertial mass is equal to $E/c^2$, where $c$ denotes the velocity of light. Now, is there an increase of gravitational mass corresponding to this increase of inertial mass? If not, then a body would fall in the same gravitational field with varying acceleration according to the energy it contained. And then the highly satisfactory result of the theory of relativity, by which the law of the conservation of mass leads to the law of conservation of energy, could not be maintained, because it would compel us to abandon the law of the conservation of mass in its old form for inertial mass, but maintain it for gravitational mass. This must be regarded as a very bad model. On the other hand, the usual theory of relativity does not provide us with any argument from which to infer that the weight of a body depends on the energy contained in it. However Einstein has shown that gravitation of energy is a necessary consequence. However, some very serious issues are raised when these arguments for maintaining the law of the conservation of both the inertial and the gravitational mass are applied to the red shift of a photon influenced by the gravitational field of a body M. When doing so we arrive at the following solution when resorting to certain well-known physical expressions: $$ E = h\nu $$ $$ E = mc^2 $$ $$ m = \frac{h\nu}{c^2} $$ $$ F = \frac{GMm}{r^2} $$ $$ F = \frac{GMh\nu}{r^2 c^2} $$ From the work done against the gravity force in bringing a photon in from infinity where the potential energy is assigned the value zero, the expression for gravitational potential energy $U$ is $$ U = -\frac{GMh\nu}{rc^2} $$ If the _original_ frequency and energy of a photon “launched” from a body $M$ were equal in magnitude to the potential energy, then when would it have enough energy to escape from $M$? This _escape energy_ would be the _original_ energy $h\nu$ of a photon which is totally red shifted to total extinguishment by the gravitational field of the body $M$. That would mean that any photon with an _original_ energy less than the _escape energy_ would be extinguished before it leaves the gravitational field of the body $M$ and that photons with higher _original_ frequencies, and thus higher _original_ energies, would escape that field less red shifted the more the _original_ frequency of the photon is increased. However, as far as I know this kind of redshift has never been observed. My question to Red Bunn is: what is then the reason for using the metaphor: "In Newtonian language, if you imagine the source of the light at the centre of a spherically symmetric expanding spacetime, then the light travels 'uphill' in a gravitational potential all the way to the observer. The observed redshift is partially due to this redshift and partially due to the observer's motion. Conversely, if you put the observer at the centre, the light 'falls downhill' all the way to the observer. This gives a different breakdown of the observed redshift into gravitational and Doppler contributions." I would rather ask whether it's proven or not that the photon could have no such gravitational mass which interacts with a gravitational field in the way it would be expected if the photon would act as a mass particle?


title: Electrolysis of liquid hydrogen

text: say i used electrolysis to extract hydrogen from water, then froze the hydrogen into a liquid and then again used electrolysis. What would happen ?


title: Do the laws of physics that apply to all observers also apply to a non-observer?

text: The Timelessness of a photon https://www.youtube.com/watch?v=5ELA3ReWQJY An observer's laws of physics are time based. "When you're traveling at the speed of light, time does not exist" - Neil deGrasse Tyson. So a photon's laws of physics can not include time because it does not exist. How does the Photon exist in "space-TIME", if Time doesn't exist for the Photon? The Photon would not exist in "space time", it would exist only in "space". The physics of "space time", which is where we are, would not apply to "space without time", where the Photon is.   1. The rules of physics are the same for all observers in uniform motion relative to each other.   2. The Photon is never in uniform motion relative to any or all observer.   3. A Photon in an observer's frame is not the same as a Photon in a Photon's frame.   4. The Photon must have "a frame" (although it is not compatible with our own), because the Photon occupies coordinates in space as a particle.   5. The Photon's frame would not define Time.   6. The Photon does not exist in any observer's frame, because the Photon is never in uniform motion relative to any observer, but the Photon does exist.   7. If the Photon does not exist in any observer's frame, then the Photon must have a frame of its own that it does its existing in.   8. The laws of physics for all Observers includes a definition for time.   9. The Photon's frame has no time coordinates, so time coordinates from any observer's frame can not be meaningfully associated with the Photon or the Photon's frame. Time is relative to all "observers" but light is not an observer. Time can't be meaningfully applied to light because time doesn't exist to light. Time is not relative between an observer and light because they are not both "observers". If one physicist says that a particle is instantaneous And another physicist says the same particle takes 8 minutes to travel from the Sun to the Earth That's a contradiction 8 Minutes > Instant All physical laws should remain unchanged under a Lorentz transformation. An observer's physical laws include time laws. A Photon's physical laws do not include time laws. All physical laws can't remain unchanged when transforming an observer's physical laws into a photons physical laws. This would cause the application of time laws to the photon, but time laws and photons are incongruent. Assume that "space time" is a prison. In the prison there are guards and inmates. Everyone in the prison follows rules, but the guards follow one list of rules and the inmates follow a different list of rules. Some of the rules for the inmates and the guards are the same, some of the rules for the inmates and the guards are not the same. Among the inmates, all inmates must follow all of the inmate rules, no inmate receives special treatment. Also among the guards, all guards must follow all of the guard rules, no guard receives special treatment. The two lists are written in different languages. All of the inmates speak different languages, but one inmate speaks the language that the inmate rules are written in, and all of the languages that the inmates speak. All of the guards only speak the language that the guard rules are written in. It's possible for the one inmate who can read the inmate rules, to translate those rules into all of the languages that the inmates speak. And because all of the inmates follow exactly the same set of rules, the number of rules would be the same in each of the inmate languages. It's also possible for the inmate to translate the list of guard rules entirely into the language of the inmates, and the list of inmate rules into the language of the guards. This doesn't matter though, because the inmates and the guards still follow different rules. Writing the rules of the guard in the language of the inmate does not allow the inmate to follow the rules of the guard, and writing the rules of the inmate in the language of the guard does not subject the guard to the rules of the inmate. The laws of physics for any observer include laws that define the behavior of time. The entire system of physics for all observers then, is inherently based on the existence of time, and time is one of the defining features of the "existence" or "reality" that all observers occupy. It is the presence of time that allows an observer's laws of physics to establish a frame of reference. Because all observers follow exactly the same list of rules, like all inmates, all of the rules of "observer physics" can be translated (by the one inmate, "man") from one observer to the next, even though all observers speak a different language, or have differing personal frames of reference. However, the laws of physics for "light" or "the speed of light", do not recognize the existence of time. The entire system of physics for "light", is inherently without time, and this lack of time is one of the defining features of the "existence" or "reality" of "light" or, "anything 'traveling' at the 'speed' of light". It is the lack of "time", and therefore the lack of a definition between "at rest" and "moving", which is THE REASON why a photon can't be assigned a frame of reference when trying to translate the photon's physics to the observer's physics. It only APPEARS that photons exist by the same laws of physics as an observer because some of the laws cross over from one reality to the next. It appears that the physics of photons and the physics of observers are the same because the existence of time in our reality prevents you from observing the photon in it's "natural habitat" to see how we different we really are.


title: How to get rotation speed after disk-disk collision?

text: Assume two circular disks A and B collide. They have both initial linear momentum and angular momentum. If their surface has no friction, their angular velocity does not change after collision, so I can easily calculate their final linear and angular momentum. But what if their surface has some friction? In that case, their angular velocity will change after collision, and I can't guess how they will change. If the friction coefficient $\mu$ is given, can I calculate their final linear and angular momentum?


title: Gravitational force and time dilation

text: Suppose the radius of the earth is reduced by half but the mass is same, then how long will it take to complete one rotation, 24, 48, 12 or 6 h.? please give the mathematical relations and solution.


title: Calculate Potential Gravity Energy converted when star collapses

text: We want to calculate how much gravitational potential energy converts to heat, when the star has no nuclear fusion, the gravity will cause the star to shrink in nano seconds. Now assuming the Sun shrinks to 10km radius (an event we know is not possible), calculate the gravity potential energy that this will release. I simply assume to 0km radius, for any point on Sun, it has gravity potential energy as $$ U = mgh = m_i g r_i = \rho_{density} dV r_{distance\;to\;core} $$ So the total energy as below, I'm using triple integral $$ \begin{align} \Delta{U} &= \int_0^{2\pi} \int_0^{\pi} \int_0^r g \;\rho_{sun}\; \rho^3 \sin\theta\; dr\; d\phi \;d\theta\\\ &= \int_0^{2\pi} \int_0^{\pi} g \frac{1}{4}r^4 \rho_{sun} \sin\theta\;d\theta \; d\phi \; \\\ &= \int_0^{2\pi} - g \frac{1}{4}r^4 \rho_{sun} \cos\theta \;|_0^{\pi}d\phi \\\ &= \int_0^{2\pi} 2 g \frac{1}{4}r^4 \rho_{sun} d\phi \\\ &= 2\pi 2 g \frac{1}{4}r^4 \rho_{sun} \\\ &= r^4 \pi g \rho_{sun} \end{align} $$ I'm not sure if my way is wrong or not, because as the teacher's the result is $$ 10^{46} J $$ while my result is $$ 10^{40}J $$ The result is calculated in some lines of code in the Ruby language ` r=7e8 #sun radius in meter rho = 1411 #density kg/m^3 g = 10 u= r**4 * Math::PI * g * rho p u ` It would print "1.0643122149350688e+40"


Why the initial spectrum of perturbation of inflation must be Gaussian? I heared it was because of Central Limit theorem. But I don't know how use this theorem explicitly in this question to get this result.


title: The Great Atomic Clock of Kansas

text: It is said that astronauts on the ISS experience time slightly slower than the rest of us. (I believe that the lesser gravitational field would increase their rate of time, so that affect must be more than canceled by the dilation affect of their velocity) One could imagine setting up an atomic clock in a flat sparsely populated area such as Kansas, with a huge display that can be seen from space. We could than synchronize this clock with an atomic clock on the ISS. The above wikipedia article mentions that the ISS looses about 0.007 seconds every 6 months. When the astronauts of the ISS pass over Kansas, will they see their clock losing time or gaining time versus the Great Atomic Clock of Kansas?


title: What's the best way to start out with astrophotography on a tight budget?

text: I'm new to astronomy and I don't have a great deal of cash to spend. I currently have a 3" reflector telescope which I've had great fun with. I also have a Pentax DSLR which I've been using to take long exposure photos of various constellations (+ brighter deep sky objects such as the Orion nebula). I've managed to take some surprisingly good photos of the moon and jupiter's moons combining my mobile phone with my telescope (which requires a very steady hand and alot of patience) but I'd really like a better way of taking photos. I'm wondering whether I should investigate getting an SLR mount to attach my Pentax to my scope, or whether to go for one of these webcam eyepeiece attachments. Any advice?


title: Assuming an observer is 50 light years away, in the plane of the solar system and observing earth, what is the light flux of earth he would see?

text: As in, from what the planet emits and re-radiates out into space (this is going to be important if we are to image any Earth-like planet)


title: Bernoulli's principle on a curve ball

text: I've seen a few excellent answers here on the Magnus force, which explains why balls with a spin will curve. However, my intuition is still telling me that the Bernoulli's principle would push it the opposite way and I need help understanding why my reasoning is flawed. Imagine that you kick a soccer ball on the left side so that it's spinning clockwise (viewing the ball from above) and the ball will curve to the right. Since the left side of the ball is spinning against the air, wouldn't this mean faster relative speeds and thus a lower pressure than the right side? And wouldn't this lower pressure on the left side cause it to curve _left_ instead of right?


title: Thermodynamics of thermometer

text: Mercury is used in thermometers because it increases in length significantly due to rise in temperature, However, mercury has high density relative to water, which means more inter-molecular forces which makes it harder to expand than water. Then,why is mercury preferred to water in a thermometer?


title: Using a lemon's energy

text: Some simple exercises i need some confirmations on. Let's say a lemon has U = 1V and an average current of 0.1mA for about an hour. Q1. How much lemons do you need to light a 100W bulb. Is the answer 1 million lemons ? Q2.The Atmega1284P processor has an average energy consumption of 0.18nJ/instruction. How much instructions can be executed from a single lemon. Is the answer (6*10^6)/0.18 ? And a bonus one i haven't figured : A battery that functions at 1Ah is draining with 4C on a resistance of 2W. How much time till the battery is fully drained.


title: Planet orbits: what's the difference between gravity and centripetal force?

text: My physics teacher says that centripetal force is caused by gravity. I'm not entirely sure how this works? How can force cause another in space (ie where there's nothing). My astronomy teacher says that gravity is (note: not like) a 3D blanket and when you put mass on it, the mass causes a dip/dent in the blanket and so if you put another object with less mass it will roll down the dip onto the bigger mass. Is this true and is this what causes the centripetal force.


title: Angular Momentum and Average Torque

text: ![alt text](http://i.stack.imgur.com/X4Ht1.png) Refer to number 6. This is the one I'm stuck on. So angular momentum is conserved right, so initial angular momentum is equal to final angular momentum. Initial is 7.87 so final must be 7.87, right? And so average torque is just change in angular momentum / change in time, so 0/7=0. What am I doing wrong?


title: Can universal continuity be experimentally falsified?

text: It is an unresolved question whether the universe is discrete or continuous in its intricate quantum level structure. See for example: Is the universe finite and discrete? How could spacetime become discretised at the Planck scale? Is time continuous? It is often stated that it is beyond our reach to resolve this issue. See for example: Is time continuous? Is this however really true? Consider a simple dynamical system, such as the Lorenz attractor. When you solve this system numerically it quickly becomes evident that the solutions found depend heavily on the numerical precision. The number of revolutions around one attractor point before the evolving curve moves to the other attractor point varies with numerical precision. At some point you can wonder if you are really studying general behavior rather than a near exact solution. Would it be possible to set up an actual experiment with a highly non-linear system, exhibiting long term iteration, to show whether or not the real-world solution at some point deviates from high-precision numerical simulation?


title: How to measure the mass of the electron?

text: I've done a little bit of research and it seems Millikan was able to measure the ratio between the charge of the electron and its mass. But how can one measure one of the two constants to get the value of the other?


title: 'Polar Vortex' Boiling Water to Snow is Mpemba Effect?

text: I am based far away from the icy storm currently blanketing the US - the 'polar vortex'. However, I have seen in the TV news footage of reporters throwing boiling water into the air, the water freezing immediately to form snow. I'm curious as to whether this would also work with cold water. If not, I presume that it is because of the, as yet unexplained, Mpemba effect. Has anyone in the US tested this?


title: Angular Momentum and Force

text: ![alt text](http://i.stack.imgur.com/9ak7P.png) I'm stuck on number 5. The answers to the first 4 are correct, but I dont know how to set up number 5. Any idea that I would have would require me having some kind of time information, but thats not given. Any suggestions?


title: Question about creation operator and its Hermitian adjoint

text: The definition of creation operator for bosonic system is $$a^{\dagger}|... n_i ...\rangle = \sqrt{n_i + 1} |... n_i + 1 ...\rangle $$ If I take Hermitian adjoint of this I will get $$(a^{\dagger}|... n_i ...\rangle)^{\dagger} = |... n_i ...\rangle^{\dagger} (a^{\dagger})^{\dagger} = \langle... n_i ...| a = \sqrt{n_i + 1} \langle... n_i + 1 ...|$$ But this can't be correct since $$\langle... n_i ...| a = \sqrt{n_i} \langle... n_i - 1 ...|$$ Can someone explain to me why my Hermitian adjoint equation is wrong. From the answer I got from JeffDror and the comment left by user26431. I infer that in dual space $A_1 = a$ acts as creation operator and $A_2 = a^{\dagger}$ as annihilation operator. I am a bit confused by what JeffDror wrote "if you are acting backwards with the operator then you need to use the Hermitian adjoint". In my mind it sounds like that to act with operator A on some bra-vector I must first take Hermitian adjoint of it and than act on bra. It make sense to me if imagine that bra-vector is row vector that I get for transposing ket-vector and non hermitian operator A in ket space is not represented by square matrix. Then in order to multiply matrix by column vector from the left I must transpose matrix that represents A. Is this correct way of thinking about operator how operator A acts in dual space?


title: Vortex shedding

text: So I was reading about vortex shedding, and got to know that it causes the building to resonate. Is there any way to use this resonance to generate electricity (maybe use quartz?) I am trying to make this model for a science fair. I am in grade 9 so it would help if the answers are not too complicated. Thanks.


title: Why are oxygen and hydrogen compressible, but water is barely compressible

text: What makes the two gases compressible, but does not apply to a liquid like water?


title: Temperature behavior over time of black or white cars in hot, sunny regions

text: How does the color of a car influence its inner temperature change over time when parked outside in windless, hot and sunny regions? I know what's the common idea about that: black cars are supposed to build up high temperatures faster because black objects absorb radiations instead of reflecting them off. Is it true? And then, what happens during the steady state? Some claim the black car will stay hotter, some others claim it will be the same whatever the color. Do all cars have the same temperature inside in the long run, or are some of them hotter? I've Googled it but the best I could find was http://phoenix.about.com/od/car/qt/carcolor.htm. It claims to be based upon ~20 articles. But there's not even a mention of absorption or emission spectrums. A priori, a black car could absorb all visible radiations and emit it as infrared while reflecting all of the Sun's infrared. And it's still only qualitative. I've found nothing on Physics stackexchange, the closest being Heat in the car during sunny day.


title: Why do electric motors draw current even when they are not moving?

text: After testing electric motors, I realized that these motors draw current even when they are not moving. I do feel that these motors are trying to move, but they are not really moving, in the end. Why do these motors draw current even though they are not moving?


title: Intuitive explanation for angular momentum uncertainty?

text: The basic commutator relation $$[J_1,J_2]=i \hbar J_3$$ of quantum mechanics yields the uncertainty relation $$\Delta(J_1)\Delta(J_2)\ge \frac{\hbar}{2}|\langle J_3\rangle|.$$ However, unlike the position-momentum or energy-time uncertainty relations, I'm not familiar with any intuitive explanation of this uncertainty. I would like to see a heuristic derivation for this uncertainty relation which can be understood by a mathematically untrained layman (i. e. something you could tell your non-physicist friends or print in a book on popular physics). If possible, the explanation should be based on a real-life experiment in which this uncertainty has immediately visible consequences.


title: Oscillator, angular frequency equation

text: ![wikipedia screenshot](http://i.stack.imgur.com/bbNP2.png) I found the highlighted equation on the Wikipedia on angular frequency, however it doesn't say how it was obtained, could someone please explain that? Also, it says that the spring is massless, if it has mass do i simply add it?


title: Determining the minimum pull force of a magnet required to hold it in place

text: If I place a magnet on the underside of a metal object so that it is held there by its attraction to the metal, how can I determine the minimum pull force the magnet needs to have in order to keep it attracted to the metal and not fall off? Would the required pull force be equivalent to the magnet's weight?


title: Isotropic systems and homogeneity

text: In isotropic systems, the atomic arrangement is homogeneous in all directions. In the case of glass, which has the atomic structure of a liquid and, therefore, a random atomic structure that is definitely not homogeneous, is it that the atomic arrangements in each direction are equally disordered and therefore homogeneous in that sense?


title: Solution to the "cubic" Helmholtz equation

text: What is known about the solutions of the differential equation in three- dimensions $$ \nabla^2 \phi = -\kappa^2 (\phi + (1/3!)\phi^3) $$ Without the cubic term, this gives a linear operator $\mathcal{L} = \nabla^2 + \kappa^2$. In this case I can get a solution via the Green's function $G=\exp{(i\kappa r)}(4\pi r)^{-1}$. In my equation however, the presence of $\phi^3$ does not give me a linear operator. Is anything known about the solution to this equation? **Context** : The Poisson-Boltzmann equation can be put into the functional form of $\nabla^2 \phi = -\kappa^2 \sinh \phi$. Expanding sinh to first order gives the Helmholtz equation as mentioned above. The second order term is zero and the third order term gives the equation in question.


title: Block on block with friction

text: I couldn't find a similar question here - I'm guessing because it's kind of elementary. Lets say we have two blocks, $B_1$ and $B_2$, of mass $m_1$ and $m_2$ (respectively), where $B_1$ is directly on top of $B_2$, and $B_2$ rests on the ground. I put a diagram together using draw.io: ![Diagram](http://i.stack.imgur.com/uvLWU.png) The coefficient of kinetic friction between $B_1$ and $B_2$ is $\mu_1$. The coefficient of kinetic friction between $B_2$ and the ground is $\mu_2$. The resultant friction forces acting on the top and bottom sides of $B_2$ are thus $F_{\mu_1}$ and $F_{\mu_2}$, respectively. **What is the horizontal force, $F_a$, that must be applied to $B_2$ in order to result in an horizontal acceleration of $B_1$ with magnitude $a_{1}$?** $$ \\\F_a = fxn(a_{1}) $$ Assumptions   * _Block $B_2$ is sufficiently long such that $B_1$ will not fall off $B_2$ during the time I'm interested in._   * _Both blocks are already sliding ($B_1$ is sliding relative to $B_2$)._ * * * EDIT: Here is what I've tried: Sum of the horizontal forces on $B_1$: $$ \\\\\Sigma(F_{m1x}) = m_1 * a_1 = F_{\mu_1} \\\a_1 = F_{\mu_1} / m_1 (1) $$ Because kinetic friction force is proportional to normal force: $$ \\\F_{\mu_1} = m_1 * g * \mu_1 (2) $$ Combining $(1)$ and $(2)$ $$ \\\a_1 = m_1 * g * \mu_1 / m_1 = g * \mu_1 (3) $$ Meaning $a_1$ is independent of the applied force $F_a$ and its mass $m_1$, which seems odd to me.


title: Special relativity: moving charge and twisting bar magnet

text: **ETA:** Huh. It's been more than three months since I posed this question. Is it really possible that no one knows the answer? I thought for sure someone would know. Oh well. You have a small bar magnet that is able to pivot about its middle (like a compass needle). You fix the middle of the bar magnet to a point on the positive half of the y-axis. Initially the bar magnet is pointing in some random direction. Now a proton moves along the x-axis in the positive x-direction with speed v. This moving charge generates a magnetic field, so the bar magnet will twist itself to align with that field, parallel to the z-axis. The above description is in the rest-frame of the bar magnet. But what about in the rest-frame of the proton? Now the proton is at rest, so it generates no magnetic field. Nevertheless, the bar magnet (now moving in the negative x-direction with speed v) must still pivot around to point in the z-direction -- if this happens in one reference frame, it must happen in every frame. But what is the explanation for the twisting of the bar magnet in the proton's rest-frame? I have come up with what may be a partial solution, but 1) I am not sure if it is correct, and 2) it only seems to work when the bar magnet is originally oriented along the y-axis. If the bar magnet is originally pointing parallel to the x-axis, my explanation fails. To start, let's replace the bar magnet with a circular loop of current- carrying wire, which has stationary positive ions and negative conduction electrons moving with drift speed v_d. The ions and electrons have the same charge density, so the loop is electrically neutral. This current loop is more or less equivalent to the bar magnet in terms of its own magnetic field. Say that the bar magnet is originally aligned along the y-axis. So the current loop we are replacing it with is originally perpendicular to the y-axis. In the rest-frame of the proton, the current loop moves in the negative x-direction at speed v, and is therefore Lorentz-contracted into an ellipse, with its major axis in the z-direction and its minor axis in the x-direction. Due to this contraction, the positive ions in the wire (all moving at speed v) will have a higher concentration at the ends of the loop's major axis. At one of those two spots, the conduction electrons will have speed v + v_d, so they will experience more Lorentz-contraction than the ions and have an even higher concentration; thus the net charge there will be negative, and that part of the loop will be electrically attracted towards the stationary proton. Conversely, at the other end of the loop's major axis, the conduction electrons will have speed v - v_d, so they will experience less Lorentz- contraction and have a lower concentration than the ions, resulting in a net positive charge that will be electrically repelled away from the proton. Result: these two electrical forces torque the current loop until it is perpendicular to the z-direction -- which is to say, the original bar magnet will align itself with the z-direction, just like in the bar magnet's rest- frame. However, this explanation won't work if the bar magnet is originally aligned parallel to the x-axis. In that case, the current loop I'm replacing it with is originally perpendicular to the x-axis. In the rest-frame of the proton, the circular current loop (moving along the x-axis) now remains a circle -- the Lorentz contraction doesn't alter its shape. And all conduction electrons are traveling at the same speed in this frame, so I don't see how I would get parts of the loop to become positively and negatively charged, as I did previously. And anyway, in order to twist the ring so as to be perpendicular to the z-direction, there must be a pair of forces pulling the ring in directions parallel to the x-axis. These forces can't be electrical attractions or repulsions, as they don't point towards or away from the stationary proton. And they can't be magnetic forces because the only magnetic field is the one from the current loop itself, and that can't cause the loop to twist (can it?). So... what am I missing? Much thanks for any help you can provide.


title: How to find particle number fluctuation under given condition?

text: So we know the particle number fluctuation of a one room. Let it be equal to **ФN** , and we have to find the particle number fluctuation of a big room, which is just **n** times bigger, than a smaller one. **n** is a finite number, the number of particle in each room is equal to **N** , which is infinite number. In addition, what gas is located in a room, is unknown. Any suggestion, how to solve this problem?


title: Where is Strong Equivalence Principle stronger than Weak Equivalence Principle

text: In my note, the two equivalence principles are stated as follows **Weak Equivalence Principle:** _Gravitational and inertial masses are equal._ **Strong Equivalence Principle:** _There is no observable distinction between the local effects of gravity and acceleration._ I think the weak one will imply that the acceleration **at a point** and the gravitational field **at that point** are equal, thus we can remove the gravitational effect by using an accelerating frame. But, what does this differ from the strong version? Is the change from **at a point** to **local** playing the role?


title: Acceleration of chairlift

text: So I'm struggling with this question, and am wondering if anyone can give me the right direction to go. For the sake of not cheating, I've changed the figures etc. I just need help on the approach. I can do similar questions on a horizontal plane, but I'm stuck now the acceleration isn't perpendicular to gravity. _Edit: realized I gave the wrong description/ sketch for the angle I have_ > A person is being lifted up a slope with an incline from horizontal of 6 deg > on a ski chairlift. The winch pulling the chairlift accelerates the > chairlift up the slope, which results in the person and seat tilting back > with an angle of 9 degrees from what would be perpendicular to motion. What > is the acceleration of the winch? Treat the cable connecting the chairlift > to the winch-cable as weightless, ie the person & chairlift act as a > pendulum. ![sketch](http://i.stack.imgur.com/9nx96.jpg)


title: Quantum mechanics and atomic bonding

text: I'm learning quantum mechanics in high school this year, and I have several doubts. I've done my research on various websites but my understanding is still fuzzy. I understand that when I punch a wall or sit on a chair I don"t go through it due to quantum degeneracy pressure. I've studied the Pauli exclusion principle, but here"s my first question:   1. What exactly is quantum degeneracy pressure? I've read answers that say "Atomic orbitals resist squishing", and the like, but I don"t understand why.   2. If orbitals resist squishing, why do covalent bonds form?  From the Wikipedia picture of a H2 bond it seems like the s orbitals of the individual atoms were squished from a circle(2-D) to an ellipse. How do we know when this squishing results in a lower energy state and when it doesn't? If the wall was made of atoms that didn't have an octet and my hand too would my hand bond with the door when I punched it?


title: Lattice model completely constrained by boundary data

text: I am dealing with a lattice model that has the peculiar property that if I specify all the spins on the boundary, by local conservation laws, the whole lattice configuration (throughout the whole volume) is fixed. This trait is true for all $N\times N \times N$ lattices with this model. I am interested if in the thermodynamic limit this behavior holds and if this fixing prohibits phase transitions. Any ideas on these two matters? Edit: These are things I think I can add. Since the internal variables are fixed by the boundary configurations, then for the partition function, there are bulk volume configurations where boundary spins are different but the internal spins are the same (compared to another configuration). Thus, I can define an equivalence between boundary configurations for two boundary configurations that yield the same interior. Then I only need to sum over equivalence class of surface configurations, and the model is somewhat 2D.


title: Heat deposition at optical focus in a clear medium

text: This is an applied physics question for an engineering problem. The well known experiment we have all done--burn paper and wood with a magnifying glass and the sun's rays. My question is, if one were to focus to a point that is in the center of a block of clear plastic (with suitably low melt point), would the plastic at the focus point melt? Or would there have to be impurities in the plastic for heat to be generated? If there are impurities, would the decreasing intensity of the light as a function of distance be linear or exponential?


title: Easy question about magnetism?

text: I have to build a simple electric motor by attaching a magnet to a battery, extending the terminals of the battery (with stiff wires so they could act as supports), and placing a coil of wire on top of it. I know that the more loops you have in the coil the stronger the magnetic field and therefore the faster the coil will rotate. However, how does the diameter of the magnetic coil affect speed of the wire coil rotating? A smaller diameter might make the magnetic field stronger, but the magnetic force which produces torque would also be be applied closer to the center of rotation, therefore creating less torque.


title: Position and momentum bases in quantum mechanics

text: I have seen the following two descriptions of the position basis: $$\tag{1}| x\rangle=\delta(x-x_0)$$ and also $$\tag{2}\langle x_0| x\rangle=\delta(x-x_0),$$ which (if either) of these is correct? Perhaps they are equivalent under change of notation? The first seems right to me, as it would solve the operator equation $$\tag{3}x| x\rangle=x_0| x\rangle,$$ but I would like to be sure. If we are working in the momentum representation, is $$\tag{4}|p\rangle=\delta(p-p_0)$$ also valid?


title: Can the hot combustion products from a large flame be in "non-local thermal equilibrium"

text: **Question:** Does it take some time for the hot combustion products from a flame to reach local thermodynamical equilibrium (i.e. for the energy state populations to follow the Boltzmann distribution)? If so, on what type of time scales might this departure from local thermodynamical equilibrium occur? **Background:** I am trying to model infrared emission spectra in the mid-infrared region to reproduce emission spectra of hot exhausts from the flame of an industrial flare stack measured with an FTIR-spectrometer. The emitted spectral radiance is calculated using the Planck function and the absorption crossections of different molecular species. The absorption crossections are calculated for different species using the HITRAN and HITEMP line databases. This seems to work fine for some species and some regimes. However, I seem to have problems especially when the exhaust is really hot. For instance, in the region 900-1000 cm$^{-1}$ I can qualitativly see that I have strong water emission lines, but with only varying the temperature parameter I cannot get the relative intensities of the different lines right. I keep thinking that one possible problem might be that the exhaust product from the combustion are not in local thermodynamical equilibrium. In that case the state populations for the species would not follow the Boltzmann distribution which is assumed for calculating the line intensities and their temperature dependence.


title: Is proper time a vector?

text: Proper time is identical with the spacetime interval of a timelike movement. A spacetime interval is the dot product of two vectors and thus a scalar. Proper time however is always pointing exactly in time direction, all space dimensions are 0. Also it may be added or multiplied with scalars. As outlined in the answer of Ross Millikan, proper time does not take part in Lorentz transforms. That means that it is not a vector within Minkowski vector space. But with its above mentioned characteristics, is there something missing for proper time being a vector? Or, in case that the physical definition of proper time is too restricted, what else is this vector pointing in time direction with the magnitude of proper time? **Edit:** The most confusing fact is the **comparability** of time (vector) and proper time (scalar?), example: A space traveler returns after 30 years, but he got only 20 years older, thus he "saved" 10 years (substraction vector / scalar??).


title: How can opaque black object occur?

text: I know the fact that a material appeared as black when all wavelength photons were absorbed. I also know that opaque object is the result of reflection and scattering of light wave. Is it right? However, how can I explain about opaque black object? If all waves are absorbed, is there still available light at the surface of the material to reflect or to scatter? If there still light to reflect and to scatter, what is ratio of light in absorption and reflection/scattering? Is there really black object exist? Obviously, I have very limited understanding of physics.


title: Number density of LO and LA phonons as a function of temperature?

text: I'd like to know the how the number density of longitudinal optical (LO) and longitudinal acoustic (LA) phonons varies as a function of temperature of the material. Is there a simple expression for these two cases? I'm guessing that this would work, $N_{LO} = \int g_{LO}(E) f(E, T) dE$ $N_{LA} = \int g_{LA}(E) f(E, T) dE$ where $g(E)$ is the density of states for LO and LA phonons and $f$ is the Bose-Einstein distribution. What would be appropriate limits for the integrals. Does anybody know a reference where the density of states for these two modes is given? **EDIT** To improve the question, I'm interested in semiconductor 3D crystals. But maybe I left this too long, sorry. Best regards,


title: The relationship between spin and spinor curvature

text: The identity, $$ -\gamma^b{\mathcal{R}}_{ab} = {\mathcal{R}}_{ab}\gamma^b = \frac{1}{2}\gamma^b R_{ab}$$ is presented in the answer to the question Dirac Equation in General Relativity. How does one prove the identity?


title: functional determinant and WKB approximation

text: let be a Hamiltonian in one dimension, i would like to evaluate the functional determinant $ det(E-H) $ in onde dimension i believe that $ det(E-H)= Cexp(iN(E)) $ here $ N(E)$ is the number of energy levels less than a given number 'E' my steps   1. i use the identity $ logDet(E-H)=TrLog(E-H)$   2. i replace the sum $\sum_{n} log(E-E_{n})$ by an integral over the phase space $ \iint_{D}dpdp log(E-p^{2}-V(x))$   3. I take the derivative respect to 'E'   4. I use the identity $ \int_{-\infty}^{\infty} \frac{dx}{x^{2}-a^{2}} = \frac{\pi i}{a}$   5. I use the Bohr-Sommerfeld quantization condition $\int_{C}dx (E-V(x))^{1/2} = (n(E)+1/2)h$   6. i use integration respect to 'E' again 7 i take the exponential is this semiclassically correct :) thanks.


title: Impulse situation

text: I am wondering if a physical system subjected to an **_impulse_** $=A\delta(x-a)$ makes any sense. I reckon that a force could take that form -- thought of as a finite impulse applied over an infinitesimal time interval. But if the impulse takes that form that would imply infinite velocity?? Thanks.


title: Poisson's Equation

text: First up, I needed to compute the potential at some external point due to charge stuffed inside the region between two concentric cylinders, the volume charge density being given.   Two methods came to mind but they are apparently yielding different answers(maybe I goofed up somewhere)   The first is to solve the Poisson's equation considering that the potential doesn't vary with $\theta$ and $z$ and setup and solve a differential equation.   With that said, what if I consider the composite object as two cylinders, the bigger one with a volume charge density $\rho_v$, radius $a$ and a smaller one inside it (along the common axis) with density $-\rho_v$, radius $b$   (In this way the stuff along the axis cancels out leaving the same resultant object) and calculate the potentials due to them at some point $r$. The resultant potential would then be the sum. Though this doesn't apparently yield the same result.


title: Why is B always not 0

text: I discovered that while applying Ampere's law, For a solenoid.. B inside is calculated. But outside we say the loop encloses no net current or hence there should not be any field.. Let's say for example a conducting wire carrying current i we have, B=Something But we can always have a current with opposite direction at infinity and hence an amperian loop of infinite radius and thus B to be a zero


Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle? By "human-sized lab" I mean a lab the size of the International Space Station, say, with typically-sized lab equipment. I also mean the absolute kind of (event) horizon, not the apparent kind. The #1 answer at this question says: > For large enough black holes, space is still weakly curved at the event > horizon, so of course we should expect that normal physics still exists > there. An infalling observer wouldn't experience anything out of the > ordinary when crossing an event horizon. This suggests that the answer to my question here is "yes". However, when I asked a question involving such a test, the highest-rated answer with 23 votes clearly says "no": > The equivalence principle only allows you to transform to an inertial frame > locally. This means that if your spacetime is curved, then the falling > observer can only choose Minkowski coordinates for an infinitesimal region > around her. I've seen this contradiction many times elsewhere. Certainly the EP has actually been tested to high precision in larger-than-infinitesimal labs. Yet once one talks about testing the EP in a lab falling through the horizon of a black hole it seem respondents _in that case_ think the lab must be infinitesimal in size, so that the EP can't be tested in any practical sense, even though "An infalling observer wouldn't experience anything out of the ordinary when crossing an event horizon" if the black hole was sufficiently large. I understand that the EP is strictly true for only a point in spacetime. But that hasn't prevented it from being validly tested to high precision in a larger lab, where the tidal force in the lab was weak enough that it didn't change the result at that precision. I'm not asking about testing the EP to _infinite_ precision, nor am I asking about a test involving a black hole of _any_ size, like one where the lab would be spaghettified by the tidal force before reaching the horizon. That's why I qualified the question with "in principle". Also note that I'm talking about a test being done as the lab equipment (temporarily) straddles the horizon, not a test limited to one side of the horizon or the other within the lab. A test using equipment straddling the horizon wouldn't be allowed according to the other answer with 23 votes, which says: > The infinitesimal flat patch in which you're allowed to play with the EP > does not include ... anything beyond the horizon ... I don't see how a test of the EP would be invalidated due to the equipment straddling the horizon.


title: Why do electromagnetic waves oscillate?

text: I've been considering this question, and found many people asking the same (or something similar) online, but none of the answers seemed to address the core point or at least I wasn't able to make sense of them in that regard. I'm looking for a layman-friendly explanation. I'll copy the most eloquent exposition of this question I found, from here: > What is it that causes an electromagnetic wave to oscillate? I.e. what is > the medium that constrains it and pulls it back from one side to the other? > > Discounting pressure waves such as sound, as they push backwards and > forwards through air, other waves, with amplitude, need something to > constrain them. For instance waves in water are constrained by surface > tension and gravity so at the end of the "up" gravity and surface tension > pulling the water flat pull it back down and vice versa at the end of the > "down". > > **So what is doing that with visible light, gamma rays, microwaves etc? What > pulls their energy back and forth causing them to oscillate?** One of the answers there claimed "The electric field constrains the magnetic field and vice versa." Is this true? I didn't see anyone else making a similar claim. * * * The above pretty much sums up my question, but for completeness' sake, I'm also including below references to some related threads I found: This guy asked "Do photons oscillate?". The responses explained nicely how his conception of photons was incorrect, but didn't clarify his question of why the wave forms. Somebody asked a pretty similar question on reddit: "Why do photons oscillate?", adding "I don't understand what makes them swing back and forth." -- again, the answer explained that photons aren't really "particles of light", and don't oscillate, but again no satisfactory answer to the "why" question was included. Finally, this page has a great applet demonstrating the basic principle of how disturbances in one charge propagate to nearby ones. The oscillation is provided by a spring for illustration purposes. The text naturally raises the question: "Yeah, that all makes sense, but don't expect me to believe that particles as small as electrons are attached to springs. **How is [the first] electron made to wiggle -- I mean, how is its speed or direction of motion changed?** " -- but I couldn't find the answer in the following pages. EDIT: I emphasized some passages above to make it clear I am not assuming the EM field moves in space (I realize what is changing is the amplitude over time), and that what I'm asking is indeed, to quote Bjorn Wesen's answer, "why does the source amplitude oscillate in the first place".


title: Testing General Relativity

text: Ever since Einstein published his GR theory in 1916, there have been numerous experimental tests to confirm its correctness--and has passed with flying colors. NASA and Stanford have just announced that their Gravity Probe B activity has confirmed GR's predicted geodetic and frame-dragging effects. Are there any other facets of GR that need experimental verification?


title: Differential Operators in Polyakov Action

text: What do the differential operators in the Polyakov action mean? How does one derive the Polyakov action and treat the differential operators?


title: Why the water remains on the surface of the Earth?

text: What makes the water stay on the surface? Why the earth does not absorb the water in it?


title: What is the curvature of an empty universe?

text: My calculations tell me an empty universe has hyperbolic curvature. Is this correct? If it is, can anyone help me understand why this is intuitively?


title: Cosmic Inflation: Lower Expansion Rate with than without?

text: When I read the Cosmic Inflation diagram at https://en.wikipedia.org/wiki/File:Horizonte_inflacionario.svg which I rotated to make it readable: ![Plot 1](http://yukterez.enabled.io/inflation.png) where the Hubbleradius, and therefore also the Hubbleparameter, which is c/Hubbleradius, is constant over inflation, then it seems to me, that with inflation the Hubbleparameter would have been much lower than without: ![Plot 2](http://yukterez.enabled.io/Inflation_Plot.gif) If the Hubble Parameter would go with Ω-Radiation (to the 4th Power), it would reach Infinity at 0, and about 10^103 m/sek/m at Planck size, which is way more than the expansion rate postulated for inflation: ![Radiation dominated Expansion Rate near 0](http://yukterez.enabled.io/Hp.PNG) Did I get this right, or do I have the wrong data? And if I have it right, is it more like the green curve with a hard inflation to radiation edge, or the blue one with a smooth blending; or is there all another way to get a plottable Hubble Parameter including inflation as a function of the scale factor? PS: the y Axis is the Hubble Parameter (c/Hubbleradius) in m/sek/m and the x Axis is the Scale Factor in m/m (dimensionless).


title: Stable Nuclei - Deviation from equal protons and neutrons

text: While studying the semi-empirical mass formula for nuclei, I came across an "asymmetry term" whose function, as far as I understand, is to build in the fact that nuclei "prefer" to have equal numbers of protons and neutrons. This is explained by the Pauli exclusion principle; the neutrons and protons are distinguishable, and hence have fill separate energy levels. Hence, if the number of neutrons and protons is close, the nuclei will have a smaller energy. Yet, it is observed that large stable nuclei have more neutrons than protons. Why is this so? If nuclei prefer to have equal protons and neutrons, shouldn't the stable nuclei lie along the N=Z line? (in the image) ![Chart of Stable Nuclei](http://i.stack.imgur.com/jHpKr.png)


title: Relativistic Lagrangian transformations

text: I need to study the relativistic lagrangian of a free particle. It's $\ L= - m c^2 \sqrt[2]{1- \frac{|u|^2}{c^2}} $ I need to study the translation, boost and rotation symmetry. I say it doesn't depend of the position, so it has translation symmetry and the momentum will conserve. It's rotation invariant because depends only of the modulus of the speed $|u|$(What is the conserved quantity derived by this symmetry?) What can I say about the boost transformation, I can use the boost of the speeed $u$, but I can't see any conclusion about that.


title: Magnetic engine

text: Is it possible to mimic crrent engine design (to some extent) by replacing the cylinders with opposed magnets? A device interupts their natural desire to push away from each other allowing them to come together (or atleast closer) at which time the device would retract into the cylinder housing allowing a powerful separation to happen which woud (when the cylinders reach the top or bottom of shaft) create enough force to work the rest of the engine parts in a similar way to current conventional engines? Please excuse me for my non academic description. This as bugged me for some time now and really have to get it off my chest!!


title: If wavefunction is just a probability function, how does an electron interfere with itself

text: I have read lots of quantum mechanics books. The chapters that are talking about De Broglie, lots of them name the chapter as "Wave-particle duality" and says: "Electrons are both waves and particles". So I start to think that (for example) an electron sometimes becomes wave sometimes becomes particle. But when I start to read the chapters about Schrödinger and wavefunction thing. I see that that wave nature thing does not belong to electron itself. It is about its location. So there is no wave particle duality. Electron is always a particle. But the location of electron is represented as wave, because of uncertainty principle. So electron can't interfere with itself because it is always a particle. The interference is about its location function. 1-) Are these all true? 2-) If true, if an electron is always a particle, in double slit experiment how does an electron interfere with itself without observer, but there is no interference pattern with observer?


title: Can wind currents form in the mesosphere?

text: Probably not the right forum for this question. How high in the atmosphere may an air-current form? Can a wind current form up in the mesosphere?


title: How is NASA's mod II Stirling engine so powerful yet so small?

text: Is it because of the temperature difference? I just don't understand how it can propel a car. Here's the link to the engine: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19880002196_1988002196.pdf


title: What's the explanation for the Giant Magnetoresistance effect?

text: I've been reading this review on Giant Magnetoresistance, and something about it is bothering me. The basic effect is that, using a special "stack" of layers (alternating between ferromagnetic and not magnetic) you can cause great variations on the electrical resistance of the material by applying a small magnetic field.   ![alt text](http://i.stack.imgur.com/jJQRA.png)   The explanation given both on the review and on Wikipedia is the following. The configuration on the left will cause scattering for all spin down electrons that cross it, but will present very low resistance for the spin up electrons (thus a small resistance overall). The one on the right, will scatter all electrons and thus have very large resistance overall. **Here's my problem** (quoting the review) > These experimental results were all obtained for the ’Current In the Plane > of the layers’ (CIP) geometry. The current is then parallel to the plane of > the layers. How can this be? CIP in the above image would mean the current is horizontal, with probes positioned on the left and right of the middle layer. But, if you don't force the current to cross the ferromagnetic layers, why would there be an increase in resistance? I checked with a professor, and he confirmed that the standard method is indeed to apply the probes horizontally, but he couldn't tell why the effect still worked. One option that came up is that electrons don't follow a straight line from one probe to the other, and thus they would still "flow" through the other layers, but I know that's not the case. Using the resistors analogy seen in the image above, applying a CIP is equivalent to setting the resistors in parallel for each of the spin orientations, and parallel resistors _always_ have less (or equal) resistance than the weakest resistor. To be clear, my question: How can the above explanation be compatible with the CIP case? If it's not, then why does it still work?


title: How do we know the universe is expanding, and not that its contents are shrinking?

text: Is there a physical reason why not to think that instead of space expanding, all physical constants and parameters are shrinking (including of course the instruments we use to measure the constants) and space is static, or is it a case of Occam's razor?


title: The exchange of photons gives rise to the electromagnetic force

text: Pardon me for my stubborn classical/semiclassical brain. But I bet I am not the only one finding such description confusing. If EM force is caused by the exchange of photons, does that mean only when there are photons exchanged shall there be a force? To my knowledge, once charged particles are placed, the electromagnetic force is always there, uninterruptedly. According to such logic, there has to be a stream of infinite photons to build EM force, and there has to be no interval between one "exchange event" to another. A free light source from an EM field? The scenario is really hard to imagine. For nuclei the scenario becomes even odder. The strong interaction between protons is caused by the exchange of massive pions. It sounds like the protons toss a stream of balls to one another to build an attractive force - and the balls should come from nothing. Please correct me if I am wrong: the excitations of photons and pions all come from nothing. So there should be EM force and strong force everywhere, no matter what type of particles out there. Say, even electrical neutral, dipole- free particles can build EM force in-between. And I find no reason such exchanges of particles cannot happen in vacuum. Hope there will be some decent firmware to refresh my classical brain with newer field language codes.


title: Why are materials that are better at conducting electricity also proportionately better at conducting heat?

text: It seems like among the electrical conductors there's a relationship between the ability to conduct heat as well as electricity. Eg: Copper is better than aluminum at conducting both electricity and heat, and silver is better yet at both. Is the reason for this known? Are there materials that are good at conducting electricity, but lousy at conducting heat?


Is the Schwinger action principle important in renormalization? I want to know if this principle could help us to see if a model is renormalizable of not. If you have any other comment or information about renormalization and quantum action principle of Schwinger, please tell me.


title: What is the name of the physical space enveloping all universes?

text: Please excuse my question, as i don't come from a physics background, but i was really wondering. Assuming we are in one of numerous universes which all have physical dimensions:   * What is the name of the physical space that envelopes all of these universes?


title: Magnetic field lines and knots

text: As I was reading the book _The Trouble With Physics,_ I encountered a small paragraph which seemed bit confusing. The paragraph goes as follows: > _Picture field lines, like the lines of magnetic field running from the > north to south pole of a magnet. The field lines can never end, unless they > end on the pole of a magnet, this is one of the Maxwell's laws. But they can > make closed circles, and those circles can tie themselves in knots. So > perhaps atoms are knots in magnetic field lines._ My questions are:   1. What exactly is the knot being described here?   2. And how are atoms related to such knots in magnetic field lines?


title: In what range the acceleration value of quantum particle lies?

text: According to Heisenberg's uncertainity principle, the position and velocity of an quantum particle cannot be determined simultaneously. Is it possible to determine position and acceleration simultaneously ? If yes, how it can be determined (or) in what range the acceleration values of quantum particles lie ?


A charged particle moves in a plane subject to the oscillatory potential: $U(r)=\frac{m\omega^2 r^2}{2}$ There is also a constant EM-field described by: $\vec{A}=\frac{1}{2}[\vec{B}\times\vec{r}]$ where B is normal to the plane. This produces the Lagrangian: $L=\frac{m}{2}\dot{\vec{r}}^2+\frac{e}{2}\dot{\vec{r}}\vec{A}-U(r)$ Now my friend says we need to transform this into polar coordinates and that produces: $L=\frac{m}{2}(\dot{r}^2+r^2\dot{\phi}^2)-mr^2\omega_L\dot{\phi}-U(r)$ where $\omega_L$ is the Larmor precession frequency: $\omega_L=-\frac{eB}{2mc}$ My question is, How does he get this transformation? I don't really understand where the second term is coming from in the mechanical kinetic energy.


title: Spin-orbit coupling constant for rubidium

text: I have come across the following question in my course notes: The $5s\to 5p$ transition in rubidium is split into two components with wavelengths of 780nm and 795nm respectively. For the $5p$ state, calculate the spin-orbit coupling constant $a$. I have calculated the spin orbit splitting energy to be $E=\frac{3}{2} a$, calculated the energy of the 795nm component to be $E=\dfrac{hc}{\lambda}=2.5\times 10^{-19} J$, suggesting that $a=1.67\times 10^{-19}J$. I'm not convinced by this answer as it gives a very large value for the magnetic field of the electron due to its orbital motion. Is the method I'm using correct, or does something seem to be out of place?


title: Is the proper interpretation of temperature missing in this book?

text: In Randall T. Knight’s textbook “Physics for Scientists and Engineers” in the first chapter on thermodynamics (Ch. 16: A Macroscopic Description of Matter) one of the first conceptual questions is stated like so: > The sample in an experiment is initially at $t_1$°C. If the sample’s > temperature is doubled, what is the new temperature in °C? The answer to that implies the reference to absolute temperature (for simplicity, to one significant figure, as the book required), i. e.: $t_2°C = (T_1 × 2)K - 273 = (t_1°C + 273) × 2 - 273$. I understand that the whole idea of this question to reiterate to the pupil that we ought to think of temperature as a specific physical property, and not in an everyday sense, but I am confused about the wording. In the section on temperature author writes: > We will begin with the commonsense idea that temperature is a measure of how > “hot” or “cold” a system is. These are properties that we can judge without > needing an elaborate theory. As we develop these ieas, we’ll find that > **temperature** _T_ is related to a system’s _thermal energy_. […] We’ll > study temperature more carefully in Chapter 18 and replace these vague > notions of hot and cold with a precise relationship between temperature and > thermal energy. That is, as yet we are still at the stage of “vague notions”. Few paragraphs later Knight introduces Kelvin scale but nowhere there or in between does he specifically insists on that idea I mentioned after the formula. At least not that I can see. Am I missing something that should be obvious to me, and I fail to grasp it instantly because my brain is depleted by 50+ hours a week of studies? Am I just plain stupid, because to my eternal shame it took me way too long to figure it out? Or was there a better way to home onto that idea by an author: what do other textbooks say on that topic, how do they word this concept? Is the question logically flawed or confusing, or is it the common way of describing the situation in scientific literature?


title: How to compute the intensity of a polarized wave going through a polaroid?

text: If an electromagnetic wave is linearly polarized, the intensity of the light that goes through a polaroid is proportional to the square of the cosine of the angle between the polarization plane and the axis of the polaroid (Malus'law). This is because we consider only the component along the axis of the polaroid. If the wave is circularly polarized, the electric field moves on a circle, but on average, if we decompose it in a component along and perpendicular to the axis of the polaroid, these two components will be equal, so that the intensity will be $I_0/2$, where $I_0$ is the intensity of the wave before going through the polaroid. Now, if the electric field varies on an arbitrary curve and we know the parametric equation of this curve (for example, it rotates around an ellipse), given a particular direction of the axis of the polaroid, how can we compute the intensity of the resulting wave?


title: Starting string theory studies in grad school

text: How is it possible for a grad student to do research in any modern area of string theory like AdS/CFT or ABJM if they need to start grad school by having to learn QFT from scratch? Is there a time-line over which this is even possible? Or one necessarily needs to come to grad school knowing at least Polchinki level string theory to be able to understand AdS/CFT or ABJM? I mean even if one has worked through enough of Polchinki's book one is likely to stare blank at the ABJM paper. Then is it even possible for someone to get to research level with something like this if they start from basic QFT in grad school? I would like to know what if is a practical implementation.


title: Delta Dirac Charge Density question

text: I have to write an expression for the charge density $\rho(\vec{r})$ of a point charge $q$ at $\vec{r}^{\prime}$, ensuring that the volume integral equals $q$. The only place any charge exists is at $\vec{r}^{\prime}$. The charge density $\rho$ is uniform: $$\rho(\vec{r}) = \delta(\vec{r} - \vec{r}^{\prime})\rho$$ But if I evaluate the total charge, I get $$ q = \int dq = \int^{\infty}_{-{\infty}}\delta(\vec{r} - \vec{r}^{\prime})\rho ~dV $$$$= \rho\int^{\infty}_{-{\infty}}\delta({x} -{x}')dx\int^{\infty}_{-{\infty}}\delta({y} -{y}')dy\int^{\infty}_{-{\infty}}\delta({z} -{z}')dz$$ The Dirac delta functions integrate to one each, but what becomes of the charge density $\rho$? For that matter, how does one integrate a zero dimensional point over 3 dimensinal space? Any help greatly appreciated. EDIT: So it seems that the charge density is just the charge itself ($\rho = q)$?


title: Van Hove Singularity at Saddle Point

text: this is another one of those examples where textbooks _always_ just gloss over it with the remark that it "can be done" and then just state the result: I want to compute the general form of a van Hove singularity if the dispersion relation expanded to second order has a saddle point. As a simple example, consider $$E = E_0 + a_x k_x^2 - a_y k_y^2$$ where the coefficients $a_x$ and $a_y$ are both positive. Now, I understand how the derivation works when all coefficients are negative or all coefficients are positive, because then the surface of constant energy is actually finite: It's an ellipsoid and we can estimate its volume. But how to proceed for saddle point? In the 2D-example above, I have $$D(E) \propto \int_{E(k_x,k_y) = E} \frac{1}{\sqrt{a_x^2 k_x^2 + a_y^2 k_y^2}}$$ and I'm not sure how to go from there. Do I actually find a parametrization for that path and compute that integral or is there a better way to arrive at the approximate form?


title: Heisenberg's principle in Quantum Cryptography

text: In quantum cryptography why do we need the Heisenberg uncertainty principle? _Edit:_ I only know the statement of the Heisenberg uncertainity principle. As I know that if Eve tries to know the polarization angle of a photon with a wrong basis then it will alert others. Then where is the use of Heisenberg uncertainity rule in it? I know this is a childish question to physics people but I really need to know the answer. Please anybody answer it.


title: Single photon and double-slit experiment

text: Laser fires single particles of light, called photons, through the slits. Even though only single photons of light are being fired through the slits and They create three pattern again. How single particles of light can create this wave pattern?


title: AdS/CFT correspondence and M-theory

text: Three questions:   1. What can be some applications of AdS/CFT correspondence on M-theory? For example, would it be possible to represent 11-dimensional world using 10-dimensional surface?   2. It seems that using AdS/CFT correspondence, we can project our world as being 100-dimensional or 1000 or more. What is wrong with this?   3. Is AdS/CFT correspondence just a conjecture, or a proven theorem? Thanks.


title: Is there an explanation for the 3:2:1 ratio between the electron, up and down quark electric charges?

text: I understand that the NNG formula relates $Q$, $I_3$, and $Y$ and can be derived in QCD; does this unambiguously predict the electric charge ratios without making assumptions about the definitions of isospin and hypercharge? If so, this is unintuitive to me! Why does a particle carrying $SU(3)$ color charge care what charge it has under the totally separate electroweak $U(1)\times SU(2)~$ symmetries? If not, is there a name for the "problem" of explaining the charge ratios?


title: What is the effect of phase transition on the thermodynamic state variables of a material?

text: When a material undergoes a phase transition, it releases an amount of heat (under a specific temperature). So the effect of the phase transition on entropy would be equal to: \begin{align} \frac{L}{T_\text{transition}} \end{align}. Does a phase transition affect entropy in any other way? Since entropy is a function of state, my question boils down to how a phase transition affects the _state variables_ of the material?


title: Why would the reflection of a lamp by a bowl look like a heart?

text: I have this bowl roughly the shape of a circular truncated cone, and the lamp shines on the bowl at an angle. The reflected lamp light hit the bottom of the bowl and created a light ring that looks just like a cardioid. Could someone help me, or give me a hint on how to really solve the equation for the light ring?


title: Solve for Initial Velocity of a projectile given Angle, Gravity, and Initial and Final positions?

text: I've found equations http://www.physicsclassroom.com/Class/1DKin/U1L6a.cfm for solving everything (and rearranged to solve everything) to do with projectile motion EXCEPT this, even though it should be possible.   * Gravity = 10 m/s^2 (for simplicity)    * Launch Angle = any angle in 0-360 degrees    * Launch Position in x,y coordinates = any position, could be a different elevation than landing position    * Landing position in x,y coordinates = any position other than Launch position, could be a different elevation than launch position  What is the general equation to solve for initial velocity for all angles 0-360 to hit a target at x2,y2 when launching from x1,y1? Note: depending on the direction you are launching the projectile, some angles will not be possible, but keep in mind that if you were at a very high altitude and were launching a projectile at a target beneath you, launch angles other than 0-180 will be viable. Just to be clear, this is the orientation of the 360 degree wheel I'm talking about, which has 90 degrees at the top and 270 at the bottom: ![degree wheel](http://img.geocaching.com/cache/large/caac028e-3a75-49c6-bb0c-5f38c2c7079d.jpg)


title: Energy of particle in electric field

text: I'm taking a physics class and the professor teaches us really basic things in lecture and then gives homework way beyond what he taught in lecture. Obviously I need to find some resource other than Stack Exchange, but in the mean time, perhaps you could explain some of the terms in this problem and give me a starting point for how to solve it. Regarding the problem, given below, I'm not sure what the significance of "exactly one mean free path through the air before hitting a molecule" is. I know eV is an electron volt, which is a unit of energy (from high school) but I'm not sure how this is related to the strength of a field. I would assume this energy is related to the force on the particle, which I can relate to the strength of the field and the force on the particle, as well as the distance the particle travels, but that doesn't seem right because no figures are given for distance or charge. I haven't got a clue what cross-sectional area might have to do with this. I do, however, know what a Maxwell distribution is from chemistry class. > (a) Assume that an ion moves, on average, exactly one mean free path through > the air before hitting a molecule. If the ion needs to acquire approximately > $1.11\ \mathrm{eV}$ of kinetic energy in order to ionize a molecule, > estimate the minimum strength of the electric field required at standard > room pressure and temperature ($300\ \mathrm{K}$). Assume that the cross- > sectional area of an air molecule is about $0.095\ \mathrm{nm^2}$. (Assume > the velocities of the particles have a Maxwell distribution of velocities.) > > (b) How does the strength of the electric field in Part (a) depend on > temperature? (Use the following variable as necessary: $T$.) > > (c) How does the strength of the electric field in Part (a) depend on > pressure? (Use the following variable as necessary: $P$.)


title: why the shape or size of Magnetosphere is different both side?

text: Two days ago, I watched a documentary about solar flares, and how Magnetosphere protect us from that to earth. I was able to understand most of it, but I'm still curious to know why the Magnetosphere's shape is different on both side? ![](http://i.stack.imgur.com/GzFVG.jpg) What is the reason behind it?


title: Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$?

text: Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$, where $k$ is the number of "hits" in a total of $N$ possible values for $|\,x\rangle$? If we know $k$, and know that it is greater than $1/2$, can't we just redefine hits as misses by modifying the oracle to produce $$-(-1)^{f(x)}\,|\,x\rangle$$ (note the additional negative sign) and then measure according to whatever strategy for $k<1/2$ produces satisfactory hit probabilities, $p_h$, since we can then say with confidence $p_h$ that one of the _unobserved_ outcomes is a hit?


title: Quick question on parallax and parsec

text: I know that 1 parsec (pc) is the distance of star at which 1 AU subtends 1 arcsecond. so $1 pc = \frac{1 AU}{1"}$ Now, if two stars in a binary with a **separation of 3"** and have a **trigonometric parallax of 0.1"** , what does it mean and what's the difference? ![enter image description here](http://i.stack.imgur.com/gNSjm.png)


title: A simple osmosis problem

text: The following is adapted from a problematic question* asked on the Bio site. I would like to ask it free of those distractions here. If there is anything unduly artificial about the problem please advise and I'll try to revise the question. I think it belongs to physics at least as much as to chemistry. Question: A bag whose walls form a semi-permeable membrane contains a mixture of 5% of solute A and 10% of solute B (both in water). The membrane allows passage of B particles but not A particles. The bag is lowered into a solution containing a 10% solution of solute B. Instead of asking a multiple choice question let me keep it open-ended. What would we expect in terms of the movement of water/solutes in this situation? Can we predict, in rough terms, a final equilibrium state? Thanks for any clarification! *The problem is that one of the solutes was poorly chosen.


title: I am interested in learning Quantum Computing what should I do?

text: I wish to learn about quantum computing which seems to be a topic of hot research and overall just intrigues me. I have a strong background in discrete mathematics and number theory. And am a pretty proficient programmer and strong problem solver. What math and physics knowledge (and in what order) should I work to be able to get the knowledge necessary for studying Quantum Computing?


title: If we are using [eV] as a unit for energy, what, then, should the unit for mass and distance be?

text: This seems obvious but it is confusing since I know that in MKS (i.e. SI) system, we use Joule with Meter with KG. But if we're using electron volt (1.6e-19 J) for energy, should we change the mass and distance units too?


title: Should the electric potential of a positively charged sphere be negative?

text: Because the indefinite integral of the electric field results in a negative value? (As the function is proportional to $r^{-2}$? I've got to be missing something... Help please!! Thanks! Also, I took the integral from infinity to the radius of the charged sphere and got $$V = \int_\infty^R{\frac{q*dr}{4*\pi*\epsilon_0*r^2}} = -\frac{q}{4*\pi*\epsilon_0*R}$$


title: Local explanation of the Aharonov-Bohm effect in terms of force fields

text: Here is an interesting paper for the Physics SE community: > On the role of potentials in the Aharonov-Bohm effect. Lev Vaidman. _Phys. > Rev. A_ **86** no. 4, 040101 (R) (2012). arXiv:1110.6169 [quant-ph]. You should check it out because it's an amusing read, but I will summarise the argument to whet your appetite, assuming you have basic familiarity with the Aharonov-Bohm (AB) effect. In the traditional AB setup, one considers an electron in a superposition of paths, taking it in two opposite directions around a solenoid treated as a **classical** source of the electromagnetic field. The observable relative phase acquired between the electron's paths is attributed to the influence of the magnetic vector potential on the electron, which cannot be globally gauged away - despite the absence of a physical field anywhere along the electron's path(s) - due to a topological obstruction. Instead, Vaidman considers the effect of the electron on the sources of the field, treating the latter as **quantum** particles. He shows that the relative phase between the two branches of the wavefunction can be considered as arising from the action of the physical field of the electron, which is **not** zero at the position of the sources. However, Vaidman uses highly contrived gedankenexperiments and completely semi-classical arguments, which begs a pair of concrete and related questions. **1) Can Vaidman's first, electric AB effect gedankenexperiment be described in a fully quantum manner, by solving (at least approximately) the three- particle Schroedinger equation? If not, why not?** **2) Is it possible to explain within this formalism the experiments of Tonomura et al. ( _Phys. Rev. Lett._ 56 no. 8, pp. 792-795 (1986)), who used a superconductor to completely shield the magnetic field of the source?**


title: Formulation of the Three-Body Newtonian problem

text: I am trying to understand three body problem in Newtonian space. I want to make formulation of differential equations for known initial conditions for the case with:   1. Identical three masses    2. Periodic solution    3. Zero Angular momentum The equations in vector form are: $$\frac{d^2 \overset{\rightharpoonup }{r}_1}{\text{dt}^2}=\frac{k^2 m_2 \left(\overset{\rightharpoonup }{r}_2-\overset{\rightharpoonup }{r}_1\right)}{r_{12}^3}+\frac{k^2 m_3 \left(\overset{\rightharpoonup }{r}_3-\overset{\rightharpoonup }{r}_1\right)}{r_{13}^3}$$ $$\frac{d^2 \overset{\rightharpoonup }{r}_2}{\text{dt}^2}=\frac{k^2 m_1 \left(\overset{\rightharpoonup }{r}_1-\overset{\rightharpoonup }{r}_2\right)}{r_{12}^3}+\frac{k^2 m_3 \left(\overset{\rightharpoonup }{r}_3-\overset{\rightharpoonup }{r}_2\right)}{r_{23}^3}$$ $$\frac{d^2 \overset{\rightharpoonup }{r}_3}{\text{dt}^2}=\frac{k^2 m_1 \left(\overset{\rightharpoonup }{r}_1-\overset{\rightharpoonup }{r}_3\right)}{r_{13}^3}+\frac{k^2 m_2 \left(\overset{\rightharpoonup }{r}_2-\overset{\rightharpoonup }{r}_3\right)}{r_{23}^3}$$ where $k$ denotes the gravity constant. I want to formulate (not solve) this problem properly. I've found this reference can help understand zero angular momentum. I don't understand it well.


Within the Solar System (or any other system for that matter) - Is it feasible for an unmanned vehicle to travel from outside the atmosphere of one planet to another without additional propulsion? That is to say Given a vehicle in orbit around a planet, say Mercury, suppose a body were launched with the destination Earth with the caveat that it have sufficient velocity to travel the distance so it reaches Earth at velocity necessary to be at Geosynchronous orbit. Could this be achieved merely by using launch velocity so that the launched body does not need carry it's own propulsion?


title: How would you design an experiment to grok optical phenomena?

text: I've been toying with the idea of making a 3D scanner that uses an IR distance sensor to find position vectors of an object in space and then translates that into a 3D computer model. One of the greatest challenges in this case is optical phenomena. If the surface has holes, or dimples that reflect the IR beam or cause diffraction, then getting an accurate reading would be nearly impossible, but that's an engineering problem. It would require several different passes from different angles to figure out what that real distance actually is. What I would like to understand is there a way to use these "glitches" in the data to model the phenomena itself? I think that this would make for a great experiment, but I don't know where to start and what to study. Essentially, I would like to derive from the data a theory of what interference was observed from the sensors and then model it to understand what it means. So, how should I try to;   1. Setting up the experiment   2. Setting controls to verify the data   3. Model the data   4. Fabricate a theory to fit the observation **Update:** What I want to do is to create an experiment that uses these mistakes in data (weird readings upon hitting distorted surfaces) and create a model that shows what optical phenomena are at play over here. Well, you could say why not just see the surface and judge? That wouldn't be fun, now, would it? On a more serious note, what I am trying to do is just make my own experiment to actually measure whatever optical phenomena is at play. Explain it and perhaps derive an expression for it from the data itself. Basically, I want to look at the data set correspond it with the physical model and see the variation in the distance reading vs. what it should have been and the surface and try to model why that happened with the 3D diagram. As I am someone who just got out of high school. What do I learn and how do I go about actually doing this? Note: I use optical phenomena as a sort of place holder for reflection, refraction, diffraction or whatever combination of these is at play. Sorry, for the confusion. **Update 2:** I guess the question title is misleading and so is the text. I changed / rephrased it to get more participation. Moreover, I know that it's hard to give a perfect answer to my question, but I would love to discuss this with someone and figure out what to learn and how. So, please go ahead take a shot. I would love to hear what you have on your mind.


title: negative vectors (eg velocity)

text: If you said someone had a velocity of -12mph and they were traveling north? Wouldn't it mean that they were traveling 12mph south? This is a quote from here: > if something [object-x] moving to the right was taken to have positive > momentum, then one should consider something [object-y] moving to the left > to have negative momentum. But isn't Momentum a vector, so the direction should be specified separately to the number. What I mean is, object-y with -1200kg m/s and object-x with 1200kg m/s should both have momentum in the same direction. But this can't be because as the quote says they are moving in opposite direction.


title: Grandfather Paradox

text: This question related to the Grandfather Paradox. Assume that time travel to the past is a reality. **What experiment/test could the time traveler perform in order to determine if he is in his own timeline or an alternate timeline/universe?** If the time traveler was in his own timeline and kills his grandfather, that means he would have never been born -- and thus cannot travel back in time to kill his grandfather. If his grandfather was not killed, that means he would have been born -- and thus could travel back in time to kill his grandfather. And so on ... At the moment the time traveler kills his grandfather, what would happen if the time traveler was in his own timeline/universe? Would it be any different if the time traveler was in a different timeline/universe? How could the time traveler know for sure if he is in his own timeline/universe or not?


title: How does charge work if photons are neutral?

text: How can an electron distinguish between another electron and a positron? They use photons as exchange particles and photons are neutral, so how does it know to repel or attract?


title: Estimate the difference between two sets of atoms

text: I've been working on amorphous structures derived from a crystalline one (using MD) containing $N$ atoms. I want to prove that these structures are different and to **quantify** their "differentness". One could think of simply displaying the structures, but:   * I actually have 20 of them and I don't want to show them 2 by 2 (poor information density)   * This does not quantify these differences (the "differentness" metric) I thought about calculating the RMS of the corresponding atom pairs distances using two different structures, but:   * I have to associate pairs so that the RMS is minimized   * A single atom **cannot** form two pairs   * A rotation and a shift (of unknown magnitude) should be allowed due to the periodic and symmetric nature of the reference cell to help minimizing the RMS I've been working on this for a week with mitigated success: the algorithm is slow and incomplete, the execution time is too slow but it kinda works. But the algorithm(/method?) is too sensitive to outliers: when I compare 3 structures, 2 close from each other (visually) and one more different, I get almost the same RMS (due to outliers). I think now that the RMS might not be a good idea after all, what figure/graph would you use to quantify the differences between these structures?


title: Is it possible to detect fake Tungsten aka Wolfram gold bars with a strong magnet?

text: Tungsten aka Wolfram is paramagnetic so it is weakly attracted to magnets. A guy devised the following to test for Tungsten in gold bars: http://www.youtube.com/watch?v=foELQ7T8_90 But he is using a paperclip and not real Tungsten. Question: How strong a magnet do I need in order to achieve a significant attraction to Tungsten. By significant I mean that it should exert a force of several (1/100)*grams so that it can be measured with a scale as in the YouTube video. Will a Neodymium magnet do? If yes, what should be the strength of the magnet in kg?


title: How does measuring redshift make us conclude that rate universe expansion is accelerating?

text: The universe is expanding in all directions. We can detect this by the redshift of electromagnetic radiation from other galaxies. We detect a larger redshift in galaxies which are further away, and I understand it is from this that we infer that the expansion of the universe is **accelerating.** Why do we infer this, and not that expansion was faster in the past (when the light from those galaxies was generated) * * * I read this question but I didn't understand the physics equations used in the answer.


title: Is light from more distant stars attracted by the gravity at black holes, or is it an optical illusion caused by the curvature of spacetime?

text: Can light really be stopped or attracted by a strong enough gravitational field, such as at a black hole? Or could it be explained as an optical effect of the spacetime curvature?