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<p>I am working on the following problem:</p>
<p>The braking acceleration for a car based on data in a driver’s handbook is –12.2 m/s2. If the car has a mass of 925 kg, find the frictional force and state the direction. </p>
<p>So far I have done the following:
F = ma
F = (925)(-12.2)
F = -11285N</p>
<p>I believe that the net force (-11285) = the force of friction. </p>
<p>Is there any way to calculate the <strong>coefficient of friction</strong> in this problem with only the above information?</p>
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] |
<p>I am having trouble getting from one line to the next from <a href="http://en.wikipedia.org/wiki/Screened_Poisson_equation" rel="nofollow">this</a> wiki page. I am referring to the text line </p>
<blockquote>
<p><em>Green's function in $r$ is therefore given by the inverse Fourier transform,</em> </p>
</blockquote>
<p>where</p>
<blockquote>
<p>$$G(r) ~=~ \frac{1}{(2\pi)^3} \iiint d^3k \frac{e^{i{\bf k}\cdot{\bf r}}}{k^2+\lambda^2}$$</p>
</blockquote>
<p>goes to</p>
<blockquote>
<p>$$G(r) ~=~ \frac{1}{2\pi^2r} \int^{\infty}_0 \!dk_r \frac{k_r \sin(k_r r)}{k_r^2+\lambda^2}.$$</p>
</blockquote>
<p>Where does the $\frac{1}{r}$ term come from and what is $k_r$? How did they simplify the triple integral? Divergence theorem? Stokes? Detailed steps would be much appreciated.</p>
| 10,930 |
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<p>I don't know about all the details of Bell tests using methods like parametric down conversion, but at least in some versions of the EPR paradox you get two photons moving apart in opposite directions. I wonder if you can look for detection coincidences by using photographic plates instead of coincidence counters? The idea would be that if you had two photographic plates on opposite sides of the source, you would get some instances where you would have a perfect matchup of reduced silver crystals, or dots. And that if you inserted crossed polarizers in front of the plates, the coincidences would disappear. I wonder if this analysis is correct, and if so, whether such experiments have been done or proposed? </p>
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<p>Is it possible to check from the EM waves(basically Light rays), if there are any extraterrestrial objects interference/passage during its travel from the Sun? I mean, can these EMs from the Sun be visually reproduced to pictures to see what has happened to these waves en route from the Sun? </p>
| 10,932 |
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] |
<p>Is it possible to calculate the weight of a person by only
using his smartphone, some action he must perform (jump, rotate etc.) and
some data like his height or age.</p>
<p>Current smartphones have the following sensors/instruments:
G-Sensor
Digital compass
Proximity sensor
Ambient light sensor
GPS</p>
<p>In conjunction with the data those devices would provide could we somehow
get the approx. weight of a person?</p>
<p>I was thinking of like asking the person to jump and then calculate the downward
velocity but that is more indicative of the persons physical strength then weight...</p>
| 10,933 |
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<p>I'm trying to calculate coexistence curves and get a rough estimate for the critical point of simple fluids using the well-known Gibbs Ensemble Monte Carlo (GEMC) (c.f. Panagiotopoulos, Molecular Physics 61 1987). In doing so, my test has been the square-well potential (SW) since there exist numerous literature data already. It seems however, that GEMC is <em>highly</em> dependent on the total initial concentration. If the initial concentration is set to a known critical point, everything works fine. However, if it is set to low, the fluid phase separates but the coexistence densities for the liquid are underestimated. On the flip side, if it is initially set to high, the fluid fails to decompose due to a low probability of acceptance for particle transfer moves.</p>
<p><strong>My question</strong>: How do you determine the initial concentrations for a GEMC simulation when the critical point is not known?</p>
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<p>There is a closed system that is just a windmill attached to a rotating shaft that can mechanically power something. I know the system produces work on the surroundings from the rotating shaft and this is positive work, but is there also a negative work input from the wind pushing the blades of the windmill?</p>
<p>Also, would there be any heat transfer in this scenario?</p>
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<p>suppose you place a number of rotating black holes in linear sequence (rotating around the same axis) between two stars at distance $d$ (assume as tightly packed as practical for purposes of calculation). If a ship enters each ergosphere and goes out into the next one, can it make the roundtrip back to home in less time than $2d/c$ (<em>home local time</em>) ?</p>
<p>What would be the simplest calculation to see that it cannot?</p>
<p><strong>Edit</strong> to make the ergosphere overlapping region more symmetric, imagine there is a symmetric sequence of black holes in front of the treadmill arranged like this:</p>
<p><img src="http://i.stack.imgur.com/rQHSU.png" alt="a kerr blackhole treadmill with an overlapping region of ergospheres"></p>
<p>the symmetry in this arrangement should cancel the angular components (at least in a small region in the middle of overlapping region). Obviously the geometry for this thing is highly unstable.</p>
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<p>What are those white lines connecting the ground to the sky on the left side of this photo?</p>
<p>I've see these before in the nuclear bomb test films too. They're apparently already in place upon detonation, as the bright backlight from the mushroom cloud suddenly makes these lines appear in the foreground.</p>
<p>I imagine test devices are being shot into the sky before detonation but I'd like to know more about this. Google searching has been fruitless as I don't even know what words I'm supposed to be searching for.</p>
<p>Looking for a brief explanation along with a source citation.</p>
<p><img src="http://i.stack.imgur.com/p508r.jpg" alt="enter image description here"></p>
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<p>I usually think of gravitational potential energy as representing just what it sounds like: the energy that we could potentially gain, using gravity. However, the equation for it (derived by integrating Newton's law of gravitational force)...</p>
<p>$PE_1 = -\frac{GMm}{r}$</p>
<p>..has me thrown for a loop, especially after <a href="http://physics.stackexchange.com/questions/13184/can-an-object-accelerate-to-infinite-speed-in-finite-time-newtonian/13189#13189">this answer</a>.</p>
<ul>
<li>If potential energy really meant what I thought it did, then it would always have to be non-negative... but this equation is <em>always</em> negative. So what does "negative potential energy" mean!?</li>
<li>If $KE + PE$ is always a constant, but PE is not only negative but becomes <strong>more</strong> negative as the particles attract, doesn't that mean the kinetic energy will become arbitrarily large? Shouldn't this mean all particles increase to infinite KE before a collision?</li>
<li>If we are near the surface of the earth, we can estimate PE as $PE_2 = mgh$ by treating Earth as a flat gravitational plane. However, <code>h</code> in this equation plays exactly the same role as <code>r</code> in the first equation, doesn't it?
<ul>
<li>So why is $PE_1$ negative while $PE_2$ is positive? Why does one increase with <code>h</code> while the other increases inversely with <code>r</code>?</li>
<li>Do they both represent the same "form" of energy? Since $PE_2$ is just an approximation of $PE_1$, we should get nearly the same answer using either equation, if we were near Earth's surface and knew our distance to its center-of-mass. However, the two equations give <em>completely</em> different answers! What gives!?</li>
</ul></li>
</ul>
<p>Can anyone help clear up my confusion?</p>
| 27 |
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<p>The <a href="https://en.wikipedia.org/wiki/Poynting_vector" rel="nofollow">Poynting vector</a> is a representation of the <a href="https://en.wikipedia.org/wiki/Energy_flux" rel="nofollow">energy flux</a> in electromagnetics, showing the amount and direction of power flow at different points in space. In electric circuits, the energy is not carried inside the wires (meaning the vector is just 0 inside them?), but by the electric and magnetic fields surrounding the wires. The DC circuit is the simplest case:</p>
<p><img src="http://i.stack.imgur.com/HJtlD.png" alt="enter image description here"></p>
<ul>
<li><a href="http://sydney.edu.au/science/uniserve_science/school/curric/stage6/phys/stw2002/sefton.pdf" rel="nofollow">Understanding Electricity and Circuits: What the Text Books Don’t Tell You</a></li>
<li><a href="http://amasci.com/elect/poynt/poynt.html" rel="nofollow">IN A SIMPLE CIRCUIT, WHERE DOES THE ENERGY FLOW?</a></li>
</ul>
<p>Is there an equivalent concept of energy flux for an equivalent hydraulic circuit? </p>
<p><img src="http://i.stack.imgur.com/RdcrC.gif" alt="enter image description here"></p>
<p>Does the energy flow inside the pipes in this case? I'm guessing the energy flux has some kind of parabolic profile inside the pipes proportional to the flow rate?</p>
| 10,938 |
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<p>I'm not new to QFT, yet there are some matters which are quite puzzling to me. I often come across the statement that real particles (the ones we actually measure in experiments, not virtual ones) are "slightly off-shell". What does this actually mean? To my knowledge, something being off-shell means that it violates the relativistic energy-momentum relation. But how can this be possible for particles we actually consider to be "physical"? Please fill me in on the mathematical/experimental backing for such a statement to any degree of detail necessary.</p>
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<p>If we were to build a high speed rail up the side of a mountain like in some ScFi movies, what is the velocity needed at the point of living the mountain excluding angular momentum from earth’s rotation to achieve escape velocity?</p>
| 10,940 |
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<p>Why <em>should</em> the mass of elementary particles be theoretically of the magnitude of the Planck mass?</p>
<p>I've read that already a few times but I don't understand why it should be that way.</p>
<p>For example: Zwiebach - <em>A first course in string theory</em>, p.55</p>
<blockquote>
<p>If the fundamental theory of nature is based on the basic constants $G$, $c$, $\hbar$ it is a great mystery why the masses of the elementary particles are so much smaller than the "obvious" mass $m_p$ that can be built from the basic constants.</p>
</blockquote>
<p>$m_p$= Planck mass</p>
<p>Zwiebach sounds to me as if it would be very logical that the mass of the elementary particles should theoretically be around $m_p$. Could you explain me this connection?</p>
<p>Edit: It is not about the problem that there is a gap between the masses.</p>
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<p>If a particle in a delta potential well has negative energy, why the particle will be bound in the well? And if it has positive well, why it is free to move in either half-space: x < 0 or x > 0?</p>
<p>I just read these in a wikipedia page:
<a href="http://en.wikipedia.org/wiki/Delta_potential" rel="nofollow">http://en.wikipedia.org/wiki/Delta_potential</a></p>
<p>I don't know how the energy of the particle influence its motion.</p>
<p>And by the way, why $e^{ikx}$ represents a wave traveling to the right, and $e^{-ikx}$ one traveling to the left?</p>
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<p>What effect does the quantum world have on radio waves? For example, if I could shrink myself down and stand on the nucleus (or even smaller sub atomic particles making up the nucleus) with a device which could measure radio waves of the surrounding world (ie with all the signals modern day humanity produces), what readings would I pick up? Would they be the same as normal or would the quantum aspects somehow effect the signals and if so, in what way would they be effected?</p>
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<p>I am reading Landau's Volume 2 of the course of theoretical physics. I have a doubt after reading the first few pages of it which I explain below.</p>
<p>Landau first defines intervals and on pages 5 and 6 shows that two events having time like interval between them can never occur simultaneously in any reference system. Then he goes on to construct a 2D space-time graph (for visualization) with an event O occurring at (0,0,0,0). Then he considers any event which occurs in future in that frame and is time-like w.r.t. origin and says on page no. 7, </p>
<blockquote>
<p>But two events which are separated by a time-like interval cannot
occur simultaneously in any reference system. Consequently, it is
impossible to find a reference frame in which any of the events in
region aOc occurred "before" the event O, i.e. at time t<0.</p>
</blockquote>
<p>The argument above just proves that because interval square should be positive, i.e. the events can't be simultaneous. But, if I replace the difference in time in the original frame with its negative in my proposed frame and let the space distance between them to be same in both frames, then I get an in my proposed frame an interval which is time like but in it the order of events is changed. Am I making some gross error or Landau has missed some argument?</p>
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<p>How would the quantum mechanical treatment of the moon as a gravitationally-bound object differ from the usual treatment of the hydrogen atom using Schrödinger's equation?</p>
<p>[The earth's gravitational potential V(r) = -GM/r where M is the mass of the earth: 6 x 10<sup>24</sup> kg. The mass of the moon is 7.4 x 10<sup>22</sup> kg and its orbital velocity is 1,023 metres/sec. The moon's mean distance from the earth is 385 million metres.]</p>
| 10,945 |
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<p>Let me justify my question before I go on. In string theory, gravitons are strings extended over space. Longitudinal gravitons are pure gauge modes of the diffeomorphism group. However, in string theory, longitudinal gravitons are also extended objects. A condensate of longitudinal gravitons is equivalent to a diffeomorphism, but this diffeomorphism has to be smeared out over the string scale. Is the diffeomorphism group in string theory a quantum deformation smeared out over space?</p>
<p>In the weak field small string coupling limit, the string theory algebra and the classical diffeomorphism algebra ought to coincide, but in this limit, all such algebras over a Poincare invariant background are isomorphic. Away from this limit, what is the form of this quantum deformation?</p>
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<p>Why when we quantize EM field, whe quantize the vector potential $A^\mu$ obtaining vectorial particles (photons) like the elastic field (phonons) and we can't quantize directly the EM-field tensor $F^{\mu\nu}$? We in that situation should obtain tensorial particles of spin 2 like graviton..It's wrong? Why?</p>
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] |
<p>Why is using a <a href="http://en.wikipedia.org/wiki/Wheatstone_bridge" rel="nofollow">Wheatstone bridge</a> such an accurate way of calculating an unknown resistance? What are the benefits of using it over Ohm's law?</p>
<p>It seems that it has something to do with the wires heating up during ohm's law calculations, and the fact that an ammeter/voltmeter still draw some current and provide some resistance which makes results unreliable.</p>
| 10,948 |
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<p>According to general relativity, speed is relative, so for example if you are running at
20 km/h and a car passes you at 30 km/h, the runner is actually moving at 50 km/h relative to the car.</p>
<p>Now imagine that 2 spaceships are traveling both at 99% the speed of light, and they pass each other in a linear fashion. Could it be argued that from 1 spaceships perspective, you are traveling at 198% the speed of light relative to the other spaceship, according to special relativity, yet violating the constant speed of light?</p>
| 109 |
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] |
<p>I am trying to compute the $\vec{E}$ and $\vec{B}$ fields in the Axial gauge ($n \cdot \vec{A}=0$) where $n^2=1$, but I'm having trouble seeing the usefulness/how it simplifies the equations.</p>
| 10,949 |
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] |
<p>Doesn't lead, according to its electron configuration, have unpaired electrons? Yet why isn't it paramagnetic?</p>
| 352 |
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<p>I have two related questions that I would like help on:</p>
<ol>
<li><p>When a power plant creates power like the <a href="http://en.wikipedia.org/wiki/Electricity_generation" rel="nofollow">Hoover Dam</a>, it can provide 2.07 GW of electrical power. My question is what does this mean? I assume from Faraday’s law that the induced voltage across the generator coil produces an current, and this combination (P = VI) is the output power. So in the case of the Hoover Dam, P = VI = 2.07 GW. I feel that this is naïve thinking but when I do a search to get more information, I am not able to find any. Can someone roughly sketch out how the electrical power of a power plant is computed?</p></li>
<li><p>If possible, what kind of voltages and currents are power plants producing before the Step Up transformers?</p></li>
</ol>
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<p>I have following exercise:
If $[C,D]$ is a c-number and $f(x)$ is a well-behaved function (i.e. all derivatives exist and are finite), show that:
$$[C, f(D)]=[C,D]f'(D)$$
where $f'(D) = \frac{d}{dx}f(x)$</p>
<p>I used expansion:
$$f(D) = \sum_{k} a_k D^k $$
that way:
$$\sum_k a_k [C,D^k]=\sum_k a_k k [C,D]D^{k-1}$$
I don't know how to show that
$$[C,D^k]=k[C,D]D^{k-1} $$</p>
<p>Do I need to expand function from operator in another way?</p>
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<p>A recent estimate by the Kavli Institute for
Particle Astrophysics and Cosmology (a joint
institute of Stanford and SLAC) is that there
are <a href="http://news.stanford.edu/news/2012/february/slac-nomad-planets-022312.html" rel="nofollow">circa 100000 times as many 'nomad planets' as stars</a></p>
<p>I found "<a href="http://articles.adsabs.harvard.edu//full/1994QJRAS..35....1M/0000005.000.html" rel="nofollow">The Close Approach of Stars in the Solar Neighborhood, Matthews, R. A. J., Quarterly Journal of the Royal Astronomical Society, Vol. 35, NO. 1, P. 1, 1994</a>"
which estimated that the frequency of other stars passing within a given
distance to be</p>
<p>$$
F_{r}(r) = \sqrt{2} \pi r^{2}\rho_{s}V_{s}
$$</p>
<p>where </p>
<p>$$
V_{s} \approx 19.5 \text{ km}/\text{second}
$$</p>
<p>and
$$
\rho_{s} \approx 0.11 \text{ stars}/\text{parsec}^3
$$</p>
<p>resulting in</p>
<p>$$
F_{r}(r) \approx 10^{-5} r[\text{pc}]^{2} \text{year}^{-1}
$$</p>
<p>Assuming that those estimates are accurate and substituting</p>
<p>$$
\rho_{s} \approx 11000 \text{ planets}/\text{parsec}^{3}
$$</p>
<p>and </p>
<p>$$
r[\text{pc}] \approx 0.000145 \text{ parsecs}
$$</p>
<p>we get a frequency of </p>
<p>$$
F_{r} \approx (10^{-5})(0.000145^{2})(10^{5})/\text{year}
$$</p>
<p>or</p>
<p>$$
F_{r} \approx 2 \times 10^{-8}/\text{year}
$$</p>
<p>This gives us a net 'close encounter' of the solar system with a nomad planet roughly every 50 million years.</p>
<p>Does this seem a reasonable estimate?</p>
| 10,952 |
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<p>In Einstein A., Zur Quantentheorie der Strahlung, Phys.ZS., 18, 121-137 (1917) spontaneous emission is considered to occur together with induced radiation so that one can write the following condition for equilibrium (which also includes induced absorption): $$ p_n e^{-\frac{\varepsilon_n} {kT}} B_n^m \rho = p_m e^{-\frac{\varepsilon_m} {kT}} \left( B_m^n \rho + A_m^n \right) $$ where $p_n$ and $p_m$ are statistical weights of the states $n$ and $m$, $\rho$ is radiation density of frequency $\nu$, $A_m^n$ is a constant characteristic of the spontaneous $m \rightarrow n$ transition (spontaneous emission), $B_m^n$ and $B_n^m$ are constants expressing the change of state under induced emission and absorption. </p>
<p>To arrive at Planck's radiation density law it is considered that at high temperatures the above equation becomes $$p_n B_n^m = p_m B_m^n .$$ What is the justification, however, to substitute $B_n^m$ expressed through the latter equality (valid for extreme temperatures) into the initial equation above (valid for lower temperatures)?</p>
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<p>This is a <em>very</em> basic question about the concepts of force and acceleration. Consider the following situations:</p>
<ol>
<li>I sit on the floor of my room on earth</li>
<li>I sit on the floor of a spaceship that accelerates with 1g (in a direction perpendicular to its "floor")</li>
</ol>
<p>In both situations I feel the same (a force that presses me towards the floor). Both situations involve an acceleration of 1g. BUT: in situation (2) my velocity changes, while in (1) it does not.</p>
<p>My question: what is the essential difference between these situations?</p>
| 10,954 |
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] |
<p>In Landau course, vol.1 Mechanics, one finds the statement: </p>
<blockquote>
<p>...the absoluteness of time necessarily implies that the ordinary law of composition of velocities is applicable to all phenomena.</p>
</blockquote>
<p>I don't see this implication clearly.</p>
| 10,955 |
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<p>What is it about conformal transformations that make them so widely applicable in physics?</p>
<p>These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, I gather this is equivalent to scale invariance, which seems like another handy feature.</p>
<p>Are those the main properties that make them useful, or are they incidental features and there are other (differential?) aspects that are more the determining factor in their use?</p>
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] |
<p>If you want to maximize the maximum velocity a child could go, what would be the optimum height?</p>
<p>If you wanted to maximize the efficiency of a child "pumping" their legs to gain velocity, what would be the optimum height?</p>
<p>I hope that I am correctly understanding how a child pumping their legs makes it possible for them to gain momentum. They shift the center of mass of the swing+child outside the normal position of being in-line with the rope/chain. By shifting the center of mass behind t's normal position, they are allowing gravity to place a small amount of force in their direction of motion. When their center of mass and the rope is parallel with the force of gravity (like a plumb bob), they cannot impart any additional velocity on their swing motion. When they are at the apex, they can impart the most force.</p>
<p>I imagine too short a swing, and the child will not have a very high maximum velocity, and the time between pumps will be too short.</p>
<p>I imagine too long, and the wind resistance will be too great, and the childs mass compared to the entire swing will be too little.</p>
| 10,957 |
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] |
<p>What is the permeability of magnesium sulphate and therefore the magnetic susceptibility?</p>
| 10,958 |
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<p>In this paper,</p>
<blockquote>
<p>Localization of an atom by homodyne measurement. A. M. Herkommer et al. <a href="http://dx.doi.org/10.1088/1355-5111/8/1/014" rel="nofollow"><em>Quantum Semiclass. Opt.</em> <strong>8</strong> no. 1, p. 189 (1996)</a> (paywalled).</p>
</blockquote>
<p>the authors are able to localize atoms using homodyne measurement. Would it be too naive to consider we can measure the position of atoms that make up molecules? I know that the LCAO (Linear Combination of Atomic Orbitals) is a widely used method to approximate molecular orbitals. This leads me to think, whether or not we can use homodyne measurements to measure the position of atoms in a molecule. If homodyne measurements don't work, what other ways are there to gain information about the position wavefunction of molecules for let's say, H<sub>2</sub>?</p>
<p>Example I'm considering:
I'm thinking that the position wavefunction for H<sub>2</sub> would be its molecular orbitals. If we estimated its molecular wavefunction as a linear combination of two atomic H orbitals that are in close proximity to each other, then... can't there be <em>some</em> way of applying homodyne measurement techniques to gain information about the position wavefunction of the two H atoms?</p>
| 10,959 |
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<p>How to get energy of collision if you know force of gravity of an object($m \rightarrow F=mg$)?
You get energy of collision by kinetic energy $E_k= \frac{1}{2}mv^2$, but if you use just force of gravity($F=mg$), how you get then the energy of collision? I know that work(energy?) $W$ made by object is $W=F \Delta s$, where $F$ is force exerted to object and $\Delta s$ traveled distance, but this distance makes it hard to calculate any collision energy of a meteorite for example.</p>
| 10,960 |
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<p>According to wikipedia, <a href="http://en.wikipedia.org/wiki/List_of_moment_of_inertia_tensors" rel="nofollow">the inertia tensor of an ellipsoid</a> with semi-axes $a,b,c$ and mass $m$ is </p>
<p>$\left[\begin{array}{ccc}
\frac{m}{5}(b^2+c^2)&0&0\\
0&\frac{m}{5}(a^2+c^2)&0\\
0&0&\frac{m}{5}(a^2+b^2)\\
\end{array}\right]$</p>
<p>If you create an arbitrary 3x3 positive diagonal matrix and try to solve for the $a,b,c$, it's very easy to wind up with imaginary dimensions. If I try to place separate point masses, I seem to run into the same problem. </p>
<p>Does that mean that the tensor doesn't represent a physically possible distribution of mass, or just not a uniform density solid? Intuitively, at least, it seems that it must be impossible for an inertia tensor to a have a single large value and two small values since a single point mass with a non-zero radius will always affect two dimensions equally and an ring of infinitesimal height still leaves the two minor dimensions with half the momentum of the large principal axis.</p>
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/7823/is-time-travel-possible">Is time travel possible?</a> </p>
</blockquote>
<p>Is time travel possible? According to my friend, it is possible to go to the future but not the past. </p>
<p>In Physics, particles move faster than the speed of light,$c$. However, consider a train moving close to the speed of light along the Earth's equator, and a particle moves in that train in the opposite direction of the train's motion. Thus, the speed of the particle with respect to Earth now becomes the products of the two velocities. Since the particle cannot travel faster than light, what happens? Is it theoretically possible to time travel into the future using this concept?</p>
| 104 |
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<p>Suppose that we have two fluids $A$ and $B$ in a container $\Omega$, and we notice that $A,B$ do not mix. </p>
<ul>
<li>Can you pleas explain to me what is the cause of this property?</li>
<li>What properties of the two fluids create the superficial tension between them? </li>
<li>Is the superficial tension between the two fluids independent of the 'sizes' of the two considered fluids? I mean, if we have a big container, with $100l$ of $A$ and $120l$ of $B$ and a small container with $40l$ of $A$ and $30l$ of $B$, the superficial tensions are the same?</li>
<li>Do walls of the container $\Omega$ influence the final equilibrium position of the considered fluids?</li>
</ul>
<p>I know that I wrote many questions above. If you can, please give me some good references to understand better the given phenomena. If you can, please give references that do not contain too advanced physics, since I'm kind of a beginner in physics. (I'm a math student) Thank you.</p>
| 10,962 |
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<p>I'm studying for a test of static rigid body and I'm having doubts on how to solve problems involving levers with weight.
If I have, for example, a lever 10 kilograms and 3 meters long and one support point at 1 meter from one end, how much force must be applied to the other side to achieve equilibrium?</p>
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<p>Suppose someone manages to evaluate the string theory $S$-matrix to all orders for any and all vertex operator insertions including non-perturbative contributions from world-sheet instantons and re-sum the whole series to obtain the exact non-perturbative string theory $S$-matrix for any combination of in- and out-states. Suppose further that the analytic result is compact, tractable, and easily amenable to numerical evaluations (say, some special function). Would such a result tell us "what string theory is"? Would it be enough in principle to answer all sensible questions about physics described by string theory? If not, what else is there we should care about?</p>
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<p>I read this intriguing statement in <a href="http://math.ucr.edu/home/baez/twf.html" rel="nofollow">John Baez' week 197</a> the other day, and I've been giving it some thought. The post in question is from 2003, so I was wondering if there has been any progress in formulating or even settling the conjecture in the title.</p>
<p>Here tmf$(n)$ is the spectrum of topological modular forms, defining a sort of generalized elliptic cohomology theory. These have a very nice construction by Lurie involving a certain moduli stack, so I was hoping one could use this construction to give a description of conformal field theory. Even if the statement </p>
<blockquote>
<p><em>tmf$(n)$ is the space of supersymmetric conformal field theories of central charge $-n$</em> </p>
</blockquote>
<p>is just a moral statement I am interested in the intuition behind it.</p>
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] |
<p>Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this
theory has 3 different topological twists. One was studied a lot during the 1990's and leads
mathematically to Donaldson theory, another one was studied by Kapustin and Witten (and mathematically it is related to geometric Langlands). My question is this: has anyone studied the 3rd twist? Is it possible to say anything about the corresponding topological field
theory?</p>
| 10,966 |
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<p>What exactly does it imply about a condensed matter system to have particle number conserved or not conserved?</p>
<p>For example, why does the superconducting phase break particle number conservation while the insulating phase does not? What exactly brings about the breaking of this conservation?</p>
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<p>My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics?</p>
<p>This probably sounds like rather strange question, or rather like one of the trivial to ask but often unhelpful questions like "give some examples of topic A occurring in relation to topic B", so let me try to motivate it.</p>
<p>In quantum computing one well known question is to quantify the number of mutually unbiased (orthonormal) bases (MUBs) in a $d$-dimensional Hilbert space. A set of bases is said to be mutually unbiased if $|\langle a_i | b_j \rangle|^2 = d^{-1}$ for every pair of vectors from chosen from different bases within the set. As each basis is orthonormal we also have $\langle a_i | a_j \rangle =\delta_{ij}$ for vectors within the same basis. We know the answer when $d$ is prime (it's $d+1$) or when $d$ is an exact power of a prime (still $d+1$), but have been unable to determine the number for other composite $d$ (even the case of $d=6$ is open). Further, there is a reasonable amount of evidence that for $d=6$ there are significantly less than $7$ MUBs. If correct, this strikes me as very weird. It feels (to me at least) like number theoretic properties like primality have no business showing up in physics like this. Are there other examples of this kind of thing showing up in physics in a fundamental way?</p>
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<p>Ptolemy's model of universe assumes that our earth is the static center of universe and everything else move relative to it (ref: <a href="http://en.wikipedia.org/wiki/The_Grand_Design_%28book%29" rel="nofollow">The grand design</a> ch:3). This model would give us a consistent picture of universe the only complication would be that the trajectories of other heavenly bodies would be fairly complicated with our earth on center. So assuming any center doesn't contradict fundamental property of nature.</p>
<p>Similarly could we have assumed that the speed of light too was not the same on different frames and had similar properties as speed of sound (for example) which is different on different frame and still not contradict fundamental property of nature only giving some other complicated (may be) equations describing nature? </p>
| 10,969 |
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<p>I was using Waves - Berkley Physics Volume III, and in explaining Snell's Law the author claims that as a wave is on the boundary between glass and air (going from glass to air) that the number of wave crests per unit length along the $y$-axis must be equal in both mediums.</p>
<p>I still don't understand this claim and was wondering if anyone could help explain it.</p>
<p>Also the boundary runs along the $y$ axis, ie the boundary is vertical and so is the $y$-axis.</p>
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<p>An object of mass $m = 5.00 g$ is moving at constant velocity $v_0 = 3.10 m/s$. At $t = 0$ and
$x = 1.50 m$, it is subjected to a resistive force $F_{res} = −mbv^2$ where $b = 0.520 m^{−1}$
is a constant. (Assume that the initial velocity is pointing in the positive direction.)</p>
<p>Express the velocity as a function of time. (Use the following as necessary: $m$, $b$, $t$, and $v_0$. Do not substitute numerical values; use variables only. Indicate the direction with the sign of your answer.) </p>
<hr>
<p>An attempt at this solution started with stating</p>
<p>$a(t)=-bv^2$</p>
<p>Then integrating to find</p>
<p>$v(t) = -t(bv^2) + C$</p>
<p>@ $t=0$, $v=v_0$. </p>
<p>So, $C = v_0$</p>
<p>and then we end up with this:</p>
<p>$v(t) = -t(bv^2) + v_0$</p>
<p>I can't seem to solve for $v$ correctly, even when using the quadratic formula.</p>
<p>Could someone point me in the right direction? Thanks in advance.</p>
| 10,971 |
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<p>Take a <em>classical</em> field theory described by a local Lagrangian depending on a set of fields and their derivatives. Suppose that the action possesses some global symmetry. What conditions have to be satisfied so that this symmetry can be gauged? To give an example, the free Schrödinger field theory is given by the Lagrangian
$$
\mathscr L=\psi^\dagger\biggl(i\partial_t+\frac{\nabla^2}{2m}\biggr)\psi.
$$
Apart from the usual $U(1)$ phase transformation, the action is also invariant under independent shifts, $\psi\to\psi+\theta_1+i\theta_2$, of the real and imaginary parts of $\psi$. It seems that such shift symmetry cannot be gauged, although I cannot prove this claim (correct me if I am wrong). This seems to be related to the fact that the Lie algebra of the symmetry necessarily contains a central charge.</p>
<p>So my questions are: (i) how is the (im)possibility to gauge a global symmetry related to central charges in its Lie algebra?; (ii) can one formulate the criterion for "gaugability" directly in terms of the Lagrangian, without referring to the canonical structure such as Poisson brackets of the generators? (I have in mind Lagrangians with higher field derivatives.)</p>
<p>N.B.: By gauging the symmetry I mean adding a background, not dynamical, gauge field which makes the action gauge invariant. </p>
| 10,972 |
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<p>I have just basic understanding of Physics from elementary school. But I still wonder, why after 10 years of cameras in cellphones, there is no "small-pack" optical zoom.</p>
<p>I think there should be no problem to make small, but still precise lenses. It should not be a problem to make small light sensor, while keeping large resolution. It should not be a problem to make tiny electric motor or servomotor to move the lenses and pack all that into 1 cm x 1 cm x 0.5 cm packing.</p>
<p>So what is the problem? I think there may be 3 explanations:</p>
<ol>
<li><p>There is some limit in physics (nature), that does not allow to
do that (which one?)</p></li>
<li><p>There is some limit in engineering, which makes tiny optical zoom extremely expensive.</p></li>
<li><p>It might work, but nobody came yet with the idea to make tiny optical zoom.</p></li>
</ol>
<p>Can you validate or disprove any of 1/2/3?</p>
| 10,973 |
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<p>I took this photo. Above the horizon there is a thick layer that looks like a cloud, but it surely isn't. Is this a <a href="http://en.wikipedia.org/wiki/Fata_Morgana_%28mirage%29">Fata Morgana</a>? What do you think?</p>
<p>EDIT: I think the more appropriate name is <a href="http://en.wikipedia.org/wiki/Mirage#Superior_mirage">superior mirage</a>, not Fata Morgana.</p>
<p><a href="https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-frc1/328722_522453751101668_74932549_o.jpg">The Image</a></p>
<p><img src="http://i.stack.imgur.com/o7gZI.jpg" alt="Fata Morgana?"></p>
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<p>Can someone name a paper or book which calculates the critical temperature of the Ising model from scratch? It might be a book and should contain the necessary prerequisites. I have had a basic course in stat physics and thermodynamics.</p>
<p>Edit:
The two suggested books have 500 pages of preface, is this necessary or is there a more compact source available?</p>
| 10,975 |
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] |
<p>What materials cause radio waves to refract? What are the radio IOR's of these materials?</p>
| 10,976 |
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<p>Recently I read that some results are obtained in directions of tricking the uncertainty principle. The relevant link is here: <a href="http://www.caltech.edu/content/tricking-uncertainty-principle" rel="nofollow">http://www.caltech.edu/content/tricking-uncertainty-principle</a> , and the paper is on the Arxiv.</p>
<p>Now the problem I have is that if we can trick the uncertainty principle, doesn't this mean that the uncertainty principle just as a restriction in our current ability to make measurements rather than a fundamental limitation?</p>
<p>If so, we can we assert that actually the universe does have certain physical knowledge of each particle's impulse and position as well, and the interaction of the rest of the universe with that particle is not uncertain. But isn't this simply Newtonian Determinism?</p>
<p>So were is the catch?</p>
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<p>I've read that Wilson lines are the effective degrees of freedom for high-energy partons, when you consider collinear gluon emission. But I'm struggling to find a readable account of this topic. Does anyone have suggestions?</p>
| 10,978 |
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<p>For photons (and any massless particle) we consider only a spin projection into the direction of motion (helicity). Why it's meaningless to talk about projection of photon's spin into some arbitrary direction? Is this because we can't measure it (photon does not have a rest frame)?</p>
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<p>I understand the physical meaning of electrostatic energy of a system of charges (or a distribution with given density) as the energy stored in the system while working to carry the charges from infinity to their actual place in the system. According to <a href="http://en.wikipedia.org/wiki/Electric_energy" rel="nofollow">this</a> article on Wikipedia, in the case of a static field you can also compute that energy as the integral of energy density $U=\int\frac{1}{2}\epsilon_{0}|\vec{E}|^2dV$. What is the physical interpretation of this density? What is the physical meaning of the expression <em>energy of an electrostatic field</em> and can this concept be used also in the non-static case? And with other fields as the gravitational one?</p>
<p>P.S. I hope this question doesn't seem obvious or useless. Being a student of mathematics, I really like to think about an abstract field $\vec{E}$ governed by Maxwell equations and <em>then</em> give it some physical meaning, unfortunatly I have not seen any theoretical physics yet, only some general physics.</p>
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<p>Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it was being thrown and at one point I ended up on the second floor of one of my high school buildings and when I threw it, my partner caught it. For the last part of my experiment I went up to the third floor of the building and threw it, my partner caught the water balloon (it burst in her hands) I am assuming that the balloon had so much force behind it that the impact caused it to burst. I know that momentum is measured using mass and velocity but I do not know how to calculate the momentum when it reaches my partner. I would say that there is no momentum because once the balloon is caught, it will not be moving. But apparently that is incorrect so I am assuming the momentum will need to be that of the split second right before it is caught. My final question: How do I calculate the momentum of the balloon when it reaches the hands of my partner?</p>
| 10,981 |
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<p>I've done an intro course on QM and I'm now hoping to understand exactly how to use probability theory rigorously in solving problems. My question is: <strong>How do I do the same thing, or the closest thing possible, in <a href="http://en.wikipedia.org/wiki/Quantum_mechanics" rel="nofollow">quantum mechanics</a>?</strong></p>
<p>To make my question more concrete, it's best to use an example - when solving problems with <a href="http://en.wikipedia.org/wiki/Probability_theory" rel="nofollow">classical probability theory</a>, I find you can set up problems using the following pattern</p>
<ul>
<li>Random experiment: Toss two coins</li>
<li>Example of an outcome: $10 = (Heads, Tails)$</li>
<li>Sample space: $S = {11,10,01,00}$, $|S| = 4$</li>
<li>Examples of events: 2 Heads $= 2H = \{11\}$, $|2H| = 1$, $1H = \{10,01\}$, $|1H| = 2$, $0H = \{00\}$, $|0H| = 1$ </li>
<li>Random variable: "Number of heads in $\omega$, $X(10)=1$</li>
</ul>
<p>Translating this to quantum mechanics, my best attempt is:</p>
<ul>
<li>Random experiment: Modelled by operators, Energy $\mathcal{H}$, Spin $S_x$,... Position or momoentum,</li>
<li>Example of an outcome: The result of applying an operator to a state vector, expressible as a linear combination of basis vectors. </li>
<li>Sample space: Set of all normalized l.c.'s of basis state vectors</li>
<li>Examples of events: Defining $\mathcal{H}|\phi_1>=\frac{\sqrt{2}}{3}|\phi_1>$, $\mathcal{H}|\phi_2>=\frac{\sqrt{3}}{3}|\phi_2>$ and $\mathcal{H}|\phi_3>=\frac{2}{3}|\phi_3>$ implies that $|\phi> = \frac{\sqrt{2}}{3}|\phi_1> + \frac{\sqrt{3}}{3}|\phi_2> + \frac{2}{3}|\phi_3>$ is a valid normalized state.</li>
<li>Random variable: a function assigning an outcome to it's eigenvalue, i.e. dual vector functionals, so $<\phi_1|$ is such that $<\phi_1|\mathcal{H}|\phi_1>= <\phi_1| \frac{\sqrt{2}}{3}|\phi_1>= \frac{\sqrt{2}}{3}<\phi_1|\phi_1> = \frac{\sqrt{2}}{3}$</li>
</ul>
<p>It seems like all the work of quantum mechanics goes into constructing the domain on which the operator in your random experiment is operating on, so to me it is a complete mystery as to what the sample space actually is, thus the potentially a more concrete question: <strong>How do I fit the construction of quantum mechanical sample spaces containing state vectors into the framework of classical probability theory as closely as possible?</strong> </p>
<p>To clarify: any time I'm solving a problem like the harmonic oscillator or a new problem I'd like to be able to think about the mathematical principles behind what I'm doing, before solving the <a href="http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" rel="nofollow">Schrodinger equation</a> or anything like that. In classical probability you're just using set theory and you know what everything is going to look like the second you've figured out what your random experiment is, what is the analogue in QM?</p>
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<p>I'm confused by <a href="http://en.wikipedia.org/wiki/Airfoil" rel="nofollow">wikipedia's page on aerofoils</a>, the <a href="http://en.wikipedia.org/wiki/Aerodynamic_center" rel="nofollow">aerodynamic center</a>, and <a href="http://en.wikipedia.org/wiki/Center_of_pressure_%28fluid_mechanics%29" rel="nofollow">center of pressure</a>; it seems to contradict itself.</p>
<p>The <a href="http://en.wikipedia.org/wiki/Airfoil" rel="nofollow">airofoils page</a> says the center of pressure is at the same position as the aerodynamic center. It says they are both the position on the wing where the moment is zero, and that they are one quarter of the chord length from the leading edge.</p>
<p>Yet the <a href="http://en.wikipedia.org/wiki/Aerodynamic_center" rel="nofollow">Aerodynamic center</a> page says:</p>
<blockquote>
<p>For non-symmetric (cambered) airfoils the quarter-chord is only an
approximation for the aerodynamic center.</p>
</blockquote>
<p>And the <a href="http://en.wikipedia.org/wiki/Center_of_pressure_%28fluid_mechanics%29" rel="nofollow">center of pressure</a> page says:</p>
<blockquote>
<p>The location of the center of pressure varies with changes of lift
coefficient and angle of attack.</p>
</blockquote>
<p>I would appreciate an explanation of the difference between center of pressure and aerodynamic center - e.g. are they both the point at which there is no moment? What's the difference between the two? Please keep terminology as close to layman's terms as possible, particularly as little maths as possible.</p>
<p>Thanks!</p>
| 10,983 |
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<p>I have calculated that because Venus is $d = 12,103.6~\mathrm{km}$ in diameter and moves at $v = 35.02~\mathrm{km}/\mathrm{s}$, it would take
$$ t=\frac{d}{v} = \frac{12,103.6~\mathrm{km}}{35.02~\mathrm{km}/\mathrm{s}} = 345.62~\mathrm{s} = 5~\mathrm{min}~46~\mathrm{s} $$
for Venus to appear totally in front of the Sun. This time would be from the edge of Venus being against the edge of the Sun to when the opposite edge of Venus is "in touch" with the same edge of the Sun.</p>
<p>But now I think this in reality takes more than just $6$ minutes (about $20$ minutes). If this is true, then why does this measurement not agree with theory?</p>
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] |
<p>I'm thinking about starting my work of physics with this question but do not know how to answer.</p>
| 10,985 |
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<p>If I take a closed circuit with two capacitors and a voltage difference, the circuit is apparently in parallel, but if I introduce a battery, the circuit is in series. Why does the presence of the battery make a difference? </p>
<p>Here's a diagram of what I mean:</p>
<p><img src="http://i.stack.imgur.com/CRwHQ.png" alt="enter image description here"></p>
<p>According to my book, the left circuit is in parallel, but the right circuit is in series. I don't see why—after all, for any voltage to run through the circuit on the left, it has to pass through C1 before C2 (or vice versa).</p>
| 10,986 |
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<p>Consider a scalar field doublet $(\phi_1, \phi_2)$ with a Mexican hat potential </p>
<p>$$V~=~\lambda (\phi_1^2+\phi_2^2-a^2)^2.$$</p>
<p>When $a=0$ this is a quartic potential and the symmetry is not spontaneously broken. However when the field acquire a VEV, the fields splits into a massive mode and a massless boson mode called the <a href="http://en.wikipedia.org/wiki/Goldstone_boson" rel="nofollow">Goldstone boson</a>.</p>
<p>I am wondering about the initial potential with $a=0$: does it have 2 massive modes?</p>
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<p>I'm trying to plot a maxwell-boltzman velocity distribution in matlab. </p>
<p>I have also asked this question at cross validated without much luck</p>
<p>The PDF is </p>
<p>f(v)=sqrt(m/2*pi*k*T) * exp(-m*v^2/2*k*T)</p>
<p><a href="http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution" rel="nofollow" title="See this link under Distribution for the velocity vectorquot;">See this link under Distribution for the velocity vector</a></p>
<p>I have defined the following function:</p>
<p>(This simple function is split over so many lines for debugging purposes.)</p>
<pre><code>function [ output_args ] = mypdf( V_i )
m=2.18e-25;
k=1.38e-23;
T=500;
intm = m/(2*pi*k*T);
intmsqr = sqrt(intm);
exponent = -m*V_i .*V_i;
exponent = exponent/(2*k*T);
exponent = exp(exponent);
output_args = intmsqr*exponent;
end
</code></pre>
<p>I then ran this function for a variety of input velocities, saved them and plotted them like this:</p>
<pre><code>>> velocities=-1000:1000;
>> results=mypdf(velocities);
>> plot(results)
</code></pre>
<p>To my horror I simply get a perfectly symmetrical distribution rather than classic maxwell-boltzman shape.</p>
<p>I also tried simply plotting the speeds of particles using another matlab function:</p>
<pre><code>function [ output_args ] = mb_speed( V_i )
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
m=2.18e-25;
k=1.38e-23;
T=500;
term1 = m/(2*pi*k*T);
term1 = term1* term1 * term1;
term1 = sqrt(term1);
term2 = 4*pi*V_i .* V_i;
term3 = -m*V_i.*V_i;
term3= term3/2*k*T;
term3 = exp(term3);
output_args = term1 * term2 .* term3;
end
</code></pre>
<p>I then plotted it using</p>
<pre><code>>> speeds=0:1000;
>> r2=mb_speed(speeds);
>> plot(r2)
</code></pre>
<p>This just produces an exponential curve and not the classic shape.</p>
<p>What am I doing wrong in both of these cases?</p>
<p>Thanks.</p>
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<p>So I guess I don't really understand the situation in question... I heard a radio piece about the <a href="http://en.wikipedia.org/wiki/Costa_Concordia">Costa Concordia shipwreck</a> in Italy taking 7-10 months to remove the vessel from its place of resting, and I was reminded of the <a href="http://www.iusmentis.com/patents/priorart/donaldduck/">Donald-Duck-ping-pong-balls-solution for raising a sunken ship</a>.</p>
<p>How come they're not using that solution in this case? (or is someone just forgetting about it?) Are there things about a very large cruise ship that would make the ping-pong ball solution impractical?</p>
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<p>When a substance changes state from solid to liquid, the temperature of the substance remains the same and the heat energy from the external source is converted to potential energy within the substance.</p>
<p>My question is that If I think of it in the reverse direction, I mean when the state changes from liquid to solid, will the potential energy that was stored be released as heat energy to the surrounding?</p>
| 10,990 |
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<p>I am designing a "glider" of sorts, and I have some basic questions about the physics involved to get me started. How much lift is required to overcome the weight of an average person, say 150 pounds? Is the lift required simply 150 pounds?</p>
| 10,991 |
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<p>Sometimes when I bicycle against hard wind, I find it difficult to breathe. Others I have discussed it with have also noticed this effect.</p>
<p>A possible related phenomenon that I heard from an acquaintance who went motorcycling in Arizona was that when it was really hot, he had to drive very slowly in order to be able to breathe. This seems related even though I have never noticed temperature affecting this before.</p>
<p>So:<br>
1. What causes this?<br>
2. Why is it more noticeable when the air is hot? (I assume it would happen to motor-bikers going sufficiently fast in cold air as well.)</p>
<p><strong>EDIT :</strong><br>
When it happens, it's usually when facing the wind directly. If you angle your head so that your mouth is not facing directly forward, it is much less noticeable. Might be psychological, but several other people I asked had experienced the same feeling as well even before I asked them.</p>
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<p>I was wonder why cameras the good ones have two lenses instead of one?</p>
<p>what benfit does it carry with this fact?</p>
<p>I have told that old cellular phones have camera with one lens and hence it blurring the </p>
<p>picture, why is that? and why 2 or more lenses are solving this or other problems?</p>
<p>Has I know every configuration of lenses are equivalent to "one lens" isn't it?</p>
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<p>A couple of weeks ago I was travelling in a car (120 km/h approximately) and I saw a <a href="http://en.wikipedia.org/wiki/Fly" rel="nofollow">fly</a> flying in front of me (inside the car, near my nose, windows closed). I wonder how was that possible. </p>
<p>Does it mean is really flying at 120 km/h or the fly is being affected by some kind of gravity/force?</p>
| 432 |
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<p>I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on. </p>
<p>I'm particularity fond of abstract algebra and topology and if possible any topics that involve abstract algebra would/topology/calculus of variations would be especially appreciated </p>
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<p>I was browsing through <a href="http://arxiv.org/abs/gr-qc/0108040">this</a> and was wondering what progress in <a href="http://en.wikipedia.org/wiki/Quantum_gravity">quantum gravity</a> research has taken place since the (preprint) publication.</p>
<p>If anyone can provide some helpful feedback I would be greatly appreciative.</p>
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<p>One formulation of Maxwell's Gauss Law for electric field is:</p>
<p>$$\bigtriangledown E = 4 \pi k \rho $$</p>
<p>This can be worked into the Divergence Theorem as follows:</p>
<p>$$\int\int_{A} F_\perp \:dA= 4\pi k \int\int\int_V \rho\:dV$$</p>
<p>As far as I can tell, the "outward pointing area normal" $F_\perp$ is the same as the current density or flux $J$ magnitude. I.e., $$F_\perp=J\cdot n=\frac{d}{dA}\left(\frac{dq}{dt}\right) \cdot n$$</p>
<p>$$\int\int_{A} J \cdot n \:dA\sim 4\pi k \int\int\int_V \rho\:dV$$</p>
<p>Now, if we assume the vector field is isotropic (flowing across a spherical surface), then
$J \cdot n$ is constant across the surface, and so the LHS integral evaluates to the surface area of the sphere times the constant $J\cdot n$:</p>
<p>$$\int\int_{A} J \cdot n \:dA=J \cdot n \int\int_{A} \:dA=J\cdot n 4\pi r^2$$</p>
<p>where $r$ is the radius of the sphere. And then we get:</p>
<p>$$ J\cdot n 4 \pi r^2\sim 4\pi k \int\int\int_V \rho\:dV$$</p>
<p>$$ J \cdot n 4 \pi r^2\sim 4\pi k E$$</p>
<p>$$J \cdot n \sim \frac{kE}{r^2}$$</p>
<p>This already seems suspect since I believe by Coloumb's Law the RHS is proportional to the acceleration of a charged particle in the field. So this equation is tantamount to equating current density to acceleration. I do not have enough background in electromagnetism to know if such a statement makes sense or not.</p>
<p>But then also consider that by the conservation of charge we know that (continuity equation):</p>
<p>$$ \bigtriangledown J = -\dot{\rho} $$</p>
<p>Substituing in the result obtained from the Divergence Theorem ($J\cdot n\sim \frac{kE}{r^2}$) gives:</p>
<p>$$ \bigtriangledown \frac{k E}{r^2} \cdot n = -\dot{\rho} $$</p>
<p>Working out $\bigtriangledown \frac{k E}{r^2} \cdot n$ gives a mess that doesn't seem related to $\dot{\rho}$. Please help show how it is true or where I have gone wrong in my derivation.</p>
| 10,996 |
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<p>(Probably related to <a href="http://physics.stackexchange.com/questions/721">this one</a>, and probably should be CW.)</p>
<p>A very long time ago, I had the good fortune to read George Gamow's excellent series of <em>Mr. Tompkins</em> books. That introduced me to the idea of a world where the usual physical constants (e.g. the speed of light and Planck's constant) were changed such that "paradoxical" effects became apparent in the macroworld.</p>
<p>My memory is hazy now, but I do recall the concepts of relativity (e.g. dilation) becoming more pronounced when the speed of light is reduced to "human-sized" speeds.</p>
<p>In this vein, I ask this: assuming all other physical constants being fixed, what exactly can be expected to happen if (<em>physical constant of your choice</em>) is increased/or decreased?</p>
<p>One physical constant per answer, please.</p>
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<p>I'm working on low budget small solar power project.</p>
<p>I want to transport heat (peak heat power about 1kW) over ~10 meter (~30ft) long pipe or hose.</p>
<p>I was thinking about thin hose (6-8mm / about 1/4 inch inner diameter ) to keep small surface area and make water flow faster (and loose less energy) - <strong>im right?</strong></p>
<p>Im thinking about some kind of synthetic, transparent hose. I dont know how this material is called in english, it's similar to fuel hoses used in old motocycles.</p>
<p>I want to cover pipe/hose with some kind of thermal insulation (maybe mineral wool) and maybe aluminium foil to keep/reflect IR radiation inside - <strong>it's good idea?</strong></p>
<p><strong>1. I need help to decide what pipe/hose diameter shall I use.</strong></p>
<p><strong>2. Any suggestions about "im right" and "it's good idea" questions above?</strong></p>
<p>I don't need exact formulas, just want to know what is proportional to what etc.</p>
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] |
<p><img src="http://i.stack.imgur.com/PF3Z7.jpg" alt="enter image description here"></p>
<p>(Zoom in <a href="http://i.stack.imgur.com/PF3Z7.jpg" rel="nofollow">here</a> to see the scales.)<br>
About the result of plotting running of 3 coupling constant, we think that we should get the correct one(MSSM).</p>
<p>But we get discontinuity at $ M_{susy}$.</p>
<p>If there something wrong in our formulae?
If you have the correct formulae of $1/\alpha$, please provide them for me.</p>
| 10,999 |
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<p>I am trying to compute the amount of energy released in the form of heat if I compress 1 cubic meter of Hydrogen to 0.1 cubic meter while submerged in a large body of water of a given temperature - say 300 degrees Kelvin.</p>
<p>Would someone smarter that I am be able to show me the appropriate formula and the computations to arrive at the result in Joules?</p>
<p>Many thanks in advance!</p>
| 11,000 |
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<p>I have solved the Killing vector equations for a 2-sphere and got the following answer. $A,B,C$ are three integration constants as expected.</p>
<p>$$\xi_{\theta}=A \sin{\phi}+B\cos{\phi}$$
$$\xi_{\phi}=\cos{\theta} \sin{\theta}(A \cos{\phi}-B\sin\phi)+c \sin^2{\theta}$$</p>
<p>From this, how do I find the basis elements in terms of the tangent vectors $\frac{\partial}{\partial \phi}$ and $\frac{\partial}{\partial \theta}$? One obvious elements if $\frac{\partial}{\partial \phi}$ itself, as the metric is independent of $\phi$. Another method IMO could be to derive it from the angular momentum generators $x\frac{\partial}{\partial y}-y\frac{\partial}{\partial x}$ etc. Is this correct? Would changing the coordinates of these generators give the right answer?</p>
<p>Lastly, How do I do this for any general metric? Is there a standard procedure to find the killing vector fields, as a basis. </p>
| 11,001 |
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<p>So I know that $V=IR$ works for circuits, but for the case of an arc-before the arc jumps, there is a potential difference, but no current, but there isn't infinite resistance is there?
I don't understand how to compute a finite resistance for an arc that would come out as infinite in some other cases.</p>
| 11,002 |
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<p>Assuming Minkowski spacetime, we know that the longest proper time curve joining two points is the rect joinining both events, While the shortest time-like curve is not a compact set (because there are sequences with limits that do not belong to the set) the proper acceleration is unbounded in such curves.</p>
<p>My question is this: is there an easy way to prove that, time-like curves between $p_0$ and $p_1$, with </p>
<p>$$ \bigl |\bigl| \frac{d^2 z}{d \tau^2} \bigr|\bigr| \le K $$</p>
<p>Have a shortest proper time curve joining two given points belonging to the set, and here it comes the hard part: <strong>That the minimal proper time curve is not of constant acceleration</strong>. </p>
<p>Is this assertion even true? How can i see it intuitively.</p>
<p>The curves must be at rest at $p_0$ and $p_1$ in some reference frame where both planets are at rest. So, the curve needs to accelerate in order to reach destination </p>
| 11,003 |
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<p>I am using Di Francesco's book P.39. The equation that the generators of the transformations satisfy is given by: $$iG_a \Phi = \frac{\delta x^{\mu}}{\delta w_a} \partial_{\mu} \Phi - \frac{\delta F}{\delta w_a},$$ where $\left\{w_a\right\}$ are a set of parameters for the transformation and $G_a$ is the corresponding generator. $F = F(\Phi(\mathbf{x}) )= \Phi'(\mathbf{x'})$ and $\Phi \equiv \Phi(\mathbf{x})$</p>
<p>He then considers some examples. For a translation, $\mathbf{x'} = \mathbf{x} + \mathbf{a}$ and $F = \Phi'(\mathbf{x+a}) = \Phi(\mathbf{x})$. I suppose the last equality there is a supposition (i.e we impose the condition that the field is invariant under translations in the coordinates). In this case, $F = \text{Id}$. I guess this warrants Francesco's statement that $\delta F/\delta w^v = 0$, but this is not general right? It is only in the case when the fields are not affected by the transformation?</p>
<p>Now consider a dilation. $\mathbf{x'} = \lambda \mathbf{x}$ and $F = \Phi'(\lambda \mathbf{x}) = \lambda^{-\Delta} \Phi(\mathbf{x})$, where $\Delta$ is the scaling dimension of the field. Could someone explain this last equality? </p>
<p>We can use the first equation above to find the generator of dilations. In this case, $w_a = \lambda$ and $x'^{\mu} - x^{\mu} = \lambda x^{\mu} - x^{\mu} \Rightarrow \delta x^{\mu}/\delta \lambda = x^{\mu}.$ I know that the generator is supposed to be $D = -ix^{\mu} \partial_{\mu}$ which seems to mean that $\delta F/\delta \lambda = 0$ But how so? By chain rule, $$\frac{\delta F}{\delta \lambda^{-\Delta}} \frac{\delta \lambda^{-\Delta}}{\delta \lambda} = -\Delta \lambda^{-1-\Delta} \Phi,$$</p>
<p>Many thanks.</p>
| 11,004 |
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<p>I am an amateur of experimental physics, and I would like to use a Stanford dual sr400 counter to make the photons coincidence counting to see quantum optical effects. Right now I am about to set up an optical experiment. </p>
<p>I have questions about the coincidence counting of my counter:</p>
<p>First of all, the Stanford dual sr400 counter only has an A FOR B PRESET mode but doesn't have a B FOR A PRESET mode. Is this what I need to set the optical path into counter A a little bit longer than the optical path into counter B such that I can record more cases of coincidences?</p>
<p>Besides, the insertion delay of this counter is 25ns. Do I need to consider this delay into my optical path of the second counter?</p>
| 11,005 |
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<p>I'm looking for a reference (books, notes, lectures) which helps a physicist to understand the language of measure theory in the context of stochastic processes (in particular markov chains).</p>
<p>I've studied markov chains and measure theory but now I'm looking for something which helps me filling the gap and making this two topics converge.</p>
<p>I've already read: <em>Measure, Integral and Probability</em> - Marek Capinski, Peter E. Kopp</p>
<p>Maybe something with direct comparison (which writes the same probability both at a basic level and in measure theory) would be great!</p>
<p>Thanks in advance!</p>
| 11,006 |
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<p>I already apologize for my medium english... I'm a french guy, not really gifted to recognize electronic circuits :</p>
<p>In fact, I need to identify a circuit from is function. So, here is the block (called OCT)</p>
<p><img src="http://i.stack.imgur.com/azzeG.jpg" alt="enter image description here"></p>
<p>I only know that the components are organized in the following manner</p>
<p><img src="http://i.stack.imgur.com/3Aq1y.jpg" alt="enter image description here"></p>
<p>where INT is an integrator, COMP is a hysteresis comparator (which compares the entering signal with zero), and $\epsilon=sign(v_{s_4}(t))$. Thus, it gives when $\mathcal{V}_A(t)=v_0$ :</p>
<p><img src="http://i.stack.imgur.com/GpJ3V.jpg" alt="enter image description here"></p>
<p>Or in the general case </p>
<p><img src="http://i.stack.imgur.com/ekfmr.jpg" alt="enter image description here"></p>
<p>So, it seems that my OCT is a kind of <a href="http://en.wikipedia.org/wiki/Voltage-controlled_oscillator" rel="nofollow">Voltage-controlled oscillator</a>, but which one ? (I'm due to buy it...).</p>
<p>Thanks everyone and again, sorry for my approximative english.</p>
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<p>I am trying to get my hands on an English or German translation of the seminal work by Gauss on fluid shapes in equilibrium: "Principia generalia Theoriae Figurae Fluidorum in statu Aequilibrii [General principles of the theory of fluid shapes in a state of equilibrium]" from 1830.</p>
<p>I have found a <a href="http://babel.hathitrust.org/cgi/pt?id=nyp.33433069098576;view=1up;seq=9" rel="nofollow">Latin version at hathitrust</a>, but my Latin is virtually non-existent so that won't help me much.</p>
<p>Does someone know where I can find a German (Gauss was German after all) or English translation of this text? Or more in general, where I can find translations of scientific papers that where originally in Latin? </p>
<p>I have tried <a href="http://www.gutenberg.org/" rel="nofollow">Project Gutenberg</a>, which seemed like a good place to start, but the specific paper I'm looking for is not there. Are there any other websites/projects that have similar databases that I might try?</p>
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] |
<p>Suppose we have two wheels attached to axis (each wheel has its own axis). One wheel is heavy compared to the other. The moment arm of force is same for the both wheels. A force F is applied on both the wheels. The applied force is also same for both wheels.</p>
<p>The light wheel will rotate fast compared to the heavy wheel. Will the torque for both wheels be same? Torque is also defined as "The turning effect of a body." But the turning effect of both the bodies is different here so, will their torque be different?</p>
| 11,009 |
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<p>How to solve the <a href="http://en.wikipedia.org/wiki/Ising_model" rel="nofollow">Ising model</a> in <a href="http://en.wikipedia.org/wiki/Ising_model#One_dimension" rel="nofollow">1D</a> by low temperature, and high temperature expansion, and by change of variable method? Can you please give me some reference links?</p>
| 11,010 |
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<p>My nephew showed me an exercise from his school-textbook about boiling eggs. Here is the exercise (translated from german):</p>
<ol>
<li>To make one hard-boiled egg in a pot of water one has to put it for 8 minutes into boiling water. How long does it if you put 10 eggs into the boiling water instead of one to make hard-boiled eggs?</li>
<li>Using an electric egg cooker (something like this: <a href="https://www.buyegggenie.com/" rel="nofollow">https://www.buyegggenie.com/</a>) one needs 7 minutes to make 3 hard-boiled eggs. How long does it take to make 6 or 10 hard-boiled eggs?</li>
</ol>
<p>The chapter in the textbook is about simple calculations with proportionalities ("Dreisatz" in german). For my nephew it was not problem to solve the exercises if one assumes that the cooking time and the number of eggs are proportional. But for him and also for me it is not clear why and when one can assume proportionalty and how to justify it physically. </p>
<p>My intuition (which is probably wrong in this case) says that in both cases we don't have a proportionality moreover that the cooking time is independent of the number of eggs. </p>
<p>To the second part of the problem: I don't own a electic egg cooker. From googling around I have found that it works with water steam (whereas in the first case the eggs are in the water). And that one needs less water in the electric egg cooker to boil more eggs. It is not clear to me how to interprete the second problem. One could assume that one uses always the same amount of water in the electric egg cooker or that one fit's the amount of water to the number of eggs (which will result in different cooking time - number of eggs relationships, perhaps one proportional and one constant...)</p>
<p>So it would be great if someone could clarify this physically. I.e. how does the cooking time depends on the number of eggs and why and under which assumptions in each case. </p>
<p>How does the situation change if one puts the eggs not in the already cooking water but into cold water at the beginning.</p>
<p>Are there methods of making hard-boiled eggs such that the cooking time is proportional to the number of eggs and are there methods such that the cooking time is (roughly) independent of the number of eggs? How to justify it physically?</p>
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] |
<p>Suppose I had a ray of unpolarized light, and I was sitting inside the beam and looking at the electric fields oscillating, then , if I am looking at a point how would the oscillations look like? I cannot seem to understand it.</p>
| 11,012 |
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<p>One problem that I'm having trouble with (as opposed to the other):</p>
<blockquote>
<p>The Messenger is a probe that orbits Mercury $700 \rm km$ from the surface. What is the tangential velocity it should be rotating at so that it doesn't precipitate towards the planet, in $\rm m/s$? </p>
<p><strong>Data</strong>: Mercury's mass $3,3 \times 10 ^{23} \rm kg$ Diameter: $4870 \rm km $ . Gravitational constant: $G=6,67 \times 10^{-11} \rm m^{3}kg^{-1}s^{-2}$</p>
</blockquote>
<p>I assume I need to use the following $$a_{c}=\frac {V^2} r$$</p>
<p>$$F=G\frac{m_1 m_2}{d^2}$$</p>
<p>EDIT:</p>
<p>Solving for $V$ in $$G\frac{{{m_1}{m_2}}}{{{d^2}}} = {m_1}\frac{{{V^2}}}{d}$$ did it.</p>
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] |
<p>The following is the extract from <a href="http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-lecture.pdf" rel="nofollow"><em>Albert Einstein's lecture</em></a> to the Nordic Assembly of Naturalists (July 11, 1923). </p>
<blockquote>
<p><em>If we consider that part of the theory of relativity which may nowadays in
a sense be regarded as bona fide scientific knowledge, we note two aspects
which have a major bearing on this theory. The whole development of the
theory turns on the question of whether there are physically preferred states
of motion in Nature (physical relativity problem). Also, concepts and distinctions are only admissible to the extent that observable facts can be assigned to them without ambiguity (stipulation that concepts and distinctions
should have meaning). This postulate, pertaining to <a href="http://en.wikipedia.org/wiki/Epistemology" rel="nofollow">epistemology</a>, proves to be of fundamental importance.</em> </p>
</blockquote>
<p>I am not able understand Einstein's question in the extract, i.e <em>are there physically preferred states of motion in Nature?</em> </p>
<p>As what I can think as layman, I didn't understand the meaning of <em>physically preferred states of motion</em>. Does Einstein mean physically preferred states of motion as wave motion, particle motion? </p>
<p>Einstein uses the term <em>physical relativity problem</em>, what is the problem of <em>physical relativity</em>? </p>
<p>Why does Einstein regards epistemology principle mentioned in the extract as of fundamental importance? </p>
<p>I am the beginner in this concept, if some where I have gone wrong in explaining pardon me.</p>
| 11,014 |
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<p>I have been chewing up some time ago the Schottky-Mott theory of Schottky Barrier height (which ignores the surface states). All the deduction seems to ground on fundamental thermodynamical principles (as the equality of Fermi levels- i.e. equality of chemical potential in equilibrium) but there is something which I can't clearly see and is one of the key points to calculate the height barrier: Why the energy bands on the semiconductor side just at the interface are assumed to be the same that the ones of the isolated semiconductor? It is clear that the band have to bend (because of the electric field) but I see no reason to why the bands values should "start" to bend from the original values (the values of the isolated semiconductor).</p>
<p>Thanks.</p>
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<p>For a single particle or field, I can't see how the <a href="http://en.wikipedia.org/wiki/Path_integral_formulation" rel="nofollow">path-integral formulation</a> depends on the order of terms in the Lagrangian. It seems that you integrate the classical Lagrangian to get the action on a path, then integrate over all paths.</p>
<p>Since we use the classical Lagrangian (I presume?), does this mean that the order of terms does not matter?</p>
| 353 |
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<p>Suppose that a force acting on a particle is factorable into one of the following forms:</p>
<p>$$\text{a)}\,\,F(x_{i},t)=f(x_i)g(t)\,\,\,\,\,\,\,\text{b)}\,\,F(\dot{x}_{i},t)=f(\dot{x}_{i})g(t)\,\,\,\,\,\,\text{c)}\,\,F(x_{i},\dot{x}_{i})=f(x_i)g(\dot{x}_i)$$</p>
<p>for which cases are the equations of motion integrable?</p>
<p>I know the answer is b, as this is an example. However, I don't feel that clear on why the other two aren't integrable. For instance,</p>
<p>$$\text{c)}\,\,m\frac{d\dot{x}_{i}}{dt}=f(x_i)g(\dot{x}_i)$$</p>
<p>if I do some manipulation with this equation...</p>
<p>$$m\frac{d\dot{x}_{i}}{g(\dot{x}_{i})}=\frac{f(x)}{m}dt$$</p>
<p>Why is that false for integrability?</p>
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<p>I heard that electrons accumulate at points on metals, and this clearly explains the arcing phenomenon, but how does a microwave make an electron imbalance on the fork?</p>
| 369 |
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<p>I am wondering about size of <a href="http://en.wikipedia.org/wiki/Black_hole" rel="nofollow">black hole</a>. How is it possible that we have black holes of different sizes? As I know the singularity is point which is infinite small and is infinite dense. So my question is how can infinite dense and infinite small object create different size black holes. We have different big infinite singularities?</p>
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<p>A pulley having some mass has a massless string around it, with two unequal masses at the end of the string. Sufficient friction is present between pulley and the string such that the string does not slip on the pulley .</p>
<p>The tensions in the massless string on the two sides of pulley will be same or different? </p>
<p>According to me the tensions on the two sides should be different so as to provide a net torque to the pulley .But what I have learned till now is that the tension in a massless string is same throughout.</p>
<p>Let the tensions on the two sides of the string be $T_1$ and $T_2$.</p>
<p>Writing equation for rotational motion of pulley we have (T1-T2)R = Ia</p>
<p>Since the pulley has non zero moment of inertia and angular acceleration ,T1 WILL NOT BE EQUAL TO T2.</p>
<p>I am having difficulty in understanding that how can a massless string have different tensions.</p>
| 11,018 |
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<p>Consider this situation:</p>
<p><img src="http://s3.amazonaws.com/answer-board-image/c4e9ecd2-b064-4e0f-8e5a-f938f98d2e6a.jpeg" alt="Diagram of box on ramp"></p>
<p>When the box is at the bottom of the frictionless incline, it will have a velocity of $v_f$. The person is an inertial frame of reference that moves at a constant velocity of $v_f$.</p>
<p>From the person's frame of reference, the box has kinetic energy when it is at the top of the ramp. Even if it is moving in the negative direction, velocity would be squared in $KE = mv^2/2$, so now the box has both potiental energy and kinetic energy.</p>
<p>When the box is at the bottom of the incline it is going to have no kinetic energy from the person's frame of reference. How is it that the box had both potential energy ($mgh$) and kinetic energy ($mv^2/2$) at the top of the frictionless incline but had neither potential nor kinetic energy at the bottom?</p>
<p>$$mgh + \frac{mv^2}{2} = 0$$</p>
<p>The law of conservation of energy says energy is transferred, but not lost. Where has the energy gone?</p>
<p>Basically the law of conservation of energy should not be violated no matter the frame of reference, but the final formula does that. Where has the energy gone?</p>
| 11,019 |
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<p>In a book of "LES HOUCHES - Critical Phenomena, Random systems, Gauge theories" the author Frolich says that:</p>
<p><strong>2D</strong></p>
<blockquote>
<p>In two dimensions, the mean energy of an isolated point defect in a square area of diameter $L$ is proportional to $\log(L)$. The total number of possible positions is proportional to $L^2$, i.e. the entropy grows logarithmically in $L$. Hence the free energy behaves like:</p>
<p>$F=E-TS \sim \textrm{const.} \log(L)-kT \textrm{const.}^\prime \log(L)$</p>
<p>Thus, for $T$ large enough, a dilute system of bound point defects becomes unstable in the thermodynamic limit, i.e. defects unbind and form a plasma</p>
</blockquote>
<p><strong>3D</strong></p>
<blockquote>
<p>In three dimensions, dislocations are line defects with a self-energy roughly proportional to their lenght, $L$. In a cubic area of diameter $\sim \textrm{const.} L$ the number of possible configurations of a single dislocation loop of lenght $L$ is clearly proportional to $\exp(\textrm{const.} L)$, so the entropy grows linearly in $L$. The free energy thus behaves like</p>
<p>$F \sim \textrm{const.} L - kT \textrm{const.}^\prime L$</p>
</blockquote>
<h3>I have not understood the following points:</h3>
<ol>
<li><p>What is the qualitative argument that says that the mean energy of a point defect in a square is $∼\log(L)$? </p></li>
<li><p>The same question of 1. for the 3D case.</p></li>
<li><p>How he derives the proportionality of $\exp(\textrm{const.} L)$ ?</p></li>
<li><p>The same question of 3. for the 2D case</p></li>
<li><p>How can he says that for $T$ large the system of point defects is unstable in the thermodynamic limit?</p></li>
<li><p>In 2D he speaks of "mean energy" in 3D of "self-energy". Why does he make this difference?</p></li>
</ol>
<p>Thanks!</p>
| 11,020 |
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<p>From the Gutemberg-Ricther law we know that the frequency of an earthquake is a power law so virtually any magnitude is possible on earthquake event. But the earth has a finite size so there must be an upper theoretical limit on the earthquake's magnitude. Which is this upper limit?</p>
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