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<p>what are the reasons for current appearing in a wire when wire is in a changing magnetic field?</p>
| 3,630 |
<p>In mean-field study of Bose-Hubbard model in an optical lattice, what parameter can be calculated to distinguish Bose glass and superfluid in a harmonic trap? </p>
| 3,631 |
<p>I have a very simple question(I guess )to ask</p>
<p>$$\frac{d\mathbf{m}}{dt}= \mathbf{C} \times \mathbf{m}$$</p>
<p>where $\mathbf{m}$ and $\mathbf{C}$ are vectors. Assume that $\mathbf{C}$ is constant over a certain period of time $[0,T]$.</p>
<p>Then would someone please explain me how can we find a rotation matrix using <a href="http://mathworld.wolfram.com/Cayley-KleinParameters.html" rel="nofollow">Cayley-Klein parameter</a> so that, for $t\in [0,T]$, we can express $\mathbf{m}(t)=R(t) \mathbf{m}_0$? Here $R(t)$ is a rotation matrix and $\mathbf{m}_0$ is the initial vector.</p>
<p>I know that, in $[0,T]$, it can be solved analytically as $\mathbf{m}(t)=exp(At) \mathbf{m}_0$. Moreover would anyone please explain the relation between this two solution?</p>
| 3,632 |
<p>Stability usually favours lower potential. Yet the triangular L -points (lagrange points) L4 and L5 are stable, having higher effective potential than the other collinear L points (L1,L2,L3)</p>
<p><img src="http://i.stack.imgur.com/YMDuj.png" alt="enter image description here"></p>
| 103 |
<p>For my question assume: </p>
<p>1: Big bang happened at a point (I know it happened everywhere) but after that explosion universe started to expand in all directions so it maybe considered to happened somewhere. (my imagination: water balloon popped with a pin and it start splattering away water in all directions and water continue to move forever) </p>
<p>2: Light bends around huge planets (relativity theory). </p>
<p>Question: when we look at the stars using telescopes, how we can determine if the light is bent due to nearby planets ( we can but only for the planets which we can see) but how about those planets which cant even see ? on the basis of this, is there a possibility that everything/majority of what we see in the sky is actually coming from just 1 direction but we see it everywhere because that incoming ray of light bent so much that w.r.t to earth, it looks like coming from different directions ? </p>
| 3,633 |
<p>Let's have some theory in hamilton formalism and let's assume that it has the constraints between canonical variables $Q, \pi$. By the Dirac terminology, the set of constraints $F_{a}(Q, \pi) \approx 0$ of the first class satisfies conditions $\lbrace F_{a}, F_{b}\rbrace_{P} \approx 0$, while the set of constraints of the second class have nonzero Poisson brackets. </p>
<p>Let's have massive and massless bosonic field cases with lagrangians
$$
L = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu} - \lambda m^{2} A^{2} , \quad \lambda_{EM} = 0, \quad \lambda_{massive} = 1.
$$
For first case we have the set of the second class constraints (the second one is fake equation of motion for $A_{0}$ component)
$$
\pi^{0} = \frac{\partial L}{\partial (\partial_{0}A_{0})} \approx 0, \quad F(A_{0}, \pi^{i}, j_{0}) = -\Delta A_{0} - \partial_{i}\pi^{i} + m^{2}A_{0} \approx 0,\quad \lbrace \pi_{0}(\mathbf x ), F_{b}(\mathbf y)\rbrace_{P} = -m^{2}\delta (\mathbf x - \mathbf y),
$$
while for the second one we have first class constraints:
$$
\pi^{0} = \frac{\partial L}{\partial (\partial_{0}A_{0})} \approx 0, \quad F(A_{0}, \pi^{i}, j_{0}) = -\Delta A_{0} - \partial_{i}\pi^{i} \approx 0,\quad \lbrace \pi_{0}(\mathbf x ), F_{b}(\mathbf y)\rbrace_{P} \approx 0.
$$
Why in the first case after introducing Dirac bracket we may make the equality the constraints to zero strict (i.e., we can express $A_{0}$ as the definite function of canonical momentums and current), while in the second case the impossibility of introduction of the Dirac brackets leads to the impossibility of expression of $A_{0}$ through other canonical coordinates? I.e., how the possibility of inctoruction of the Dirac brackets changes $\approx$ to $=$?</p>
| 3,634 |
<p>The non-Relativistic Doppler shift equation is $f = \left( \frac{c + v_\text{r}}{c + v_\text{s}} \right) f_0 $ where c is the speed of the medium (346.4 m/s for sound at 25 C temperature). I tried calculating the Doppler shift for the case when the source was moving towards the observer, and the case where the observer is moving with the same velocity towards the source, but I get different answers by about 0.75 m/s. Why does the frame I choose make a difference?</p>
<p><a href="http://www.wolframalpha.com/input/?i=200" rel="nofollow">http://www.wolframalpha.com/input/?i=200</a>*%28346.4+%2B+20%29%2F%28346.4+-+0%29</p>
<p>I am running the calculation for a wave with 200Hz frequency and a source(or an observer) moving with 20 m/s. $v_s$ is velocity of the source and $v_r$ is the velocity of the observer.</p>
| 3,635 |
<p>I recently saw a cat fall probably 100 feet like in this video <a href="https://www.youtube.com/watch?v=OivjNVDe5gk" rel="nofollow">Cat Falls</a>. It seemed as if the cat reached terminal velocity by the time it hit. Does this mean that cats (and other small animals) could fall any distance without much harm because of there low terminal velocity? Is there a point when (in increasing animal size) that larger animals have lower terminal velocity (so little harm to animal)? </p>
<p>Disclaimer: I will not test out these claims, nor do I hope you do. </p>
| 3,636 |
<p>Until reading the Phys.SE post <a href="http://physics.stackexchange.com/q/133904/">here</a> about the neutron decay I never feel strange the fact about the antisymmetricity of this decay. But indeed why this decay is antisymmetric. The neutron is his own antiparticle, and this is without any restriction.</p>
<p>Could I suppose that the phenomena has a purely electromagnetic cause? Put a neutron into an environment of positrons, will the result of the neutron decay be an antiproton, a positron and a neutrino? And if this is right, will an ordinary positive charged environment give the same result?</p>
<p>Comment: The question is not about the process of the decay which is explainable with the weak nuclear force. It's about the hidden parameters, which bring the neutron to the decay. </p>
| 3,637 |
<p>Lets consider this in marine seismic processsing. I am assuming you know what a first order primary reflection is, if not, I can define it. </p>
<p>Ok, so if we were to have a source $(S)$ and receiver $(R)$ lying directly on the $x$ axis seperated with a distance of $n$ meters, and a horzontial reflective surface, then the reflection point for a first order multiple would lie at the mid point $S$ and $R$, i.e at the point $\frac{n}{2}$. However, if we were to have a dip of a certain angle in the $x$ direction, then now our reflection point would change. The "aperture" is a range in which the new reflection point could lie in.</p>
<p>As this is done in the deep water marine environment, we might not know the exact angle of the wave as it goes down and the exact angle of the dip of the reflector, so how would we come up with an aperture to cover the possible location of the surface reflection point? In this case, the aperture will just be a line.</p>
<p>Similarly, if there was a dip in the $y$ direction, how would we come up with an aperture that could help us cover the surface reflection point?</p>
| 3,638 |
<p>Which balloon will have higher relative change in volume, helium balloon immersed in liquid nitrogen or air balloon immersed in liquid nitrogen? Since volume is directly proportional to temperature does the gas in the balloon matter?</p>
| 3,639 |
<p>I'm looking for an approximation for the temperature of the atmosphere at any height and pressure.</p>
<p>Both altitude and pressure are known variables,</p>
<p>I've derived this equation using maxwell's distribution:</p>
<p><img src="http://i.stack.imgur.com/Vcxk4.png" alt="Derivation"></p>
<p>Is this suitable? It only needs to be accurate to the top of the troposphere</p>
<p>Also, Latitude is another known variable, if I can take this into account that would be great.</p>
| 3,640 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/2166/is-it-possible-to-go-back-in-time">Is it possible to go back in time?</a><br>
<a href="http://physics.stackexchange.com/questions/7823/is-time-travel-possible">Is time travel possible?</a> </p>
</blockquote>
<p>I get the idea of traveling to the future and it makes perfect sense as we'd be somehow trapped in a machine that will travel at a very high speed (close to c) thus slowing down our aging wheres time would flow normally in, let's say, Earth. So years would pass faster for people on earth than for the person in the time machine, making it virtually possible to travel to the future. However, I don't see how traveling back in time could be possible following this logic.</p>
| 104 |
<p>Tyre companies boast of their wider tires for better grip on road. Also, the F1 cars have broad tires for better grip. But as far as I know Friction does not depend on the surface area of contact between the materials. Even the formula says so..
$F=\mu mg$ (where $F$ = Force of friction, $\mu$ = coefficient of friction, $m$ = mass, $g$ = gravity)</p>
<p>Can anyone please tell me the relation between broad tires and road grip ?</p>
| 460 |
<p>Why is the center-of-mass of 2 bodies (which interact only via Newtonian gravity) located at a focus of each of the elliptical orbits?</p>
<p>I know that when there are no external forces, the center of mass moves at a constant speed, but that doesn't explain it.</p>
| 3,641 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/29921/why-isnt-the-symmetric-twin-paradox-a-paradox">Why isn't the symmetric twin paradox a paradox?</a> </p>
</blockquote>
<p>Suppose there are two identical rockets, each carrying one of two identical clocks and one of two identical observers. The rockets lie on a straight line through space, face away from each other, and are completely motionless with respect to each other. The two rockets will use exactly the same flight plans except in different directions, like so:</p>
<pre>
<**********************************************************---\
|
/----------------------------------A B----------------------------------/
|
\---**********************************************************>
</pre>
<p>The direction, power, and duration of the various uses of thrust will be identical. The actions of the observers are also completely identical. It seems that the experience of the observer in either rocket should be identical to the experience of the observer in the other rocket.</p>
<p>Also, the rocket do not accelerate at all while on the portions of their paths that are composed of asterisks.</p>
<p>Consider the portions of the paths composed of asterisks and the effect of time dilation. Because of the difference in velocities, the observer in either rocket will "perceive" the clock in the other rocket showing a time earlier than the clock in his own rocket. However, because the situation is completely symmetrical, the reality in either rocket should be the same; the clocks at any given moment read exactly the same thing. For arbitrarily long "asterisk paths", the difference between real time in either rocket and the time observed in that rocket by the the observer in the other rocket becomes arbitrarily large. (I'm not entirely certain about the conclusions in this paragraph.)</p>
<p>Now suppose that both rockets also carry pairs of missiles such that the four missiles are all identical. The passenger in rocket A hates the passenger in rocket B, so he does some calculations to figure out when to fire his missiles in order to kill the passenger in rocket B. (The passenger in rocket A is a nasty fellow.) He has decided to fire his two missiles in exactly opposite directions in order to prevent his rocket from being accelerated.</p>
<p>So, when he does this, what happens?</p>
<p>Will the observer in rocket B, who is being fired upon, perceive the two missiles leaving rocket A but no longer in rocket A? Will he perceive them being in rocket A but not leaving rocket A? Will he perceive them both still being in rocket A but also leaving it?</p>
<p>If he does not perceive them leaving rocket A, and if we assume that there is a sufficiently large "time lag" between rockets A and B, will the observer in rocket A observe a collision when the observer in rocket B does not observe a collision (and does not get hurt or killed)? Will the observer in rocket B have no physical possibility of seeing the missile missile coming but get killed by it anyway?</p>
<p>What happens?</p>
| 84 |
<p>i want to know the relation between voltage,current & resistance , apart from this ohm's law V=IR.Because in zener diodes,current does not increase accordingly with the voltage.At BREAKDOWN POINT, voltage remains the same as the current increases manifold.And in several other cases,even if there is a low voltage,there exists a high current flow.How are they possible!!!</p>
| 3,642 |
<p>By studying quantum cosmology I was asking myself if the fact that the universe is expanding, so space is expanding and with it I would say that phase space is also expanding, so it's a non-unitary evolution, am I right? If yes, can unitarity be restored in a multiverse picture? Because I am always troubled when I hear that as we have experimentally verified the unitarity of low energy QM, by pushing further we arrive at the concluse that the multiverse can be extended from $t= - \infty$ to $t= + \infty$, sounds a bit dogmatic to me.</p>
| 3,643 |
<p>Suppose to have two capacitors in series:</p>
<p><img src="http://i.stack.imgur.com/gVAEX.png" alt="enter image description here"></p>
<p>The voltage in the middle point will be:</p>
<p>$$
V_X = V_1 \frac{C_1}{C_1+C_2}
$$</p>
<p>How can this be explained? It's been asked in <a href="http://electronics.stackexchange.com/questions/33647/solving-capacitor-voltage-drops">electronics</a>, and explained in terms of impedence and charge equality, but none of the explanations is satisfying to me, as I think it should involve charge conservation (Gauss theorem?) and/or electric fields/potentials.</p>
<p>Could you enlighten me?</p>
| 3,644 |
<p>I am trying to measure the acceleration and deceleration of a car by using an 3 axis accelerometer which is build in an iPhone 5s. Placing the iPhone flat inside the car with the y axis to the top of the car this works pretty ok. But now I want to be able to place the iPhone basically arbitrary inside the car. (like in the picture below)</p>
<p><img src="http://forums.everythingicafe.com/data/MetaMirrorCache/farm3.static.flickr.com_2355_2206921565_5fd67cf1b6.jpg_a4f0a23c50a330cf1bf56cae6c33a893.jpg" alt="iPhone inside a car"></p>
<p>Is there a way to calculate only the horizontal acceleration of the device in such a placement? (I am aware that you won't be able to differ a directional acceleration but that's sufficent for my project. If I am wrong, I would be glad to know if it would work)</p>
<p>To do the calculations the following data is available</p>
<ul>
<li>User Acceleration (uX,uY,uZ) - only the acceleration the user imparts to the device</li>
<li>the total acceleration of the device (tX,tY,tZ) - user acceleration plus gravity</li>
<li>Gyro Data (gX,gY,gZ) - the device’s rate of rotation around it's axes</li>
<li>the attitude of the device (quaternion, rotation matrix, (pitch,roll,yaw))</li>
</ul>
<p>Many thanks in advance!</p>
| 3,645 |
<p>Sorry people, very basic kinematic stuff here.</p>
<p>(1) Velocity:
$$v=\frac{d}{t}$$</p>
<p>(2) Acceleraton:
$$a=\frac{v_{f}-v_{i}}{t}$$</p>
<p>(3) Re-arrange acceleration:
$$v_{f} = v_{i}+at$$</p>
<p>(4) Ok here is my question, my lecturer produces this equation by "combining" (1) and (3):
$$d=v_{i}t+\frac{1}{2}at^{2}$$</p>
<p>(5) So now I want to figure out how (4) was formed, I stick to algebra and this is my process/result:</p>
<p>(5.1) If $v=\frac{d}{t}$ then place $\frac{d}{t}$ into the final velocity equation:
$$\therefore \left (\frac{d}{t}\right )_{f} = \left (\frac{d}{t}\right )_{i} + at$$
$$\therefore \left ( \left (\frac{d}{t}\right )_{f} \right )\times t= \left (\left (\frac{d}{t}\right )_{i} + at\right ) \times t$$
$$\therefore d=d+\left (at\right )\times t$$
$$\therefore d=d+at^{2}$$
Obviously:
$$\left (d=d+at^{2} \right )\neq \left (d=v_{i}t+\frac{1}{2}at^{2}\right )$$</p>
<p>So what have I done wrong?</p>
| 3,646 |
<p>I remember from an experiment about the <a href="http://en.wikipedia.org/wiki/Josephson_effect" rel="nofollow">Josephson effect</a> the state of each of the super conductors is fully described by a phase factor. From there I assume that is true for any Bose-Einstein condensate. So...</p>
<p>Let there be a huge blob of Bose condensate in vacuum. In its reference frame, you can describe the wave function as a complex phase number, which is the same over the whole condensate. It will change over time, but at all times, it is the same everywhere.</p>
<p>Enters Special Relativity: there is no simultaneousness. If someone in one reference frame "sees" the condensate in one phase constant over the whole condensate, but changing with time, another observer with relative velocity will "see" a phase gradient.</p>
<p>Does that mean, that to the moving observer it does not seem like a Bose-Einstein condensate? Or does it just seem to be an excited version of it?</p>
<p>I am confused.</p>
| 3,647 |
<p>The relevant question is <a href="http://physics.stackexchange.com/questions/83089/what-is-the-magnetic-effect-on-either-of-the-charges-moving-parallel">here</a>. The accepted answer may have explained my question in a descriptive manner. However, I want to see how things are related quantitatively.</p>
<p>Imagine we have two charges $q$ moving parallel to each other. The distance between them is $d$. </p>
<ul>
<li><p>In the frame where the charges are stationary. We have:
$$m_0 a_0=\frac{q^2}{4\pi\epsilon_0d}$$</p></li>
<li><p>In the laboratory frame, the charges also experience a force caused by the magnetic field which is generated by the other charge:
$$B=\mu_0\frac{qv}{2\pi d}$$
The total force is:
$$F=\frac{q^2}{4\pi\epsilon_0d}-\mu_0\frac{q^2v^2}{2\pi d}=\frac{m_0}{\sqrt{1-v^2/c^2}}a$$</p></li>
</ul>
<p>There is also the relation of $a_0$ and $a$ that relate these two equations of motion. However, it seems I cannot get the right result.</p>
<p>Any help in figuring out how to relate these two situations would be appreciated.</p>
| 3,648 |
<p>Suppose we try to obtain the movement equation for a particle sliding on a sphere (no friction, ideal bodies...). The only forces acting on the particle are its weight and - here's my problem - a force that keeps the particle attached to the sphere*. How I am supposed to represent mathematically this kind of forces? As a restriction on the coordinates of the particle?</p>
<p>As a side note: My teacher refers to this, in Spanish, as a "fuerza de ligadura". I don't have a clue on its correct translation; does ligature force make any sense? </p>
| 3,649 |
<p>I'm a pure mathematician by trade, but have been teaching myself classical mechanics. I've got to the chapter on <em>Work, Energy and Power</em> and I've found an example that is causing me some problems.</p>
<p><strong>Question</strong></p>
<p>A van of mass 1250 kg is travelling along a horizontal road. The van's engine is working at 24 kW. The constant force of resistance to motion has magnitude 600 N. Calculate:</p>
<ol>
<li>The acceleration of the van when it is travelling at 6 m/s.</li>
<li>The maximum speed of the van.</li>
</ol>
<p><strong>Answer</strong></p>
<p>Part 1 is fine. We know that $P = Fv$ and so $24000 = 6F$. It follows that $F = 4000$ N. To find the acceleration, we use $F=ma.$ The total resulting force is the traction minus the resistance, in other words $F = 4000 - 600 = 3400$ N. The mass is 1250 kg and so $3400 = 1250a$. It now follows that $a=2.72$ m/s/s.</p>
<p>Part 2 is the part that causes me problems. The maths isn't the problem, it's the way it's used. At maximum speed the acceleration is zero and so the resultant horizontal force will be zero. The book says that $T' = 600$. There are two problems here: I'm used to a prime denoting differentiation. I guess it just means the new tractive force. But the resistance force is working against the direction of motion, so shouldn't we have $T' = -600$?</p>
<p>Running with $T' = 600$, the book then uses $P = Fv$ to get $24000=600v$ and so $v=40$ m/s. I can see that using $T'=-600$ would give a negative velocity, which is clearly untrue. </p>
<p><strong>In short</strong></p>
<p>I don't see why the fact that at maximum speed there will be no acceleration, so the resultant horizontal force will be zero leads to us using $T'=600$ when $T > 0$ was the forwards tractive force and $-600 < 0$ was the resistance force.</p>
| 3,650 |
<p>I'm currently a junior at San Diego State University and ever since I learned on my intro physics courses that antennas are best 1/2 wavelength. I've read wimpy explanations that it is so it can "feel" the whole wave. I don't find that convincing enough. Basically, how can you prove or show that 1/2 wavelength is the best? Keep in mind that semester I am embarking on my E&M classes. Thanks! </p>
| 3,651 |
<p>I'm reading a few papers about how the optical properties of materials change when a under stress or a force acts upon them. I seem to be encountering the following three terms:</p>
<ol>
<li>Photoelastic constant </li>
<li>Photoelastic coefficient </li>
<li>Acousto-optic coefficient</li>
</ol>
<p>Is there a difference between these three terms, as they seem to be used in context of describing very similar phenomena? Also, does Acousto-optic constant exist?</p>
| 3,652 |
<p>As in the title. I know she was working with radioactive atoms and she made huge progress in the field of physics. But where would you find the application of her discoveries in our world? Is it just used in theoretical physics or does it have any meaning to us mortals?</p>
| 3,653 |
<p>Based on the <a href="http://en.wikipedia.org/wiki/Lambda-CDM_model" rel="nofollow">Lambda-CDM</a> cosmological model, our universe is not only expanding, but is accelerating in its expansion. However, the <a href="http://en.wikipedia.org/wiki/Equivalence_principle" rel="nofollow">Equivalence Principle</a> would suggest that inertia manifests itself in non-inertial reference frames as a pseudo-force, a body force similar to gravity but anti-parallel to the direction of acceleration. If this is in fact the case—with seemingly <em>no</em> reference frame being truly un-accelerated (due to the expansion of the universe)—why can't I <em>feel</em> it? Is it because the acceleration is too weak? Or is it because I have never <em>not</em> known the presence of this pseudo-force (so I am just used to it)? And if there is a small apparent force, what direction is it in given the isotropy of the expansion? </p>
| 3,654 |
<p>A phase transition occurs when for example, heat is applied continuously to a liquid and after a certain time it converts into a gas.</p>
<p>How does this process work in detail? Is their a chain reaction that causes to liquid to reach a 'critical' point? Does the liquid syncronises in some specific vector, facilitating the phase transition? Finally could it be that the liquid theromodynamically self organisises into a state that causes the transition?</p>
<p>To paraphrase, what exactly is a 'phase-transition' what occurs before, during and after one?</p>
<p>Any additional comments you think would help explain this phenomenom to me would be great.</p>
| 3,655 |
<p>Consider a 10 meter bridge that weighs 500 N supported at both ends. A person who weighs 750 N is standing 2 m from the end of the bridge. What are the forces $F_a$, $F_b$ holding the bridgeup at either end?</p>
<p>$$750 N - 2m + (500\cdot5) = F_b\cdot10 \\
1748 /10 m =F_b \\
F_b=174.8N \\
F_a=750N + 500N - 174.8N \\
F_a=1075.2N
$$</p>
<p>Can you please explain to me why they came up with this solution? I need it to explain to the class, especially the subtracting part.</p>
| 3,656 |
<p>The following quote is extracted from the book "The Field-The quest for the secret force": </p>
<blockquote>
<p>...There was other, quite practical, unfinished business with quantum theory. Bohr and his colleagues only got so far in their experiments and understanding. The experiments they’d conducted demonstrating these quantum effects had occurred in the laboratory, with non-living subatomic particles.<em>From there, scientists in their wake naturally assumed that this strange quantum world only existed in the world of dead matter. Anything alive still operated according to the laws of Newton and Descartes, a view that has informed all of modern medicine and biology.</em> Even biochemistry depends upon Newtonian force and collision to work. </p>
</blockquote>
<p>Are the above statements correct? </p>
<p>I always get stuck here, according to Newton's laws of motion, everybody continues in the state of motion or rest (w.r.t to an inertial frame), unless and until a force is applied on it. But, a rat, a dog, a girl!, always pass before me and fluctuate to rest and motion, rest and motion. Are they acted upon by any force to set them in motion or to get them into rest? </p>
<p>If muscles help them move (Pratyay gosh has noticed this significant point), which force make the muscles move. According to Newton's law, they must be acted upon by a force, right?</p>
<p>So, does Newton's laws of motion also apply for the matter which is not dead? </p>
<p>Is Quantum mechanics applicable only for dead matter?</p>
| 3,657 |
<p>I've been told my whole life that light is either a wave or a particle. When it's traveling through space, it's a wave. When it hits a wall, or a photo-sensitive chemical strip or something similar, it's a particle. </p>
<p>However, upon looking back all of the examples I've seen I can only recall instances in which we observe light as a particle. Are there in fact ways we can measure it as a wave?</p>
| 3,658 |
<p>This question is about taking the logarithm of the ideal gas law. In a fluids text book the author writes:</p>
<blockquote>
<p>First recall a couple of ideal gas relationships involving potential temperature, $\theta$, and entropy s...</p>
</blockquote>
<p>$$\log(\theta) = \log(T) - \dfrac{R}{c_{p}}\log(p) = \dfrac{1}{\gamma}\log(p) - \log(\rho),$$ where $\gamma=\dfrac{c_{p}}{c_{v}}$.</p>
<p>When I take the logarithm of the ideal gas law though I get:</p>
<p>$$\log(\theta) = \dfrac{1}{\gamma}\log(p) - \log(\rho) - \log(R) + \dfrac{R}{c_{p}}\log(p_{0}),$$</p>
<p>where $R$ is the gas constant ($p=\rho{RT}$) and $c_{p}$ is the specific heat constant. Note I have used the relationship $c_{p}-c_{v}=R$. I get the same thing if I take the logarithm of the definition for potential temperature directly. Does anyone know why the author does not have those last two constant terms? Am I doing something wrong?</p>
| 3,659 |
<p>I've just cracked open a biophysics textbook and it's all fine up until the introduction of the letter C in a wavefunction equation, and declaring C<sub>1</sub>= ±C<sub>2</sub></p>
<p>I've had lectures on eigenfunctions etc. before and no recollection of what C is, and it's not introduced earlier in the book (<em>Biophysics</em>, Pattabhi and Guatham, 2002).</p>
<p>A scan of the section in question (1.4) is below:</p>
<p><img src="http://i.stack.imgur.com/1I0at.png" alt="enter image description here"></p>
<p>Anyone care to enlighten me?</p>
| 3,660 |
<p>Let's have the S-matrix:
$$
S_{\beta \alpha} = \langle \beta | \hat{S} | \alpha\rangle .
$$
Here $|\alpha \rangle , | \beta \rangle$ are $t \to \mp \infty$ limit of the free states, $\hat {S} = \hat{T}e^{-i\int \hat{L}_{\int}d^{4}x}$, $\hat{L}_{\int}$ refers to the operator in the interaction picture. When we decide to get the matrix element of some process we will get
$$
\int d^{4}x_{1}...d^{4}x_{n}\langle \beta |\hat{T}(\hat{\varphi}_{1_{int}}(x_{1})...\hat{\varphi}_{m_{int}}(x_{n})) | \alpha \rangle .
$$
So it's convenient to introduce n-point Green function,
$$
\tag 1 G_{n}(x_{1},...x_{n}) = \langle 0| \hat{T}(\hat {\varphi}_{1_{int}}(x_{1})...\hat{\varphi}_{n_{int}}(x_{n}))| 0\rangle
$$
and generation functionals for it.</p>
<p>But recently I have read anywhere that as n-point Green function people use expression
$$
\tag 2 G^{H}_{n}(x_{1},...x_{n}) = \langle 0| \hat{T}(\hat {\varphi}_{1}(x_{1})...\hat{\varphi}_{n}(x_{n}))| 0\rangle ,
$$
where the operators of fields are in the Heisenberg picture. So they need to rewrite the operators into interaction picture:
$$
\tag 3 G^{H}_{n}(x_{1},...x_{n}) = \langle 0| \hat{T}\left( \hat {\varphi}_{1_{int}}(x_{1})...\hat{\varphi}_{n_{int}}(x_{n})\hat{S}\right)|0\rangle .
$$
I don't understand why we need the Green function $(2)$ where the fields operators are in the Heisenberg picture if $S$-matrix "generates" rather Green functions with operators in interaction picture. </p>
<p>Can you explain it why we don't use $(1)$ when talk about the Green functions?</p>
| 3,661 |
<p>How is it possible to achieve waves which are spatially, but not temporally, coherent? Can this be done with a bandpass filter?</p>
<p>Conversely, how is it possible to achieve waves which are temporally, but not spatially, coherent? Can this always be achieved with a pinhole?</p>
| 3,662 |
<p>In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to tunnel between two pieces of superconductor. </p>
<p>With a potential difference $V$ across the junction, an alternating current should flow at a frequency $f$ given by:
$$
hf = 2\times e\times V.
$$
For a potential difference of $10^9$ volts, the frequency of these alternating currents would be around $10^{24}$ Hz, and that is comparable (in terms of frequency) with the frequency of highly energetic gamma radiation. </p>
<p>Question 1. What is the maximum current carrying capacity of a Josephson tunnel junction? (we do not want the materials to brake down in the middle of the experiment).</p>
<p>In 1967, Andrei Sakharov suggested that fundamental fields such as electromagnetism cause, in their ground state, a stress in the vacuum that is perceived as gravity (induced gravity). Following this train of thought, it makes sense to ask the following question.</p>
<p>Question 2. Could these extremely high frequency alternating currents lead to new phenomena, like gravity modification effects? Basically, a network of Josephson tunnel junctions under high voltage, could this experimental setup lead to effects connected to gravity modification effects? </p>
<p>Question 3. Is the Podkletnov effect confirmed?</p>
| 3,663 |
<p>I'm confused by statistical entropy. It seems to me like the number of microstates for a given macrostate would increase without bound as finer partitionings of the phase space are chosen. Why is it that, as the <a href="http://en.wikipedia.org/wiki/Microcanonical_ensemble#Precise_expressions_for_the_ensemble" rel="nofollow">wiki article</a> states, "the size of the microstates in phase space can be chosen somewhat arbitrarily"? Is there an intuitive explanation for this? It must have something to do with the requirement that total energy is held constant, right?</p>
<p>I'm not trying to become a statistical physicist here, I'd just like to understand entropy better. Keep it simple, please! (I do have a mathematical background, though.)</p>
| 3,664 |
<p>In Gasiorowicz's <em>Quantum Physics</em>, we determined the relation: $$L_z | l,m\rangle= \hbar m | l,m \rangle$$</p>
<p>I would like to determine: $\langle l,m_1 | L_x | l,m_2 \rangle $</p>
<p>I thought about expressing $L_x$ in terms of $L_{+}$ and $L_{-}$, which gives us: </p>
<p>$$L_x= \frac12\left(L_{+}+ L_{-}\right)$$</p>
<p>We know that:
$$L_{+} | l,m\rangle= C_{+} | l,m+1 \rangle$$
and
$$L_{-} | l,m\rangle= C_{-} | l,m-1 \rangle$$</p>
<p>But I don't think that's how I should proceed.</p>
| 3,665 |
<p>A question needed for a "solid" sci-fi author: How to detect a strong magnetic monopole? (yes, I know no such thing is to be found on Earth).</p>
<p>Think of basic construction details, principles of operation and necessary components of a device capable of detecting/recognizing a macroscopic object emitting magnetic field of equivalent of order ~0.1-10 Tesla near its surface, but with only one pole, reliably distinguishing it from normal (2-pole) magnets, preferably at a distance.</p>
<p>Preferably a robust method, not involving extremely advanced technology. Detect the presence, possibly distance (or field strength) and direction.</p>
<p>I know of SQUIDs, but these concentrate on extreme sensitivity. I'm thinking of something less sensitive but more robust (like, no need for the monopole to fall through the loop) and still able to recognize a monopole against a magnet.</p>
<p>Also, how would such a macroscopic object behave practically? Such a "one-pole magnet" about the size and strength of a refrigerator magnets - how would it behave around ferromagnetics, normal magnets and so on?</p>
| 3,666 |
<p>I have a question regarding <a href="http://en.wikipedia.org/wiki/Coset" rel="nofollow">coset space</a> or <a href="http://en.wikipedia.org/wiki/Homogeneous_space" rel="nofollow">homogeneous space</a> $SO(n+1)/SO(n)$ which is simply $S^n$. I need some intuition regarding this result.</p>
<p>As everyone knows that for a simple case of $SO(3)/SO(2)$, one can have $SO(3)$ as a group acting on $\mathbb{R}^3$ and $SO(2)$ as an isotropy group of $x\in\mathbb{R}^3$, then the group $SO(3)$ acts transitively on $S^2$ and we get $S^2$ as the coset. </p>
<p>Since the result is just 2-sphere or $n$-sphere, is there an intuitive way of seeing it?</p>
| 3,667 |
<p>Is it another way of saying the ground state?</p>
| 3,668 |
<p>The edge of Jupiter <a href="http://en.wikipedia.org/wiki/File%3aJupiter-Earth-Spot_comparison.jpg">looks very sharp</a>.</p>
<p><img src="http://i.stack.imgur.com/DH0Ay.jpg" alt="Jupiter"></p>
<p>Even more bothersome, the <a href="http://en.wikipedia.org/wiki/File:171879main_LimbFlareJan12_lg.jpg">edge of the sun</a> looks sharp, aside from kind of a soup of particles floating above it.</p>
<p><img src="http://i.stack.imgur.com/DhZhI.jpg" alt="Sun edge"></p>
<p>The sun's surface has an incredibly low density. I mean, $10^{-6} g/cm^3$ kind of density (<a href="http://qdl.scs-inc.us/2ndParty/Images/Charles/Sun/Density_wbg.png">ref</a>). The Earth's atmosphere looks very hazy, and rightly so, because it's a gas.</p>
<p><img src="http://i.stack.imgur.com/inHqD.jpg" alt="Earth"></p>
<p>Since Jupiter and the sun are 100% gas, why don't they appear as smudges on our telescopes? To say "smudge" in a more scientific way, why isn't the transition zone between opacity and transparency a significant fraction of the radii of gaseous bodies?</p>
| 105 |
<p>Sorry for the long text, but I am unable to make my question more compact.</p>
<p>Any periodic function can be Fourier expanded. Usually, they say in mathematical physics books, if the function is not periodic we use Fourier transform which is more general than Fourier series expansion. </p>
<p>If Fourier transform is more general, cannot we use it to expand a periodic functions as well? Why periodic functions in textbooks are only Fourier expanded but not Fourier transformed?</p>
<p>More specifically, the boundary value problems that we solve in electromagnetism (like in chapter 3 of Griffiths) in which for example some potential is specified on the boundary of some region and we want to find the potential inside that region, this problem is usually solved by separation of variable then eventually applying Fourier series expansion to fit the boundary conditions. Those problems are never solved using Fourier transform, why is that? is it because that in Fourier series expansion one has control on truncating the series to whatever accuracy one wants whereas for Fourier transform one cannot do that? or is it an issue of convergence? </p>
<p>If both are viable there must be some criteria on using one over the other!</p>
<p>If one can point out a reference in which Laplace's equation is solved once with Fourier series and once with Fourier transform that will be greatly appreciated. </p>
| 3,669 |
<p>We consider a theory described by the Lagrangian,</p>
<p>$$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$</p>
<p>The corresponding field equations are,
$$(i\gamma^\mu\partial_\mu-m+g\bar{\Psi}\Psi)\Psi=0$$</p>
<p>Could this model have soliton solutions? Without the last term, it is just a Dirac field (if $g=0$), but it has to be included. This is similar to the <a href="http://en.wikipedia.org/wiki/Thirring_model" rel="nofollow">Thirring model</a>. I was looking for this field in books and papers but I haven't found it. If you know about it could you give me any reference? </p>
| 3,670 |
<p>I am reading a <a href="http://www.physik.uni-siegen.de/quantenoptik/forschung/publikationen/publis/epr_prl.pdf" rel="nofollow">paper</a> by Serge Haroche stating the cavity they use sustains a Gaussian mode of the e.m. field called $TEM_{900}$. I understand what Gaussian means. I found <a href="http://en.wikipedia.org/wiki/Transverse_mode" rel="nofollow">this</a> explaining what TEM means, but if I am working in a cavity, what is the "direction of propagation"? And above all, why three indices instead of two?</p>
| 3,671 |
<p>I'm having this lecture on QM and we are giving an introduction on Lie Groups. </p>
<p>So... this week we have been talking about central extensions of LG (such as Galilean) and related to this popped up the 2-cocycles. All I know is that they should relate somehow the phases of its projective representation and by that should have a concrete property that defines them. </p>
| 3,672 |
<p><a href="https://en.wikipedia.org/wiki/Rabi_problem" rel="nofollow">Rabi oscillations</a> are commonly known as the oscillations in time of the occupation probability of a quantum two-level system under the action of a coupling interaction between the two-levels.</p>
<p>Nevertheless, I think that Rabi oscillations do not really probe quantum light-matter effects until discrete Rabi frequencies are observed, as was done <em>e.g.</em> in</p>
<blockquote>
<p>M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J.-M. Raimond & S. Haroche. <em>Quantum Rabi Oscillation: A Direct Test of Field Quantization in a Cavity.</em> <a href="http://dx.doi.org/10.1103/PhysRevLett.76.1800" rel="nofollow">Physical Review Letters <strong>76</strong> 1800–1803 (1996)</a>. (<em>free to read article</em>)</p>
</blockquote>
<p>So my question follows: <strong>Are Rabi oscillations a probe of the quantum-ness or not?</strong> <em>(by quantum-ness I here mean a kind of particle-wave duality)</em> In particular: are similar effects observable between two oscillating modes? To understand a bit more this last question, it is clear that the discreteness of the Rabi frequencies are a probe of the particle-wave duality. So the question can be recast as: What if I forget the two-levels system? For instance, what happens if I replace the two-levels system with a quantum harmonic oscillator, and then take the classical limit for this oscillator?</p>
| 3,673 |
<p>I wondered whether, under the probabilistic interpretations of QM, the <em>timing</em> of the Big Bang (or perhaps any other historical event) is <em>fundamentally</em> as uncertain as (or: like) other (e.g., future) quantum-mechanical processes. That is, looking backwards, should one—<em>if one insists on being pedantic about it</em>—actually treat the Big Bang as a superposition of many "possible" (and interfering) Big Bangs?</p>
| 3,674 |
<p>In a recent Hunger Games movie, there's a scene where a certain scientist says that he invented a wire which will not melt under the current of a lightning. Is that even possible?</p>
| 3,675 |
<p>What are the various approaches to fault tolerant quantum computation ? Two examples are 1. topological quantum computation which uses topological phases in quantum states (2-Dimensional for non-abelian statistics of anyons) and 2. spin-half BEC form (refer <a href="http://jqi.umd.edu/news/new-state-fifth-state" rel="nofollow">http://jqi.umd.edu/news/new-state-fifth-state</a> (Dr. Victor Galitski's research at UMD) ) .
Can you guide me to the references mentioning various approaches and the challenges associated with them ? </p>
| 3,676 |
<p>When we find the electric field between the plates of a parallel plate capacitor we assume that the electric field from both plates is $${\bf E}=\frac{\sigma}{2\epsilon_0}\hat{n.}$$ The factor of two in the denominator comes from the fact that there is a surface charge density on both sides of the (very thin) plates. This result can be obtained easily for each plate. Therefore when we put them together the net field between the plates is $${\bf E}=\frac{\sigma}{\epsilon_0}\hat{n}$$ and zero everywhere else. Here, $\sigma$ is the surface charge density on a single side of the plate, or $Q/2A$, since half the charge will be on each side. </p>
<p>But in a real capacitor the plates are conducting, and the surface charge density will change on each plate when the <em>other</em> plate is brought closer to it. That is, in the limit that the two plates get brought closer together, <em>all</em> of the charge of each plate must be on a single side. If we let $d$ denote the distance between the plates, then we must have $$\lim_{d \rightarrow 0}{\bf E}=\frac{2\sigma}{\epsilon_0}\hat{n}$$ which disagrees with the above equation. Where is the mistake in this reasoning?</p>
<p>Or more likely, do our textbook authors commonly assume that we are in this limit, and that this is why the conductor behaves like a perfectly thin charged sheet?</p>
| 3,677 |
<p>I, a newbie in physics, often read about "near determinism", which is most probably the actual state of physics, meaning: the "big world" is deterministic, but very small things (atoms and smaller) are indeterministic (e.g. quantum physics). </p>
<p>If this is true, where is the border?</p>
<p>At which size do objects in our universe stop to be indeterministic and start to be deterministic?</p>
| 3,678 |
<blockquote>
<p>Consider the following situation. A certain quantity of ideal monatomic gas (say one mole) is confined in a cylinder by a piston and is maintained at constant temperature (say $T_0$) by thermal contact with a heat reservoir. Then the gas slowly expands from $V_1$ to $V_2$ while being held at the same temperature $T_0$.</p>
<p><strong>Question</strong>: Is this process reversible or irreversible?</p>
</blockquote>
<p><strong>Attempt</strong>: When the gas expands, the temperature must decrease, so the heat reservoir gives energy to the gas so the gas is maintained to the same temperature, right? Then If we do work on the gas so that it returns to the initial volume $V_1$, we know that due to $\Delta T=0$, then $\Delta U=0$, right? So, the work done on the gas is going to transform itself to heat that would be absorbed by the heat reservoir. My question is: how do we know if the heat given by the heat reservoir is the same that the heat absorbed by itself? If this is true, then I guess the process will be reversible, but if it's not true, does the process would be irreversible? Or it does not matter due that we have a heat reservoir?</p>
| 3,679 |
<p>There is differential identity with Weyl tensor and energy-momentum tensor:
$$
D^{\lambda}C_{\lambda \alpha \sigma \beta} = 4 \pi G \left(D_{\sigma}T_{\alpha \beta} - D_{\beta}T_{\alpha \sigma} + \frac{1}{3}(g_{\alpha \sigma}D_{\beta}T - g_{\alpha \beta}D_{\sigma}T)\right). \qquad (1)
$$
One says (Carroll, "Spacetime and geometry") that it "...can be thought of as a propagation equation for gravitational waves, in close analogy with Waxwell's equations $\partial_{\mu}F^{\mu \nu} = J^{\nu}$...".
But I don't see where is the close analogy of $(1)$ and Maxwell's equation. Can you make it clearer?</p>
| 3,680 |
<p>I would like to know how good or bad behave a metallic wall in stopping the propagation of an microwave signal.</p>
<p>To be practical, let's take the example of a GSM relay antenna. If I set up the perpendicular metallic wall between me and the signal sender,
will the wall stops the signal like a plank does it in front of a light, </p>
<p><img src="http://i.stack.imgur.com/8kn1c.png" alt="enter image description here"></p>
<p>or
more like a plank in a mountain river with only a very small protected area just behind the plank ?</p>
<p><img src="http://i.stack.imgur.com/LojRQ.png" alt="enter image description here"></p>
| 3,681 |
<p>I'm doing old exam questions, and here is one that on first glance seemed rather simple to me, but I just can't get it:</p>
<p>Given are two operators $A$ and $B$, and all we know about them is that
$$[A,B] = B$$
and
$$B^\dagger B = 1 - A^2$$</p>
<p>From this, I must find the "hermiticity properties" of $A$ and $B$. So far, the only progress I have made is to note that $A^2$ must be hermitian, because for any operator, $B^\dagger B$ is hermitian. </p>
<p>However, this does not suffice to determin the hermiticity of $A$ itself, as $A$ could be hermitian, anit-hermitian or even have one hermitian part $A_h^\dagger = A_h$ and one antihermitian part $A_a^\dagger = -A_a$ as long as $A_h A_a = -A_a A_h$, i.e. the hermitian and anti-hermitian part of $A$ anti-commute.</p>
<p>I am sure that there must be a really simple trick, but I just don't get it...</p>
| 3,682 |
<p>I've posed the question in this particular way to avoid the ambiguity usually found in the posing of the "<a href="http://pogue.blogs.nytimes.com/2006/12/11/the-airplane-treadmill-conundrum/" rel="nofollow">airplane on a treadmill</a>" puzzle, <a href="http://physics.stackexchange.com/questions/32269/what-will-happen-if-a-plane-trys-to-take-off-whilst-on-a-treadmill">e.g.</a></p>
<p>I'm not specifying how the treadmill is controlled but asking <em>if</em> it can be controlled in such a way that the thrust of the plane's engine is countered with an equal and opposite force. Assume the wheel bearings are frictionless and the wheels rotate freely. Please justify your answer.</p>
<p>[EDIT] Idealize the problem such that we can ignore rolling resistance.</p>
| 3,683 |
<p>I have recently come across two key concepts in quantum optics: <a href="https://www.google.com/search?q=%22shot+noise%22" rel="nofollow">shot noise</a> and <a href="https://www.google.com/search?q=%22back-action+noise%22" rel="nofollow">back-action noise</a>. This is very important for me to know: first, are shot noise and back-action noise the same? Please let me know if there is any other equivalent term for back-action noise among the quantum optics community.
I am also wondering whether back-action is the nature of light beam in vacuum, or is it related basically to measurement detector like homodyne?</p>
<p>I really like to know exclusively the characteristics of back-action noise to be able to model it.</p>
| 3,684 |
<p>I almost all movies where you could see an animation about an asteroid, they move in a very distinct way.</p>
<p>I don't know how to explain better, but I think what we can see in the movies is that the asteroid is rotating around the x axis with constant speed, around the y axis with constant speed and around the z axis with constant speed, where x, y and z axes are of a reference frame.</p>
<p>What is this kind of motion? Is it correct?</p>
<p>According to the Euler's rotation theorem any 3D rotation that has a fixed point also has a fixed axis. So if they are rotating around more then one axis, does it mean that they don't have any fixed point? But then what is the motion what their center of mass is doing?</p>
<p>I would suppose, that the correct movement would be when asteroids are rotating like planets, around one fixed axis. But to me the rotation commonly used is not like that. What is the correct way?</p>
| 3,685 |
<p>If I have a car (with a particular engine) optimized (shape & weight distribution-wise) for attaining the top speeds possible, and I put that engine into a car which is heavier (but otherwise the same shape & design), will the heavier car have the same top speed in the real world?</p>
<p>I'm guessing that the heavier car will accelerate at a slower rate, but I am not sure whether it would eventually hit the same top speed as the lighter car. Factors such as air resistance & the way racing cars are designed to hug the ground (as I understand it) might cause them to not have the same max speed?</p>
<p>If they don't have the same top speed, would it be possible to re-design the heavier car (i.e. change its shape and weight distribution) so that it has the same max speed as (or a higher max speed than) the lighter car? My thinking is that if the heavier car doesn't need to use the air resistance to "hug the ground" then it might be able to be designed more aerodynamically?</p>
<h3>Update 1</h3>
<p>Okay, $F_{ground}$ increases with $m$, which decreases $|v|_{max}$. That makes sense.</p>
<p>But could the heavier car go as fast or faster with a different design? Here's my reasoning: </p>
<ol>
<li>Speed increases while the car's $F_{engine}$ is greater than friction's $F_{ground} + F_{air}$. </li>
<li>$F_{air}$ increases as $|v|$ increases.</li>
<li>"Upside down wings" are used to provide extra $F_{downwards}$ (lets call it $F_{wings}$).</li>
<li>Having too little $F_{downwards}$ decreases $F_{engine}$.</li>
<li>Bigger 'wings' in #3 increases $F_{wings}$ but also increases $F_{air}$</li>
<li>$F_{downwards} = F_{gravity} + F_{wings}$</li>
</ol>
<p>Based on this logic, a lighter car will need bigger 'wings' (#6) to maintain traction (#3) in order to maintain speed (#4), but increasing $F_{wings}$ increases $F_{air}$ by #5, which decreases $|v|_{max}$ (#1 + #2). However, as $m$ increases, $F_{gravity}$ increases, therefore less $F_{wings}$ is needed (#6), and therefore less $F_{air}$ is experienced. So we have</p>
<ul>
<li>heavier car would have greater $F_{ground}$ which decreases $|v|_{max}$ by a constant amount</li>
<li>lighter car would have greater $F_{air}$ which increases as $|v|$ increases</li>
</ul>
<p>So following this reasoning, wouldn't it be possible to build a heavier car which has greater $|v|_{max}$ than a lighter car?</p>
<h3>Update 2</h3>
<p>Clarification: #4 is supposed to mean "when there's too little force pushing the car down, the wheels will slip, which reduces the amount of force the engine can provide". Is that correct?</p>
| 3,686 |
<p>I'm reading a book about string theory, and it describes <a href="http://en.wikipedia.org/wiki/Anthropic_principle" rel="nofollow">anthropic principle</a>. Idea is clear to me, I understand this principle describes certain constants in modern physics that are so fine tuned as if to imply the existence of a creator.</p>
<p>I also understand how this is not true if we imagine multiverse where each universe contains different sets of rules and constants thus leading to different physical laws, where infinite amount of universes exist 1 could easily turn out to match ours.</p>
<p>But why is it called Anthropic principle, or better yet why Anthropic?</p>
| 3,687 |
<p>I am from civil engineering, I am doing simulation and analysis (CFD and other statistical method) on flow around bluff bodies as in a wind tunnel. Different from in aerospace aerodynamics, our objects are generally very blunt and have sharp separation angles, for example flow around rectangular prisms, etc. The Re is very high (Re=1E5~1E8, incompressible, single phase).</p>
<p>Could anyone give me some advice from fluid mechanics point of view, how should I look into this type of problem and get most out of this research endeavor. I really hope that my research would be more solid and meaningful and general and fundamental! The question I have is equivalent to "How to ask the right question in the aerodynamic research."</p>
<p>Any general or specific suggestion would be highly appreciated. </p>
<p>For example, to put this in more detail, I would like to know:</p>
<ol>
<li>Any remaining problems in fluid mechanics that bluff-body flow would shed light on?</li>
<li>Anything that deserves more attention on the wake flow?</li>
<li>Is coherent structure around the surface a interesting topic?</li>
<li>Inflow turbulence impact on reattachment?</li>
</ol>
<p>...</p>
<p>Ideas from both academic and industry are welcomed. </p>
<p>Thanks</p>
| 3,688 |
<p>The question and answer are on pg.8-10 of <a href="http://web.mit.edu/8.01t/www/materials/ExamPrep/final_practice_problems%20sol_f12.pdf" rel="nofollow">this PDF</a>:</p>
<p>At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at closest approach, but an arbitrary distance away from the center of the moon?" The equation (eq.11) would be exactly the same! What does that mean? Since obviously the distance from the space junk to the moon changes continuously, yet the form of the equation remains the same.</p>
<p>Using conservation of energy:
$$\frac{1}{2}mv_i^2-\frac{GMm}{R}=\frac{1}{2}mv_f^2-\frac{GMm}{r}$$
And conservation of angular momentum:
$$mRv_i=mrv_f$$
For any $v_f$ and $r$.</p>
<p>Now look. We have two equations and two unknowns, $v_f$ and $r$. This suggests that there is a unique solution for both. If we solve for one and plug that into the other equation, we'll get a unique result (or perhaps end up with a quadratic equation, which doesn't fix the problem). How do we reconcile this?</p>
| 3,689 |
<p>Consider a long semiconductor bar is doped uniformly with donor atoms so that the concentration given by $n = N_D$ and is independent of position. Radiation falls upon the end of the bar at $x=0$, this light generates electron-hole pairs at $x=0$. light keeps on falling.</p>
<p><strong>Explanation:</strong> </p>
<p>Because the material is n-doped (many electrons) the light does not significantly change the electron concentration. However, there are initially very few holes in the material, so the illumination <em>does</em> significantly change the number of holes. Holes in a n-type semiconductor are referred to as <em>minority carriers</em>.</p>
<p>Carrier transport in semiconductors takes place by drift and diffusion. The hole drift current can be ignored (We shall make the reasonable assumption that the injected minority concentration is very small compared with the doping level.</p>
<p>The statement that the minority concentration is much smaller than the
majority concentration is called the low-level injection condition. Since the
drift current is proportional to the concentration and
we shall neglect the hole drift current but not the electron
drift current and shall assume that $i_p$ is due entirely to diffusion. This
assumption can be justified (see e.g. <em>Electronic Principles</em>, Paul E. Gray & Campbell L. Searle, John Wiley & Sons 1969, or Millman's <em>Electronic Devices</em>). The diffusion current density is proportional to the gradient in minority carrier concentration (in this case the holes) and diffusion coefficient,</p>
<p>$$j_p = -qD_p\frac{\partial p}{\partial x}$$
by Fick's law.</p>
<p><strong>I wish to determine the time it takes for this system to reach steady state.</strong></p>
<p><em>Steady state</em> is the state at which the parameters (e.g current density and carrier concentration) at a particular position $x$ do not change with time. The continuity equation related to carrier current and generation and recombination rate is</p>
<p>$$\frac{\partial p}{\partial t} = -\frac{1}{q}\frac{\partial j_p}{\partial x} + G,$$</p>
<p>where $\tau_p$ is the mean life time, from the definition of mean life time and assuming that $\tau_p$ is independent of the magnitude of the hole concentration, $p_0$ is the value of $p$ in thermal-equilibrium value, $ g = p_0/\tau_p$ is the generation rate, $p/\tau_p$ is the recombination rate, and $G$ is the sum of generation rate and recombination rate.</p>
<p>Substituting the first equation and the value of $G$ into the second gives</p>
<p>$$\frac{\partial p}{\partial t} = D_p\frac{\partial^2 p}{\partial x^2} + \frac{p_0 - p}{\tau_p}.$$</p>
<p>In the steady state $p$ doesn't vary with time but vary w.r.t position and the concentration at $x=0$ will remain constant all the time hence we can put $$\frac{\partial p}{\partial t}=0;$$</p>
<p>hence when steady state is achieved we will have</p>
<p>$$\frac{\mathrm d^2 p}{\mathrm d x^2} = \frac{p - p_0}{D\tau_p}.$$</p>
<p>How much time will it take for the minority carrier concentration to reach this steady state value?</p>
| 3,690 |
<p>I have a table of the characters of a set of wavefunctions for different points in reciprocal space and for different band indices (this is for a solid). For the case of a single irreducible representation, it is clear from the physical meaning of a 1D group that a character of 1 means operating with the symmetry operation (i) maps the wavefunction to itself and a character of -1 maps it to its inverse. So far so good. What I am more puzzled by is when a symmetry analysis gives rise to a direct sum of different irreducible representations.</p>
<p>In a given material, for the k Gamma point, I find the following character table:</p>
<pre><code> The point group is D3d
12 symmetry operations in 6 classes
Table 55 on page 58 in Koster et al [7]
Table 42.4 on page 371 in Altmann et al [8]
E 2C3 3C2 I 2IC3 3IC2
G1+ A1g 1 1 1 1 1 1
G2+ A2g 1 1 -1 1 1 -1
G3+ Eg 2 -1 0 2 -1 0
G1- A1u 1 1 1 -1 -1 -1
G2- A2u 1 1 -1 -1 -1 1
G3- Eu 2 -1 0 -2 1 0
--------------------------------------------
G4+ E1/2g 2 1 0 2 1 0
G5+ 1E3/2g 1 -1 i 1 -1 i
G6+ 2E3/2g 1 -1 -i 1 -1 -i
G4- E1/2u 2 1 0 -2 -1 0
G5- 1E3/2u 1 -1 i -1 1 -i
G6- 2E3/2u 1 -1 -i -1 1 i
</code></pre>
<p>For most bands, I find a simple relationship. Take for instance the characters of the first band:</p>
<pre><code> bnd ndg eigval E 2C3 3C2 I 2IC3 3IC2
1 2 -7.239676 2.00+0.00i 1.00+0.00i 0.00-0.00i 2.00+0.00i 1.00-0.00i 0.00-0.00i =G4+
</code></pre>
<p>e.g. as the character is that from a single irrep. and has value 2 (it is a two dimensional group), the parity must be even (+1).</p>
<p>What I am confused about is the situation when there is more than one irrep.</p>
<pre><code> bnd ndg eigval E 2C3 3C2 I 2IC3 3IC2
63 4 -1.880979 4.00-0.00i -4.00+0.00i 0.00-0.00i 0.00-0.00i -0.00+0.00i -0.00+0.00i =G5+ + G6+ + G5- + G6-
</code></pre>
<p>This implies that the character of the wavefunction for the 63rd band which is 4-fold degenerate is zero. What sort of conclusion can I make about the parity of the wavefunction using this information.</p>
<p>Thanks.</p>
| 3,691 |
<p>Why is application of probability in QM fundamentally different than
application of probability in other areas?</p>
<p><a href="http://en.wikipedia.org/wiki/Quantum_mechanics" rel="nofollow">Quantum mechanics</a> applies probability according to the same <a href="http://en.wikipedia.org/wiki/Probability_axioms" rel="nofollow">probability theory</a> that other areas of physics, engineering, etc. apply probability.</p>
<p>Why is there a difference?</p>
<p>"Naively" one would assume these cases:</p>
<ol>
<li><p>Either it is <strong>not</strong> the same probability (theory?)</p></li>
<li><p>Or it is a matter of interpretation (of the formalism?)</p></li>
<li><p>Something else?</p></li>
</ol>
<p>Thankx</p>
<p>UPDATE:</p>
<p>Many answers (which i still study) focus on the fact that the combined probability of 2 (assumed independent) events in QM is <strong>not</strong> equal to the sum of the probabilities of each event (sth that holds classicaly by definition). This fact (appears to) makes the formulation of another probability (a quantum one) a necessity. </p>
<p>Yet this again breaks down to <em>assumed independent</em>, if this is not so, the "classic probability" is applicable (as indeed in other areas).</p>
<p>This is one of the main points of the question.</p>
<p>UPDATE2: See comments on accepted answer.</p>
| 3,692 |
<p>How can I convert </p>
<p>$$ W m^{-2} sr^{-1} nmm^{-1} $$</p>
<p>to </p>
<p>$$ W m^{-2} nm^{-1} $$</p>
<p>I have the following matlab code to illustrate the spectral energy distribution of solar radiation:</p>
<pre><code>h = 6.626e-34; % Planck's Constant = 4.135 x 10^-15 eV s
c = 3e8; % speed of light (MKS)
T= 6000; % kelvin
k = 1.38066e-23; % Boltzmann constant in J/K
lamda = 0:20e-9:3200e-9;
p = 2*3.14*h*c*c./(lamda.^5);
b6000 = p./(exp(h*c./(lamda*k*T)-1));
lamda = lamda.*1000000;
plot(lamda,b6000,'.');
title('Planck Radiation Law');
xlabel('Wavelength [\mu{m}]')
ylabel('Irradiance [W m^{-2} sr^{-1} nmm^{-1}]');
xlim([0 3.2]);
</code></pre>
<p>This is my result:</p>
<p><img src="http://i.stack.imgur.com/J0fE0.png" alt="enter image description here"></p>
<p>How would I change my yaxis to be the same as the example shown?</p>
<p>but I need the yaxis to be in units of </p>
<p>$$ W m^{-2} nm^{-1} $$</p>
<p>so that the curve looks like </p>
<p><img src="http://i.stack.imgur.com/Gj4Gb.png" alt="enter image description here"></p>
<p>From the plot, it seems that dividing the irradiance by 10.^14 would do the trick, is this correct? Could someone explain the unit conversion, for a non-physicist? </p>
<p>This function is taken from here</p>
<p><a href="http://web.mit.edu/8.13/matlab/Examples/planck.m" rel="nofollow">http://web.mit.edu/8.13/matlab/Examples/planck.m</a></p>
<p>Updated version:</p>
<p>From all of the advice given here, this is the updated and hopefully correct methods:</p>
<pre><code>h = 6.626e-34; % Planck's Constant
c = 3e8; % speed of light
T = 6000; % absolute temperature
k = 1.38066e-23; % Boltzmann constant in J/K
lambda = 0:20e-9:3200e-9; % wavelength
% spectral radiance
p = 2*h*c*c./(lambda.^5);
b6000 = p./(exp(h*c./(lambda*k*T))-1);
b6000 = (1e-9).*b6000;
% multiply by the square of the ratio of the solar radius of earth's
% orbital radius
b6000 = b6000.*(2.177e-5);
% apply Lambert's cosine law
b6000 = b6000.*pi;
% convert units for lambda
lambda = lambda.*1e6;
% print result
fh = figure(1);
plot(lambda,b6000)
xlabel('Wavelength [\mu{m}]');
ylabel('Irradiance [W m^{-2} nm^{-1}]');
</code></pre>
<p><img src="http://i.stack.imgur.com/K7rMa.png" alt="enter image description here"></p>
| 3,693 |
<p>I was learning about circular motion when this question struck me:</p>
<p>In real life situations we are able to take a turn along a circular arc with our bike because friction provides us the necessary centripetal force for doing so. When we talk about cars, the road is banked which provides the centripetal force. But what if a biker wants to take a turn on an unbanked, frictionless road? Would he be able to turn? I think if he bends, then the normal reaction offered by the ground can possibly provide the centripetal force, but while bending, he will slip, and so this possibility might not be correct. I'm confused, and want a satisfactory answer to this question. </p>
| 3,694 |
<p>Recently, I happened to hear about the possibility of doing <a href="http://en.wikipedia.org/wiki/Analytic_continuation" rel="nofollow">analytic continuation</a> <strong>numerically</strong>. That sounds attractive for the ubiquitous $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ procedure, via which we go from <a href="http://en.wikipedia.org/wiki/Green%27s_function_%28many-body_theory%29" rel="nofollow">Matsubara Green's functions</a> to retarded ones.</p>
<p>So my question is about any infomation on such numerical analytic continuation algorithms. How is it done? Or, at least, where can I find any detailed description of it? Thanks in advance!</p>
<p>To be more specific, in my problem, I can evaluate a Matsubara correlation function at a series of Bose Matsubara frequencies. I want to find a way to obtain the analytic continuation, i.e., correlation function in terms of real energy/frequency. Is there any widely accepted simple recipe for this?</p>
| 3,695 |
<p>To state the title question perhaps more precisely:</p>
<p>What is the largest photon energy $E_{\gamma}$ and the corresponding mass number $A$ and atomic number $Z$ of a suitable nucleus ${}^A_ZX$ (presumably in a ground state) such that the hypothetical reaction</p>
<p>$$ {}^A_ZX + \gamma \rightarrow {}^{(A - a)}_{(Z - z)}Y + \text{whatever remains (with combined charge} +z \text{)}$$</p>
<p>is "kinematically" forbidden for any values $1 \le a < A$ and $Z \ge z \ge Z + a - A$,<br>
while conforming to the standard model?</p>
<p><strong>Edit</strong><br>
Changed the question title (removed the parenthetical qualification "whether otherwise stable or not"): for any unstable nucleus the stated question and condition is not meaningful and not relevant. </p>
| 3,696 |
<p>In contrast to a "time-like" or "causal" structure connecting space-time together, Does quantum entanglement imply the existence of a "space-like" or "non-causal" structure holding space-time together as well.</p>
<p>A more general question; is there even any relevance to the <em>discussion</em> of the existence of a non-causal structure connecting space-time together? </p>
<p>The reason I ask is because it initially seems too assuming to suggest that causal structure is the only meaningful structure just because it's intuitive; Consider the fact that two space-like separated events are even allowed to exist in a definable space (space-time diagram). Is there nothing physical <em>in principle</em> between the two events which can be defined?</p>
| 3,697 |
<p>Since by introducing <em>one</em> <a href="http://en.wikipedia.org/wiki/Higgs_boson">Higgs Boson</a> we can give a mass to the leptons and gauge bosons of the weak interaction: </p>
<p>Why should we consider more than one Higgs (doublet) once we go beyond the standard model?</p>
| 3,698 |
<p>I'm interested in learning physics. I do realize that the subject is large and that it would be easier if I had a specific area of interest. However, I do not. I suppose I want to learn about the fundamentals of it all; the axioms that combine all physics fields. Or, in other words, a high school physics class. </p>
<p>Specifically, a book or series of videos would be helpful. I looked over MIT and unfortunately the material wasn't for me. I don't mean to be "picky" so I am not completely ruling out any resource just yet. </p>
<p>Thanks in advance. </p>
| 98 |
<p>I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this Riemannian metric, which people consider to be the object, which induced the minimal symmetry requirements of spacetime.</p>
<p>1) Regarding the relation between Riemannian geometry and the Hamiltonian formalism of classical mechanisc: Does a setting for Riemannian geometry always already imply that it's possible to cook up a symplectic structre in the cotangent bundle?</p>
<p>2) Are there some some more natural structures which physicists might be tempted to put on spacetime, which might then also be restricting regarding the (spacetime) symmetry structures? Is constructing quantum group symmetries (of non-commutative coordinate algebras, alla Connes?) just this?</p>
<p>3) I'm given a solution to a differential equation which can be thought of a resulting from a Lagrangian with a set of $n$ symmetries (e.g. $n=10$ for some spacetime models). Can this solution also be the result of a Lagrangian with fewer symmetries? Here, I'm basically asking to what extend I can reconstruct the symmetries from a solution or specific sets of the soltuon. It's kind of the inverse problem of the question "are there hidden/broken symmetries?".</p>
| 3,699 |
<p>I have only just finished High school physics so my understanding is still fairly simple but I'm having trouble with this question.</p>
<p>Imagine you are in space traveling at a relativistic speed with a laser/light source. When you fire the laser do you see a straight line?</p>
<p>If you do, then when the light leaves the laser, what makes it continue to have the same velocity as you? If you sent out a pulse and aimed it exactly at a target on a side, then would it miss the target by continuing to travel in the same direction as you?</p>
<p>From a stationary observer looking down they would see a laser moving (lets say to the left) and at the instant it fires the laser is pointing in a straight line but the light will move off in a diagonal, moving to the left at the same speed as the laser.</p>
<p>If that laser stopped when it is fired then it would essentially look to be firing a laser beam diagonally!</p>
| 3,700 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/25254/why-does-the-moon-sometimes-appear-giant-and-a-orange-red-color-near-the-horizon">Why does the moon sometimes appear giant and a orange red color near the horizon?</a> </p>
</blockquote>
<p>Why does the moon look bigger at horizon or skyline than at other times e.g. at moonrise and moonset. This effect can also be observed with the sun. And I think the difference between the distance at horizon and other time is not too much to be the cause of this effect. So what is the reason behind this?</p>
| 106 |
<p>I am trying to study the canonical formulation of Yang-Mills theories so that I have direct access to the $n$-particle of the theory (<em>i.e.</em> the Hilbert Space). To that end, I am following Kugo and Ojima's (1978) 3-part paper.</p>
<p>At the outset, I am confused by their Lagrangian, and their two differences from the conventional one (I write the Lagrangian 2.3 of their paper):</p>
<p>$$\mathcal{L}=-\frac{1}{4}F^a_{\mu\nu}F^{a\,\mu\nu}-i\partial^\mu\bar{c}D_\mu^{ab}c^b-\partial^\mu B^a A_\mu^a+\alpha_0 B^a B^a/2$$</p>
<ol>
<li>They have rescaled the Ghost field so that its kinetic term has a factor of $i$ in front. </li>
<li>They have integrated by parts on $B^a\partial_\mu A^{a\,\mu}$, effectively making $B$ dynamical.</li>
</ol>
<p>The authors chose these two differences are so that (1) BRS variations (eq 2.15 in their paper) preserve Hermiticity of the Ghost fields, and (2) to make the Lagrangian BRS invariant.</p>
<p>I am totally confused by their second point. I thought the standard BRS Lagrangian appearing in standard texts, for example, in Peskin and Schroeder was already BRS invariant. Why the $\partial B.A$ term?</p>
| 3,701 |
<p>As temperature rise the density become lower,When temperature goes down, density is higher but in higher temperature the body become bigger so why density become lower?</p>
| 3,702 |
<p>I have two atoms, both of which are either bosons or fermions, with four allowed energy states: $E_1 = 0$, $E_2 = E$, $E_3 = 2E$, with degeneracies 1, 1, 2 respectively.</p>
<p>What's the difference between the partition functions of a pair of two bosons and that of a pair of two fermions?</p>
| 3,703 |
<p>How are decays related to forces, what is meant by particle X decays through the, say, strong force? </p>
<p>The way I understand forces is by how they change the acceleration of particles with the right charge (mass, electric etc), through F=ma, how does it cause one particle to turn into other? </p>
<p>How is it determined which force is responsible for which decays? </p>
<p>Can a particle decay through the gravitational interaction?</p>
| 3,704 |
<p>I have a theoretical question that has been bugging me and my peers for weeks now - and we have yet to settle on a concrete answer.</p>
<p>Imagine two balloons, one is filled with air, one with concrete. They are both the same size (and hence have the same air resistance). On the moon, we are taught at school that they would drop at the same rate, however on earth, they obviously don't - with the concrete falling faster. </p>
<p>Our reasoning was as follows:
Air resistance is not a factor in this example, therefore the only other variable is the mass (density) of the two balloons. </p>
<p>If you were to change the medium from earth's atmospheric air to water, the air ballon floats as it is less dense than water (and therefore displaces more water than its mass), and consequently has an upwards buoyancy force acting on it. The concrete sinks for the same reasons. </p>
<p>Therefore in the medium of air, there is also, albeit somewhat reduced, bouyancy effect acting on the balloons - explaining why the concrete balloon falls faster. </p>
<p>Could someone please tell me if my logic is correct, and if not explaing to us what other forces are playing their part.</p>
<p>Thank you so much for clearing this up! </p>
| 3,705 |
<p>So I am piecing together a school project on the numerous misconceptions of the universe, which I plan to "provide proof against them" with information from various sources (one of the main ones will be <em>A Brief History of Time</em> by Stephen Hawking). In coming up with the myths, I am sure that I will miss some that are very important. So, what are the most mind blowing things that you have come across that have completely changed your thoughts on the universe?</p>
<p>The main one for me is proving that the universe is finite, by the conjecture that the night sky would be extremely bright, as one would eventually encounter a star on the way to the infinite edge of the universe.</p>
<p>What else is there?</p>
<p>(note that I have a basic(ish) understanding of QM, but I do not really want to take the project in such a way)</p>
| 3,706 |
<p>Why the lowest order of matrices in Dirac equation (Relativistic Quantums) are 4x4 matrices (and can not be 2x2 matrices)?</p>
<p>How to prove it?</p>
| 3,707 |
<p>A white light, as we all know, is composed of seven lights VIBGYOR. Each of the component lights has distinct frequency ranging from one value to another. So, when the photons have wavelength of 600 nm it becomes a yellow light and when it changes to 700 nm it becomes a red light. So, does this imply that the frequency with which a group of photons vibrate determine the colour of light? Well, in that case, with what frequencies are photons vibrating for a white light?</p>
| 3,708 |
<p>One of my professors told us this semester, that the 'infinities' that arise in QFT are partly due to the use of the $\delta$-distribution in the commutator relations which read (for fermions)</p>
<p>$\left\{\Psi(r'), \Psi^\dagger(r)\right\} = \delta(r-r')$</p>
<p>In reality we would not have such a $\delta$-distribution but an extended version of it.</p>
<p>Is this view correct? And if definitely yes, is my following view wrong?</p>
<p>As far as I understand it, the $\delta$-distribution is due to the fact that we deal with point particles. If e.g. the electron was an extended particle, then the $\delta$-distribution would be 'finite'.</p>
<p>Since <a href="http://cerncourier.com/cws/article/cern/29724">experiments</a> pin down the extension of a particle to $R < 10^{-18}m$ it is also likely that the $\delta$-distribution should really be there.</p>
| 3,709 |
<p>Some people speculate that the mysterious dark matter in the universe could be tiny black holes. But on the other side, could dark matter particles attract each other by gravity and finally form a black hole? Since dark matter is even more abundant than normal matter, the dark matter black hole should not be rare.</p>
| 961 |
<p>A shopper pushes a 7.5-kg shopping cart up a 13 (degree)incline. Find the magnitude of the horizontal force, F, needed to give the cart an acceleration of 1.41 m/s$^2$.</p>
<p>I ask this because the solution to this problem is $7.5[1.41 + 9.81\sin(13)] = 27.1$, which describes the component of the force along the direction of the ramp. </p>
<p>However, the question explicitly states to find the magnitude of the "horizontal" force, which sounds to me a lot like its asking for the entire magnitude of the force, not just a component of it. The answer in that case would be, $\sqrt{27.1^2 + 7.5\cdot9.81\cos(13)} = 76.7$, would it not? Yet, this answer is not the one shown in the solutions. </p>
| 3,710 |
<p><em>Edit: I know there have been some similar questions but I don't think any had quite articulated my particular confusion.</em></p>
<p>If gauge symmetries are really just redundancies in our description accounting for nonphysical degrees of freedom, then how does one explain the deep and powerful fact that if one begins with, say, just fermions and no gauge field in one's theory (no interactions & no dynamics), but then imposes that the theory be invariant under local U(1) transformations, then one finds a vector field <em>must</em> be introduced? </p>
<p>Note that I did not have any vector field in my theory before I demanded invariance under gauge symmetry. If one thinks of the vector field as being in the theory to begin with then I can see how one could see the imposition of local symmetry as a necessary constraint to remove extra degrees of freedom - you've got an A_mu, that thing's got 4 degrees of freedom and it should only have 2. But if I imagine that I knew nothing about photons or the electromagnetic field, and I require my theory of fermions to have this U(1) symmetry, then the vector potential arises as the mechanism for enforcing that symmetry. Beginning with no interactions, axiomatically or arbitrarily requiring gauge symmetry has the power to produce not only gauge fields in the theory, but the correct number of them and with the correct self-interactions (or lack of them). </p>
<p>I suppose one could say that SU(3) just happens to work because there just happen to be 8 gluons, similarly for SU(2) and U(1), but doesn't that seem awfully random and clunky (or... unnatural)? Doesn't it seem much more natural and coherent to say that there are 8 gluons precisely because there are 8 generators of SU(3), and so on? If I begin my theory without the gauge fields then it seems to me to make no sense to say that the shockingly powerful principle of requiring gauge invariance only accounts for a redundancy in a field that I have not even put in my theory yet and might not want to.</p>
<p><em>I cannot get away with imposing gauge invariance without introducing exactly the kind of forces and interactions that we observe and that appear in the SM.</em> That statement seems way too powerful for a mere redundancy in our description. Again, maybe it's true that if you go about it from the other direction, ie, requiring one photon and three weak gauge bosons, etc., then you are forced to introduce the right gauge symmetry to account for the redundancies. But that seems much more ad-hoc to me - you have a lot of random things that happen to be true and a lot of coincidences that happen to work out - whereas if you think about the requirement of gauge symmetry as giving rise to these connections that tell you how to move around in your bundle, that sort of communicate the local transformation from one place to another, then you are only making one ad-hoc postulate, and it is a concise and elegant one with a ridiculous amount of explanatory power. It also seems weird to call the very thing that defines a theory only a dumb redundancy in the theory. </p>
<p>So, where am I wrong in all this? Is this an untenable view in the context of gauge theory (neglecting ideas that are being researched that may or may not pan out)? Or is this a viable view to take, even if one you dislike it? I know very little about spinor-helicity methods but I gather they may have something to say about this. Does their success eliminate the possibility of my interpretation?</p>
| 3,711 |
<p>I am having difficulty finding a good explanation of how potential difference and deformation of a piezoelectric relate. Is there a fixed axis along which the piezoelectric crystal will respond to voltage potential / form a voltage potential when compressed? Is the action of a piezoelectric even compression/expansion, or is it something odd like sheering, curving, etc. What about piezoelectric polymers? I can find no good answers to any of these questions, and I feel that the reason may be that the answer is complicated. So, here is a breakdown of my question.</p>
<p>I want to know if there are different kinds of piezoelectrics with different behaviors or if they all respond to potentials and mechanical stresses in a similar way.</p>
<p>I want to know how to very roughly model mechanical deformation under an applied voltage and the inverse, developed potential under mechanical stress. I don't particularly care about magnitudes, but I do care about orientations and directions.</p>
<p>I am particularly interested in a thorough explanation of Rochelle salt.</p>
| 3,712 |
<p>I am looking at <a href="http://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution" rel="nofollow">Wikipedia's article on deriving the Schwarzschild solution</a>. In the section "Simplifying the components", it says,</p>
<blockquote>
<p>On the hypersurfaces of constant $t$ and constant $r$, it is required that the metric be that of a 2-sphere:</p>
<p>$$dl^2=r^2(d\theta^2+\sin^2\theta d\phi^2)$$</p>
</blockquote>
<p>My question is why does the metric have to be this particular 2-sphere with a coefficient of $r^2$? We are not necessarily dealing with Euclidean space here.</p>
| 3,713 |
<p>Do the apperance in the atomic nucleus of virtual matter-antimatter particle pairs play a role in the random nature of radioactive decay?</p>
| 3,714 |
<p>Is it right that all units in physics can be defined in terms of only mass, length and time?</p>
<p>Why is it so? Is there some principle that explains it or is it just observational fact?</p>
| 3,715 |
<p>Reaching the ground state of a large 2D classical spin model (e.g. classical Heisenberg model) might be a relatively difficult task while using conventional "flip/reject" Monte Carlo method. The system may be easily trapped in a local minima instead of the global minima, for example, the spin domains might appear while you are trying to get a pure ground state.</p>
<p>As far as know there are some techniques can help solve this issue includes "simulated annealing" and "parallel temperature", I would like to know if there are some other techniques might be helpful?</p>
<p>Secondly, many people use Langevin dynamics as an alternative to Monte Carlo method, but I have not tried it yet, I would like to know if the dynamics method has the same "local minima" issue as well?</p>
<p>Any comments and suggestions will be very welcome.</p>
| 3,716 |
<p>Recently i found out this <a href="http://news.stanford.edu/news/2010/august/sun-082310.html" rel="nofollow">uber strange article</a> about nuclear decay rates being somehow showing seasonal variations with a high correlation with sun activity. Two very precise questions:</p>
<p>1) <strong>has this been experimentally confirmed/disproved?</strong> an experiment using neutrinos from a fission reactor would be awesome, although probably a couple orders of magnitude below the required luminosity (at least to be comparable with solar sources)</p>
<p>2) <strong>could the standard model possibly allow neutrinos to modulate decay rates in this way? or do we need new physics?</strong></p>
<p>link to the <a href="http://arxiv.org/abs/1007.0924" rel="nofollow">public version of the paper</a></p>
<p><strong>EDIT</strong> brief explanation why i tag this question as <code>cavity-qed</code>; because <em>it is the only other known mechanism we are aware that you can use to shift decay rates of energy levels</em>, it might be interesting to see if there are deeper relationships between both mechanisms involved</p>
<p><strong>EDIT 27/01/2013</strong> Another paper about this, but now the SuperKamiokande data is compared with data from Brookhaven: <a href="http://arxiv.org/abs/1301.3754" rel="nofollow">http://arxiv.org/abs/1301.3754</a> They also propose a model of the effect called neutrino "resonant spin-flavor precesion", and i'll be damned if i knew what that is.</p>
| 3,717 |
<p>What kind of object is <a href="http://en.wikipedia.org/wiki/656_Beagle" rel="nofollow">656 Beagle</a> (<a href="http://comets.universetoday.com/l/3668/656-Beagle-1908-BU" rel="nofollow">1908BU</a>)?</p>
<p>I know it's a minor planet, but that includes a large array of different stuff. Specifically, I am looking at the general chemistry/geology of the object.</p>
| 3,718 |
<p>I'll keep it simple. How does inflation drive Ω close to 1?</p>
| 3,719 |
<p>These questions are in reference to this beautiful review article by Minahan -
<a href="http://arxiv.org/pdf/1012.3983v2" rel="nofollow">http://arxiv.org/pdf/1012.3983v2</a></p>
<p>I gained a lot by reading some of its sections but not everything is clear to me.
I would like to ask a few questions to clarify some of the things in it. </p>
<ul>
<li><p>On page 5 between equation 3.7 and 3.8 it says that the R-charge representation of the $S$ are "reversed" compared to that of the $Q$. What does it exactly mean ? </p></li>
<li><p>There it does not explicitly specify the commutation relationship between $M_{\mu \nu}$ and $S^a_\alpha$ and $\bar{S}_{\dot{\alpha}a}$. Should I assume that its similar to that with $Q_{\alpha a}$ and $\bar{Q}^a_\dot{\alpha}$ ? Like if I may think - </p></li>
</ul>
<p>$[M^{\mu \nu},S^a_\alpha] = i \gamma ^{\mu \nu}_{\alpha \beta} \epsilon ^{\beta \gamma} S^a_{\gamma }$</p>
<p>$[M^{\mu \nu},\bar{S}_{\dot{\alpha} a} ] = i \gamma ^{\mu \nu}_{\dot{\alpha} \dot{\beta}} \epsilon ^{\dot{\beta} \dot{\gamma}} \bar{S}_{\dot{\gamma} a}$</p>
<p>?</p>
<ul>
<li><p>Comparing equation 3.12 to 3.9 I see some possible discrepancies. Is there a factor of $\frac{1}{2}$ missing with the term containing $D$ on the RHS of equation 3.12 ? In the same RHS of equation 3.12 in the $M_{\mu \nu}$ term why has the $\gamma ^{\mu \nu}$ of equation 3.9 become $\sigma ^{\mu \nu}$ ? </p></li>
<li><p>In the statement just below equation 3.14 it says "Hence a primary operator with R-charges $(J_1,0,0)$ is annihilated by $Q_{\alpha 1}$ and $Q_{\alpha 2}$ if $\Delta = J_1$"...Is this a consistency statement? </p></li>
</ul>
<p>From this how does it follow that thesame operator is also annihilated by $\bar{Q}^3_{\dot{\alpha}}$ and $\bar{Q}^4_{\dot{\alpha}}$</p>
<p>In the same strain can one also say that $\Delta = -J_1$ is consistent with the primary operator being annihilated by $Q^3_\alpha$ and $Q^4 _ \alpha$ ? </p>
<ul>
<li><p>I guess the above conclusions follow from taking different values of $a$ and $b$ in the equation 3.13. But one would get an extra factor of $\frac{1}{2}$ on the RHS of 3.13 if one puts in the factor of $\frac{1}{2}$ with the term containing $D$ on the RHS of equation 3.12 (..as I think it should be ..)</p></li>
<li><p>On page 8 one creates bispinors $F_{+\alpha \beta}$ and $F_{-\dot{\alpha} \dot{\beta}}$ out of $F_{\mu \nu}$. I would like to know what is the intuition/motivation/reason for doing this ?</p></li>
</ul>
<p>Is the bispinor version of $F$ still have the meaning of a field strength ? If so then how does it relate to the bispinor version (?) $D_{\alpha \dot{\beta}}$ of the covariant derivative ? </p>
<p>I think I have already put in too many questions for one question. May be I will ask some more about this review in a separate question. </p>
| 3,720 |
<p>Can someone compare the energy efficiency of human brain as a computer ? What is the energy in joules / flop ? may be some reasonable assumptions on the computational load of common tasks such as pattern recognition or speech synthesis can be used.</p>
| 3,721 |
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