question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
|
|---|---|
<p>I'm trying to set up the problem of deriving the thermodynamics of hadronic matter. I know how to proceed in the case of an effective description such as mean field (<a href="http://arxiv.org/abs/nucl-th/9701058" rel="nofollow">Walecka/linear sigma model</a>) but I'm trying to start from QCD. I do not wish to actually obtain the partition function, but I want to at least set up the complete problem.</p>
<p>In the mean field approximation, we usually write baryon and meson fields and baryon/meson couplings as the interactions, meaning that we also bypass the problem of describing the hadrons as QCD bound states. On the extreme oposite, I know how to proceed in the case of pure quark matter (it's just the "QCD Lagrangian").</p>
<p>How do I write the full Lagrangian? How do I represent the hadrons and the hadron-hadron strong (well, and EM) interaction without shifting to an effective approximation? Can it be done with quarks and gluons as the basic degrees of freedom?</p>
<p>I don't have any compromise with the "practical usefulness" of the result and I'm not particularly interested on the peculiarities of the dynamics of the bound states.</p>
| 2,813 |
<blockquote>
<p><strong>Question:</strong>
A police boat is chasing a boat with criminals along a straight river
by moving against the stream. The speed of the river stream is 3 miles
per hour, the speed of the boat with criminals relative to the river
is 30 miles per hour, and the police boat is 4 miles per hour faster
than the boat with criminals. </p>
<p>Currently the criminals are ahead of the police, and horizontally
throw a stone at the police boat at a speed 16 miles per hour relative
to their boat (i.e. relative to the boat of criminals).</p>
<p>What is the horizontal velocity of the stone relative to the police
boat and to the river bank? You need to state what the origin and the
positive direction of motion are.</p>
</blockquote>
<p>Choose the direction of the river stream to be the positive direction and choose the origin to be in front of criminals' boat.</p>
<p>Denote the velocity of the river stream by $\dot{x}_R$
Denote the velocity of the police boat by $\dot{x}_P$
Denote the velocity of the criminal boat by $\dot{x}_C$.
Denote the velocity of the stone thrown by $\dot{x}_S$.</p>
<p>From the question we have that $\dot{x}_R = 3$, and we also have that the velocity of the criminal boat relative to the river stream is
\begin{align*}
\dot{x}_C - \dot{x}_R &= -30 \\
\implies \dot{x}_C - 3 &= -30 \\
\implies \dot{x}_C &= -27
\end{align*}
Note that the minus 30 is because from the point of view of the river, the criminal boat is travelling in the negative direction.</p>
<p>Now from $\dot{x}_C$ I can calculate $\dot{x}_P$, since
\begin{align*}
\dot{x}_P &= \dot{x}_C + (-4) \\
&= -27 - 4 \\
&= -31
\end{align*}</p>
<p>Note that the minus 4 is because the police boat is 4 mph faster, but in the negative direction.</p>
<p>Also from $\dot{x}_C$ I can calculate $\dot{x}_S$. From the question we have that
\begin{align*}
\dot{x}_S - \dot{x}_C &= 16 \\
\implies \dot{x}_S - (-27) &= 16 \\
\implies \dot{x}_S &= -11
\end{align*}</p>
<p>I was wondering if my solution was right, even though $\dot{x}_S = -11$ is negative, even though it moves in the positive direction.</p>
| 2,814 |
<p>If I have a long solenoid, e.g. length $l$ and radius $r$ with $l = kr$, where k >> 1, with a nonpermeable (e.g. air) core, how much of the magnetic energy is stored outside as compared to inside?</p>
<p>If I go by the Wikipedia article on <a href="http://en.wikipedia.org/wiki/Solenoid" rel="nofollow">solenoids</a>, $B = \frac{\mu Ni}{l} \to H = \frac{Ni}{l}$ inside the coil, so the energy density should be $\frac{1}{2}\mu H^2$, and therefore the total energy inside the coil is $\frac{\mu N^2i^2}{2l^2}l\pi r^2 = \frac{\mu N^2 i^2}{2l}\pi r^2$.</p>
<p>The inductance is supposed to be $L = \frac{\mu N^2 A}{l} = \frac{\mu N^2 \pi r^2}{l}$, and if you compute energy $\frac{1}{2} Li^2$ you get $\frac{\mu N^2 i^2 \pi r^2}{2l}$ which is the same answer as the energy inside the coil calculated above, which relies on approximations, so we can't subtract these and figure out the energy stored outside.</p>
<p>Are there practical rules of thumb?</p>
| 2,815 |
<p>suppose there is a scale able to measure weight with an uncertainty of $10^{-9}kg$ . On the scale, an airtight plastic chamber is placed. Initially, a fly of mass $10^{-5}kg$ is sitting at the bottom of the chamber, which sits on the scale. At a later point in time the fly is flying around the chamber. Will there be a difference in the observed weight as measured by the scale when the fly is sitting at the bottom of the chamber compared to when it is flying around the chamber at some point in time? If so, what does the value of this difference depend on (I am most concerned with the case where the fly has not touched any surface of the container in enough time for the scale to reach some equilibrium value (or do the pressure variations induced from the flies wings cause constant fluctuations in the scale)?</p>
| 792 |
<p>I believe in Neutron Scattering the neutrons after hitting a nucleus can bounce in any of 360*3 dimensions -> 1080 degrees?</p>
<p>Why is this so? Shouldn't it only bounce "off" the neutron in approximately the same "direction" that it came in such as when a particle bounces off a mirror -> because of the cross-section ...</p>
| 2,816 |
<p>I would like to ask what are the experimental evidences that led to the conclusion that QCD is the right theory to describe strong interactions. I know that some of the key point are the decay of $\pi_{0}$ and the measurement of Jets but I'd love to see a full answer to this question. Is there a still a chance to <a href="http://en.wikipedia.org/wiki/Regge_theory">Regge theory</a> nowadays?</p>
| 2,817 |
<p>I have been wondering recently how useful programming is to a physicist. It seems fairly useful (simulations are a lot cheaper than the actual thing in many cases) in some areas (say space programs), but in other areas (for example at CERN) it seems pointless. So is it useful and perhaps how do you use it?</p>
| 2,818 |
<p>For me, the gradient of a scalar field (say, in three dimensions) is simply (formally)</p>
<p>$\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y},\frac{\partial f}{\partial z} \right)$.</p>
<p>In which way do we need a metric?</p>
<p>But some people did tell me only on a Riemann manifold (with a metric) can we define the gradient. </p>
| 2,819 |
<blockquote>
<p>The ball of mass $m$ is given a speed of $v_a = \sqrt{3gr}$ at position $A$. When it reaches $B$, the cord hits the small peg $P$ after which the ball describes a smaller circular path. Determine the position $x$ of $P$ so that the ball will be able to reach point $C$.</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/58MPI.png" alt="enter image description here"></p>
<p><strong>My Work</strong></p>
<p>Let $T$ represent kinetic energy and $V$ potential energy. Let $O$ be the datum for gravitational potential energy.</p>
<p>$T_1 + V_1 = T_2 + V_2$</p>
<p>$1/2m(3gr) - mgr = mg(r-x)$</p>
<p>$3/2r - r = r-x$</p>
<p>$x = r-3/2r + r$</p>
<p>$x = 1/2r$</p>
<p>However the correct answer is $x = 2/3r$. What's my mistake? Thanks a lot.</p>
| 2,820 |
<p>Maybe this is a silly question, but why does, say, a gasoline-powered AC generator have to use more gas depending on the load?</p>
<p>Let's say I have a 120VAC generator and either a 1A or a 10A load, and assume it can handle 1200W without issue. For 10A, the generator uses more gas and works harder compared to 1A. </p>
<p>Is this because the 10A is passively causing a magnetic field that makes the generator shaft physically more difficult to spin? If so, why does the magnetic field oppose the generators movement if the current is flowing in the direction the generator is trying to make it go to begin with? (Sorry, I know that is probably silly but I have a very limited understanding of electricity and magnetism.)</p>
<p>Or is it because the circuitry in the generator is actively sensing voltage drop due to higher load, and increasing the throttle to maintain a constant output voltage? Sort of like I'd imagine a water pump would have to work harder to maintain a constant pressure in a system with a leak in it or with flow. (Related: If so, is this type of sensing <em>necessary</em> for a generator to limit the voltage to low loads, or is it just a bonus feature to increase efficiency by not running at full throttle all the time?)</p>
<p>Or is it some combination of both? Or are both of those somehow the same thing? (It seems like it must be a little bit of the former; because the generator stalls under too high loads, which I guess means something is resisting the spin - unless the generator just actively shuts itself down?)</p>
<p>What is the process from "higher load" => "higher fuel usage"? </p>
| 2,821 |
<p>Law of equipartition predicts the heat capacity of gases correctly. It assumes that inter-molecular attraction in gases is negligible (which is true). But for solids, inter-molecular attraction is not negligible, the, how come it still predicts the correct value for molar heat capacity?</p>
<p>How can we ignore the potential energy due to inter-molecular attraction in solids?</p>
<p>Each oscillator has two degree of freedom (kinetic and potential). Solid has oscillators in all the 3 dimension. So, total degree for freedom will be $6$. Using equipartition, the internal energy of one mole a solid will be $ U = 6 \times \frac{1}{2}RT = 3RT$. </p>
<p>Heat capacity, $C = \dfrac{dQ}{dT} = \dfrac{dU + PdV}{dT} = \dfrac{dU}{dT}$ $(\because V \text{ is constant})$</p>
<p>$\implies C = \dfrac{d}{dT}[3RT] = 3R \approx 25 J mol^{-1} K^{-1}$</p>
<p>Which is a very close approximation of the <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/tables/sphtt.html" rel="nofollow">actual values</a>.</p>
<p>My question is why is this prediction in agreement with experimentally determined values, when we have ignored the potential energy due to inter-molecular attraction. Which is not negligible for solids? </p>
| 2,822 |
<p>As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper <a href="http://arxiv.org/abs/1107.5563" rel="nofollow">http://arxiv.org/abs/1107.5563</a>. I was wondering if there is some special relation involving the Ricci Curvature in 5d's relationship to one in 4d. Since with a general metric like the one given in 2.1, calculating the Christoffel symbols would seem to be an enormous and not particularly smart idea.</p>
| 2,823 |
<p>I am doing a (mostly qualitative) course on Particle Physics, and am confused about the concept of <a href="http://en.wikipedia.org/wiki/Asymptotic_freedom" rel="nofollow">asymptotic freedom</a>. The lecture notes basically say that a quark may experience no force/be "unbound" temporarily as a result of a collision. (due to properties of the strong force) Is there all there is to it?</p>
<p>Later, it mentioned that asymptotic freedom is important in electron-positron annihilation into hadrons. Were there no asymptotic freedom, the cross section of the process would be different. I can't see how this follows on from what was said above.</p>
<p>So I am seeking an qualitative explanation of this concept, and perhaps something about its consequences as well.</p>
| 2,824 |
<p>I'm trying to find the potential energy of multiple geometric shapes made entirely out of point charges.
This particular shape is a cube made out of two different point charges, A and B, each separated by a constant distance.</p>
<p>I'm not entirely sure how to go about this problem but I'm pretty sure that the equations V=Ed and E=kQ/r^2. I'm pretty sure you just add up the charges but I have no idea how to do this in a cube form..</p>
| 2,825 |
<p>I understand that the electromagnetic spectrum is made up of different frequencies of light waves, but is this true in all cases such as with longer wave frequencies? "such as with microwaves". sometimes I get the impression that with microwave ovens for example use waves of electrons, so my question is, is there some kind of threshold where somewhere between infrared to microwaves does the frequency makes the conversion from light to electrons? (and if so, how?) or is it always light and has some other correlation such as light influencing the electrons thru the air? </p>
| 2,826 |
<p>If I understand correctly, lightning is the discharge of electricity from the atmosphere into the planet. However, if I switch on a lamp, the wires are not causing thunder (or any audible sound).</p>
<p>I've also heard that the thunder comes from lightning breaking the sound barrier. This sounds weird to me since I would assume that lightning would be traveling at, well, light speed, so I'm not sure how the threshold could be crossed.</p>
<p>How does lightning cause thunder?</p>
| 2,827 |
<p>The problem of the infinite resistor grid is very common. The solution for the resistance between any 2 nodes in an infinite resistor lattice is all over the internet.</p>
<p>My question is somewhat similar but more pragmatic.
If we had a grid that was very large but yet finite... Then what would be the average voltage drop across a given grid for a given current density?</p>
<p>For arguments sake, a grid in the region of say 4000 by 4000. Maybe it would be safe to assume an infinite grid(?)</p>
<p>Very interesting Q. Can anyone shed any light?</p>
| 2,828 |
<p>Question:
A bungee jumper jumps from a bridge. The length of the loose rope is 30 m. When the jumper reach the lowest point possible, the rope stretches 10 m. What is the final stretch of the rope, when the oscillation of the rope stops? Mechanical energy loss is null. Hook law applies for the elastic.</p>
<p>I think this problem is unsolvable, because we need mass or the coefficient of the rope?</p>
| 2,829 |
<p>A system might have internal energy and/or kinetic energy. Kinetic energy in classical mechanics is a form of energy the object has, only because of its relative movement to other objects. </p>
<p>If you have a system like an oscillator, then you have a system where the amount of internal energy (energy of the spring, say) and the kinetic energy oscillate periodically. The amount of energy that is flowing from "internal energy" to "kinetic energy" and back therefore also meassures how this system is different from a system with might have the same amount of energy in total, but all its energy only stored in form of internal energy. </p>
<p>Is there a reasonable meassure of this difference, that is the ''energy-form flow''? </p>
<p>Maybe such a meassure might also be related to the entropy, because if there is kinetic energy around, I expect the entropy to be higher than otherwise.</p>
<p>Then I was thinking mabye that something like $\frac{dE_{kin}}{dt}$ might therefore be relevant. But the only quantity which directly puts energy and time together is the action. However, I'm not sure if the action has an illustative meaning, which goes beyond its definition, anyway.</p>
| 2,830 |
<p>so one uses equations of motion to describe liquids (e.g. Navier–Stokes equations). These are equations for $\vec{v}(\vec{r},t)$ with boundary conditions on the surface $S$ of the liquid (e.g. $\vec{v}(\vec{r}\in S,t) = \vec{0}$).</p>
<p>How should one incorporate surface tension $\sigma$ in these equations/boundary conditions? It seems, only boundary conditions must change, and $\Delta p = \sigma (1/R_1 + 1/R_2)$ is the first thing that comes to mind, but how to get $1/R$ from $\vec{v}(\vec{r},t)$?</p>
| 2,831 |
<p>It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi \exp\left(\frac{iq\chi}{\hbar}\right)\end{cases}$$
The Schrodinger equation $$\left[-\frac{\hbar^2}{2m}\left(\nabla-\frac{iq\vec A}{\hbar}\right)^2+q\phi \right]\psi=i\hbar\frac{\partial}{\partial t}\psi$$
gives back the same equation.</p>
<p>How does it follow that the probability current is gauge invariant?</p>
| 2,832 |
<p>Quantum fields are presented as operator-valued <em>distributions</em>, so that the <em>operators</em> in the theory are linear functionals of some test function space. This works well for free fields, giving us a particular form for VEVs, in which the 2-point connected correlation function determines the whole theory, and a trivial S-matrix.</p>
<p>For interacting fields, however, the VEVs and the statistics of S-matrix observables that are predicted by the theory depend not only on the test functions (generally given for the S-matrix in terms of pure, improper wave-number modes of the free field at $t=\pm\infty$) but also on the "energy scale of measurements". One obtains a different functional form at different energy scales.</p>
<p>The energy scales at which one is measuring are already encoded in the wave-numbers associated with the test functions, so it seems that the test functions play extra duty, to determine the functional form of the VEVs (at least in their S-matrix form) both by linearly smearing the quantum field and, more indirectly, by determining the renormalization scale. As a consequence, the VEVs, the Wightman functions, seem clearly to be nonlinear functionals of the test functions for interacting QFTs.</p>
<p>I've worried at this for a while. The argument as put brings into question the Wightman axioms' insistence that a quantum field must be a linear map from the test function space to the space of operators, although I suppose the effect would be only logarithmic in some measure of the frequencies of the test functions. The Haag-Kastler additivity axiom also seems problematic. I'm not aware of weakening this particular aspect of the Wightman or Haag-Kastler axioms so as to be able to construct models of the axioms that parallel empirically successful QFT having been discussed in the literature, but have they?</p>
<p>[Note that dropping the linearity of the map from test functions to operators in the algebra of observables does not affect the linearity of the algebra. There's still a perfectly good probability interpretation of a state over a *-algebra and a perfectly good Hilbert space, but the relationship of measurements to space-time is somewhat modified.]</p>
<p>EDIT: I'll <em>attempt</em> to make the Question slightly more accessible. It turns out that what follows makes it significantly longer. The Wightman functions (effectively a different name for Vacuum Expectation Values (VEVs)) allow the reconstruction of a Wightman (quantum) field. That is, given the vacuum state over the algebra one can construct the Wightman functions, $$W(x_1,x_2,...x_n)=\left<0\right|\hat\phi(x_1)\hat\phi(x_2)...\hat\phi(x_n)\left|0\right>,$$ but also, given the Wightman functions one can construct the algebra. Wightman functions satisfy somewhat arcane relationships, so that just any function $VV(x_1,x_2,...,x_n)$ is almost certainly not a Wightman function and cannot be used to reconstruct a Wightman field.</p>
<p>The object $\hat\phi(x)$ is not an operator in the algebra of observables, it is an <em>operator-valued distribution</em>, so that if we have a well-behaved "test function" $f(x)$, where "well-behaved" most often means that it is smooth (infinitely differentiable) and has a smooth fourier transform, then $\hat\phi_f=\int\hat\phi(x)f(x)\mathrm{d}^4x$ <em>is</em> an operator. This is often called "smearing" with the test function $f(x)$. The test function $f(x)$ effectively tells us what relative amplification we apply to the field at each point in space-time for a given measurement, and its fourier transform $\tilde f(k)$ tells us what relative amplification we apply to the field at each point in momentum space. In signal analysis the same object is called a "window function", which can be looked up on Wikipedia. One can talk about the bandwidth of a measurement, or say that a signal transformation is high-pass or low-pass. If it were not for non-commutativity of measurement operators at time-like separation, quantum field theory would be <em>exactly</em> what one would want for a mathematical formalism for modeling stochastic signal processing. If one only talks about measurements that are space-like separated —admittedly a tight constraint—, QFT <em>is</em> a stochastic signal processing formalism.</p>
<p>In contrast to $\hat\phi(x)$, $\hat\phi_f$ is not a singular mathematical object; the difference is comparable to the difference between a smooth function and the Dirac delta function. In terms of these operators, the Wightman functions become $$W(f_1,f_2,...,f_n)=\left<0\right|\hat\phi_{f_1}\hat\phi_{f_2}...\hat\phi_{f_n}\left|0\right>,$$
which is linear in all the test functions.
When we move to the practical formalisms of interacting QFT, however, the VEVs predicted by the bare theory are infinite. Renormalization fixes that in a Lorentz invariant way, but it leaves the VEVs a function of the energy scale $\mu$ of the measurements that are involved in an experiment. Thus, one finds that the Wightman functions are now a function of $\mu$ as well as of the points $x_i$, $W_\mu(x_1,x_2,...x_n)$, or, in terms of operators, $W_\mu(f_1,f_2,...f_n)$. [It's perhaps worth noting that we don't know whether these $W_\mu(...)$ satisfy the relationships required for them to be Wightman functions, so that we could reconstruct a Wightman field, but I've never seen a discussion of perturbative QFT conducted in such terms.] The Wightman functions in terms of positions do not encode energy scales, but they are <em>not</em> observables, they are only a template for constructing observables. The fourier transforms of the test functions, $\tilde f_i(k)$, however, already determine various energy scales at which the measurements made in an experiment operate, potentially in <em>much</em> more detail than a single number $\mu$. We could just say that the energy scale of measurements $\mu$ is separate from the energy scales determined by the test functions $f_i$, but it seems more natural <em>to me</em> to say that $\mu$ is a functional of the test functions $f_i$, in which case we can write $W'(f_1,f_2,...f_n)=W_\mu(f_1,f_2,...f_n)$, where $W'$ is now a non-linear functional of the $f_i$. I suppose we expect $W'$ to be a symmetric function of each of the $f_i$.</p>
<p>For a more-or-less trivial example, suppose we have two ordinary quantized Klein-Gordon fields $\hat\phi_f$ and $\hat\xi_f$, not necessarily having the same mass spectrum, then we could construct a quantum field $\hat\Phi_f=\hat\phi_f+\hat\xi_{f+\epsilon f^2}$ (where the square $f^2$ is $[f^2](x)=[f(x)]^2$, so that $\hat\Phi_f$ satisfies microcausality), so that $\hat\Phi:\mathcal{S}\rightarrow\mathcal{A};\hat\Phi:f\mapsto\hat\Phi_f$ is a nonlinear map from the test function space into the algebra of observables. This is still a Gaussian field, so not interacting. Already there start to be significant complications. One of the most fundamental Wightman axioms is the restriction to positive spectrum, which in terms of test functions is a projection to forward light-cone components of the test functions. Only components of $\tilde f(k)$ for which $k_\alpha$ is in the forward light-cone have any effect on measurement results. In the above, however, forward light-cone components of $f^2(x)$ contribute, which in fourier space, where $f^2(x)$ is a convolution, means that negative frequency components of $f(x)$ will contribute. Although this means that this kind of nonlinearity apparently does not satisfy positivity of the energy, it's not clear that this means such a system is not <strong><em>stable</em></strong>, which is the (non-axiomatic) reason why we insist on positivity of the energy as an axiom. Which, whoops, brings into question positivity of the energy, one of the <em>big</em> axioms, which I asked about <a href="http://physics.stackexchange.com/q/5812/2451">here</a>.</p>
<p>Now, of course, I'm trying out doing research here as if it was a virtual blackboard. Many of the ideas above ought to be rubbed out, different ideas tried and equally or more vigorously discarded. I've got lots of pieces of paper that have discarded ideas on them that you don't want to see, because I hope you have your own discarded ideas, as anyone who doesn't get too fixed in their ways should, most of which I probably don't want to see (not that I'm not a little fixed in my ways, but I've discarded <em>some</em> ideas). The trouble is that I can't see how we can go forward from me just typing away, I think the feedback loop may be too long for this to work. Still, the alternative is to write a paper and get feedback six months later. This introduces Questions that I may try to put on meta.</p>
<p>By the way, making a Question Favorite counts for no Reps, but it's much appreciated. </p>
| 2,833 |
<p>Source:
<a href="http://www.engineeringtoolbox.com/sound-power-intensity-pressure-d_57.html" rel="nofollow">http://www.engineeringtoolbox.com/sound-power-intensity-pressure-d_57.html</a></p>
<p>Both sound intesity and pressure level are measured in dB. Given a specific sound, are these two dB values the same?</p>
| 2,834 |
<p>I read that </p>
<p>$(FF(f))(x)=2\pi f(-x)$, where $F$ is the Fourier transform</p>
<p><em>and</em> $F(f(x-a))(k)=\exp(-ika) X(k)$ where $X(k)=F(f(x))$</p>
<p><em>implies</em> $F(\exp(iax)f(x))(k)=X(k-a)$.</p>
<p>But I don't see how that is done... I am quite happy with getting $F^{-1}X(k-a)=\exp(iax)f(x)$ by brute force calculation. I would like to see how to use duality though.</p>
| 2,835 |
<p>Suppose you a have an ordinary Luttinger liquid with<br>
$$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). $$</p>
<p>You then bosonize it using
$$\psi_{\eta,\sigma}=\frac{1}{\sqrt{2 \pi \alpha}} F_{\eta ,\sigma} e^{-i \phi_{\eta, \sigma}}$$
where F is the Klein factor and $\phi$ a bosonic field.</p>
<p>My question is, what happens to F and $\phi$ under time reversal? </p>
<p>The problem here is that the usual result for fermions,
$$T c_{i,\uparrow} T^{-1}= c_{i,\downarrow}$$
$$T c_{i,\downarrow} T^{-1}=- c_{i,\uparrow}$$</p>
<p>where T is the time reversal operator,
is not so obvious when there is separation between the Klein factor and the phase.
I mean, why would $\phi_\uparrow$ turn into $\phi_\downarrow$ ?</p>
| 2,836 |
<p>How can it be shown that the Dirac spinor is the direct sum of a right handed Weyl spinor and a left handed Weyl spinor?</p>
<p>EDIT:- Let $\psi_L$ and $\psi_R$ be 2 component left-handed and right-handed Weyl spinors. Their transformation properties are known. When I put these two spinors in a column and construct a four-component column which is a direct sum of $\psi_L$ and $\psi_R$ i.e., $\psi_D=\psi_L\oplus\psi_R$. This I <strong>define</strong> to be the dirac spinor. Right? Since it is a direct sum under Lorentz transformation, the corresponding Lorentz transformation matrix is diagonal. Right? Then it is easy to show that, it satisfies the Dirac equation in Chiral basis. Right? This is possible because we started from the definition of left-handed and right handed weyl spinors and their transformation properties are known. Right? This is explicitly carried out in the book by Lewis Ryder. But suppose I start the other way around. I solve the dirac equation in chiral basis. Then no one tells me that the upper two components are really left-handed and lower two are really right-handed. Suppose I take this chiral basis solution of dirac equation and now take that to be my <strong>definition</strong> of dirac spinor. Then how can I show the opposite, that it is made up of two irreps of Lorentz group i.e., $\psi_D=\psi_L\oplus\psi_R$ ? </p>
| 2,837 |
<p>For two particles, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) \rangle = \langle
a(t_1) a^\dagger (t_2)\rangle \theta (t_1-t_2) + \xi \langle a^\dagger (t_2)a(t_1) \rangle \theta (t_2-t_1)$ with $\xi$ is a plus sign for bosons and a minus sign for fermions.</p>
<p>How would I write, for example, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) a(t_3) a^\dagger (t_4) \rangle$ ?</p>
| 2,838 |
<p>Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The observers don't know the exact color (state) of their balls, they know only the probability of having one or another color, until they look at them (measure). If the observer A looks at his ball he will see its color, which is white, so he immediately knows the color of the second ball. Lets call this “classical entanglement”.</p>
<p>My question is: What is the difference between this “classical entanglement” and the quantum entanglement, for example, of two entangled electrons with opposite spins states? Can this analogy be used to explain the quantum entanglement?</p>
| 2,839 |
<p>The time is treated differently in special relativity and quantum mechanics. What is the exact difference and why relativistic quantum mechanics (Dirac equation etc.) works?</p>
| 2,840 |
<p>Am I correct in assuming it is the weight of all that liquid + gravity?</p>
| 2,841 |
<p>By chance(playing around really) I saw that a spring(mainly from a pen) placed on a neodymium hard-disk magnet(and then flicked by your finger at the top) makes a nice-effect (see youtube video ). It appears to oscillate in slow-motion(looks like tornado).</p>
<p>Of course, "slow-motion" is purposely simplistic and unscientific - I am very far from a physicist. </p>
<p>Here's the video - <a href="http://www.youtube.com/watch?v=n0OJQ1iXZg0&feature=channel_video_title" rel="nofollow">http://www.youtube.com/watch?v=n0OJQ1iXZg0&feature=channel_video_title</a> </p>
<p>I was too impatient in the video though, I should have zoomed in on the spring and waited. Sorry about that.. </p>
<p>Here's a page about the magnets used:
<a href="http://www.reuk.co.uk/Hard-Disk-Drive-Magnets-For-Wind-Turbines.htm" rel="nofollow">http://www.reuk.co.uk/Hard-Disk-Drive-Magnets-For-Wind-Turbines.htm</a></p>
<p>Here are the polarities, plus a horizontal profile below:</p>
<p><img src="http://i.stack.imgur.com/7krCW.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/fPLEl.png" alt="enter image description here"></p>
<p>More details: You really want to use a retractable pen spring, the thin kind. And Hard-drive magnets are key - I think it doesn't work with others. I think it's partly because of the 4-poles of a neodymium magnet. i.e, it's actually two-magnets-in-one.
Cigarette lighters also have a long delicate magnet, which is good but too tipsy.<br>
LBNL, supposedly you can stack these magnets, but they seem impossible to separate from the backing-piece. I appreciate any tips or advice.</p>
| 2,842 |
<p>Will <a href="http://en.wikipedia.org/wiki/Timbre" rel="nofollow">timbre</a>/quality be different if two different people play the same guitar? Assume that frequency/pitch and amplitude are same.</p>
| 2,843 |
<blockquote>
<p>Four rods A, B, C, D of same length and material but of different
radii r, 2r , 3r and 4r respectively are held between two rigid
walls. The temperature of all rods is increased by same amount. If the
rods do not bend, then which of these are correct:</p>
<ol>
<li>The stress in the rods are in the ratio 1 : 2 : 3 : 4.</li>
<li>The force on the rod exerted by the wall are in the ratio 1 : 2 : 3 : 4.</li>
<li>The energy stored in the rods due to elasticity are in the ratio 1 : 2 : 3 : 4.</li>
<li>The strains produced in the rods are in the ratio 1 : 2 : 3 : 4.</li>
</ol>
</blockquote>
<p><em>Four rods A, B, C, D of same length and material</em> => Same Youngs Modulus, Same coefficient of linear expansion, Same Length.</p>
<p>Also, <em>The temperature of all rods is increased by same amount.</em> </p>
<p>Before answering the above question I've few other questions:</p>
<ol>
<li><p>Suppose rods were not held between two rigid walls. Then there would have been change in length. In that case, would there be stress? Intuitively it feels like stress would be zero, as there seems to be no restoring forces developed. But Stress = Youngs modulus * strain. Strain is definitely not zero. So, stress should not be zero. Confused!</p></li>
<li><p>No say, rods were held between two rigid walls. Assuming rods are not bending. There length will not change. So, strain would be zero. Stress = Youngs modulus * strain. So, Stress must be zero. But intuitively it seems there will be stress, because there will be restoring forces in the rod pushing walls away. Again confused!</p></li>
</ol>
<p>Now coming back to the original problem. The above two confusions are causing trouble. But just going by intuition. There will be stress developed even though there is no strain. But stress = Restoring Force/Area. Here areas for all rods are different pi*r^2, because r is different. But Restoring force is same. So, the ratio must be 1/1 : 1/4 : 1/9 : 1/16. Right?</p>
<p>Surprisingly answers are 3,4. There is lot of confusion. Kindly clarify</p>
| 2,844 |
<p>See this related question: <a href="http://physics.stackexchange.com/questions/118927/if-particles-are-excitations-what-are-their-fields">If particles are excitations what are their fields?</a></p>
<p>I ask this question because, according to a lecture, the higgs boson was frozen into a "matrix" at some point before recombination (otherwise we would not have atoms). Is this considered a field in the same way an electron field is a field? It was described that higgs was everywhere ... Is that another way of saying there is Higgs field?</p>
<p>This means the electron interacts with the higgs field and not with excitations of the higgs field? Or probably Higgs bosons are only excited momentarily. </p>
<p>Was the electron field also created like the higgs field at some point? </p>
<p>See here <a href="https://www.youtube.com/watch?v=hL2BLAOVbDA" rel="nofollow">https://www.youtube.com/watch?v=hL2BLAOVbDA</a></p>
| 2,845 |
<p>My home town (Iran, Lamerd) has very hot summer (always > 45+ degree) with dry weather and sharp sun shine. I used some black tubes under glassy box to heat up water. It was a natural thermal siphon and did not need pimping. definite volume of salty water in the container was connected to the tube glassy box. the empty space of the container was filled with hot humid. I have just connected this humid to a condenser. finally I had the distilled water but production rate was slow. Is that economically feasible to scale it up and be used for drinking water?<img src="http://i.stack.imgur.com/V0Qqz.jpg" alt="My home made apparatus"></p>
| 2,846 |
<p>When a polished piece of metal (or steel in particular) is heated to incandescence, how do its reflective properties change?</p>
<p>Given a mirror-like surface, would the object temporarily cease to act like a mirror at a certain temperature?
Would the specular reflection of light turn into diffuse reflection; in other words, would the surface temporarily become matte/dull?</p>
<p>I am not asking about permanent changes to the object such as melting, but rather can there be a temporary change in the reflectivity only while the the object is hot, that disappears when the object is cooled down?</p>
<p>Background of the question: I have a laser scanner that usually has trouble scanning shiny surfaces with high specular/ low diffuse reflectivity; and it seems to work a lot better for hot steel pieces than for cold ones. Glowing steel also <em>looks</em> less shiny to me than cold steel, but of course that is hard to tell with all the glowing </p>
| 2,847 |
<p>According to the definition of potential energy, we use $U= mhg .
$
In the figure below , </p>
<p><strong>A thin uniform rod of mass m and length h is positioned vertically above an anchored frictionless pivot point.</strong></p>
<p>Why does a author say that potential energy is $U =\dfrac{mgh}2$ why not $U =mgh$</p>
<p><img src="http://i.stack.imgur.com/DfGcJ.png" alt="enter image description here"></p>
<p>Similar problem I faced on a problem, when I had to find out the potential energy for lifting water from a hole with height h.</p>
<blockquote>
<p>So my problem is, when should I consider center of mass and when I should not?</p>
</blockquote>
| 2,848 |
<p>It is said that in Minkowski spacetime, the current conservation law for the number current $N^\mu$ where $N^0$ is the number density and $N^i, i=1,2,3$ is the particle flux in the $x^i $ direction, is given by </p>
<p>$$\partial_\mu N^\mu=0 ....................(*)$$</p>
<p>What I don't understand is he following.</p>
<p>I would have thought that $$\partial_t N^0=-\nabla\cdot \vec N$$ where $\vec N$ has components $N^i, i=1,2,3$.</p>
<p>But using the Minkowski metric, $(*)$ reads
$$\partial_t N^0=\nabla\cdot \vec N$$</p>
<p>Why is there not a minus sign on the RHS?</p>
<p>Thank you.</p>
| 2,849 |
<p>I'm investigating the velocity field induced by a continuous distribution of 2D vortex points distributed along an ellipse $\{a\cos\theta,b\sin\theta\}$. I'm interested in the field inside the ellipse, and I need some help to prove whether this field is zero or not.</p>
<p>The intensity of each vortex point is proportional to $d\theta$ and not to the length along the ellipse. A vortex point located at a point $\boldsymbol{x'}$ induces a velocity field $\boldsymbol{u}(\boldsymbol{x})=\frac{d\theta}{2\pi |\boldsymbol{x}-\boldsymbol{x'}|} \boldsymbol{e}_\perp$ where ${e}_\perp$ is the unitary vector orthogonal to $(\boldsymbol{x}-\boldsymbol{x'})$ which is in 2D: $\boldsymbol{e}_z\times(\boldsymbol{x}-\boldsymbol{x'})/|\boldsymbol{x}-\boldsymbol{x'}|$.
The total velocity field at a point $(x,y)$ inside the ellipse is obtained by integration over $\theta$. Numerical experiments seem to show that the field is zero inside the ellipse, but I cannot prove it. Dropping the factor $2\pi$, the field is in cartesian coordinates:</p>
<p>$$\boldsymbol{u}=\int_0^{2\pi} \left\{\frac{-y + b \sin\theta}{(x - a \cos\theta)^2 + (y -
b \sin\theta)^2}, \frac{x - a \cos\theta}{(x - a \cos\theta)^2 + (y -
b \sin\theta)^2}\right\} d\theta \stackrel{?}{=}\{0,0\}$$</p>
<p>Is the field really zero?</p>
<p>Maybe there is no need for the integrals to prove it. Maybe complex analysis is of help?
I should mention that the following property is true in this problem: For any closed contour inside the ellipse the circulation is zero:
$$\oint \boldsymbol{u}\cdot\boldsymbol{dl} =0$$</p>
<p>Since we are in a simply connected region, the velocity is the gradient of a potential which is single valued. But then is this potential constant?...</p>
<p>I'm able to prove that the velocity is zero on both the $x$ and the $y$ axis. Also $u_x$ is an even function of $x$ and an odd function of $y$. The opposite applies for $u_y$. I'm able to prove the result for a circle $a=b$.
Can somebody help me for the ellipse? Any idea?</p>
| 2,850 |
<p>Consider a "wavefunction" $\psi(x)$, which has a Fourier transform $\tilde \psi(p)$</p>
<p>Suppose that we know, for each $x$, $|\psi(x)|^2$, and that we know, for each $p$, $|\tilde \psi(p)|^2$.</p>
<p>Have we enough information to reconstruct the "wavefunction" $\psi(x)$, that is, obtain the phase of the "wavefunction" for all $x$ (up to a global phase, we are only interesting to the relative phases between the $x$)?</p>
| 2,851 |
<p>The PACER project is described in this question: <a href="http://physics.stackexchange.com/questions/21405/how-much-of-the-energy-from-1-megaton-h-bomb-explosion-could-we-capture-to-do-us">How much of the energy from 1 megaton H Bomb explosion could we capture to do useful work?</a></p>
<p>Why was it abandoned? It seems that it is the only readily economical and engineeringwise useful path to fusion power, and it seems that its breeder possibilities can easily let it pay for itself for generating fissile elements and helium (which is getting to be rare too nowadays!) </p>
<p>Was it political or technical limitations that killed it? Is there hope for a renewed interest in this in todays energy conscious politics?</p>
| 2,852 |
<p>The other day I was wondering: When a <a href="http://en.wikipedia.org/wiki/Tachyon" rel="nofollow">tachyon</a> is coming towards you faster than the speed of light, will you see it before it hits you? Then I thought of course not, since the light waves aren't traveling faster than the tachyon then how could you see it before it hits you? Now I thought today, if an tachyon is traveling away from you faster than the speed of light, would you see it?</p>
<p>If you fire a ball at an initial velocity of 20mph south out of a car that is going 50mph north, the final velocity of the ball would be 30mph north, is this also how light acts when the initial velocity of the object it is reflecting off is not equal to 0? </p>
<p>So in my case, if the speed of light were 100mph (dummy math) and a tachyon was traveling at 110mph north that means the light reflecting off the tachyon would be traveling at 10mph north, so then really would you be able to see it?
More generally, how does <a href="http://en.wikipedia.org/wiki/Velocity-addition_formula" rel="nofollow">relativistic addition of velocities</a> work for tachyons?</p>
<p>update:</p>
<p>This question is a hypothetical question: IF tachyons exist, then what would happen? After a few hours of research I see why a usual massive object CAN'T travel faster than (or even reach) the speed of light, but this question is about tachyons.</p>
| 2,853 |
<p>Given a parallel plate capacitor of width $w$, length $l$, with a dielectric moving along the length $l$. Let the dielectric be from $x$ onwards.</p>
<p>The capacitance will be $\frac{w \epsilon_0}{d} (\epsilon_r l - \chi_e x)$. Griffiths (p. 195) says that the total charge $Q$ in the $C=\frac{Q}{V}$ expression is constant as the dielectric moves. But $Q$ here refers to the free charge, and the free charge definitely increases as you move the dielectric in increasing $x$. What am I misunderstanding?</p>
| 2,854 |
<p>I was just wondering... I believe that if a car travelling 50 miles per hour crashes into a wall, the result should be the same as crashing to another car also travelling 50 miles per hour (but in the other direction of course)</p>
<p>Is this true? Why is that?</p>
| 58 |
<p>Let's say there is a fin that is 1mm thick, extends 8mm from the surface, and is 10 mm wide. The fin is exposed to a moving fluid. Can we assume the adiabatic tip condition and use the characteristic, "Corrected", length for calculations?</p>
| 2,855 |
<p>Can you trigger a thermonuclear explosion from a smaller thermonuclear explosion in a scaling way, so that starting from a small laser ignited fusion within a small fissile container, using the X-rays from the first explosion to implode a tiny adjacent Li-d wire, which is then used to implode a bigger wire, and so on to a big explosion after a few cycles? Or does the Teller-Ulam design not scale to miniature explosions?</p>
<p>If there is a russian-doll design, can you then trigger the first explosion using a free-electron x-ray laser available today? Any other laser trigger? I am asking because from the answer to this question: <a href="http://physics.stackexchange.com/questions/21405/how-much-of-the-energy-from-1-megaton-h-bomb-explosion-could-we-capture-to-do-us">How much of the energy from 1 megaton H Bomb explosion could we capture to do useful work?</a> , the PACER power-plant design presumably relies on a fission triggered bombs, and fission resources are limited and non-renewable. Further, the PACER folks suggested that future thermonuclear explosions can be laser-triggered, and this was the only way I could think of doing this. Is this really possible?</p>
<p>(I should add that it would also help with regards to proliferation and terrorism safety if the trigger was an expensive bulky free electron laser, as opposed to a standalone explosive nuclear bomb.)</p>
| 2,856 |
<p>One method of introducing electric field is based on the measurement of the force acting on moving charged particle. By equating F to qE we determine the electric field E if the electric charge q is known. Similarly, one can determine magnetic field. </p>
<p>This approach is fine for vacuum but it generally fails for fields in a medium, especially for dispersive medium since one needs first to distigush Lorentz force from other forces that act on a particle there, e.g., from friction force. Once I met the above cited description somewhere but I forgot where it was written. Could some one direct me to an approriate reference? I also cannot remember tha name of scientist who pointed out on the above cited difficulty in determining the field. Perhaps, it was Rosenfeld or something like that. And finally, is there a better definition of the electric / magnetic field in a medium?</p>
| 2,857 |
<p>Please help me with an answer to my dilemma:</p>
<p>Is there a liquid that could be used to fill an ice rink (non-explosive, non-poisonous, etc), and have the freezing point above 0 Celsius?</p>
| 2,858 |
<p>A recent paper, titled <a href="http://arxiv.org/abs/1302.2775">Inertia from an Asymmetric Casimir Effect</a>, discusses the universal horizons relative to an accelerating observer (Rindler space). A figure it used to demonstrate its point challenged a view I held.</p>
<p><img src="http://i.stack.imgur.com/BAWzq.png" alt="Figure 1"></p>
<p>I previously asked a question about Rindler space, <a href="http://physics.stackexchange.com/questions/10811/do-apparent-event-horizons-have-hawking-radiation">Do apparent event horizons have Hawking radiation?</a>. My take-away from the (very good) answers was that an the Rindler Horizon (in the above figure) emits Hawking radiation in the same way that a black hole or the cosmic horizon does. This is called Unruh radiation.</p>
<p>This leads me to the obvious question: Does the accelerating observer see the new Unruh radiation <strong>and</strong> the old cosmic horizon's radiation?</p>
<p>As you accelerate to the <em>right</em>, then you replace the cosmic horizon to you <em>left</em> with a new horizon, closer to you. Radiation thus appears out of nowhere, but does that mean that the existing radiation from the prior horizon disappears?</p>
<hr>
<p>EDITED, new material follows:</p>
<p>In my first version of this question I referenced <em>both</em> the CMB and cosmic horizon radiation. These are two different things, but I treated them as the same thing. The question was answered for the CMB - it remains just as the light from any galaxy would.</p>
<p>I've reformulated this so it can be about the Rindler Horizon's radiation versus radiation from the original cosmic horizon. To illustrate this, I made my own version of Figure 1 above, with more detail for the old versus new horizon. Here:</p>
<ul>
<li>Cosmic horizon - horizon according to an inertial observer </li>
<li>Cosmic horizon prime - horizon according to an accelerating observer with same position and velocity as the inertial one</li>
</ul>
<p><img src="http://i.stack.imgur.com/UJ1wg.png" alt="My Figure 1"></p>
<p>This corresponds to Figure 1, since his surface labeled "COSMIC HORIZON" is the rightmost part of the horizon that remains the same for the accelerating observer as well as the inertial observer. His "RINDLER HORIZON" on the left is only the new horizon, leaving out the old horizon, which I have included.</p>
<p>If we say that $O$ <em>just started</em> accelerating, then what do we expect? Logical possibilities include:</p>
<ul>
<li>Sees Hawking radiation from both horizons</li>
<li>Sees Hawking radiation from old horizon, which transforms into the characteristic of the new horizon over time</li>
<li>Instantly sees Hawking radiation from new horizon</li>
</ul>
<p>I'm also not sure if I've drawn the new horizon correctly. I would think that you couldn't "reveal" any galaxy beyond the cosmic horizon at the rightmost point, but to $O$, its dark-energy acceleration is less than to the inertial observer. Maybe I should have just moved the horizon to the right instead of shrinking it? I'm not sure, but I <em>think</em> the paper assumed no change in the cosmic horizon Hawking radiation from the right.</p>
| 2,859 |
<p>This is the known equation of air drag:</p>
<p>$$m{\bf a}=mg-\mathcal D=mg-b{\bf v}.$$</p>
<p>Considering this, is air drag equation in term of momentum still valid?</p>
<p>$$m{\bf v}=mv_g-b{\bf r}.$$</p>
| 2,860 |
<p>I have created a simulation of <strong>one</strong> electron bouncing through a 3D mesh of molecules. The electron hopping is determined by a calculation of electron transfer rate using the Marcus equation (a result in units of $1/s$). In order to force the electron to reach one end of this 3D mesh I have applied a driving energy $dE$ (negative) to <strong>each</strong> molecule.</p>
<p>I am familiar with the electric field equation but I do not see how it applies to one electron
bouncing through many molecules. How do I go about calculating the electric field that I applied?</p>
| 2,861 |
<p>I am interested in gravitational lensing caused by a cluster of galaxies (say it has a diameter of 1 Mpc and mass of $10^{12}$ solar masses). How close must a light travel as it passes by to be notably bent - if compared to a case where there would be much smaller object in a spot where is now a center of cluster, like one isolated galaxy?</p>
<p>I am trying to determine angle of deflection for a special case of gravitational potential and I have no feeling for the distances at which lens still has an effect on light.</p>
| 2,862 |
<p>I just started learning physics 3 days ago and am having trouble understanding what I am doing wrong. Can someone please explain my error(s)? Thanks!</p>
<p>We have a 1kg object on a plane at a 30 degree angle from horizontal. Force of friction is 1.5N. We are asked to calculate the net force. </p>
<p>I assume the object is moving along a line with negative slope (toward positive x and negative y quadrant). All vectors are as they would be interpreted in $\mathbb{R}^2$ Euclidean space. </p>
<p>I solved to get:</p>
<p>Force normal = [5.66, 9.8], I am assuming that the y component is 9.8N because otherwise the object would move vertically through the plane, right? I got to this assumption because I didn't understand how a vertical force, gravity, could cause motion at a non-vertical angle, so I assumed that the normal force must be pushing the object forward, rather than gravity pulling it forward.</p>
<ul>
<li>Force g = [0, -9.8]</li>
<li>Force friction = [-1.3, .75]</li>
</ul>
<p>adding to get</p>
<ul>
<li>Force net = [4.3, -.75]</li>
</ul>
<p>which is a 4.42N force acting at 30 degree angle.</p>
<p>The book I am using says the force should be 3.4N. The book rotates the the x,y axes by 30 degrees, I don't really like their way. I feel my main problem is not properly understanding the relationship between the normal force and gravity, and how it leads to motion at an angle.</p>
| 2,863 |
<p>In quantum mechanical systems which have classical counterparts, we can typically recover classical mechanics by letting $\hbar \rightarrow 0$. Is recovering Einstein's field equations (conceptually) that simple in string theory?</p>
| 59 |
<p>This is really a basic question whose answer I guess may have to do with the way we construct Feynman rules and diagrams. The question is: Suppose I have been given a two-point function (found in some other ways, say for example some gauge/gravity duality or some symmetry in the theory). How can we construct the Lagrangian of that theory from there?</p>
<p>Is there a general rule for that? Can you give me a reference?</p>
| 2,864 |
<p>Here's an example to describe the issue</p>
<p>Supossed a high power laser (eg a 100 kW laser, ie, electromagnetic weapons)
is fired to a target, then it will receive energy and move.
(and likely to burn or explode, but that's not the point)</p>
<p>My question is, statting that photons have no mass</p>
<p>Would the laser transmitter get a kickback/recoil like in a "normal" gun?</p>
| 2,865 |
<p>Suppose there's a radioactive material and a 1/2 quantum probability of detecting it by a Geiger counter. This puts the system in a superposition. Also suppose you are in the same room, and the walls of the room are perfectly decoherence-proof. You observe the Geiger counter and get a definite result. Either it had gone off, or it hadn't. The Copenhagen interpretation tells you the decay or nondecay only became real when it was measured, and the result reached you. Your friend is waiting outside the room. After a very long delay, you open the door, and he observes whether or not you had seen the Geiger counter go off.</p>
<p>He then has the nerve to tell you </p>
<blockquote>
<p>There is only one observer, and that's me, not you. You are nothing more than a dull bound state of electrons and protons. Before the door opened, you never had the property of knowing whether the Geiger counter went off. Only when the door opened did you acquire that property.</p>
</blockquote>
<p>Unnerving, but you reason, your friend is just like you. Both of you are humans and made up of a bound state of electrons and protons. What applies to you ought to apply to him and vice versa. Or are you special and inherently different from him?</p>
<p>You object that you remember very distinctly whether or not you heard the Geiger counter go off. He counters</p>
<blockquote>
<p>Your memory of having known whether or not the Geiger counter went off only came into being when the door opened. Just because you have that memory now does not mean it was real before the door opened. </p>
</blockquote>
<p>You object that applying the Copenhagen interpretation to yourself tells you you did have a definite knowledge before the door opened. He counters</p>
<blockquote>
<p>It's a meaningless question whether or not you knew the state of the Geiger counter before the door opened and I measured you because there is no way in principle for me to find out. There is no inconsistency here.</p>
</blockquote>
<p>Don't all observers have to agree? Both of you agree on your current memory of having had a definite state and that is observable.</p>
<p>Did you have a definite knowledge of the state of the Geiger counter before the door opened? Change the story a little. You haven't opened the door yet, but you know your friend is waiting outside. Do you have a definite knowledge now? You think you do, but does that make it so?</p>
<p>After some further reflection, you realize the present you is a different observer from your past selves. How definite was the past?</p>
| 2,866 |
<p>Let us consider Bloch wave function solutions for a particle confined to a 2D square lattice with a potential of the form
$V=V(x) + V(y)$
(that is, one that can be factorized).</p>
<p>In this case we can factorize the Hamiltonian to
$\hat{H} = \hat{H}_x + \hat{H}_y$
and the band spectrum structure (the energy dispersion for states) can be presented as
$E( \vec{q}) = E_x(q_x) + E_y(q_y)$. </p>
<p>One-dimensional dispersion spectrum has gaps between the bands for quasimomentum values of $q_{x} = n \frac{\pi}{a}$, here $n$ is integer. It means that the energy gaps between the bands are situated at the quasimomentum border values of $q_{x,y} = n \frac{\pi}{a}$.</p>
<p>Am I correct?
Is it a specific case of some general principle regarding the positions of band gaps I need to know about? What can be said about the band gap positions generally?</p>
| 2,867 |
<p>How many virtual gravitons do the sun and earth exchange in one year?<br>
What are their wavelengths?</p>
| 2,868 |
<p>A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. </p>
<ol>
<li>Is there a one to one correspondence between the potential and its spectrum? </li>
<li>If the answer to the previous question is yes, then given the spectrum, is there a systematic way to calculate the corresponding potential?</li>
</ol>
| 2,869 |
<p>A mass spring system is in equilibrium. If I pull on the load by $x$ meters, the energy stored in the spring is (this is what is given in my book):</p>
<p>$$E=\frac12kx^2 $$</p>
<p>However, doesn't the load lose gravitational potential energy as it moves down? Where would this energy go? By conservation law, shouldn't the energy equation be:
$$E_{stored}= \frac12kx^2 + mgx$$</p>
<p>In short, where does the loss of gravitational potential energy (mgx) of the load get transferred to if it is not stored in the spring?</p>
<p>(Referring to a vertical mass spring system)</p>
<p>The picture in my mind:
<img src="http://i.stack.imgur.com/OdVee.png" alt="enter image description here"></p>
| 2,870 |
<p>I was wondering what voltage or current, if any, would be produced if the basic magnet through a copper coil experiment had the poles rotated 90 degrees so north and south faced the top/bottom of the coil rather than the entry/exit points?</p>
<p>The attached image has a basic illustration of this.</p>
<p>Thanks</p>
<p><img src="http://i.stack.imgur.com/YUv75.jpg" alt="enter image description here"></p>
| 2,871 |
<p><img src="http://i.stack.imgur.com/crCx4.png" alt="enter image description here"></p>
<p>The spectrum of a filament has been given before, the left one having the lowest temperature, the middle with a medium temperature and the right one with the highest. My question is this: Why does the region of yellow light on the left have a small range of spectrum while the red and green ones both have a large range? </p>
<p>Also, why the temperature increasing results in the shrinking of red and green region and the expansion of yellow region? It seems strange that the continous wavelenth has different pattern.</p>
| 2,872 |
<p>I was thinking about an apparently simple question about quantum mechanics, if I am looking at a quantum system described by a Hilbert space $\cal{H}$ under what hypothesis can I define A and B as subsystems whose union gives the full former system and decompose $\cal{H} = \cal{H_A}\otimes \cal{H_B}$. The other way, it is evident, if I join two quantum systems, their state will evolve in the tensorial products of the two, and the states are factorizable if there is no quantum correlation. But starting with the first joined system, I am puzzled by the meaning of this decomposition.</p>
<p>Thank you. And sorry if that question is a no brainer, it's just not that evident to me. =)</p>
| 2,873 |
<p>What I mean is, the nuclear chain reactions take microseconds for every generation and that is the reason that nuclear weapons exist. Because in nuclear reactors the reaction rate is much slower thus it can be controlled and prevent it from exploding.
So my question here is about the speed of matter-antimatter reaction. Just imagine we have a kilogram of antimatter, is the annihilation speed enough to make it usable as a weapon ?</p>
| 2,874 |
<p>I apologize if I am missing something obvious, but I am in my first class with tensors and I am still learning the notation. I am running into a problem with the transformation of the transformation of the four-tensor for electromagnetism that is given by</p>
<p>$$
F^{\mu \nu} =
\left[
\matrix
{
0 & - \cal{E}_x/c & - \cal{E}_y /c & - \cal{E}_z /c \\
\cal{E}_x/c & 0 & -B_z & B_y \\
\cal{E}_y/c & B_z & 0 & -B_x \\
\cal{E}_z/c & -B_y & B_x & 0
}
\right]
$$</p>
<p>And the Lorentz transformation of this tensor is given by</p>
<p>$$
F^{' \mu \nu} = \sum\limits^3_{\alpha, \beta = 0}{\Lambda^\mu_\alpha \Lambda^\nu_\beta F^{\alpha \beta}}
$$</p>
<p>From what I understand, this is just a single sum and $\alpha = \beta$ over every iteration; however, by this $F^{00} = F^{11} = F^{22} = F^{33} = 0$, so the transformation of any element would result in a zero.</p>
<p>Where have I gone wrong here?</p>
| 2,875 |
<p>It's my understanding that Earth's core is hot and molten because of the high pressure from gravity compressing the planet's mass towards the center. How does this heat reconcile with thermodynamics, meaning, would it be possible for all the heat to bleed away into space through infrared radiation etc., such that the Earth eventually had about the same mass in about the same configuration, but was instead cold at the core? Or would it always be the case that as long as the planet holds together, it will be hot at the center due to gravity?</p>
<p>How are these two processes reconciled, meaning, why would there eventually be a "heat death" of the universe so long as there is gravity making masses come together into a form that causes local hot spots (or in larger cases, new suns)? Wouldn't the planet have to fly apart to get much colder, and why would it do that? Is it possible for the mass to stay together while all the energy dissipates (ie temperature eventually goes to zero K)?</p>
<p>[I'm not a physicist, so if I'm way off the rails, please help me understand what's really going on.]</p>
| 2,876 |
<p>I've studied something so I'm able to explain better what I'm thinking about.</p>
<p>'t Hooft duality states:</p>
<p>In a gauge theory with fields in the adjoint representation in presence of a mass gap only the following alternatives are allowed:</p>
<p>1 Magnetic condensation and electric confinement</p>
<p>2 Electric condensation and magnetic confinement.</p>
<p>I've also learnt that the object of electric nature are the ones that are affected by gauge transformation while the magnetic ones are not.
Moreover, but I'm not so sure of that, magnetic objects in an electric theory can be admitted only as singularities (such as Dirac delta) in analogy to the Meissner effect in which the magnetic field can penetrate a superconductor only via tiny tubes.</p>
<p>So I would appreciate if someone would give me a better insight of this characterization of electric and magnetic objects since they have been presented to me only as facts to accept.</p>
<p>Thank you in advance.</p>
<p>The previous, less clear, version of my question was:</p>
<p>Approaching the study of QCD, I've read about the 't Hooft duality that is similar to the Meissner effect for superconductors: magnetic condensation implies electric confinement and vice versa.
At first I'm not sure about what is magnetic and what is electric in QCD. Then I would appreciate if someone could give me a formal description of this phenomenon, cause I've only found this naive description.
Thanks.</p>
| 2,877 |
<p>There was a reason why I constantly failed physics at school and university, and that reason was, apart from the fact I was immensely lazy, that I mentally refused to "believe" more advanced stuff until I understand the fundamentals (which I, eventually, never did).</p>
<p>As such, one of the most fundamental things in physics that I still don't understand (a year after dropping out from the university) is <strong>the concept of <a href="http://en.wikipedia.org/wiki/Field_%28physics%29">field</a></strong>. No one cared to explain what a field <em>actually is</em>, they just used to throw in a bunch of formulas and everyone was content. The school textbook definition for a field (electromagnetic in this particular case, but they were similar), as I remember it, goes like:</p>
<blockquote>
<p>An electromagnetic field is a special kind of substance by which charged moving particles or physical bodies with a magnetic moment interact.</p>
</blockquote>
<p><em>A special kind of substance</em>, are they for real? This sounds like the authors themselves didn't quite understand what a field is so they decided to throw in a bunch of buzzwords to make it sounds right. I'm fine with the second half but <em>a special kind of substance</em> really bugs me, so I'd like to focus on that.</p>
<h3>Is a field <em>material</em>?</h3>
<p>Apparently, it isn't. It doesn't consist of particles like my laptop or even the light. </p>
<p>If it isn't material, <strong>is it <em>real</em> or is it just <em>a concept that helps to explain our observations</em></strong>? While this is prone to speculations, I think we can agree that in scope of this discussion particles actually do exist and laws of physics don't (the latter are nothing but human ideas so I suspect Universe doesn't "know" a thing about them, at least if we're talking raw matter and don't take it on metalevel where human knowledge, being a part of the Universe, makes the Universe contain laws of physics). Any laws are only a product of human thinking while the stars are likely to exist without us homo sapiens messing around. Or am I wrong here too? I hope you already see why I hate physics.</p>
<h3>Is a field <em>not material but still real</em>?</h3>
<p>Can something "not touchable" by definition be considered part of our Universe by physicians? I used to imagine that a "snapshot" of our Universe in time would contain information about each particle and its position, and this would've been enough to "de<a href="http://en.wikipedia.org/wiki/Serialization">seralize</a>" it but I guess my programmer metaphors are largely off the track. (Oh, and I know that the uncertainty principle makes such (de)serialization impossible — I only mean that I thought the Universe can be "defined" as the set of all material objects in it). Is such assumption false?</p>
<p>At this point, if fields indeed are <em>not</em> material but <em>are</em> part of the Universe, I don't really see how they are different from <a href="http://en.wikipedia.org/wiki/Hindu_deities">the whole Hindu pantheon</a> except for perhaps a more geeky flavor.</p>
<p>When I talked about this with the teacher who helped me to prepare for the exams (which I did pass, by the way, it was before I dropped out), she said to me that, if I wanted hardcore definitions,</p>
<blockquote>
<p>a field is a function that returns a value for a point in space.</p>
</blockquote>
<p>Now this finally makes a hell lot of sense to me but I still don't understand how mathematical functions can be a part of the Universe and shape the reality.</p>
<p>I'm afraid the question will seem ambiguous and get closed but I had a really hard time trying to shape my confusion into sentences, and I will highly appreciate if someone clears it up, suggests a link or confirms that there is no definitive answer to my question.</p>
| 558 |
<p>Assuming I rotate a disk, I want to know how long it takes to completely stop, and the number of revolutions it made since I removed my fingers off the disk.</p>
<p>Lets say a DVD I rotate with my fingers. I only know the radians per second (velocity) of the last moment I touched the disc.</p>
<p>Can you guys tell me where to start?</p>
<p>Im trying to implement this on an iPhone app. So it would be nice if you mention <strong>equations</strong>. It should not be exact. </p>
| 2,878 |
<p>I'm trying to understand a particular case of gauge theories, namely discrete spaces on which a group G can act transitively, with a gauge group H which is discrete as well.</p>
<p>From what I've already read about continuous and discrete gauge theory (I can provide the necessary references if needed*), it seems that the full gauge transformation group will be the semidirect product of G by H. However I'm unable to prove it...</p>
<p>Can someone point me to the proof of this fact ?</p>
<p>Any help greatly appreciated !</p>
<p>*Edit :
The bottom of page 2 in this reference describes this kind of thing without giving any proof : <a href="http://arxiv.org/pdf/1106.2759">http://arxiv.org/pdf/1106.2759</a></p>
| 2,879 |
<p>I am not exactly sure how the physics work here. If we take a car tow rope, which is manufactured for towing a 3500 kg car and we actually start towing such a car on this rope, what force do we really apply to the rope?</p>
<p>Could the same rope <strong>safely</strong> withhold an adult person (100 kg) hanging on it?</p>
| 2,880 |
<p>I'm thinking about a project to tackle, and I'd like to make a simulation that allows the user to define a rope or chain of length L, pin it at arbitrary points r1, r2.... etc. and draw the resulting curve in real time.</p>
<p>Also, I'd like the user to be able to alter the field that the rope exists in, for example more complex vector fields than just a straight gravitational field. This is a bonus, however, and I'd like to get the basic example working.</p>
<p>Could you recommend some resources, preferably free/online, for me to learn the physics involved (I'm not exactly sure what to CALL this area of classical mechanics)? I learn through concepts and then math so a resource that is concept-heavy would be nice. </p>
<p>Thanks! </p>
| 2,881 |
<p>I'm wondering if it would be possible to map out all the different types of molecules, atoms and nuclei and their energy levels on one page (even if in a generalised way)? But perhaps I'm referring to the periodic table here? Do representations differ according to whether one is looking at things from a Classical perspective or a Quantum perspective?</p>
<p>Apologies in advance for all the question marks! I'm generally interested in ways of visually conveying concepts- so would be curious to discover different approaches to the above.</p>
| 2,882 |
<p>I learned that as the earth rotates about its axis, the bodies on the earth also follow a circular path. In most books I read, they give the example of a person standing on a weight balance at the equator... and I did understand that. However, by doing the following calculation, I am seeing that the apparent weight at other points on the earth (apart from the poles) is the same</p>
<p>This is the picture on my mind:
<img src="http://i.stack.imgur.com/4C73k.png" alt="enter image description here"></p>
<p>At B,</p>
<p>$$W-N=m{\omega}^2 R$$</p>
<p>At A, a component of weight will provides the centripetal force to rotate around the circle with the radius $r$,
$$Wcos{\theta} - Ncos\theta =m{\omega}^2r $$
as $r=Rcos\theta$,
$$Wcos{\theta} - Ncos\theta =m{\omega}^2R\cos\theta$$</p>
<p>The equation eventually ends up as...
$$W - N =m{\omega}^2R $$</p>
<p>So from this, I think that the normal reaction force which is the apparent weight remains the same as to the apparent weight at the equator.</p>
<p>However the book states that the apparent weight varies along $A$ and $B$</p>
<p>Also, we assume that the earth is spherical.</p>
<p>I am really sorry for making the question so long. Could someone please tell me which part of my concept is wrong.</p>
| 2,883 |
<p>In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle. </p>
| 2,884 |
<p>If you stick a tissue to the bottom of a glass and immerse this glass fully (upside down) into a tumbler of water, then this tissue remains dry. Why is this so? / What conclusion would you draw from this?</p>
<p>a) Air occupies a definite volume.</p>
<p>b) Air has mass.</p>
<p>c) Both</p>
<p>Now, I think it should be both. Reason:</p>
<p>If air had a volume but zero mass (hypothetically speaking), then it will not exert any pressure, so therefore water would rise till it hits the tissue (pressure due to air is the reason water level is lower, right?)!</p>
<p>Also, we can say that if an object has zero mass, we can have 100 % compressibility for any definite volume.</p>
<p>Pls tell me if my approach is right? </p>
<p>PS: I am not in junior school, my sister is, and this is from her weekly test.</p>
| 2,885 |
<p>I'm trying to imagine in my head what happens to the universe in ten billion years, twenty billion years, etc. </p>
<p>I imagine that all mass in the universe turns to black holes, as when mass reaches the temperature of absolute zero, it automatically collapses the atoms, or is that true?</p>
<p>If all of the mass in the universe is black holes, it would still be in galaxies of black holes that used to have stars in them, around a central black hole, but some of those galaxies would have merged with each other, like how our nearest galaxy is moving towards us. </p>
<p>Over time, with all the mass in the universe existing as black holes, and all energy having gravity including dark energy, then the dark energy that fell into the black holes would be captured, and the black holes would get larger and larger. </p>
<p>If dark energy is not a constant, which seems unlikely to me, and if it changes over time, and it's density decreases, and it has no pushing effect on black holes, because they suck it in, then eventually all the energy and mass would be contained within the black holes. </p>
<p>I'm trying to understand why anyone thinks that black holes can evaporate when energy has gravity, based on the stress energy tensor of general relativity, and the escape velocity of a black hole is higher than the speed of light. </p>
<p>If a photon could pop out, wouldn't it be sucked straight back in again? There are two theories really, one says the universe will collapse, causing another big bang, and explaining why the big bang happened in the first place. </p>
<p>The other says that the universe keeps expanding until the black holes evaporate into photons which fly around forever, never causing a universe again, but this fails to explain why it ever happened in the first place. </p>
| 2,886 |
<p>If a detector is kept at the two slits the fringes disappear. But, when the detectors are removes do the fringes come up immediately without any significant time lag? </p>
<p>Can there be a way to switch on and off the detector so fast that it all happens within the time required for the light to reach the screen form the source? What would be the result if it is possible? </p>
| 2,887 |
<p>This question seems to have been asked a few times in different configurations, but none of them answer my variation. I've struggled to understand this for nearly 15 years and had conflicting answers from my school physics teachers and more recently friends who are physicists.</p>
<p>So a round leaves my gun barrel at $40$ m/s. Its initial Airspeed is $40$ m/s.</p>
<p>In another question they asked about firing down the length of a train traveling the same speed. I understand that firing toward the front of the train would result in a ground speed of $80$ m/s and an airspeed of $40$ m/s. Also, firing toward the back of the train results in a ground speed of $0$ m/s and an airspeed of $40$ m/s.</p>
<p>My question... if you were to walk to the back of the train, open the door and fire directly out the back, would you end up with a ground <strong>and</strong> airspeed of $0$ m/s? Meaning the projectile would literally just tumble in a straight trajectory down to the ground?</p>
<p>Plenty of people have thrown spanners into this one over the years - like talking about the way an explosive force will 'hang' in a certain space if not pushed, pushing the projectile away from itself as well as the firing pin of the gun, giving it extra forward momentum in that instance. (unlike firing from the front of the train would always equal $80$ m/s for air and ground. The explosion cannot be 'left behind'). I personally don't buy this one... But i don't know enough to judge.</p>
| 2,888 |
<p>So far I'm only tasting the quantum mechanics. Haven't gone very deep into the mathematics of it yet.</p>
<p>I read about the double slit experiment, and the weird consequences of it: if you put a detector at the slits you won't have an interference pattern. Since you basically absorbed and recorded the photon then you reemitted another one at that slit: now you have single probability wave emitted at that slit which won't interfere with the another one since it's not there: no interference pattern. At least this is my understanding so far.</p>
<p>Ok, now let's cheat: at the source you detect (absorb) and reemit the photon. You won't measure the reemitted photon again till it hits the detector. So it pass the slits in a fuzzy state and you should have an interference pattern at the detector then. Anyway the photon hits detector at a point somewhere, you record it. If you have atomic clocks you can have interval between the reemission and detection at the screen. Based on the location of the hit and the travel time measured, and knowing the light travels with $c$ the path length travelled can be estimated. From the path length you can deduce which slit it passed through.</p>
<p>Of course nature doesn't like cheaters: you cannot have "which slit" information and "interference pattern" (went through both slits) at the same time. So my thoughts:</p>
<ul>
<li><p>I think nature cannot prohibit to have a low rate photon source: you can put some lead screen in front of your radioactive gamma source, to reduce the rate. So you should be able to measure travel times occasionally when the next photon comes late enough.</p></li>
<li><p>Nature cannot mess with travel times too since from that would mean light would't go woth $c$ but slower or faster - the latter would have nasty consequences. </p></li>
<li><p>Another thing I can think of is that there will be enough uncertainty in detector response times or the reemitting apparatus so I cannot reliably measure the travel times. But this would mean that this uncertainty depends on the distance between the slits: the bigger the distance the bigger possible difference in travel times to a point on the detector through the slits. It's very hard to believe the the sole fact of changing the slit spacing can affect uncertainty of the detector response times...</p></li>
</ul>
<p><strong>So what do you think will happen?</strong> Do you know of experiment that tested this?</p>
| 2,889 |
<p>Question on Section 9.1.3 in "Conformal Field Theory" by Philippe Di Francesco et. al.</p>
<blockquote>
<p><em>The basic idea of the Coulomb-gas formalism is to place a background charge in the system, making the $U(1)$ symmetry anomalous. This has the effect of modifying the conformal dimensions of the vertex operators and the central charge[...]</em></p>
</blockquote>
<p>Could anyone tell me what does he mean by $U(1)$ symmetry? I didn't see any $U(1)$ symmetry here in the context...</p>
| 2,890 |
<p>$E = h\nu$ and $P = h\nu/c$ in vacuum.
If a photon enters water, it's frequency $\nu$ doesn't change.
What are its energy and momentum : $h\nu$ ? and $h\nu/c$ ?
Since part of it's energy and momentum have been transferred to water, it should be less.</p>
<p>If water's refractive index is $n$, Are the energy and momentum equal to $h\nu/n$ and $h\nu/c/n$ ? </p>
| 1,006 |
<p>consider the following:
<img src="http://i.stack.imgur.com/tpCcw.jpg" alt="enter image description here"></p>
<p>I need to find the minimal coeeficient of friction $\mu _{min}$ so that both recatngle boxes would remain static. The lower angle in the triangle is $2\alpha$ as indicated.
I ended up with this expression: $$\mu _{min}=\frac{m_2}{2\cdot m_1 \cdot \tan \alpha}$$
but the answer in the book is rather this one:
$$\frac{m_2}{(2m_1+m_2)\tan\alpha}$$
Who is correct?I know that the normal force that that the triangle is exerting on both is like this:
<img src="http://i.stack.imgur.com/qYGQr.jpg" alt="enter image description here">
(on both sides of course) so with geometry and soome FBD that's what I came out with.</p>
<p>Would like to hear your thoughts!</p>
| 2,891 |
<p>I have seen a lot of places talking about the Reynolds number and how it is calculated, but I have never seen an equation that actually made use of this number to calculate lift, drag, or other aerodynamic properties.</p>
<p>So, what is this number actually used for?</p>
| 2,892 |
<p>I just read that in the Gaussian Units of charge The Final equation in Coulomb's law is as simple as $$\boldsymbol{F}=\frac{q_1q_2}{r^2}$$</p>
<p>No $\epsilon_0$ no $4\pi$ like you have in the $\mbox{SI}$ units of measurement . </p>
<p>The permittivity constant was the factor in the $\mbox{SI}$ system of Coulombic Force that determined the intensity of force in a medium. </p>
<p>In the Gaussian system i see no such constant . So that would mean that some other factor would govern the Quantity of charge on a body.</p>
<p>What is that factor ?</p>
<p>(I vaguely remember it as being related to the speed of light $c_0$)</p>
| 2,893 |
<p>What was the proportion of dark matter/energy to other matters/energy at the moments after the beginning of the universe (standard Big Bang model)?</p>
| 2,894 |
<p>When correlation function has branch cut in momentum space,
how to find correlation in coordinate space?
For example
$$ \tilde {G}(\omega) = \frac{2i}{\omega+(\omega^2-\nu^2)^{1/2}}$$
How to get the $G(t)$ usng Fourier transformation ?<br>
t>0 HERE.
This problem is from matrix model of Iizuka and Polchinski. They discuss the propagator in the model and find that the propagator $G(t)$ has power law decay behavior if there is branch cut in $\tilde{G}(\omega)$. If there is a pole in the lower half plane for $\tilde{G}(\omega)$, there is an exponential decay in $G(t)$.</p>
| 2,895 |
<p>The masses of the Z and W particle sum almost exactly to the mass of the Top quark,within the errors:</p>
<p>Z + W = 80.385±0.015 + 91.1876±0.0021 = 171.57 ±0.0171 GeV</p>
<p>Top quark 172.9± 1.5 GeV</p>
<p>A: Is this one of those simple coincidences?</p>
<p>B: The Z,W particles are decays of the T?</p>
<p>C: Someone has a not too cranky idea connecting them?</p>
<p>EDIT:
After consideration of dmckee and Lubos posts.</p>
<p>How about instead of a decay from a t quark, collide a $W^\pm$ and a $Z$ to produce a red top and anti-red bottom. </p>
<p>$$W^+ + Z^0 \to t(r) + \bar{b}(\bar{r})$$</p>
<p>this conserves charge, spin, color, confinement and energy - provided the excess energy of the bottom quark comes from the kinetic term of the collision. It immediately decays as <a href="http://physics.stackexchange.com/questions/29132/is-there-a-tb-meson">lubos and dmckee pointed out in an early question</a> </p>
<p>EDIT 2:
Also note decay time of t-quark is $4.2\ 10^{-25} s$, nearly matching the W,Z decays times of $3.0\ 10^{-25} s$ , although I'm yet to find an uncertainty for these.</p>
<p>And with incredible hubris I'm calling this the Metzgeer Momentary Meson $t\bar{b} $<br>
:) joke</p>
| 2,896 |
<p>So a slackline is basically a bouncy tight rope. </p>
<p>I found a site that has a calculator for the tension of a static slackline </p>
<p><a href="http://www.slacklineexpress.com/force.php?linelength=40&sag=1&w=170" rel="nofollow">http://www.slacklineexpress.com/force.php?linelength=40&sag=1&w=170</a> </p>
<p>What I want to figure out is how much this tension increases when bouncing on the slackline. Is there an equation I can use to calculate this? </p>
<p>What are the variables? weight? height of jump? original tension? What else? </p>
<p>Thanks! </p>
| 2,897 |
<p>Consider 2 uncorrelated photon pairs (a1,a2), (b1,b2) such that (a1,a2) are entangled, and separately (b1,b2) are entangled. We wish to entangle-swap so as to end up with a new entanglement (a1,b1) by using the ancillary photon pair (a3,b3), such that (a1,a3) are entangled and (b1,b3) are entangled. This suggests that we do a multipartite (3-way in this case) entanglement preparation prior to the swap, such that (a1,a2,a3) are entangled, and separately (b1,b2,b3) are entangled.</p>
<p>The swap proceeds in the usual way by Bell state measurement on a3 and b3, and we end up having entangled (a1,b1).</p>
<p>The question is whether, after this operation, the entanglements (a1,a2) and (b1,b2) remain intact? If not, can we modify the procedure to guarantee this? If yes, will (a2,b2) now be entangled as a result of the swap? (they were uncorrelated before it). If not, how can we arrange that they are entangled, by only manipulating the other 4 photons?</p>
| 2,898 |
<p>Why does dust stick to rotating fan propeller?</p>
<p>Intuitively, most people (including I) think of the dust will not stick to rotating fan propellers.</p>
<p><strong>EDIT 1:</strong></p>
<p>Thank you for the great explanations. I am still waiting for the "better" one if any.</p>
| 945 |
<p>If the light velocity is a vector quantity, why vector addition cannot be applied to it?</p>
<p>Or the light velocity is not a vector quantity?</p>
| 2,899 |
<p>In quantum information and quantum computation, we generally use Bell type states which are maximally entangled. I find that the set of entangled states as interesting objects from a mathematical point of view and one can ask many questions regarding their structure and so on. But my question is, what are the practical uses of such states and why are they physically interesting.</p>
<p>The only case I can find out is, when due to some environmental interaction such states are created. However I can only see the use of maximally entangled states in literature. Caveat: In multipartite cases, maximal entanglement can be tricky.</p>
<p>I am not sure, whether I have have phrased the question correctly. Feel free to ask and edit. Advanced thanks for any help, suggestion etc.</p>
| 2,900 |
<p>A circuit, has current $A$ flowing at a certain $V$.</p>
<p>When there is a change in magnetic-flux, based on Faraday's law of induction & Lenz's law, we know that there is change in <strong>Potential Difference</strong> now, aside from the source $V$ now we have a induced $-V$ due to the change in magnetic-flux, and it opposes the current, why would it? I understood from lenz's law that it will, but not great detail as to why.</p>
<p>Another thing, if the power-source can be increased, $V$ can potentially increase to oppose the $-V$? And maintain $A$ at the same value it was?</p>
| 2,901 |
<p>I've known for a long time that if you heat a magnet, there is a point it loses its magnetism (the <a href="https://en.wikipedia.org/wiki/Curie_temperature" rel="nofollow">Curie temperature</a>). It isn't clear to me if this applies to induced magnetism like iron sticking to a magnet.</p>
<p>Will molten iron behave like a ferrofluid and be attracted to a magnet or will it just have a very weak paramagnetic attraction?</p>
| 2,902 |
<p>In an alternating current, the flow of electric charge periodically reverses direction, and the number of times it does that is called the frequency of the current. However, if the frequency of an AC is made infinite, would any current flow? I asked this question to my school teacher and he was unable to provide me with an answer unfortunately.</p>
<p>If I consider a horizontal wire, through which an AC is flowing, then I can say that an electron in the wire is moving 50 times left and 50 times right, if the frequency is assumed to be 50Hz. It seems to me that if I increase the frequency, the displacement of the electrons in both the directions, that is left and right, will gradually decrease, and finally become 0, when frequency is infinite, thus making I = 0.</p>
<p>What have I got wrong?</p>
| 2,903 |
<p><strong>Space-like</strong> separated events are events that, in a well-chosen reference frame, can take place at the <strong>same time</strong> but <em>never</em> happen at the <em>same</em> <em>location</em>.</p>
<p>On the other hand for <a href="http://en.wikipedia.org/wiki/Spacetime#Time-like_interval" rel="nofollow"><strong>time-like events</strong></a>, one can chose a reference frame such that they happen at the <strong>same</strong> <strong>place</strong> but <em>never</em> <em>simultaneously</em>.</p>
<p>I can't help thinking that the labels are therefore very ill-chosen... Is there another motivation for these names?</p>
| 2,904 |
<p><img src="http://i.stack.imgur.com/in7Xf.jpg" alt="enter image description here"></p>
<p>A sends out a series of flashes of light to B, where the interval between flashes is denoted by T according to A's clock. Then it is plausible to assume that the intervals of reception by B's clock are proportional to T, say KT. (K is the K-factor)</p>
<p>I dont understand this at all. How is it plausible to assume the proportionality of K?</p>
<p>Source : Ray D'Inverno's Relativity Book.</p>
| 2,905 |
<p>Given that in the ballistic regime a particle (electron) can move freely without scattering (there are no impurities ), is the resistance through a ballistic sample zero?</p>
| 2,906 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.