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<p>I understand that the fundamental representation of $U(1)$ amounts to a multiplication by a phase factor, e.g. EM. I thought that when it is extended to higher dimensional representations, it would just become a phase factor times the identity matrix.</p>
<p>Can someone explain where the hypercharge comes into the $U(1)$ generator matrices in $SU(2)\times U(1)$ model, e.g. $Y = -(1/2) I$ in $(2, -1/2)$ representation? I don't quite understand where the "$-1/2$" comes from.</p>
<p>Where do all these hypercharges come from? What is the logic behind choosing a particular value like $-1/2$?</p>
<p>Hope someone can clarify. </p>
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<p>why do two observers measure the same order of events if we are inside the light cone?</p>
<p>(e.g. if ds^2 > 0 time order is preserved according to the class mech book I am reading, but it doesn't give any proof of this) I assume there is some simple geometrical argument I am missing</p>
<p>and analgously why do two observers measure possible different order of events if we are outside the light cone?</p>
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<p>In a common wood fire such as a campfire, is matter converted to energy or is it simply an exothermic chemical reaction and all the mass can be accounted for in the ash and soot?</p>
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<p>Consider the following example:</p>
<blockquote>
<p><em>A bullet of mass 45g is fired at a speed of 220 m/s into a 5.0 kg sandbag hanging from a string from the ceiling. The sandbag absorbs the bullet and begins to swing. To what maximum vertical height will it rise? (Assuming negligent air resistance and heat loss due to friction)</em></p>
</blockquote>
<p>The way to solve this would be to calculate the kinetic energy of the bullet and then convert it to gravitational potential energy of the bullet + sandbag.</p>
<p>$$E_{k} = \frac12 * 0.045\,{\rm kg} * (220\,{\rm m/s})^2=1089\,{\rm J}$$</p>
<p>We could then find the gravitational potential energy here by substituting in $E_{p} = E_{k}$.</p>
<p>But, what I'm curious about here is, what would be the speed immediately after the bullet impacts the sandbag? Either the kinetic energy, or the momentum could be conserved, but not both.</p>
<p>$$P = 0.045\,{\rm kg} * 220 \,{\rm m/s} = 9.9 \,{\rm kg} \cdot \,{\rm m/s}$$</p>
<p>Then we find the speed after the collision of the sandbag + bullet to be:</p>
<p>$$9.9 \,{\rm kg} \cdot \,{\rm m/s} = 5.0\,{\rm kg} + 0.045\,{\rm kg} * X \,{\rm m/s}\to 1.96234 \,{\rm m/s} = X$$</p>
<p>So if momentum is conserved then the kinetic energy would be:</p>
<p>$$E_{k} = \frac12(5.0\,{\rm kg} + 0.045\,{\rm kg}) * (1.96324 \,{\rm m/s})^2=9.72\,{\rm J}$$</p>
<p>Should this question specifically state whether momentum or energy was conserved? How can you tell which one will be conserved?</p>
| 8,342 |
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<p>The abstract Weyl Algebra $W_n$ is the *-algebra generated by a family of elements $U(u),V(v)$ with $u,v\in\mathbb{R}^n$ such that (Weyl relations)
$$U(u)V(v)=V(v)U(u)e^{i u\cdot v}\ \ Commutation\ Relations$$
$$U(u+u')=U(u)U(u'),\qquad V(v+v')=V(v)V(v')$$
$$U(u)^*=U(-u),\qquad V(v)^*=V(-v)$$
It is a well known fact (Stone- von Neumann theorem) that all irreducible representations $\pi:W_n\rightarrow B(H)$ of this algebra such that
$$s-\lim_{u\rightarrow 0}\pi(U(u))=U(0),\qquad s-\lim_{v\rightarrow 0}\pi(V(v))=V(0)$$
are unitary equivalent to the Schroedinger one:
$$H\equiv L^2(\mathbb{R}^n)$$ $$\pi(U(u))\equiv e^{i\overline{u\cdot X}},\qquad \pi(V(v))\equiv e^{i\overline{v\cdot P}}$$ where $X,P$ are the usual position and momentum operators defined (and essentially self-adjoint) on the Schwartz space $S(\mathbb{R}^n)$.
For this reason, this algebra is usually associated to the quantization of a spinless non relativistic particle in $\mathbb{R}^n$. But what happen if one considers a spinless particle confined in a subregion $K\subset\mathbb{R}^n$, for example a circle $S^1\subset\mathbb{R}^2$, a sphere $S^2\subset\mathbb{R}^n$ or a generic open subset? The state space could still be chosen as $L^2(K)$, but what about the associated Weyl Algebra? I think it can still be defined abstractly but, while the commutation relations must be conserved in some way, the parameters domain $(u,v)$ cannot still be taken as $\mathbb{R}^n\times\mathbb{R}^n$ otherwise we fall in the previous context.</p>
<p>Is there some prescription for such a general situation? To be more precise:
Given a bosonic particle confined in a sub region K, is it possibile to associate a family of abstract elements $U(u),V(v)$, $u,v$ belonging for example to some additive groups, such that the above Weyl properties are satisfied? </p>
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<p>Given a system of two particles with spin up and down, I have troubles to understand the possible states of this system.</p>
<p>I would have normally thought, that the possible states are the tensor products of the states of each particle with one of the other.
This would have given us the states that are listed in Wikipedia under: substituting in the four basis states.
So why do we define these new states(three with total spin $1$ and one with total spin $0$) that are given by triplet and singlet representations? So maybe you don't know what I am asking so I repeat my question: What is the meaning of these triplet and singlet states, because I would have thought that the four states listed above are the possible states of a system?
The reference to what I am talking about:
<a href="http://en.wikipedia.org/wiki/Triplet_state" rel="nofollow">wikipedia reference</a></p>
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<p>I have seen on this site some questions regarding the nature of gravitational-force, and the ways in which it could be interpreted. Most of them mention that the space-time fabric came into existence due to the big-bang. But I cannot understand why it came into existence during the big-bang, and had no earlier existence. Also, how should I develop my notion regarding the form of a gravitational-singularity? My current concept holds it that a gravitational singularity, is a compact-clump of spatial and temporal curves, where laws of Classical Physics are rarely(?) valid. But more often, I "like" to compare a garvitational-singularity with a huge go-down of energy, that is longing to burst open, and thus, decrease its entropy, as well as energy. If in-any way my current-notion is to a-certain degree acceptable, would it then be correct for me to guess that "minute"(?)-fabrics of space-time come into existence whenever there is a conversion of matter into an equivalent amount of energy, according to Einstein's equation E=m.(c^2) ?</p>
<hr>
<p>Please take care of the fact that I am a high-school student-with a corresponding limited-knowledge on Physics, and especially, Quantum-Mechanics.</p>
| 8,345 |
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<p>My question is, <em>can the (classical) Lagrangian be thought of as a metric</em>? That is, is there a meaningful sense in which we can think of the <em>least-action</em> path from the initial to the final configuration as being the <em>shortest</em> one? Then the equations of motion would be geodesics - not in physical space, but in phase space, with the metric defined by the Lagrangian. Below is a slightly expanded outline of this idea, outlining why I think it might make sense.</p>
<p>(Classical) Lagrangian mechanics is derived by assuming the system takes the path of minimum action from its initial state to its final one. In the formalism of classical mechanics we normally write time $t$ as a special type of coordinate, quite distinct from the other (generalised) coordinates $\mathbf{q}$. </p>
<p>However, if we want we can lump these together into a single set of "generalised space-time coordinates" $\mathbf{r} = (t, q_0, q_1, \dots)$, to be considered a vector space of dimension $1+n$, where $n$ is the number of degrees of freedom. Then the action is just a function of curves in $\mathbf{r}$-space, and the equations of motion are determined by choosing the least-action path between two points, $\mathbf{r_0}$ and $\mathbf{r_1}$. In this picture, $L$ depends upon the position and direction of the curve at each point along it, and the action is obtained by a line integral along the curve.</p>
<p>This has a pleasingly geometrical feel, and so my question is, is there a meaningful sense in which I can think of the least-action path as being the <em>shortest</em> path, with the Lagrangian playing the role of a metric on $\mathbf{r}$-space? Or is there some technical reason why $L$ can't be thought of as a metric in this sense?</p>
<p>Note that this isn't in general the same as a metric defined on space-time. For an $m$-particle system in $3+1$ space-time, $\mathbf{r}$ will have $3m+1$ dimensions, rather than 4. I'm interested in the notion of a metric in $\mathbf{r}$-space defined by $L$, rather than the more usual picture of $L$ being defined in terms of a metric on space-time.</p>
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<p>I know perfectly well how to derive the magnitude of the electric field near a conductor,
$$E = \frac{\sigma}{\varepsilon_0}$$ and near a sheet of charge, $$ E = \frac{\sigma}{2\varepsilon_0} .$$</p>
<p>In fact, I can explain with clarity each step of the derivation and I understand why is one two times larger than the other. But here's what bothers me...</p>
<p>When I try to think about it <em>purely</em> intuitively (whatever the heck that actually means), I find it difficult to accept that a planar charge distribution with the same surface density can produce a different field.</p>
<p>Why should it <em>care</em> whether there's a conductor behind it or not... ?</p>
<p>I repeat, I understand Gauss' law and everything formally required, but I want to understand where my intuition went wrong.</p>
<p><strong>EDIT:</strong> <em>Thanks to you people, I developed my own intuition to deal with this problem, and I'm happy with it, you can see it posted as an answer!</em></p>
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] |
<p>I've been wondering: </p>
<p>Are there, still, some advantages, for current research, to study Newtonian gravity? I mean, not experimentally, where Newton gravity is a very good approximation to everyday phenomenon or, even, to the solar system (aside some perihelion problems, gravitational lensing, etc...) but to some study of General Relativity or some approximation to the Einstein field equations where knowing the Newton potential is needed.</p>
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] |
<p>How can we construct a <a href="http://en.wikipedia.org/wiki/Tauc_plot" rel="nofollow">tauc plot</a> using data from the transmission spectra? How does one calculate the absorption coefficient for plotting tauc plots? </p>
| 8,349 |
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<ol>
<li><p>Mathematically, (by mathematically I means by equations) what is path of light in the accelerating elevator?</p></li>
<li><p>What is the difference between an ordinary derivative and covariant derivative (which is used in curved geodesic)?</p></li>
</ol>
| 8,350 |
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<p>I have read about the application of railguns and other ground powered launch, where there is no need to carry any propellant in the rocket.</p>
<p>I am wondering, to <strong>what velocity should the vehicle achieve to enter into the orbit of earth?</strong>
I know the orbital velocity and escape velocity calculations and their values too. I want to know the practical velocity needed, <strong><em>by accounting for the atmospheric resistance</em></strong>. </p>
<p>Will the rocket enter into an orbit when launched at any angle? Or <em>is there a range of angle of launch</em> to achieve orbit?</p>
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<p>I'd like to know if the sign in front of a kinetic term in QFT important. For the scalar field we conventionally write (in the $ + --- $ metric),
\begin{equation}
{\cal L} _{ kin} = \frac{1}{2} \partial _\mu \phi \partial ^\mu \phi
\end{equation}
Based on the answer given <a href="http://physics.stackexchange.com/questions/99252/meaning-of-kinetic-part-in-the-lagrangian-density">here</a>, this makes perfect sense since we want to have positive kinetic energy $\propto \dot{\phi}^2$. So would the Hamiltonian with a negative in front of the kinetic term be unbounded?</p>
<p>Does this logic extend to the Dirac Lagrangian typically given by,
\begin{equation}
\bar{\psi} i \partial _\mu \gamma ^\mu \psi \quad ?
\end{equation}
i.e., would having a negative in front of the Dirac Lagrangian make the Hamiltonian unbounded?</p>
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<p>What happens when the photon which hits a metal surface has energy equal to the work function of that surface?
$$\phi = hf$$
I realise the emitted electron will have no kinetic energy after escape, but then what does it do? Hover above the surface? Or does it have momentum from escaping? I also don't understand what the work function is caused by - is it the electrostatic attraction between nuclei and the electrons?</p>
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<p>The annihilation and creation operators are given below
$$
\hat a|n\rangle=\sqrt{n}|n-1\rangle\qquad\text{and}\qquad\hat a^\dagger|n\rangle=\sqrt{n+1}|n+1\rangle
$$</p>
<p>Now I know the operator a^ is not Hermitian but as to why I'm a little confused.
Is it because they 'create' and 'annihilate' photons hence they're not hermitian? I don't think that explanation would be good for an exam if this question was asked though...</p>
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<p>When I learn QFT, I am bothered by many problems in complex analysis.</p>
<p>1) $$\frac{1}{x-x_0+i\epsilon}=P\frac{1}{x-x_0}-i\pi\delta(x-x_0)$$</p>
<p>I can't understand why $1/x$ can have a principal value because it's not a multivalued function. I'm very confused. And when I learned the complex analysis, I've not watched <a href="http://en.wikipedia.org/wiki/Sokhotski%E2%80%93Plemelj_theorem" rel="nofollow">this formula</a>, can anybody tell me where I can find this formula's proof.</p>
<p>2) $$\frac{d}{dx}\ln(x+i\epsilon)=P\frac{1}{x}-i\pi\delta(x)$$</p>
<p>3)
And I also find this formula. Seemingly $f(x)$ has a branch cut, then
$$f(z)=\frac{1}{\pi}\int_Z^{\infty}dz^{\prime}\frac{{\rm Im} f(z^{\prime})}{z^{\prime}-z}$$
Can anyone can tell the whole theorem and its proof, and what it wants to express.
<img src="http://i.stack.imgur.com/oK0o1.png" alt="enter image description here"></p>
<p>Now I am very confused by these formula, because I haven't read it in any complex analysis book and never been taught how to handle an integral with branch cut. Can anyone give me the whole proof and where I can consult. </p>
| 8,355 |
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<p>Consider the 3-dimensional Minkowski space
$$
ds^2=dt'^2-dr'^2-r'^2d\phi'^2
$$</p>
<p>Now we transform it into a rotating frame:
$$
t'=t,r'=r,\phi'=\phi+\omega t
$$</p>
<p>Then the metric becomes
$$
ds^2=(1-r^2\omega^2)dt^2-dr^2-2\omega r^2d\phi dt-r^2 d\phi^2
$$</p>
<p>Consider a static observer in the rotating frame with coordinate $(r,\phi)=(R,0)$. Could anyone show me how to compute the 4-acceleration of this observer?</p>
<p>I am expecting the answer to be $(0,-\omega^2 R,0)$ based on my knowledge of Newtonian mechanics. But my calculation does not give this.</p>
<p>I have calculated the 4-velocity to be
$$
u=\left(\frac{1}{\sqrt{1-R^2\omega^2}},0,0\right)
$$</p>
<p>Then I use the formula
$$
a^\mu=u^\nu\nabla_\nu u^\mu=u^t\nabla_tu^\mu=u^t(\partial_tu^\mu+\Gamma^\mu_{t\alpha}u^\alpha)=u^tu^\alpha\Gamma^\mu_{t\alpha}
$$
Then it turns out only $\alpha=t,\mu=r$ is meaningful, and
$$
a^r=-\frac{2R\omega^2}{1-R^2\omega^2}R^2(1-2\omega^2R^2)
$$
which I think is definitely wrong...</p>
| 8,356 |
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<p>I have studied from Griffiths, the relativistic form of momentum is
$$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$ </p>
<p>Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I get $p= 0/0$. How does it make sense? </p>
<p>Can you tell me that where I am wrong?</p>
| 195 |
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<p>I am attempting to validate an accelerometer. I have a triaxial accelerometer and placed it on a wheel which goes at various frequencies from 1 to 3 Hz.
Am I right in thinking that I would expect the acceleration in <em>z</em> to be 1g?</p>
<p>Then in the <em>x</em> and <em>y</em> plane I would expect a read out of acceleration in $X(t) = -2\pi fr\cos{(2\pi f t)}$ and acceleration in $Y(t) = -2\pi fr\sin{(2\pi f t)}$ where $r$ is the radius of the wheel and $f$ is frequency.</p>
<p>How can I compare these with my readout from the sensor, and what is the best way to report accuracy? I'm confused as surely I will need to quite accurately time align the two traces.</p>
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<p>Let $\psi (x,y,z)$ be a scalar field. I found the following statement in Morse & Feshbach Methods of Theoretical Physics:</p>
<blockquote>
<p>The limiting value of the difference between $\psi$ at a point and the average value of $\psi$ at neighboring points is $-\frac{1}{6}(dxdydz)^2\nabla ^2\psi$</p>
</blockquote>
<p>By taking a small sphere centered at the point of radius $r$, I was able to show that the difference between $\psi$ at a point and the average value of $\psi$ at neighboring points equals $-\frac{1}{6}r^2\nabla ^2\psi$. But I have not been able to get the expression given in the book. Thanks.</p>
<p>Edit: To obtain $-\frac{1}{6}r^2\nabla ^2\psi$ I first expanded $\psi$ in a Taylor series up to quadratic terms about the point in question. Then I integrated $\psi$ (rather, its Taylor expansion up to quadratic terms) over the surface of a small sphere of radius $r$ centered at the given point and divided this by the surface are of the sphere (this gives the average value of $\psi$ in the sphere). Subtracting this average from the value of $\psi$ at the center of the sphere gives the result $-\frac{1}{6}r^2\nabla ^2\psi$.</p>
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<p>I'm trying to relate the concept of entropy to keeping my room clean as suggested by my high school teacher ~1993...</p>
<p>Comparing the two scenarios:</p>
<ol>
<li><p>Every day I come home and throw an empty can on the floor and every night before bed I pick it up and throw it in the trash.</p></li>
<li><p>Every day I come home and throw an empty can on the floor and every six months I bag them all up at once.</p></li>
</ol>
<p>So to me it's obviously more efficient to let entropy run its course and then undo it in a "batch" as opposed to constantly undoing it.</p>
<p>Is that right though? I'm thinking since entropy is related to energy, then is has to be conserved and the same amount of effort should be required to keep a room clean than to clean it after its become horribly messy.</p>
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<p>I suppose this is also an English question, but I'll ask it here first.</p>
<p>Why does the milli- prefix mean 1/1000 when it sounds so much like million? According to the internet, this dates back to the 18-19th centuries. Did it make more sense back then? Are we stubbornly holding on to meanings from borrowed prefix's languages (such as milli meaning 1000 in Latin)?</p>
<p>Not that I'm qualified in any way to make this kind of statement, but if I were able to rename our unit prefixes, I would shift everything from milli- to femto- down 3 orders of magnitude and eliminate atto-. The resulting pairs would be:</p>
<pre><code>thousand- kilo (placeholder)
million- mega milli
billion- giga micro
trillion- terra nano
quadrillion- peta pico
quintillion- exa femto
sextillion- zetta zepto
...
</code></pre>
<p>Which to me, sounds better. But I suppose I answered my own question by saying that since they are the units everyone uses, social inertia prevents us from changing. Would this be correct?</p>
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] |
<p>I took an empty clear sphere with radius r, put some weight inside this sphere, and put in into the water. I calculate the buoyancy force as:</p>
<p>Volume of the sphere = Volume of the water displaced (Vdisplaced) = (4/3)<em>pi</em>(r^3);
Weight of the displaced water = Buoyancy force (B) = Vdisplaced * density of water;
Wtotal= Wsphere + Wweight;</p>
<p>Then, the sphere will float when Buoyancy (B) > Wtotal, otherwise it will sink. I assume that I am right so far?? So the air inside the sphere will affect sphere's ability to float. My confusion is that I assume that I have already considered this effect during the aforementioned calculations (since density of the sphere itself is low). Is that right? Please note that the sphere is not flexible. </p>
| 8,361 |
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<p>Could anyone suggest where can I find absorption spectra & refractive index of Glycerol?</p>
<p>I am specifically interested in UV range, 200-400nm, everything I was able to find out was for standard conditions only...</p>
<p>Is there any software which can get these parameters through simulation?</p>
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<p>When a Electron gets promoted to the conduction band from valence band (In generation) lets say for example in Silicon at room temperature.</p>
<p>Is there any way to determine (on average) how long it will last before falling back down in the hole it just left.</p>
<p>What about with a Voltage Applied?</p>
<p>Thanks</p>
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<p>So we can define a particle by defining its kinetic and potential energy, knowing that we can get a wavefunction describing a particle.</p>
<p>But the kinetic energy involves motion, and motion can be described in many different frames of reference as different quantities, so is the Hamiltionian not uniquely defined?</p>
<p>I mean, is the quantum state than dependant on in which frame of reference you look at the particle? Or it is just taken as a velocity in the Earths frame of reference as we cannot extract the energy contained in the velocity due to rotational motion around the Sun and the center of Galaxy?</p>
<p>And also what is the same case with temperature? I found some things about it but I don't fully understand I think. relevant: <a href="http://en.wikipedia.org/wiki/Unruh_effect" rel="nofollow">Unruh effect</a></p>
<p>I searched over the physics stackexchange and read about the energy in different frames of reference and the temperature and so on, and well I still don't feel that I understand it, but the main question is: <strong>isn't the wavefunction absolute description of the state of the particle?</strong></p>
| 8,364 |
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<p>A while ago, during my introductory physics course, my professor purposefully neglected to tell us about the existence of the anti-electron neutrino in beta decay; he made it an assignment(on our honor) to propose a theory to explain where the missing energy ran off to. Since I was not very experienced at the time, I did not come to the conclusion that the culprit had to be neutral (to conserve charge), but I was aware of basic particle collisions and how scientists smashed particles together in order to observe smaller, more basic ones. Consequently, I came to the conclusion that when the electron broke away from the nucleus, particle fragments (where the electron broke off) were released as well (so, a bit like detritus which would have accounted for the deviation in the missing energy, as a different number of particles could have broken off each time). Now, clearly, I had an advantage over Pauli (since I was aware of particle diversity, and the separable nature of baryons), yet I am still not certain exactly how he was able to narrow his choices down to a single particle (especially since he was decades away from being able to detect such an elusive creature). How would you have come to such a conclusion (if possible, perhaps another response besides Occam's Razor)?</p>
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] |
<p>Does it make sense to say that the quantum field of a photon is exactly proportional to the photon's electromagnetic field?</p>
<p>\begin{align}
\bar{\Psi}
=
\dfrac{\bar{E}+i\bar{B}}{\sqrt{\int (E^2+B^2)dV}}
\end{align}</p>
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<p>I've been studying Bagger & Giannakis paper on the SuperHiggs Mechanism found <a href="http://arxiv.org/abs/hep-th/0502107v1" rel="nofollow">here</a>. </p>
<p>The paper shows how SUSY is broken by a $B_{\mu\nu}$ gauge field background restricted to $T^3$ in $M^7\times T^3$ Compactification of the heterotic string.</p>
<p><em>My question is, have these results been generalised to different Backgrounds and/or Compactifications (Perhaps even Calabi Yau 3-folds)?</em> </p>
<p>So far my search has shown up no results, any pointers in the right direction are greatly appreciated, Thanks!</p>
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<p>Let's say I've got an Earth-like planet with no atmosphere: it's just a barren ball of rock. I want to live there, but I don't like domes, so instead I'm just going to dig a big hole and let gravity keep the air in.</p>
<p>How deep a hole do I need?</p>
<p>According to a chart I found, the density of the atmosphere drops to pretty much zero by about 50km, at the top of the stratosphere. But 'pretty much zero' is not zero; the mesosphere beyond that extends up to about 80km and while vanishingly thin is responsible for dealing with most meteors.</p>
<p>If my hole is a mere 50km deep, then, some of my air is going to diffuse out of the hole and onto the planet's surface. But the surface of my planet is largely flat; there's nowhere for the air to <em>go</em>, so it's just going to hang around and form a dynamic equilibrium. (Unlike, say, if I built a 50km wall and tried to keep the air inside. Air would leak over the top of the wall, fall down into the vacuum on the other side, and be lost forever. Which is why the Ringworld had walls 1000km high.)</p>
<p>So I don't really know how shallow a hole I can get away with. I <em>can</em> replace the air, but I would like it to go without maintenance for at least small geological timescales. Any advice before I start up the earth-moving equipment?</p>
<p>(Yes, it's SF worldbuilding.)</p>
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<p>I do not remember when, but a while a ago I was told that for a spring with stiffness $k$ and a mass $m$, the equation $-kx = ma$ never holds. (assume a horizontal spring)</p>
<p>So if I was given a problem like this:</p>
<blockquote>
<p>You pull a mass $m$ attached to a spring with stiffness $k$ to the right of the equilibrium point $x = 5\text{ m}$ of the spring and you let it go, what is the acceleration of the mass?</p>
</blockquote>
<p>Then is this question meaningless (or any other that is similar)? I forgot what the real question is like, but I have seem such a method was used to tackle these problems? As such an attempt to write $-kx = ma$?</p>
<p>Could someone please jog my memory? I realize I am asking you guys to 'read my mind', but please bear with me.</p>
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<p>Considering how low the power density is at the sun's core, I seem not to be able to expect what would happen to matter in case it was thrown inside the sun's core.
For example, let's assume an Earth-like planet is placed at the center of the Sun's core, and with the power density of 276.5 $watts$/$m^3$ which is very low to even raise the temperature of the Earth by any noticeable degree. That was one thought.
The other thought was that, the temperature in the core is already 15 million degrees K, so any matter there should get close to this temperature quickly enough.</p>
<p>So now I'm very confused, like will the planet stay there intact for thousands or even millions of years until it has accumulated enough energy to melt or vaporize ?
Or there are other types of energy absorption the planet would experience and thus have a shorter time staying as one piece in the core ?</p>
<p>Just for trying to get a practical and numerical answer to this question, let it be : how long can the Earth as a whole survive in the core of the sun ? </p>
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<p>WHAT I KNOW: </p>
<p>classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states.
Now when we make a "measurement" (to determine the state of qubit), it changes the state of qubit, collapsing it from its superposition of 0 and 1 to the specific state consistent with the measurement result.</p>
<p>MY QUESTION:</p>
<p>If, from measurement of a qubit we obtain only a single bit of information (0 or 1 beacuse the qubit collapses to either of the states) then how is a qubit better than a classical bit..... since ultimately we are only able to get either 0 or 1 from either classical or quantum bit.</p>
<p>[I hope that i have made the question clear enough to convey what i think].</p>
<p>To those who answer this please try to explain with an example if you can.</p>
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<p>This assignment is about the one dimensional harmonic oscillator (HO).
The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at $t = 0$, is given by:</p>
<p>$\psi \left( x,\,\,t=0 \right)=A\left( {{\phi }_{0}}\left( x \right)+2i{{\phi }_{2}}\left( x \right) \right)$</p>
<p>Now I have to calculate A, so that $\psi$ is normalized.</p>
<p>My question is, what is ${{\phi }_{0}}\left( x \right)$ and ${{\phi }_{2}}\left( x \right)$ given by ?</p>
<p>Otherwise I guess is just doing the usual:</p>
<p>$\int_{-\infty }^{\infty }{{{\left| \Psi \left( x,\,\,t \right) \right|}^{2}}}dx=1$</p>
<p>To figure out A.</p>
| 8,372 |
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] |
<p>If two balls collide (elastically) and there is no friction between them, will their angular momentum change after the collision?</p>
| 8,373 |
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<p>I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that</p>
<p>$$\Delta S\geq0$$</p>
<p>via <a href="http://en.wikipedia.org/wiki/Clausius_theorem" rel="nofollow">Clausius' theorem</a>. My question is, how can I prove this in a mathematical way?</p>
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<p>I am looking into the decay of a $\Phi$-meson decaying into $K^+$, $K^-$. My problem is, the $\Phi$-meson has a total angular momentum of 1 and the two Kaons have a total angular momentum of 0. On the first glance this seems to be a violation of the angular momentum conservation law.</p>
<p>I tried to explain it to myself using the quark picture of the system. So the $\Phi (s \bar{s})$ goes under the production of a $u\bar{u}$ pair into $K^+(u \bar{s})$ and $K^- (\bar{u}s)$. Using Clebsch Gordon coefficients i noted down the possible combinations and that works out so far.</p>
<p>My question is, how can the 'effective' total angular momentum be explained as it seems to me, that the conservation law is not conserved, which can not be. Do i miss something or have i got something wrong?</p>
| 8,375 |
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] |
<p>If space itself is expanding, then why would it have any effect on matter (separates distant galaxies)? </p>
<ul>
<li><p>Space is "nothing", and if "nothing" becomes bigger "nothing" it's still a "nothing" that shouldn't interact with matter in any way (it doesn't have mass, energy, etc).</p></li>
<li><p>Gravity doesn't have a cutoff distance afaik, so even the most distant galaxies should be attracted to each other. Gravity force would be very very tiny, but it would still dominate "nothing" from space expansion.</p></li>
<li><p>Lets take inertia from Big Bang into account. Inertia would be the primary force that moves galaxies away comparing to their tiny gravity and even more tiny, if any, force of our "nothing" that is still expanding inbetween. Wouldn't expansion decelerate if driven mostly by inertia?</p></li>
</ul>
| 56 |
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<p>If I'm correct a quark can change color by emitting a gluon. For example a blue up quark $u_b$ can change into a red up quark by emitting a gluon:
$$u_b \longrightarrow u_r + g_{b\overline{r}}$$
(Here, the subscript indicates color and $\overline{r}$ means anti-red). This is needed to keep the color balance (left hand side: $b$, right hand side $r+b+\overline{r}=b$).</p>
<p>My question is then, do color-neutral gluons exist? Eg a gluon that is blue-anti-blue?
If it would, it could be created by any quark then:
$$u_b \longrightarrow u_b + g_{b\overline{b}}$$</p>
<p>I'm learning about the Standard Model in school, but the text isn't always that clear. </p>
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<p>The Higgs boson propagator can be written $$\frac{1}{p^2-m^2+\Sigma(p^2)}$$. If we take $p^2=m_P^2$ the physical mass, we get $m_P^2=m^2-\Sigma(m_P^2)$. Now, if $\Sigma\sim \Lambda^2$, we get $m^2\sim\Lambda^2+m_P^2$.</p>
<p>It had assumed that the mass correction from fermion loops was positive, but from this it appears that the Higgs mass is renormalized to be smaller than the bare mass. Is this physical ?</p>
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<p>Assuming it is possible in principle to entangle the degrees of freedom of the event horizons of two black holes, and that this is something that can be done, either after the black hole is formed, or only by careful preparation before collapse. </p>
<blockquote>
<p><strong>Question:</strong> Could exist a physically realisable entanglement configuration of the horizons that behaves as a traversable wormhole,
in the sense that infalling information on one mouth becomes
non-thermal Hawking radiation on the other mouth, that preserves some
or all the original information?</p>
</blockquote>
<p>A while ago I made a relevant <a href="http://physics.stackexchange.com/q/48511/955">question regarding creating black holes with entangled light</a>. That method suggested there could provide two such entangled black holes</p>
| 8,378 |
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<p><a href="http://physics.stackexchange.com/questions/80773/the-example-of-relativity-of-simultaneity-given-by-einstein/80776#80776">This answer</a> to a recent question related to <a href="http://archive.org/details/relativitythespe00einsuoft#chapters.8.and.9" rel="nofollow">Einstein's thought-experimental definition of (how to determine) simultaneity</a> contained the following statement:</p>
<blockquote>Suppose two people, $C$ and $D$, stand equal distances from you and are known to pitch balls at exactly the same speed. With everyone standing at rest, $C$ and $D$ each toss you a ball. You get the ball from $C$ *before* the one from $D$. This is not a logical inconsistency. It simply means $C$ threw a ball *before* $D$ <b>in your reference frame</b> [emphasis added].</blockquote>
<p>I believe that I understand the described setup and the conclusion ("<i>It simply means $C$ threw a ball <em>before</em> $D$</i>") as such. But I question whether it is necessary to add the qualification "<i>in your reference frame</i>".</p>
<p>Carefully applying Einstein's definition of (how to determine) simultaneity, as referenced above, which for the given setup involves a suitable observer "<i>at the midpoint between</i> $C$ and $D$", is there even any reference frame at all (necessarily other than "<i>your reference frame</i>") "in which" $C$ threw a ball *simultaneous to* $D$ throwing a ball ?</p>
<p>Or is there even any reference frame at all (again necessarily other than "<i>your reference frame</i>") "in which" $C$ threw a ball *after* $D$ ?</p>
<p>(If there are no such reference frames, then the qualification "<i>in your reference frame</i>" is apparently not necessary; and, indeed, it would seem inappropriate and misleading to add such a qualification as if it were necessary.) </p>
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<p>This is quite embarrassing to ask, but I haven't done a fluid flow calculation in a very long time and when you don't use it, you lose it!</p>
<p>I have a natural gas pipeline that I want to purge of air with natural gas. It's a 3" and 4" line totalling about 6,600 feet. I'll be injecting natural gas into the line through a 2" hose with a pressure of 15 psi and the outlet will be another 2" hose at the other end.</p>
<p>My question is:
How long will it take to push all of the air out of the pipe and fill it with natural gas (purge the line of air)?</p>
<p>I've spent the last few hours Googling fluid flow questions and answers and just can't figure it out. Thanks in advance!</p>
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<p>We have a long, cylindrical wire carrying a constant current I in an inertial frame. At a distance of R from the center of the wire, the magnitude of magnetic field is $μI/2πR$.
What is the magnitude of magnetic field in another inertial frame moving at a certain speed opposite to the direction of electric current? </p>
<p>Since the observed drift speed of the electrons is now greater, does this mean that the current as observed from this frame is greater? </p>
<p>If so, what about the magnetic field due to this current? Does this change too? </p>
<p>In general how do currents vary between different frames of reference?</p>
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<p>I ran into a bit of physics yesterday, and couldn't understand the physics at work. I've been scouring the Internet, but haven't found the answer yet. I'm guessing there's a basic principle I'm misinterpreting or ignorant of.</p>
<p>Basically, the sewer backed up into my house. Among other points of entry, water flowed up the shower drain, and up the toilet bowl.</p>
<p>The shower filled to a bit under the lip of its basin. The toilet filled to a bit under the lip of the bowl, but neither overflowed.</p>
<p>So basically I had a reservoir (the sewer), with one pipe (shower) extending to floor height + 4 inches, and another pipe (toilet) extending to floor height + 24 inches.</p>
<p>Where I'm getting confused is that in my physics textbooks I recall seeing a diagram of a U-shaped vessel with differently sized "legs." I think that the water level in each leg of the U had to be the same, because otherwise there'd be a pressure differential at the base of the U preventing the system from stabilizing.</p>
<p>Edit: Here's <a href="http://physics.stackexchange.com/questions/799/why-does-the-water-level-equalize-in-a-series-of-tubes">an example of what I'm talking about</a>.</p>
<p>What would allow for this difference in water levels?</p>
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] |
<p>Suppose we have a disc with a hole, when computing moment of inertia of this about the disc's centre. Why do we subtract the moment of inertia of the removed part from the moment of inertia of complete disc? </p>
| 8,383 |
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] |
<p>$\vec F=m\vec a$ ,for moving object with 10 $km/s$ in a constant manner ,where acceleration is zero. ie No force on object ?</p>
<p><a href="http://www.physicsforums.com/showthread.php?t=622711" rel="nofollow">http://www.physicsforums.com/showthread.php?t=622711</a></p>
| 275 |
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<p>Water on earth has been theorized to have come through comets trapped inside crystals. But why wouldn't that water evaporate on impact, and wouldn't the atmosphere at that time allow the vapours to escape Earth?</p>
<p>Also, what is the current scientific opinion of the validity of this theory ?</p>
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<p>Why do we need to use the sign convention again in the mirror equation while solving numericals when we know we have already used a convention while deriving the mirror equation? The question is not about the importance of sign conventions but why do we need to use the sign conventions twice? Doesn't the equation already include a sign convention?</p>
<p>1/u + 1/v = 1/ f</p>
<p>Or say, in the magification formula: height of image/ height of object = - (v/u)</p>
<p>Why do I need to bother about the signs ( -u or - v or +f) while using the above equations? </p>
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<p>We know that near a massive object, light's wavelength and frequency changes, but its speed remains same. I'd like to know how it is possible for frequency to change, unless we change the light source? </p>
| 8,386 |
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<p>I am not sure if I understand spin operators correctly. Given a two spin system in state $|++\rangle$ and an operator $S = S^{(1)} + S^{(2)}$</p>
<p>Then I have</p>
<p>$$
S_z |++\rangle
= (S^{(1)}_z + S^{(2)}_z) (|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes |\tfrac{1}{2}, \tfrac{1}{2}\rangle)
= (S_z|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes S_z|\tfrac{1}{2}, \tfrac{1}{2}\rangle)
= (\tfrac{\hbar}{2} |\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes \tfrac{\hbar}{2} |\tfrac{1}{2}, \tfrac{1}{2}\rangle)
= \tfrac{\hbar}{2} (|\tfrac{1}{2}, \tfrac{1}{2}\rangle \otimes |\tfrac{1}{2},\tfrac{1}{2}\rangle)
= \tfrac{\hbar}{2} |++\rangle
$$</p>
<p>But everywhere I read, I see
$$
S_z |++\rangle = \hbar |++\rangle
$$</p>
<p>What did I do wrong?</p>
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<p>Does a black body (imagine like a square of solid black-body-matter) thermally conduct well at room temperature?</p>
| 8,388 |
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<p>There's a question on my homework about the process $e^{-} e^{+} \rightarrow \tau^{+} \tau^{-}$. Specifically, it is claimed that the minimum energy required of the colliding positron and electron beams is slightly less than twice the $\tau$ mass, and I am asked to explain this deviation and compute it. In the context of this course, we have only discussed the relativistic kinematics of such processes (which would predict a minimum energy of twice the $\tau$ mass), so I am not sure what might be responsible. I'm grasping at straws here, but might it have something to do with the Coulomb interaction between the opposite charges? Thanks in advance.</p>
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<p>In the Schrödinger equation in the position representation
$$
i\hbar\frac{\partial}{\partial t}\Psi(x,t)
~=~[\frac{-\hbar^2}{2m}\nabla^2+V(x,t)]\Psi(x,t),
$$
is the potential $V(x,t)$ an operator acting on $\Psi$ or merely a scalar?</p>
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] |
<p>I found this solid-solid transformation in wikipedia. <a href="http://en.wikipedia.org/wiki/Phase_transition#Types_of_phase_transition" rel="nofollow">http://en.wikipedia.org/wiki/Phase_transition#Types_of_phase_transition</a>
Please tell me what it is?
It's present in types of phase transition in wiki.</p>
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<p>Type I superstring theory is unoriented, and it seems that it needs to be so in order to exist. </p>
<p>Now, we always have open-closed duality, that connects at least the ultraviolet sector of a theory with the infrared sector of another, so in principle we should have some oriented open strings coming from it, by duality with a closed oriented theory.</p>
<p>And we have all the D-brane stuff, that surely produces another kinds of open string theories with the restriction of terminating there in the branes.</p>
<p>¿Is some of these D-brane examples an oriented theory? ¿Is there some canonical, well known, example of a consistent oriented theory with open strings?</p>
| 8,392 |
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<p>I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do this, I need the parametric equations for the body's position for any given time (i.e. I need an $x(t)$ and $y(t)$ function). I have access to each body's position, velocity, and mass. I have no other accessible variables.</p>
<p>P.S. <a href="http://www.colekito.com/projects/orbit" rel="nofollow">Here</a> is a link to what I have so far. The equations currently used to plot the orbit are $x(t)=x+v_xt$ and $y(t)=y+v_yt$.</p>
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<p>Suppose you are doing an experiment to determine the work function of a metal.
You get $KE_1$, $\nu_1$ and $KE_2$, $\nu_2$.
We know that $KE = h\nu - W$ but when you solve the simultaneous equations, we have a $h$ slightly different from the textbook value.</p>
<p>Question: In such a situation should you</p>
<ol>
<li><p>Use the textbook $h$ then average {$W_1,W_2$}; or</p></li>
<li><p>Simply solve the simultaneous equations for $W$</p></li>
</ol>
<p>I believe that the values obtained will be different.</p>
<p>Thank you.</p>
<p>Added: Assume you don't get to do more repeats etc.</p>
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<p>I'm currently taking an introduction to Solid State Physics class, and is now on the subject of superconductivity (SC). Currently I'm reading about the BCS theory, and how this works on a microscopic scale. I then get presented with this picture (Electron-Phonon Interaction):</p>
<p><img src="http://i.stack.imgur.com/ZJiFm.png" alt="Electron-Phonon interaction"></p>
<p>Now, as far as I have understood, the electrons, when below $T_{C}$, attract the ions, but are too fast compared to the ions, which means that the ions contract after the electron is gone. This creates a higher potential in the area where they are "squeezed" together which the next electron is much more attracted to that usually. This again means that all electrons pretty much follow the same path, and somehow bond together in Cooper Pairs (Is this the way they get entangled?).</p>
<p>Now, my main question is: Does this attraction of ions, after an electron has moved past them, not happen to a normal metal ? I mean, the electrons move in a normal metal, and also past ions. So don't they attract the ions as well, and make this attraction that another electron then can follow as well ?</p>
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<p>To external fields(H, - H) not equal to each other are acting on that material. <strong>Based on the hysteresis loop</strong> what would be the result?
The hysteresis area of that materials is very narrow(i.e easy to magnetize & demagnetize) H = 1000 A/m and, - H = 500 A/m. I know they are both vectors so it would be H - H = H(total).
However, the material's coercively is 0.1 A/m.</p>
<p>The thing is I can't imagine this condition properly, because both fields are opposing each other, and that ferromagnetic material is placed in-between them both. What would be the result? </p>
<p>The material responds based on it's hysteresis... H points on the hysteresis loop.
Why is it incorrect to state magnetization = 0?</p>
<p>I'm relating this to an object that has to forces acting on it, they are both on opposite directions. F1 = 10N F2= 5N
[x]= is the object. 10N ->[x]<- 5N = 5N ->[x]
Although it makes sense... The hysteresis loop changes everything. Magnetization depends on how the material reacts. The material could become magnetized and fully saturated at 100A/m, now we have both of those conditions...
So M should = zero?!</p>
<p>To picture what I mean, please take a look at this:
<a href="http://uk.tdk-lambda.com/content/glossary/128522219667677500_Hysteresis%20Loop%20image.png" rel="nofollow">http://uk.tdk-lambda.com/content/glossary/128522219667677500_Hysteresis%20Loop%20image.png</a></p>
<p>The two points on the loop on the H axis are 100 A/m(that is the force needed to magnetize the material), however, the field applied H = 1000 A/m and - H = 500 A/m</p>
<p>Hope it helps!</p>
| 8,396 |
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<p>I am trying to determine the self-inductance of a toroidal coil of mean radius $R$ with $N$ loops of radius $a$ with a current $I$ flowing within them.</p>
<p>I have calculated the magnetic field by noting that it must be in the circumferential direction (i.e. in the $\hat{\boldsymbol{\theta}}$ direction) and then using Ampéres Law to get:</p>
<p>$$\oint_{\partial \Sigma} \mathbf{B}\cdot \mathrm{d}\boldsymbol{\ell}=\mu_{0}I_{\text{enc}} \implies \mathbf{B}=\frac{\mu_{0}NI}{2\pi r}\hat{\boldsymbol{\theta}}$$</p>
<p>I know that we can get the self-inductance $L$ by using the relation:</p>
<p>$$\Phi=LI$$</p>
<p>And we know that:</p>
<p>$$\Phi=N\iint_{\Sigma}\mathbf{B}\cdot\mathrm{d}\mathbf{A}$$</p>
<p>Where $\Sigma$ is the area of a single loop. However, I am not sure how evaluate the surface integral, I'm not sure if perhaps I should be using the mean radius $R$ to give us:</p>
<p>$$\Phi=\frac{\mu_{0}N^{2}}{2\pi R}\pi a^{2}I=\frac{\mu_{0}a^{2}N^{2}}{2R}I$$</p>
<p>Or if I need to evalute the integral in a more complete way?</p>
| 8,397 |
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<p>What does <a href="http://www.google.com/search?as_q=&as_epq=smooth+dynamical+system" rel="nofollow">smooth dynamical system</a> mean? It is the title of a paper I am supposed to read in non linear systems.</p>
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<p>Ok, this is definitely a silly question and is partly inspired by the last 20 minutes or so of the film <em>The Avengers</em>, so look to that if you can't picture the situation.</p>
<p>In the film a portal is opened up above new york, to somewhere in deep space. I.e. from an area where the gravitational field is effectively uniform and field lines would be parallel, to an area with negligible net gravitational acceleration.</p>
<p>My question is, assuming this portal has literally linked the two bits of space, it makes sense that the gravity of the earth would be transmitted through the portal in some way, but in what form would the field take on the other side of the portal?</p>
<p>Would it behave like a point source, or similarly to a diffraction slits? Would a mass slightly off to one side from the portal experience a force?</p>
<p>Let's ignore all the practical factors like the air rushing out into the vacuum and the question of what happens on the "other side" of the portal (the bit you'd be looking at if you flew up from new york to above the portal) although there's plenty of scope for interesting things happening there as well.</p>
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<p>We know that Spin is described with $SU(2)$ and that $SU(2)$ is a double cover of the rotation group $SO(3)$. This suggests a simple thought experiment, to be described below. The question then is in three parts: </p>
<ol>
<li><p>Is this thought experiment theoretically sound? </p></li>
<li><p>Can it be conducted experimentally? </p></li>
<li><p>If so what has been the result?</p></li>
</ol>
<p>The experiment is to take a slab of material in which there are spin objects e.g. electrons all (or most) with spin $\uparrow$. Then rotate that object $360$ degrees (around an axis perpendicular to the spin direction), so that macroscopically we are back to where we started. Measure the electron spins. Do they point $\downarrow$?</p>
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<p>I am having some troubles trying to classify a modified photon gas into which phase transition it belongs (if it really is a phase transition).</p>
<p>First of all, it is a photon gas that interacts with an external electric field, so the q-potential (from the grand canonical ensemble) depends on the external field and the temperature alone. The potential is continuous but not analytic only when the external field is varied (if the external field is maintained fixed it might be on one side or the other of the critical point, independently of the temperature). Because the density of energy is the derivative with respect to $\beta$, it has the same qualitative properties of the q-potential.</p>
<p>Now, I've found two definitions for phase transitions, Ehrenfest's one and the "modern" one. Following Ehrenfest's classification I found that it's a first order transition since the discontinuity appears in the first derivative of the potential with respect to a thermodynamic variable, the electric field. But, following the "modern" definition, I found that it is a second order phase transition, or, in the modern classification, a continuous phase transition, because the entropy doesn't have a discontinuity and thus the system doesn't require a latent heat to perform the transition.</p>
<p>My questions are, have I well understood the definitions? Is the system really having a phase transition? And, if it does, which one is it having or it is of a third kind I didn't mention?</p>
<p>Thanks</p>
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<p>I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...</p>
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<p>Pre-face: My step-father and I were turning the heat down on the water heater. He demonstrated that touching the ground wire doesn't shock you.</p>
<p>My understanding is that the ground wire doesn't have current unless the case of a short-circuit, or over-abundance of energy. The wire also has very little resistance.</p>
<p>My question, if the water heater had a short-circuit or had an access flow of energy. Would he have been shocked? Please explain instead of yes or no.</p>
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<p>Although they have never been observed, theoretically gluons can exist outside of the nucleus of an atom in the form of a "glue ball". Since the predominant mechanism of Higgs creation at the LHC was observed to be a gluon-gluon interaction (with various virtual particles playing out in the conversion), what are the chances that a "glue ball" as predicted by QCD is the same animal from the particle zoo as a Higgs boson?</p>
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<p>I'm aware that electron pair-production from a single photon requires the presence of matter — say some large nucleus — able to absorb momentum, as in the process
\begin{align}
N \gamma \rightarrow N e^- e^+
\end{align}
where $N$ represents the nucleus. My question is, how would one represent this process with a Feynman diagram? I'm having trouble constructing one with valid vertices that makes sense. Would the neutron interact with the photon? With the electron-positron pair? Both? Any help would be appreciated.</p>
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<p>I know that recent advances in technology are doing amazing things with very low amounts of electricity, with RFID being one of the most familiar examples, but I'm not very familiar with the principles involved. It makes me wonder: is it possible (with current technology, not "is it theoretically possible?") to use ambient sources (including body heat) to generate enough power to light up an LED, all in a device small enough for a person to hold in their hand? If so, how small could the whole assembly be made?</p>
<p>I've actually got a very specific application in mind, but if it turns out we don't have the capability for it, that'll save a lot of time right there.</p>
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] |
<p>Is there a good way to directly measure a moment of inertia of the Earth, or say, other planet?</p>
| 8,407 |
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<p>What state is <a href="http://en.wikipedia.org/wiki/Fire" rel="nofollow">fire</a>? Solid, Liquid or Gas or Plasma? </p>
<p>I was just roaming around when this question popped out of my mind. In what state is FIRE? </p>
| 276 |
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<p>Do magnets redshift light? </p>
<p>Suppose we have an extremely powerful magnet (say the size of the Sun) and we have a smaller paramagnetic material above it (say. Titanium Brick which is indestructible) . Due to magnetic attraction it will fall toward the big magnet. </p>
<p>Now suppose that when it hits the surface of the bigger magnet, the smaller paramagnetic material (Titanium Brick) is somehow converted into photons (light) equivalent to its mass using $E=mc^2$, plus its kinetic energy, $KE_1$. These photons are shot upwards via an perfect mirror perpendicular to the paramagnetic material above. When they reach the magnet's original position they are again converted into mass in the form of the titanium brick.</p>
<p>If this is repeated many times it seems we will gain free energy, since the iron brick gains kinetic energy when it falls, but light is not effected by magnetic fields. (Or am I wrong?) But this will breach the energy conservation laws in specific "Energy cannot be created nor destroyed". </p>
<p>Therefore I must conclude light is (or should be) redshifted (loses energy) as it travels through magnetic field. The problem arises when you take into consideration that light is not charged so it should not be effected by any magnetic fields but my intuition tells me light should still be affected so is my conclusion valid or not? Is light red shifted in presence of an magnetic field? </p>
<p>If light is not red shifted then what is lost to ensure the system is not gaining energy but in this experiment it does not make sense since we are using photons which are not effected by magnetic fields and then recreating the para magnetic material (like Iron brick we used) so we should not loose energy as we are simply recreating the same object again. </p>
| 8,408 |
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<p>Suppose you know everything about Quantum Field Theory, but nothing about the very specific interactions and particles which exist in our real word.</p>
<p>Which physical or mathematical principles could be used to reduce the infinite number of possibilities of QFT, to finish with some class of theories, in which the Standard Model, for instance, would belong.</p>
<p>[If the question is too "extreme", one may soften it by considering having some partial information, to be detailed, about our real world]</p>
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<p>I can understand that animals need some battaries to run. But, we learn that plants serve like batteries for animals because they accumulate the sun energy in the first place! You can eat them or burn to extract the accumulated energy. This means that they consist of structures that they want to blow-up and disintegrate to fall apart at the lower energy level. But why? </p>
<p>This is strange to me since the <a href="http://en.wikipedia.org/wiki/Principle_of_minimum_energy" rel="nofollow">most fundamental law of nature</a> says that battaries spontaneously leak and discharge themselves. This means that the hydrocarbon structures that all life organisms are made of on the Earth are not stable. The photosinthesis, $\mathrm{H_2 O + CO_2 + \text{photo} \mapsto O_2 + CH_2O}$, is costly. It not only needs (photo) energy but uses it to produces the hydrocarbons, the $\mathrm{CH_2O}$-like spontaneously degrading structures! Why do you want to consist of something unstable that has tendency to blow up as soon as possible (why not immediatly, BTW?) if your purpose is survival, as any life organism on the Earth?</p>
<p>I watched the <a href="http://www.youtube.com/watch?v=DPjMPeU5OeM&feature=youtu.be" rel="nofollow">Gibbs Free Energy</a> but could not understand anything. Is it because of the min. energy law we have everything at the min energy already on the Earth and if you want to produce some structures (fortunately, there is a Sun), you have no other choice but to make them unstable?</p>
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<p>Space isn't a perfect vacuum and I wonder how an image of a galaxy can travel billions of years without becoming diffused by photon collisions with space matter?</p>
| 8,411 |
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] |
<p>I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.</p>
| 8,412 |
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<p>Say there is $\hat{J} = \exp[-i \hat{p} l/ \hbar]$ and $\hat{U}= \exp[-i\hat{H}t/ \hbar]$, where $\hat{H}$ is time-independent. </p>
<p>Can we say anything about $[\hat{J},\hat{U}]$? Is it zero? How do we show this? </p>
<p>For example if $\hat{H} = \hat{p}^2 /2m + m\omega^2 \hat{x}^2/2$.</p>
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] |
<p>I want to know the properties and the behavior of the gapless excitation for the traditional <a href="http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate" rel="nofollow">BEC</a>s. Could you give me some idea or references about this? </p>
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] |
<p>For rigid body we need to know position of three points and their velocities to determine everything. So that would make 12 DOF. Why do text books say it has six DOFs?</p>
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<p>If my understanding of wormholes is correct, anything that moves into a wormhole can be transported from one region of space-time to another. Consider a situation where an object of mass $m$ in space at $(x_1,y_1,z_1)$ and time $t_1$ travels through a wormhole and appears at $(x_2,y_2,z_2)$ in a distant future time $t_2$. In between time $t_1$ and $t_2$, it seems this object of mass $m$ doesn't exist. Hence during this span of time, the total mass-energy of the universe should be less than before. Doesn't this violate law of conservation of mass-energy?</p>
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<p>I know I should have listened to my teacher in physics class but I didn't. I need help on a thing I am trying to do for a game.</p>
<p>I want to be able to calculate Gravity pushing down on a object over a certain amount of time. (I want the object to slow down to a stop and then go back down due to gravity).</p>
<p>I've been looking on the internet and I guess I'm not using the right search terms. So I am hoping that this fine community can help me.</p>
<p>*The object(Player) is only moving upward. The Player is not moving forward or anything. Just Up</p>
<p>Given the initial velocity, how do I compute the motion (position, velocity) of the object as a function of time?</p>
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<p>I was drawing a diagram and trying to resolve all the forces. It seems to me that because of gravity, centrifugal force will produce a sort of "dragging" motion along the surface of the earth. The centrifugal force is quite small (I got around 2.5 N at the equator). This force is easily neutralized by friction. Is this right?</p>
<p>EDIT: I did not consider any complexities that may arise due to revolution, I just considered rotation.</p>
| 18 |
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<p>Long ago, I realized this: (super)string theory can NOT give a well-defined/unique prediction of why the electron (muon, tau) or the neutrino (any flavor) masses have the masses we measure. String theory can NOT give a concrete prediction of any SM particle mass (even resonances like the Higgs and other particles). The question is: Is this lack of predictive ability of the mass of the SM "elementary particles" a hint that string theory in its current status is not complete or wrong? Or perhaps even better:</p>
<p><strong>Even when string theory provides a framework in which you can accomodate every Standard Model field, and hence, a priori you can have the SM spectrum, we have not a string theory explanation of the values of the masses and charges. Should a explicit derivation of particle properties like (rest) masses and (bare) charges (like the electron charge value) be "predicted" and "derived" in a more fundamental version of the theory?</strong></p>
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<p>There are the eddy currents in thin circular copper plate thickness h and radius a, in a harmonic magnetic field which is perpendicular to plate and the effect of auto-induction is negligible. Now we must get average heat generated on it.</p>
<p>As I said, I have final equation, but how do you get to this eqution. Does anyone know solution from first step to this?
$$
\overline P=\frac{1}{16}\pi\gamma ha^4B_0^2\omega
$$</p>
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<p>In an ideal situation, we can use a simple formula to determine the velocity at which a body revolves around a massive body at a particular distance. I was wondering if there is an intuitive way to understand the motion of a body influenced by two other massive bodies (say the moon being influenced by the earth and the Sun). Is there any analogy to the motion of a wheel that can be considered as a combination as translational and rotational motion (and both these motions can be mathematically treated separately)? Or do we need a simulator to visualize the actual path?</p>
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] |
<p>There seems to have some (deep) relation between <a href="http://ncatlab.org/nlab/show/Seiberg-Witten+theory" rel="nofollow">Seiberg-Witten theory</a> and <a href="http://en.wikipedia.org/wiki/Superconductivity" rel="nofollow">superconductivity</a>. e.g. <a href="http://www.ams.org/journals/bull/2007-44-03/S0273-0979-07-01167-6/S0273-0979-07-01167-6.pdf" rel="nofollow">this Witten paper</a>.</p>
<blockquote>
<p>Q: Could someone introduce the relations between the twos both <strong>physically in terms of intuition</strong>? and <strong>mathematically in terms of formalism</strong>? How exactly is the relation?</p>
</blockquote>
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] |
<blockquote>
<p>A chip has a thermal resistance of 0.007 K/J s and thermal capacitance
of 1.6 J/K. You give it an impulse of heat equal to 100 J. How long
does it take for the chip to cool to within 10% of the ambient
temperature?</p>
</blockquote>
<p>I understand that I have to implement Newton's Law of Cooling, but I can't seem to grasp how I can find the ambient temperature nor the initial temperature.</p>
<p>Any and all help is greatly appreciated.</p>
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<p>I've been struggling with this question all morning, yet I get the feeling the answer is frightfully simple. </p>
<p>If Orion appears upside down in the Southern Hemisphere and the right way up in the Northern Hemisphere, what does it look like in equatorial countries such as Kenya, Colombia, and Ecuador, bearing in mind that Orion itself is in the equatorial region of the celestial sphere?</p>
<p>I initially thought it could just be a matter of perspective: If you're on the equator and facing North you'll see it the right way up,but see it upside down if you're facing South. But then surely that approach would apply even if you were in the Northern or Southern Hemisphere. </p>
<p>I reckon the times Orion is visible in various parts of the world will also have to be factored in. For example, it is visible at night late spring to summer in the Southern Hemisphere.</p>
<p>Could anyone offer me some advice? I fear I may be over-thinking this.</p>
<p>Thanks in advance.</p>
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<p>Ancient Greek astronomer Aristarchos who lived around 300 BC found a method to compute the Eart-Sun distance by applying geometry. </p>
<p><a href="http://www.youtube.com/watch?v=7ne0GArfeMs" rel="nofollow">In this video about the cosmic distance ladder</a>, at 26:30, Terence Tao explains that Aristarchos was basically limited by nonexisting clock technology.
So he was not able to accurately measure the time difference between the time of (1/2 (new moon - fullmoon)) and time at which sun-moon distance was exactly at 90 degrees to the intersection of earthorbit - moonorbit. See screenshots.</p>
<p><img src="http://i.stack.imgur.com/YnS0l.jpg" alt="Aristarchos 1"></p>
<p><img src="http://i.stack.imgur.com/bGR9e.jpg" alt="Aristachos 2"></p>
<p>Why was his method never refined in more modern times? Someone could have independently discovered the computation by a similar way of reasoning, but with better clocks.</p>
<p>Or <em>did</em> some European Astronomer else do this after mechanical clocks were invented, and it was just not accurate enough so they went for the transit-of-venus-method? </p>
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<p>Let us pretend for a moment that there are two identical planets that are exactly opposite their star from each other and are the same distance from said star. (This would make them, at all times, double the distance from their star apart from each other.)</p>
<p>Would they, under the definition of a planet, be considered planets? One could argue they have not cleared their neighborhood by virtue of one not having cleared the other. But, it would seem strange to assume a planet would be capable of clearing something that always has its sun in the way.</p>
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<p>I'd like to understand the physics of dynamic light scattering experiment. In particular I want to understand the basic relation between relaxation time $\tau_q$ and the diffusion coefficient $D$:</p>
<p>$\tau_q=(q^2 D)^{-1}.$</p>
<p>I suppose that more or less the following steps are necessary:</p>
<p>1) Calculate the scattered wave from Maxwell equations.
2) Find a relation between the scattered intensity autocorrelation function and the brownian motion of the particles.</p>
<p>I found this book by Berne and Pecora, but at least for point 1 I got lost because there seem to a strange version (or an approximation) of maxwell equations that I don't understand (it is citing Landau but looking at this book was not such an help).</p>
<p>Is there any book were I can find what I need or at least point 1 written with some detail?</p>
<p>thank you</p>
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<p>Using a <a href="http://www.fluke.com/fluke/usen/electrical-test-tools/thermometers/fluke-62.htm?PID=56096" rel="nofollow">Fluke 62 Mini Infrared Thermometer</a> today on a stainless steel pipe with coolant I noticed that it gives incorrect temperature readings. There is a temperature sensor inside the coolant saying about 90° Celsius. I spray painted a spot on the pipe and the IR thermometer instantly gave more correct readings on the painted spot.</p>
<p>So why?
Why is it the coolant fluid is about 90° Celsius (both the painted spot and the temperature sensor suggest that), while the unpainted clear stainless steel says about 50° Celcius? I.e. apx 55%</p>
| 8,427 |
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<p>It's a physics club for undergraduates (first three years of university); I'm looking for projects idea that aren't too obvious like a small rocket or an electromagnet (school projects) but also not too advanced. Since most members know Newtonian mechanics, electrostatics & magnetostatics and some simple notions of thermodynamics, waves, special relativity & geometric optics, I came up with the project "<em>The Solar System</em>" with the following objectives:<br/></p>
<ul>
<li>Study the motion of the earth in the gravitational field of the fixed sun (analytical solution) and compare the results to the available data.</li>
<li>Study the earth as a 2-body system (analytical solution)</li>
<li>Study the sun-earth-moon system numerically (3-body problem)</li>
<li>Study the sun-earth-moon-other planets as a 10-body problem</li>
<li>Treat the bodies as point particles and then as rotating solid bodies</li>
<li>Calculate the value of the year</li>
</ul>
<p>Any refinements to this projects are welcomed. Any other project?</p>
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<p>Once day, I talked to my Prof. about Computational Physics and he showed me his work. I'm quite surprised that why Prof. use C++ for computation because C++ quite complicated. I heard he talked about memory talk about pointer. Why didn't he use Python or Java that more easier? no need to manage memory no need to busy with pointer.</p>
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<p>Well the following question I really struggle to find an answer</p>
<blockquote>
<p>A thin lens creates an image of an object with magnification -3. A
second identical lens is positioned very close to the first lens such
that the distance between the two lenses can be neglected. What is the
magnification with this two lens system assuming that the object
distance has not changed?</p>
</blockquote>
<p>At first the solution seemed very simple, name the distances between some virtual objects $d_0$, $d_1$ & $d_2$. </p>
<p>Then the total magnifying factor can be found using:
$$M_t = -\frac{d_2}{d_0}$$
$$M = -3 = -\frac{d_1}{d_0}$$
$$M = -3 = -\frac{d_2}{-d_1}$$</p>
<p>(last equation has an extra minus sign as the image is a virtual location, the image $d_1$ is behind the lens, the distance of this virtual image to the lens is $d_1$ given that the lenses are "positioned very close".</p>
<p>Now the problem is: I can't solve this, 4 unknowns and only 3 equations. Also going by hand and stating simply "well the magnification factor is the combination of both lenses so $M_t = M * M = 9$ results in a "wrong answer".</p>
| 8,430 |
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<p>My book starts section 2.2 like this:</p>
<p><img src="http://i.stack.imgur.com/obS89.png" alt="enter image description here"></p>
<p>Equation 1.1 is this:
$$q_x=-k\frac {\partial T}{\partial x}$$</p>
<p>As you can see in the picture I posted, my book says that one can go from equation 1.1 to equation 2.1 by integration. I don't see how this is done by integration at all.</p>
<p>Thank you</p>
| 8,431 |
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<p>I've always been not so bad in mathematics, but I'm terribly bad at physics. For me, abstract concept are totally understandable, but when it come to reality, I'm lost !</p>
<p>So, for my job, I need to understand something.</p>
<p>I have an object, travelling during $t_o$ on a distance $d_o$.</p>
<p>It has an inital speed $v_1$, and a final speed $v_2$.</p>
<p>I need to find an exponential curve which fits the condition, and I'm lost in my equation, I don't know where to begin.</p>
<p>I try to start from the equation of the acceleration. I wan't it to be exponential, so </p>
<p>$$ a = e^{kt} $$</p>
<p>The speed curve is then the integration of the acceleration</p>
<p>$$ v = \frac{e^{kt}}{k}$$</p>
<p>I can substitute condition for finding k, </p>
<p>$$ v_1 = \frac{e^{k\cdot0}}{k} \implies k = \frac{1}{v_1}$$
$$ v_2 = \frac{e^{k\cdot t_0}}k \implies v_2 = v_1\cdot e^{{t_0}\cdot{v_1^{-1}}}$$</p>
<p>Which makes no sense. Where did I go wrong ?</p>
<p>My final idea is to have something like $$ t = f(d) $$ so I can find the time with the distance, and vice verse.</p>
| 8,432 |
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<p>I am studying quantum statistical mechanics from the mathematician's perspective. I don't quite understand what the duality formula for entropy is <em>really</em> saying (or why there is a "duality"). </p>
<p>If $A$ is an $n\times n$ Hermitian (self-adjoint, diagonalizable) matrix, then $$S(A)=\sup\bigl[{\operatorname{Tr}(AH) - \ln\bigl(\operatorname{Tr}[E^H]\bigr) : H \in H_n}\bigr]$$
where $H_n$ is the set of Hermitean matrices. </p>
<p>What does this even mean? </p>
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