question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>I'm currently doing some calculations which require evaluating various standard thermal expectation values in the canonical ensemble (both bosons and fermions). Now, in order to make my theoretical machinations easier, I am actually using the grand canonical ensemble, where the chemical potential acts as a Lagrange multiplier enforcing the constraint $\langle \hat{N} \rangle = N$, where $N/V$ is the fixed density of the physical system. The justification for this is that the relative fluctuations in $\langle \hat{N} \rangle$ should vanish in the thermodynamic limit, in which case I expect fixing the average number to be physically equivalent to fixing the number once and for all. (Also, this approach seems to be adopted by a several presumably trustworthy references, see for example <a href="http://archive.org/details/CondensedMatterFieldTheory" rel="nofollow">Simons & Altland</a> Section 6.3.) This intuition seems reasonable, but I wonder if matters may be more subtle than this argument implies.</p>
<blockquote>
<p>Do thermal averages in the thermodynamic limit of the grand canonical and canonical ensembles coincide?</p>
</blockquote>
<p>I'm hoping for either a more rigorous justification supporting this procedure, or examples where it can go horribly wrong. Pointers to appropriate references would also be much appreciated.</p> | g13506 | [
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<p>In thermodynamics, the heat $Q$ is defined as a type of energy in transfer, and is not a state function, which function denotes the energy of thermal motion within a system?</p>
<p>1) $TS$, (there is a contradictory, for an idea gas, $dU=TdS-pdV=C_vdT$)</p>
<p>2) Enthalpy $H$, ($H=U-Yx+pV =TS+pV+\sum_j\mu_jN_j$)</p>
<p>3) Neither of the two, the function has not been well defined,</p>
<p>4) The function cannot be defined.</p>
<p>5) Others.</p> | g13507 | [
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<p>My question is related to simulation of racing ball demonstration.
<a href="http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=142" rel="nofollow">http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=142</a></p>
<p>One ball goes on a straight path, while another one goes on a curved path. On the simulation the second ball going on the blue part down hill which is parabola has a constant component of the velocity in the x direction. Why is that the case when the slope changes?</p> | g13508 | [
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<p>This question follows a previous one of mine: <a href="http://physics.stackexchange.com/questions/70707/">Adiabatic theorem and Berry phase</a>. </p>
<p>In his original paper [ M. V. Berry, <a href="http://www.jstor.org/stable/2397741" rel="nofollow">Proc. R. Soc. Lond. A. Math. Phys. Sci. 392, 45 (1984)</a> ], Berry discussed the possibility for an old-forgotten phase factor to arise after one loop is done in a <em>parameter space</em>, using the adiabatic theorem. This became famously known as a <a href="http://en.wikipedia.org/wiki/Geometric_phase" rel="nofollow">Berry's phase</a>, see also <a href="http://en.wikipedia.org/wiki/Berry_connection_and_curvature" rel="nofollow">Berry's curvature</a> article on Wikipedia.</p>
<p>Soon after, [ Y. Aharonov and J. Anandan, <a href="http://dx.doi.org/10.1103/PhysRevLett.58.1593" rel="nofollow">Phys. Rev. Lett. 58, 1593 (1987)</a> ], AA proposed to generalised this adiabatic phase to non-adiabatic -- still cyclic -- evolutions. </p>
<p>What confused me is the sentence: </p>
<blockquote>
<p>[..] we regard $\beta$ [the AA geometric phase] as a geometric phase associated with a closed curve in the projective Hilbert space and not the parameter space [...]</p>
</blockquote>
<p>I would like to make this sentence a bit more clear, especially regarding the degeneracy point discussed in the previous question <a href="http://physics.stackexchange.com/questions/70707/">Adiabatic theorem and Berry phase</a>. </p>
<p><strong>What is the space in which the degeneracy appears?</strong> </p>
<p>Any comment to improve this question is welcome.</p> | g13509 | [
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<p>A plane mirror image approaches the object at the same rate the object approaches the mirror. So the speed of approach is twice the speed at which the object approaches the mirror. If the object approaches the mirror at a speed greater than half the speed of light (c), does that mean that the speed of approach between object and image will exceed the speed of light?</p> | g13510 | [
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<p>I'm sure a simple question.</p>
<p>I have a video of me jumping off a cliff into a river. I want to calculate how high it is. I know my weight, acceleration due to gravity of course, and I can get the time it took to hit the water.</p>
<p>Can I calculate (albeit roughly) how high the cliff was?</p>
<p>Cheers,</p>
<p>Tim.</p> | g13511 | [
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<p>Do we take gravity = 9.8 m/s² for all heights when solving problems?</p> | g13512 | [
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<p>How can the <a href="https://en.wikipedia.org/wiki/Hanbury_Brown_and_Twiss_effect" rel="nofollow">Hanbury Brown and Twiss effect</a> (photon bunching) be explained if photons don't interact in free space?</p>
<p>To explain it with the influence of the two photons on the two detectors simultaneously would seem strange to me, because of the fact that "if the source consists of a single atom which can only emit one photon at a time, simultaneous detection in two closely spaced detectors is clearly impossible" (same Wiki under the "Quantum interpretation" heading).</p>
<p>Comment: The question is not about uniting or dividing two photons, which is possible only on the atomic level. The question is about synchronizing two photons from different sources like the sun.</p> | g13513 | [
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<p>I have recently taken an interest in shadows. I know that in order for a shadow to exist that you must have a solid in the way of the light. My hypothesis is that there can be a light so strong, like a laser beam, that it acts like a solid in the sense where it doesn't let light pass through... is this plausible? </p> | g13514 | [
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<p>I have a couple of conceptual questions regarding the thermodynamics of scattering. Any partial answer or argument will be appreciated.</p>
<p>For the sake of discussion, consider the scattering of electromagnetic waves. I understand that the physics would be different for other particles or fields, feel free to base your discussion on those to provide your perspective.</p>
<p>The first questions are on the definition of entropy and its governing laws in a scattering process. More specifically:</p>
<p>(1) How do we define entropy for electromagnetic waves? I guess, one can always start from the general definition of entropy and perhaps calculate the density matrix of electromagnetic waves (though I've not seen such calculations). While such a first-principles approach might be helpful, I'm more of looking for a phenomenological definition that would capture the physics in relatively simple terms and mathematics. There seems to be arguments saying that electromagnetic waves do not have entropy, but given the fundamental nature of entropy, I think everything has entropy but it may not be well defined (please correct me if I'm wrong).</p>
<p>(2) How does entropy change in a scattering event? The second law would be a correct answer to this question, but is there a tighter bound regarding its change? Or, assuming that we now know how to define entropy for the electromagnetic waves, how are the entropies of incoming and outgoing waves related to the properties of the scatterer? (To better illustrate my question, in the case of energy, the difference between energies of incoming and outgoing waves is the dissipation in the scatterer.)</p>
<p>My final question is what I'm really after, though it might sound stupid: are the 1st and 2nd laws of thermodynamics independent in such scattering theories? (Can we derive the 2nd law from the 1st law plus something else in the framework of scattering theory?) This is not a random question but has basis in my research. I've been unable to reach clarity in this thought, but feel free to ask me to elaborate on any confusing statement.</p> | g13515 | [
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<p>After moving onto some of the practice textbook exercises in the section covering Kirchhoff's current law and Ohm's law, I came across a problem which evades my best attempts at solving it.</p>
<p><img src="http://i.stack.imgur.com/KybEy.png" alt="problem text"></p>
<p><img src="http://i.stack.imgur.com/goNxE.png" alt="circuit diagram"></p>
<p>Using Ohm's law, it was relatively easy to determine a equation involving voltage drops around the right loop:$$(1000\,\Omega)I_C+(1000\,\Omega)I_E=V_2\\(1000\,\Omega)(I_C+I_E)=V_2$$Similarly, it was simple to write an equation for the node where $I_B,I_E$ meet:$$I_B+I_C+150I_B=I_E\\151I_B+I_C=I_E$$... but given just $I_B=100\,\mu A=10^{-4}\,A$ it seems impossible to determine a numerical value for $I_C,I_E$.</p>
<p>Nevertheless it's straightforward to solve for $I_C,I_E$ in terms of $I_B,V_2$:$$I_C+I_E=\frac1{1000}V_2\\-I_C+I_E=151I_B\\\implies\begin{align*}2I_E&=151I_B+\frac1{1000}V_2\\2I_C&=-151I_B+\frac1{1000}V_2\end{align*}$$</p>
<p>Substituting $I_B=10^{-4}\,A$ yields $I_C=\frac1{20000}(10V_2-151),I_E=\frac1{20000}(10V_2+151)$</p>
<p>Am I approaching the problem correctly? Am I justified in ignoring the unlabeled voltage source bridging the two loops along with the labelled elements in the left one (i.e. $V_1,R_1,R_2$)? Am I treating the CCCS properly in writing my nodal equation?</p> | g13516 | [
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<p>I have two doubts:
Exactly when does this happen?
and
If we are in a superposition of states (lets say E1 and E2) and the particle absorbs a photon, what will happen? If E3-E1 = hf, will it go to E3?</p>
<p>Thanks!</p> | g13517 | [
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<p>...And you jumped in.</p>
<p>What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up? </p> | g76 | [
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<p>I saw this question in a test. I would have answered kinectic energy due to rotation and translation. It that correct. Else what is the answer?</p>
<p>Oh no, i forgot to mention it was objective type question.There were three other options.I just looked them up</p>
<p>1)kinetic energy due to rotation
2)kinetic energy due to translation
3)none of the above</p>
<p>the question looked confusing and the choices looked misleading at that time.
Thanks for all your resopnses</p> | g13518 | [
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<p>According to <a href="http://en.wikipedia.org/wiki/Water_rocket#World_record" rel="nofollow">this page</a>, the current record for greatest altitude achieved by a water and air propelled rocket is 2044 feet (623 meters).<br>
In this connection, i had one question: How the greatest altitude depends of the density of the liquid used in the rocket?<br>
Suppose that we have the opportunity to choose a liquid with an arbitrary density and with the same hydrodynamic properties as water. Then there must be a density at which the greatest altitude has its absolute maximum, i think. </p>
<p>To be more specific let's consider a simpler problem: </p>
<p>Let a two-liter soda bottle rocket, filled with some amount of a liquid mentioned above and air at the atmospheric pressure, is launched in deep space($g=0$)(say an astronaut is experimenting). What is the absolute maximum of the speed the rocket can achieve? For simplicity let's assume the expansion of the air to be isothermal (which it is not).</p>
<p><img src="http://i.stack.imgur.com/RVXX7.png" alt="enter image description here"></p> | g13519 | [
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<p>What is the meaning of expansion, shear and viscosity in context of universe? How can we conclude a result after getting a numerical value of above terms?</p> | g13520 | [
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<p>If I have a strong vessel that I've cooled to say -20°C, and lowered the pressure below 0.006 atmospheres, the water in food placed inside will sublimate and freeze dry the food.</p>
<p>But what happens to the water vapor? Does the moisture rise to the top or fall to the bottom of the vessel itself? Or does it just expand to fill the container equally?</p> | g13521 | [
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<p>I currently make my living as an electrophysicist, so am a bit embarassed at having not thought this one through, before.</p>
<p>Magnetically, the North pole is.... North. We get out our compass, and wait for the North-seeking needle to line up. I've always thought of this end of the needle as the north end.</p>
<p>In a current carrying loop, if we use the right-hand rule and point our thumb in the direction of conventional current, the fingers show the direction of the mag field lines around the wire. The direction the mag field lines point "north" when they pass through the interior of the loop. By stacking many such loops we can create a cylindrical electromagnet, for which it is easy to see which end is the "north" end. I resume permanent physical magnets follow the same naming convention: that is, mag field lines emanate from the north end and cycle around to the south.</p>
<p>We know that like poles of a magnet repel and opposites attract.</p>
<p>So, now, hanging a magnet from a string (or going back and using our trusty compass), if the north pole of the magnet points towards teh magnetic north pole of Earth, doesn't that mean that the pole near the Arctic circle is really magnetically-speaking the south pole? Or conversely, when we say "north-seeking" pole of a magnet, is that really the south pole of the magnet?</p>
<p>Which is it?</p> | g13522 | [
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<p>I'm aware of Sidney Coleman's 1975/76 sequence of <a href="http://www.physics.harvard.edu/about/Phys253.html">54 lectures</a> on Quantum Field Theory. Are there any other high-quality QFT lecture series available online?</p> | g371 | [
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<p>Given a DeSitter-space metric from the line element:</p>
<p>$$ ds^2=\left(1-\frac{r^2}{R^2}\right)dt^2-\left(1-\frac{r^2}{R^2}\right)^{-1}dr^2-r^2d\Omega^2 $$</p>
<p>Where $R=\sqrt{\frac{3}{\Lambda}}$, and $\Lambda$ is a positive cosmological constant, I am trying to derive the equations for radial null geodesics. I derived the geodesic equations from the definition and Christoffel symbols, but I'm a little suspicious of my solution to these equations. So, the differential equations I derived are ($\lambda$ is an "affine" parameter):</p>
<p>$$ \frac{d^2r}{d\lambda^2}-\frac{r}{R^2}\left(1-\frac{r^2}{R^2}\right)\left(\frac{dt}{d\lambda}\right)^2+\frac{r}{R^2-r^2}\left(\frac{dr}{d\lambda}\right)^2=0 $$</p>
<p>$$ \frac{d^2t}{d\lambda^2}+\frac{2r}{r^2-R^2}\frac{dt}{d\lambda}\frac{dr}{d\lambda}=0 $$</p>
<p>Now, I tried to use the identity $\textbf{u}\cdot\textbf{u}=0$ where $\bf u$ is the four velocity (or I guess a vector tangent to the light ray's world line if I'm thinking about this correctly). Thus, because $u^2=u^3=0$:</p>
<p>$$g_{\mu\nu}u^{\mu}u^{\nu}=\left(1-\frac{r^2}{R^2}\right)(u^0)^2-\left(1-\frac{r^2}{R^2}\right)^{-1}(u^1)^2=0 $$</p>
<p>$$\implies -\frac{r}{R^2}\left(1-\frac{r^2}{R^2}\right)(u^0)^2+\frac{r}{R^2-r^2}(u^1)^2=0$$</p>
<p>Then, substituting this into the first (radial) geodesic equation, I get:</p>
<p>$$\frac{d^2r}{d\lambda^2}=0$$</p>
<p>This is what I am suspicious of. It seems too easy and simple. Do you think this is correct? If I carry on anyways and integrate to find $u^0(r)$ then substitute $r(\lambda)$ I get the following for $t(\lambda)$:</p>
<p>$$ r(\lambda)=A\lambda+B $$</p>
<p>$$ t(\lambda)=\frac{D}{AR}\tanh^{-1}\left[\frac{A\lambda+B}{R} \right]+E $$</p>
<p>Where, $A,B,D,E$ are constants of integration. To sum up, is this a viable way to solve these equations or am I missing something? If this is correct, how does one define initial conditions for these solutions. Specifically, the derivative conditions $t'(0)$ and $r'(0)$.</p> | g13523 | [
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... |
<p>The speed of light is the same in all frames of reference. But imagine a scenario in which you passed by a ship which had (B=.78), while your ship had (B=.94). While somehow being able to look through the window of the ship you were passing, you see someone pointing a green laser into a fish tank, and of course the light refracts. Solving for the new angle is simple,(a bit of linear algebra, using the Lorentz matrix with angular components), but we all know that the speed of that light changes after it was refracted. So, would I measure the same velocity of that light as someone who is in the rest frame of the refraction incidence? I mean it is light, so all observers should measure it moving the same speed, correct? But, my gut tells me that I would clearly have to add the velocities using the velocity component Lorentz matrix. Where is the kicker?</p> | g13524 | [
0.03538060188293457,
-0.01465445477515459,
-0.0013958312338218093,
0.02077891118824482,
0.036130234599113464,
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0.05619180202484131,
0.013594410382211208,
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-0.03070559911429882,
0.03787991777062416,
0.06773542612791061,
0.02005651779472828,
0.022706... |
<p>For a given scalar potential $V$, it is known that the corresponding force field $\mathbf{F}$ can be computed from </p>
<p>$$
\mathbf{F} = -\nabla V
$$</p>
<p>Suppose a rigid body is placed inside this potential. The torque on the body $\mathbf{T}$ exerted by the scalar field will be</p>
<p>$$
\begin{align}
\mathbf{T} &= \int_M \left( \mathbf{r} \times \mathbf{F}(\mathbf{r}) \right) dm \\
&= \int_M \left( \mathbf{r} \times -\nabla V(\mathbf{r}) \right) dm \\
&= \int_M \left( \nabla V(\mathbf{r}) \times \mathbf{r} \right) dm
\end{align}
$$</p>
<p>with $\mathbf{r}$ the position vector to the mass element $dm$, and the integration carried out over the entire body $M$.</p>
<p>So, being not too familiar with rigid body dynamics, I was wondering -- does something like a (vector/scalar) potential $P$ exist, such that the local torque induced by the potential $V$ can be expressed as</p>
<p>$$ \matrix{
\mathbf{T} = I \cdot \nabla P & & &\text{(or some similar form)}
}
$$</p>
<p>with $I$ the moment of inertia tensor of the rigid body? </p>
<p>If such a thing exists: </p>
<ul>
<li>what is its name?</li>
<li>where should I start reading?</li>
<li>What is the proper expression for the torque $\mathbf{T}$?</li>
<li>how does $P$ relate to $V$?</li>
</ul>
<p>If such a thing <em>doesn't</em> exist: </p>
<ul>
<li>why not? :) </li>
</ul> | g13525 | [
0.06673746556043625,
-0.010040213353931904,
-0.010789130814373493,
0.007841922342777252,
0.04048604518175125,
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0.06114486977458,
0.040907878428697586,
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0.010874639265239239,
-0.018240146338939667,
-0.02394779771566391,
0.01110299676656723,
-0.044483... |
<p>Will it be possible to fry eggs in <a href="http://en.wikipedia.org/wiki/Sahara_Desert_%28ecoregion%29" rel="nofollow">Sahara desert</a> by just keeping them under the sun? If so, then will the radiated eggs be any different? Or will we have to use the <a href="https://en.wikipedia.org/wiki/Solar_cooker" rel="nofollow">solar cooking</a> concept to some extent? What is the minimum Intensity required and the temperature to achieve this?
(With and without solar cooker)</p> | g13526 | [
-0.00012479581346269697,
0.05623156577348709,
-0.013947459869086742,
0.003979193512350321,
-0.05377785861492157,
0.009336068294942379,
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-0.03914714977145195,
-0.041097041219472885,
0.026954062283039093,
0.035897739231586456,
0.040308307856321335,
... |
<p>I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum systems. This is what I have so far:</p>
<ul>
<li>superposed: A superposition of two states which a system $A$ can occupy, so $\frac{1}{\sqrt{2}}(|1\rangle_A+|1\rangle_A)$</li>
<li>seperable: $|1\rangle_A|0\rangle_B$ A state is called separable, if its an element of the (tensor)product basis of system $A$ and $B$ (for all possible choices of bases)</li>
<li>entangled: $\frac{1}{\sqrt{2}}(|0\rangle_A|1\rangle_B+|1\rangle_A|0\rangle_B)$ is not a state within the product basis (again for all possible bases).</li>
<li>mixed state: Is a statistical mixture, so for instance $|1\rangle$ with probability $1/2$ and $|0\rangle$ with probability $1/2$</li>
<li>pure state: Not a mixed state, no statistical mixture</li>
</ul>
<p>I hope that the above examples and classifications are correct. If not it would be great if you could correct me. Or add further cases, if this list is incomplete. </p>
<p>On wikipedia I read about <a href="http://en.wikipedia.org/wiki/Quantum_entanglement" rel="nofollow">quantum entanglement</a></p>
<blockquote>
<p>Another way to say this is that while the von Neumann entropy of the whole state is zero (as it is for any pure state), the entropy of the subsystems is greater than zero.</p>
</blockquote>
<p>which is perfectly fine. However I also read on wikipedia a criterion for <a href="http://en.wikipedia.org/wiki/Mixed_state_%28physics%29#Mixed_states" rel="nofollow">mixed states</a>:</p>
<blockquote>
<p>Another, equivalent, criterion is that the von Neumann entropy is 0 for a pure state, and strictly positive for a mixed state.</p>
</blockquote>
<p>So does this imply that if I look at the subsystems of an entangled state, that they are in a mixed state? Sounds strange... What would be the statistical mixture in that case?</p>
<p>Moreover I also wanted to ask, whether you had further illustrative examples for the different states I tried to describe above. Or any dangerous cases, where one might think a state of one kind to be the other?</p> | g13527 | [
0.005850040819495916,
0.017883678898215294,
0.021440710872411728,
-0.04264339059591293,
-0.02984713949263096,
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0.06565626710653305,
0.032594580203294754,
0.07321201264858246,
-0.03446219488978386,
-0.04291452467441559,
-0.04653873294591904,
0.03187824413180351,
-0.0059... |
<p>How occurs the <a href="http://en.wikipedia.org/wiki/Chirality_%28mathematics%29" rel="nofollow">enantiomorph</a> of the mirror?</p>
<p>I would like to know how occurs the RELATIONS OF THE RAYS with the mirror and the image, everything that happens to be flipped image from the right to the left.</p> | g421 | [
-0.05476254224777222,
0.000700735894497484,
-0.014879646711051464,
-0.018341748043894768,
0.10336283594369888,
-0.02159256301820278,
0.05461791157722473,
0.06977184116840363,
-0.006741843651980162,
0.016297245398163795,
-0.0028837101999670267,
0.037129826843738556,
0.05559059977531433,
0.0... |
<p>A curiosity question.</p>
<p><a href="http://en.wikipedia.org/wiki/Radio_propagation" rel="nofollow">Radio Propagation</a> within Earth's atmosphere is via atmosphere. Broadly speaking a signal loses strength between bouncing off the ionized layer, and absorption by various earthy elements.</p>
<p>If an identical signal were to be produced in free space, how far would it travel as compared to it's range within Earth's atmosphere? </p>
<p>EDIT: A commercial FM transmitter on Earth probably has a range no more than 25 miles where the listener uses a broadcast receiver. For the purpose of elaboration assume the the receiver being placed in static orbit - how far out could the same signal be generated, and still be intelligible?</p> | g13528 | [
-0.008291371166706085,
0.05456877127289772,
-0.009398736990988255,
0.00447146175429225,
-0.04422038421034813,
0.009038806892931461,
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-0.032193075865507126,
-0.06003912538290024,
0.0010732035152614117,
0.0650184154510498,
0.02833583764731884,
-0.... |
<p>The problem description for the <a href="http://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap" rel="nofollow">Yang-Mills Existence and Mass Gap</a> problem (<a href="http://www.claymath.org/sites/default/files/yangmills.pdf" rel="nofollow">http://www.claymath.org/sites/default/files/yangmills.pdf</a>) says in its "Mathematical Perspective" section that</p>
<blockquote>
<p><em>Some results are known for Yang-Mills theory on a 4-torus $\mathbb{T}^{4}$ approximating $\mathbb{R}^{4}$ and, while the construction is not complete, there is ample indication that known methods could be extended to construct Yang–Mills theory on $\mathbb{T}^{4}$.</em></p>
<p><em>In fact, at present we do not know any non-trivial relativistic field theory that satisfies the Wightman (or any other reasonable) axioms in four dimensions. So even having a detailed mathematical construction of Yang–Mills theory on a compact space would represent a major breakthrough. Yet, even if this were accomplished, no present ideas point the direction to establish the existence of a mass gap that is uniform in the volume. Nor do present methods suggest how to obtain the existence of the infinite volume limit $\mathbb{T}^{4}\rightarrow\mathbb{R}^{4}$.</em></p>
</blockquote>
<p>Could someone point me in the direction of a paper that describes the use of compact torus manifolds to construct 4d Quantum Yang-Mills, or else describe some of these attempts? Also, is the difficulty alluded to by Witten and Jaffe solely that a toroidal space is compact whereas a Euclidean space is unbounded, or is there more to the story?</p> | g13529 | [
0.007218125741928816,
0.010670389980077744,
-0.01988474279642105,
-0.04924343153834343,
-0.018273556604981422,
0.035270269960165024,
0.05808380991220474,
0.0009355478687211871,
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0.01391110010445118,
0.06000373512506485,
-0.07898374646902084,
0.04359283670783043,
0.0058... |
<p>I'm a programmer and a game developer, not a mathematician or a physicist. So please go easy on the math :)</p>
<p>I know two things:</p>
<ul>
<li>How to find the new velocities of two objects after an <a href="http://en.wikipedia.org/wiki/Elastic_collision">elastic collision</a>.</li>
<li>How to find the velocity of the new object formed by two objects in an <a href="http://en.wikipedia.org/wiki/Inelastic_collision">inelastic collision</a>.</li>
</ul>
<p>However what I need to know is: given the mass, the velocity, and the 'angle' the two objects are going two be when they collide - how can I know if I need to compute an elastic or an inelastic collision?</p>
<p>I need this for the 2D game I'm developing, that tries to simulate relatively-realistic physics. Thanks for your help</p> | g13530 | [
0.056678663939237595,
-0.014417598024010658,
-0.013626334257423878,
-0.004111053422093391,
0.0657576322555542,
-0.03526303172111511,
-0.0028834128752350807,
0.01592238061130047,
-0.059655044227838516,
-0.01790895126760006,
-0.01896100677549839,
-0.006796079687774181,
0.052620355039834976,
... |
<p>Consider an acoustic wave in some medium, expressed as particle displacement:</p>
<p>$$s(t,x) = e^{j(-\omega t + kx)} $$</p>
<p>I understand that pressure must be at its maximum when the particle displacement is zero and vice versa. But there are many functions that satisfy that criterion.</p>
<p>How can the pressure be expressed in terms of particle displacement?</p> | g13531 | [
0.06332341581583023,
-0.02485458180308342,
-0.015522399917244911,
-0.04900835454463959,
0.07817944884300232,
0.02596237324178219,
-0.04432385787367821,
0.013211317360401154,
-0.035691969096660614,
0.03497694432735443,
-0.08597280830144882,
0.00452144630253315,
0.025944825261831284,
0.00636... |
<p>I am trying to understand how a real world beam of laser actually reflects the physics description of oscillating electromagnetic waves.</p>
<p>So say we are looking side on at a vertically polarized laser beam, and this is section of it propagating through free space:</p>
<p><img src="http://i.stack.imgur.com/9qqwi.png" alt="enter image description here"></p>
<p>Ive cut down the opacity and zoomed in now to illustrate my question on what would the waves look like? Something like...</p>
<p><img src="http://i.stack.imgur.com/47Ngz.png" alt="enter image description here"></p>
<p>But how can this form a Gaussian intensity profile? Maybe there are more of these waves dispersed through out it, and their amplitude denotes the intensity e.g:</p>
<p><img src="http://i.stack.imgur.com/D4wX5.png" alt="enter image description here"></p>
<p>Where the waves closer to the edge of the beam are the same wavelength but smaller amplitude than the main section...? But now we have only considered a horizontal cross section, what would it be like if you looked at it from above? </p>
<p>Thanks</p> | g13532 | [
0.03881416842341423,
-0.019114498049020767,
-0.01666744239628315,
-0.015805739909410477,
0.0008976023527793586,
0.06014120951294899,
0.002786159049719572,
0.018626322969794273,
-0.008561208844184875,
-0.02509087696671486,
0.0017730151303112507,
0.04675273224711418,
0.058668043464422226,
-0... |
<h2>Does this integral converge?</h2>
<p>My question is related to this one:
<a href="http://physics.stackexchange.com/questions/23682/free-particle-propagation-amplitude-calculation">Free particle propagation amplitude calculation</a></p>
<p>I am reading the book of Peskin and Schroesder. In the second page of their chapter 2, they estimated the propagator for the Klein-Gorden equation. The final step of the calculation is to calculate an integral of the form</p>
<p>$$\int_0^\infty \mathrm{d}p\;p\;\sin(px)e^{-\mathrm{i}t\sqrt{p^2+m^2}}.$$</p>
<p>My question is very simple: does this integral converge in the first place? Note that the integrand is an oscillating function whose amplitude grows without bound. If we take $m=0$, then for sure the integral does not converge.</p>
<p>In fact, I can reproduce their result very easily (namely, the $e^{-m\sqrt{x^2-t^2}}$ behavior). But I am not sure whether my calculation makes sense because I don't know whether the integral has a finite value.</p>
<p>I know this integral can be converted into a loop integral in the complex plane, and then be estimated using stationary-phase method. But since the amplitude of the integrand does not go to zero uniformly at infinity, I feel such a procedure may not be valid.</p>
<p>We may multiply a factor $e^{-\epsilon p}$ ($\epsilon>0$) to the integrand to make it converge, but then we are not calculating what we wanted to calculate in the beginning, right?</p>
<p>Then, if the integral does not converge by itself, how should I make sense of the result in the Peskin and Schroesder book?
I am quite confused by this. Thanks for any hints!</p> | g13533 | [
0.04221083223819733,
0.013613495044410229,
0.03594610467553139,
-0.04867707937955856,
-0.03318898379802704,
0.006417796481400728,
0.008064853958785534,
0.009922794997692108,
-0.05666537210345268,
0.027264177799224854,
-0.04915634170174599,
0.013355394825339317,
-0.0172578077763319,
0.03839... |
<p>The question:</p>
<p>How would you make a semi transparent mirror (50% reflection, 50% transmission) with glass with a layer of copper. For light $\lambda$ = 500nm Try to be as realistic as possible</p>
<p>What I've done so far. </p>
<p>The reflection coefficient of copper for 500nm light is 50%. So that's great. But I'm not sure whether that's enough. (It is an exam question, so I guess not).
I'm guessing it'll have to do something with skin depth, but I'm not sure.</p>
<p>Any suggestions on how to continue ?</p> | g13534 | [
-0.030067365616559982,
0.012245689518749714,
0.020469950512051582,
-0.03717607632279396,
-0.014750664122402668,
0.0015503939939662814,
0.04062946140766144,
0.038848333060741425,
0.003575962735339999,
-0.00360513711348176,
-0.005577854812145233,
0.07327672839164734,
0.028645707294344902,
0.... |
<p>I was reading the article <em><a href="http://cdn.makezine.com/make/24/Make24_weatherballoon_11x17.pdf" rel="nofollow">Weather Balloon Space Probes</a></em> that says you can put your own balloon probe at 65,000 ft temporarily. </p>
<p>Is it even remotely possible to raise the probe high enough using <a href="http://kaymontballoons.com/Near_Space_Photography.html" rel="nofollow">balloons</a>, and then put it in orbit or escape the field using an on-board propulsion system?</p>
<p>Can it be done with easily purchased materials?</p>
<p>How much mass can be added for instrumentation?</p>
<p>How much fuel of is required? What kind?</p>
<p>I know it's kind of a broad question, but I just want to know a rough estimate.</p> | g13535 | [
-0.03796255216002464,
0.017751114442944527,
0.0004915516474284232,
-0.026098307222127914,
-0.022810861468315125,
0.01705981232225895,
-0.0517691932618618,
0.006424080114811659,
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0.04227038472890854,
0.014695699326694012,
0.05561504513025284,
-0.0016041601775214076,
-0... |
<p>In 1+1 dim bosonization, one introduce the Klein factors, which are Hermitian and satisfies Clifford algebra. </p>
<p>(1) In the case of <strong>1 dim space is a 1D ring ($S^1$ circle)</strong>, then one have left-right boson field commutes
$$[\phi_L, \phi_R]=0$$
but introduces Klein factor to reproduce the fermionized fermion field anti-commute:
$$\{ \psi_L, \psi_R\}=0.$$</p>
<p>(2) However, according to this <a href="http://arxiv.org/abs/cond-mat/9908262" rel="nofollow">Ref</a>, in page 21, footnote 8, for <strong>1 dim space as an infinite line</strong>, one requires
$$[\phi_L, \phi_R]=i \frac{1}{4}$$
to reproduces the fermionized fermion field anti-commute:
$$\{ \psi_L, \psi_R\}=0.$$</p>
<blockquote>
<p><strong>How can I see, how can one show that $[\phi_L, \phi_R]=i \frac{1}{4}$ for 1 dim space as an infinite line</strong>?</p>
</blockquote> | g13536 | [
-0.014120233245193958,
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0.09129711240530014,
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0.0540810227394104,
0.06746914237737656,
0.006366313900798559,
-0.04608386382460594,
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0.003818701719865203,
-0.060712508857250214,
0... |
<p>Consider a system in which atoms are located in a regular lattice, each atom having a spin $1/2$ and an associated intrinsic magnetic moment $\mu_0>0$. Assume that each atom interacts only weakly with other atoms so that all the other atoms act as a heat reservior. If the system is placed in an external magnetic field $H_0 \hat{z}$, then the Hamiltonian is given by:
$$\hat{H}=-\mu_0H_0\sum_i\sigma^z_i$$
where $\sigma_i^z$ are (the $z$ components of) the <a href="http://en.wikipedia.org/wiki/Pauli_matrices" rel="nofollow">Pauli matrices</a>, at the $i$th site. </p>
<p>For the magnetic moment $\mu= \pm\mu_0$, the corresponding magnetic energy of the atom is $E=\mp\mu_0 H_0$. </p>
<p>What would be the mean magnetic moment?</p> | g13537 | [
-0.01829197071492672,
0.011161881498992443,
-0.024510737508535385,
-0.05690458416938782,
-0.00634413119405508,
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0.0542290173470974,
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0.04236065596342087,
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0.05704006925225258,
-0.0332363061606884,
-0.03... |
<p>Conceptually, I understand that coaxial cables operate in a TEM mode due to the central conductor, and hence the electric field is directed radially outward from the voltage $V_0$ at the centre of the cable, to the supposedly grounded outer cable (the derivation for this involving Poisson's equation and such). Similarly, as the current flows down the cable, the magnetic field around this conductor has direction only in terms of $\phi$ and does not change with $z$. However, I've been asked:</p>
<p><em>How are the electric and magnetic fields inside a coaxial cable related to the V and I in the wave of the equation:</em></p>
<p>$V_+(t-z/v) = Z_0I_+(t-z/v)$</p>
<p><em>where the subscript $+$ signifies the voltage and current in the $+z$ direction</em> (Note that there is a similar formula for the -ve reflected direction).</p>
<p>I've been searching all night, but I have yet to find a solid explanation for this that doesn't involve derivations from first principles. How can I turn the above equation into something involving B and E fields?</p> | g13538 | [
-0.03322143480181694,
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-0.03216038644313812,
-0.012841074727475643,
0.08280542492866516,
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0.05989465117454529,
0.019645050168037415,
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-0.002203752752393484,
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0.010820101946592331,
0.022461693733930588,
0.... |
<p>I've read that electroweak symmetry breaking occurred "at a picosecond or so" after the Big Bang (in <a href="http://delphiwww.cern.ch/talks/general/Treille.tianjin2012/origin_tianjin_corr_reduced.pdf" rel="nofollow">a source I found</a>).</p>
<p>I can't help wondering why it took so long to get started. For instance, was something missing up until then, which was needed by the <a href="http://en.wikipedia.org/wiki/Higgs_mechanism" rel="nofollow">Higgs mechanism</a>?</p>
<p>What feature(s) of the Higgs mechanism, or perhaps what other theoretical consideration(s), was/were seemingly responsible for this very brief delay?</p> | g13539 | [
0.03974686190485954,
0.059105582535266876,
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0.03701093792915344,
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-0.05284838378429413,
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-0.029964903369545937,
0.007620486430823803,
0.04836... |
<p>The problem in Sredniki's textbook 10.5 :</p>
<p>For a free scalar field $\psi$, the Lagrangian is
$$\cal{L}= -\frac{1}{2}\partial^\mu\psi\partial_\mu\psi-\frac{1}{2}m^2\psi^2$$
Here we use the metric $\operatorname{diag}(- + + +)$</p>
<p>If I make $\psi=\phi+\lambda \phi^2$, then the Lagrangian is
$$\cal{L}= -\frac{1}{2}\partial^\mu\phi\partial_\mu\phi-\frac{1}{2}m^2\phi^2-2\lambda\phi\partial^\mu\phi\partial_\mu\phi-\lambda m^2\phi^3-2\lambda^2\phi^2\partial^\mu\phi\partial_\mu\phi-\frac{1}{2}\lambda^2m^2\phi^4$$</p>
<p>For scattering $\phi\phi \to \phi\phi $, how do I calculate the loop correction? Since the Lagrangian is now nonrenormalizable. In loop correction we need to take ghost into consideration. </p> | g13540 | [
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0.0165473073720932,
-0.0013075383612886071,
0.06525609642267227,
0.026531675830483437,
0.067435... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/843/maxwells-demon-constant-information-energy-equivalence">Maxwell's Demon Constant (information-energy equivalence)</a> </p>
</blockquote>
<p>I was reading:</p>
<p><a href="http://www.scientificamerican.com/article.cfm?id=demonic-device-converts-inform" rel="nofollow">Demonic device converts information to energy : Experiment inspired by a paradox tempts a bead uphill.</a></p>
<p>Its good to see conservation of energy is violated. :)</p>
<p>I want to know more about it. What other resources are available (that doesn't involve too much math). Especially, I want to see that beed experiment. Are there any demonstrations available on net?</p>
<p><strong>EDIT:</strong> I did learn more about maxwell's daemon from this:
<img src="http://i.stack.imgur.com/yrLNz.png" alt="alt text"></p> | g422 | [
0.04584064334630966,
0.03750830516219139,
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0.004179932177066803,
0.033022888004779816,
0.013021639548242092,
0.04740952327847481,
0.0052... |
<p>What do you guys think of <a href="http://www.dilbert.com/blog/entry/what_is_the_universe_made_of/" rel="nofollow">Scott Adams' theory</a> that the Universe might be made of recursions, created by observation?</p>
<p>I find it fascinating but have no strong opinion yet if it makes sense.</p> | g13541 | [
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0... |
<p>The mistery of the mass of the top being in the electroweak scale can be justified by the Higgs mechanism itself; in some sense the top mass is the only "natural" mass, the other masses of fermions being protected by some unknown mechanism so that they are "zero" relative to the electroweak: the typical values of the Yukawas are in the $10^{-3}$ range and even smaller. The masses are still "natural" relative to GUT or Planck Scale cutoffs, because then their corrections are logarithmic and about the same order of magnitude that the mass itself, in fact about a 30%.</p>
<p>My question is about the mass of tau and mu. Is there some reason for them to be in the GeV range, where QCD masses -proton and pion, if you wish, or glue and chiral scales- are?</p>
<p>I am asking for theories justifying this. For instance, Alejandro Cabo tries to produce first the quark masses from the one of the top quark via QCD, very much as <a href="http://prd.aps.org/abstract/PRD/v7/i8/p2457_1" rel="nofollow">Georgi-Glashow electron-muon</a> in the early seventies, and then he expects that the leptons should have masses similar to the quarks via the electromagnetic/electroweak coupling (albeit some group theoretical reason could be enough).</p>
<hr>
<p>Hierarchically, and from the point of view that any near zero value for a coupling is a hint for a broken symmetry (so that in the limit where this symmetry is unbroken, the coupling is exactly zero), what I would expect is a symmetry protecting all the yukawas except the top, and then still a subgroup protecting the first generation.</p> | g13542 | [
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<p><sup>[Remark: I admit that my first attempt on <a href="http://physics.stackexchange.com/questions/994/what-makes-a-space-a-real-space">What makes a space a real space?</a> was rather ill-posed and led to some confusion. Sorry for that, but please give me a second try. Part of the confusion arose from the ununsual term "real space". The far better term would have been "<a href="http://en.wikipedia.org/wiki/Physical_space" rel="nofollow">physical space</a>" which I hope to be unambiguous.]</sup></p>
<p>In the following let a "mechanical system" be a system of $n$ spatial objects moving in physical space.</p>
<p>Consider you are given a function $q:\mathbb{R} \rightarrow \mathcal{M}^n$ with $\mathcal{M}$ a mathematical space.</p>
<p><strong>Question 1</strong></p>
<blockquote>
<p>When would you assume that $q$ describes the evolution of a mechanical system?</p>
</blockquote>
<p>I would, if I found or was given a function $\mathcal{L}(x,\dot{x},t)$ such that the Lagrange equations hold for all times $t$ when inserting $q(t)$ for $x$ and $\dot{q}(t)$ for $\dot{x}$, and which I can consider physically plausible. In this case I would interpret $\mathcal{M}$ as physical space, maybe distorted by generalized coordinates.</p>
<p>I would <em>not</em>, if there is provably no such function. In this case $q$ describes the evolution of a general dynamical system, but not a mechanical one.</p>
<p><strong>Question 2</strong></p>
<blockquote>
<p>Are there mathematically definable conditions on $\mathcal{L}$ for being physically plausible, or possible, let's say? </p>
</blockquote>
<p>Besides, maybe, that $\mathcal{L}$ must be of the form $\mathcal{T} - \mathcal{V}$.</p>
<p><strong>Question 3</strong></p>
<blockquote>
<p>Can anyone give an example of a non-mechanical system that <em>behaves</em> like a mechanical one (in the narrow sense above)?</p>
</blockquote>
<p>One answer to this question comes immediately in mind: a system that is <em>designed</em> to behave like a mechanical one, e.g. a computer running a simulation. I'd like to exclude such cases if I could, and restrict the question to "natural" systems.</p>
<p><strong>Question 4</strong></p>
<blockquote>
<p>What about possible worlds with a physical space like ours but in which the Lagrange equations do not hold?</p>
</blockquote> | g13543 | [
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<p>In my physics class, we did an experiment in which we supported Ohm's law. We used a simple circuit that includes one resistor. The relationship of I = VR, and variants thereof, became apparent. We mainly looked at the relationship between potential difference and the current in series.</p>
<p>What we have not done is see if this relationship is apparent in a series circuit with multiple resistors. I've did further research and read about Non-ohmic resistors, do they have anything to do with this? I can't really make the connection.</p>
<p>So my question is, what is the relationship between the potential difference across two resistors in series and the current through them? We are moving towards parallel, but I would like to know this question better. </p> | g13544 | [
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0.04... |
<p>Because of the image forced barrier lowering the barrier potential reduces in reverse bias . What happens to barrier height (potential) in forward bias??</p> | g13545 | [
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<p>I have been taught in school that atoms cannot have more than 8 electrons in the outer shell. <a href="http://en.wikipedia.org/wiki/Palladium" rel="nofollow">Palladium</a> atom's electron configuration is 2,8,18,18. Why isn't it 2,8,18,17,1 like the case of Platinum 2,8,18,32,17,1 or Nickel 2,8,17,1 and they are all in the same group?</p> | g13546 | [
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<p>This is more of a theoretical thought-experiment question.</p>
<p>Basically, how much geothermal energy can we extract before the loss of the magnetic field makes it a terribly bad idea?</p>
<p>Will the geothermal energy inside the earth now, which is lost through "natural processes", last until the end of the Sun (say, another 5billion years?) And if so, how much excess is leftover?</p>
<p>a) do we know how much thermal energy there is? Call this: A</p>
<p>b) do we know at what point the core would stop producing a magnetic field? (ie: is it when the iron in the core is no longer molten?) Call this: B</p>
<p>c) do we know the rate that heat is radiated out naturally? Call the annual rate: C</p>
<p>So I guess: A-B - (5.0 * 10^9 * C) is the amount of heat for "safe" geothermal extraction?</p>
<p>also: Considering such extreme timescales -- are there any other factors adding heat into the Earth? Maybe tidal interactions with Sun/Moon/etc add anything over billions of years?</p>
<p>Thanks!</p> | g13547 | [
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<p>Gell-Mann and Hartle came up with the <a href="http://arxiv.org/abs/1106.0767" rel="nofollow">extended probability ensemble interpretation</a> over <a href="http://arxiv.org/abs/0801.0688" rel="nofollow">here</a>.</p>
<p>Basically, they extended probability theory to include real numbers which may be negative or greater than 1. This necessitates an unconventional interpretation of probabilities, and for that, they used the "no Dutch book" interpretation of probability theory. For the "no Dutch book" interpretation to even make any sense, they have to introduce cybernetic agents, which they call Information Gathering and Utilizing Systems (IGUS). These agents can make bets, and a Dutch book against them is a collection of bets made with the agent such that individually, the agent would prefer to make the bet, but collectively, the agent will lose a fixed amount <em>no matter what the outcome of the bet is</em>. The condition that no Dutch book can be made against an agent is equivalent to the agent's belief system satisfying the axioms of classical probability theory. An agent with negative probabilities or a probability greater than one is susceptible to Dutch books.</p>
<p>Only bets on outcomes which can be recorded can be settled, but such outcomes aren't susceptible to Dutch books, or so they claim. Otherwise, don't bet. This already brings up a whole host of issues. Do the bets really have to happen, or is it enough to merely imagine them? Or is it enough that the agent is prepared to bet should the need arise? Or does the bet happen at the meta level? Is the agent free to choose whether or not to bet?
Besides, an agent which always loses isn't necessarily an inconsistent agent, merely one which fails to satisfies its goals.</p>
<p>An agent can have a belief system not susceptible to Dutch books but is still lousy anyway. Another more knowledgeable agent can exploit their better knowledge to offer a series of bets, which while not guaranteeing a profit all the time, is likely to bring a profit most of the time, and only a loss rarely (whatever "most of the time" and "rarely" really mean). </p>
<p>The authors state that the preferred basis is the basis of the Feynman path integral, but what about S-dualities? Even without S-dualities, a quantum field theory can be described equivalently either as a path integral over field configurations, or a path integral over Feynman diagrams with edges and vertices. Which basis is preferred?</p>
<p>The fine-grained probability distribution can have negative probabilities, but there are coarse-grainings with only non-negative probabilities, and at least one such coarse-graining always exists; the coarse-graining with no resolution. A maximal coarse-graining is one associated with non-negative marginal probabilities for which any extension of it will contain negative probabilities. Such coarse-grainings are referred to as realms. Unfortunately, mutually incompatible realms are the norm, and not the exception.</p>
<p>No problem, they write. There "really" is a "real" fine-grained history, and whichever realm we choose, the "real" history is the one containing the "real" fine-grained history, which is <em>unobservable</em>. We may choose incompatible realms if we so wish, and whichever one we choose, there is a corresponding "real" history. But what is the probability distribution for the "real" fine-grained history? It can be <strong>negative</strong> or greater than 1! How can something with <em>negative</em> probability happen? So just how real is it anyway?</p>
<p>As they so clearly pointed out, the past history is unobservable. Only present records are observable. But there's always the possibility that the present record is misleadingly deceptive about the past history, assuming an actual past history even exists. When should we choose to measure the records? Now? When is "now"? Why isn't now one second ago or a year from now?</p>
<p>The records are only approximately recorded and approximately decoherent anyway. So, we can in principle make a Dutch book with exponentially small payoff against such agents.</p>
<p>Realms which are "typical" are preferred over realms which are not. Typicality means the log of the coarse-grained probability for the "real" coarse-grained history is much less than the Shannon entropy. But why is typicality preferred?</p> | g13548 | [
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<p>Today, I tried creating a very basic Faraday cage by surrounding a radio with two baking trays made out of iron. It didn't seem to affect the radio's signal (AM was being used, not FM).</p>
<p>In theory, should what I used block the radio's signal?</p>
<p>I can't remember how thick the baking trays were. There was some gaps totalling a few square centimetres, because the two baking trays were not identical. I didn't attempt to "Ground" the baking trays.</p> | g13549 | [
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<p>As given on this <a href="http://en.wikipedia.org/wiki/Supercritical_fluid" rel="nofollow">link</a>, supercritical fluids are viewed more as a continuum which has both liquid and gas properties. This continuum is obtained when a gas is brought to a pressure and a temperature higher than its critical values. The intermolecular distances of a pure supercritical fluid are in between that of a liquid and gas. With so many qualitative differences between a supercritical fluid and a gas and a liquid. Why is it not considered a separate state of matter?</p> | g13550 | [
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<p>With crude calculations following densities can be approximated:</p>
<p>Given that radius of proton is $1.75×10^{−15} m$ and it's mass is $1.67 × 10^{-27}kg$, this gives density of proton to be $\dfrac {1.67 × 10^{-27}kg} {\frac{4}{3}(1.75×10^{−15} m)^3}=\dfrac {3}{4} \dfrac{1.67 × 10^{-27}}{5.36×10^{−45}} \dfrac{kg}{m^3}=2.34 \times 10^{15} \dfrac{kg}{m^3}$</p>
<p>Density of the heaviest naturally occurring solid $\mathrm U^{238}$: 1 cubic meter of Uranium is about $2 \times 10^4 kg$, and since there are 238 protons+neutrons in Uranium, this gives the density $8 \times 10^{-3} \times 10^4 \dfrac{kg}{m^3}=8\times10 \dfrac{kg}{m^3}$</p>
<p>This means the protons are dispersed by a factor of $2.92\times10^{13}$, in other words there are $2.92\times10^{13}$ empty space units to each unit of space filled with proton.</p>
<p>Density of water $=\frac{1}{20}\times10 \dfrac{kg}{m^3}=5\times10^{-1}\dfrac{kg}{m^3}$ </p>
<p>The density in the core of neutron star is $8×10^{17} kg/m^3$, and the density of a black hole is supposedly infinite according to Wikipedia, but then again before transitioning to a black hole there must have been some finite mass distributed over a non zero volume of space therefore having a finite density.</p>
<p>So far on logarithmic scale (base 10) followings look obvious for $\operatorname {log}_{10}(density \dfrac {kg}{m^3}) = \operatorname {log}_{10} \dfrac{kg}{m^3} + \operatorname {log}_{10}density$ </p>
<p>Let $ d =\operatorname {log}_{10}density,\quad \operatorname {log}_{10} \dfrac{kg}{m^3}= \text{what is one to make of this}?$</p>
<p>Then following crude observations can be made: </p>
<p>$-1\leq\mathcal O(d)\leq1$: Order of density of life as we know it.</p>
<p>$\mathcal O(d)\approx 15$: Order of density of matter packed space</p>
<p>$\mathcal O(d)\approx 17$:Order of density at the core of a Neutron star</p>
<p>$\mathcal O(d)\geq x$:Order of density of black holes, (collapse of space to contain matter?) what is $x$?</p>
<p>My question is: does these calculations make sense and is there anything more to the order of densities than these naïve observations?</p> | g13551 | [
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<p>Using classical mechanics, the formula for gravitational attraction is </p>
<p>$$F = G\frac{m_1m_2}{r^2}.$$ </p>
<p>This formula does not work for photons, and we need to use Einstein's theory of gravity to account for that, as the photon is massless. What if, instead of using the mass of the photon, we rather used the inertia of it?</p>
<p>The momentum of a photon is </p>
<p>$$p=\frac{h}{\lambda}.$$</p>
<p>Thus, using that, we can calculate its supposed 'mass' (inertia) as momentum is also equal to mass times velocity. So 'mass' of a photon is </p>
<p>$$m=\frac{p}{v}=\frac{h}{\lambda c}.$$ </p>
<p>If we use this mass as the mass of a photon, can we use Newton's equation for gravitational attraction?</p> | g13552 | [
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<p>Ammeter (A1) and voltmeter (V) in series have parallel connection to another ammeter (A2). Currents in A1 and A2 are respectively 0.2 and 1.7 amp. Voltmeter's voltage is 6 volts.</p>
<p><img src="http://i.stack.imgur.com/w9oZl.png" alt="enter image description here"></p>
<p>How should I find resistances of all elements?</p> | g13553 | [
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<p>Could a ship equipped with Alcubierre drive theoretically escape from a black hole?</p>
<p>Also, could it reach parts of the universe that are receding faster than the speed of light from us?</p> | g13554 | [
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<p>Could the Opera result be interpreted as some kind of hint to a discrete spacetime that is only seen for high enough energy neutrinos?</p>
<p>I think I've read (some time ago) something like this in a popular article where among other things tests of quantum gravity theories, that assume a discrete spacetime, are explained.</p>
<p>Looking around in blogs and other places in the web, I notice that this is disussed seldom or not at all... `` </p> | g13555 | [
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<p>Let there be given two Hamiltonians</p>
<p>$$H_1~=~ p^{2}+f(x) \qquad \mathrm{and} \qquad H_2~=~ p^{2}+g(x). $$</p>
<p>Let's suppose that for big big $x$, the potentials are asymptotically similar in the sense that the quotient</p>
<p>$$ \frac{f(x)}{g(x)}~\to~1 \qquad \mathrm{for}\qquad x \to \infty.$$</p>
<p>Then if we quantize these Hamiltonians, </p>
<p>$$ \hat{H}_1y(x)~=~E_{n}y(x) \qquad \mathrm{and} \qquad \hat{H}_2y(x)~=~B_{n}y(x), $$ </p>
<p>since the potentials $ f(x)$ and $g(x)$ are asymptotically close to each other, does it mean that for big quantum number $n$
$$ \frac{E_{n}}{B_{n}}~\to~1 \qquad \mathrm{for}\qquad n \to \infty,$$</p>
<p>at least in one dimension?</p> | g13556 | [
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<p>Nuclearity is a postulate in algebraic quantum field theory (AQFT). Basically, it says thermal states at any temperature always have a thermodynamic limit with extensive quantities. This is violated by string theory at the Hagedorn temperature. Does this mean anything?</p> | g13557 | [
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-0.0051439316011965275,
-... |
<p>I am not a physiologist, but whatever little I know about human eyes always makes me wonder by its details of optical subtleties. A question always comes to mind. Are human eyes the best possible optical instrument evolved by natural selection? Is there any possible room for further major improvement as per the laws of physics in principle? Can there be any camera prepared by human beings which can be superior to human eyes?</p> | g13558 | [
0.005875792820006609,
0.008388356305658817,
0.02722409926354885,
0.06421659886837006,
0.024722548201680183,
0.006632745731621981,
0.030107291415333748,
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0.012035015039145947,
-0.014154247008264065,
0.046874891966581345,
0.0028881686739623547,
0.04385020583868027,
0.01... |
<p>UFOs as shown in movies are shown as disk like objects with raised centers that emit some sort of light from bottom. Can such a thing fly?</p>
<p>My very limited knowledge in physics tell me that a disk like object may not be able to maneuver unless it has thrusters on sides and simple light can not be enough to make any object go up in the air.</p>
<p>Is it possible?</p> | g13559 | [
-0.049248430877923965,
0.08086168020963669,
0.023554742336273193,
0.034796927124261856,
0.03440145030617714,
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-0.04129141569137573,
0.00565695995464921,
0.022998875007033348,
0.03159404918551445,
-0.000... |
<p>Magnetic field lines depict the strength of the magnetic field, dense lines in a region imply a strong field. </p>
<p>Lines are drawn as per our convenience. We needn't draw infinite lines but just relative amounts: where the field is stronger, more lines; where it isn't, less lines. </p>
<p>What I wanted to know was what do these lines imply when they are formed in the magnet and iron filings experiment. All this while we find that these lines can be infinite with relative spacings to depict field strength. It seems that these lines are imaginary and only for our convenience. Yet iron filings form them. So what do they imply? </p>
<p>Why do the iron filings follow only specific lines around the magnet? What about the spaces in between two adjacent lines? What are those spaces supposed to be? Why wouldn't the iron filings fill those up as well? Are those spaces supposed to imply absence in field? </p> | g423 | [
-0.0021327033173292875,
0.04621531069278717,
-0.0011549257906153798,
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0.028496842831373215,
0.023... |
<p>I have read the explanation for this in several textbooks, but I am struggling to understand it via Archimedes' principle. If someone can clarify with a diagram or something so I can understand or a clear equation explanation that would be great. </p> | g13560 | [
0.01972297392785549,
0.11811604350805283,
-0.015753773972392082,
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0.004966396372765303,
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0.025118067860603333,
0.03914336487650871,
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<p>If an object is dropped from a roof with no initial velocity and wind is blowing along the side of the building exerting a constant force on the object, then its trajectory will be a straight line. But if the object has an initial velocity downwards, then its trajectory will be a parabola instead (according to my book). I don't understand why! </p>
<p>Why does it not just become a steeper straight line? It will still have the same vertical and horizontal accelerations right?</p> | g13561 | [
0.0998399630188942,
0.007620796095579863,
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0.0042146299965679646,
0.010872668586671352,
0.0273577... |
<p>I read <a href="http://en.wikipedia.org/wiki/Magnetic_dipole" rel="nofollow">Magnetic Dipole</a> point source in computational electro-magnetic literatures where it is used as exciting source. But I do not know how to plug this source into <a href="http://www.spec2000.net/06-electromag.htm" rel="nofollow">Maxwell's equations</a>. </p>
<p>Does it go into the free electric current density $J_f$? </p>
<p>Does the point dipole gives a Dirac function somewhere in Maxwell's equation?</p> | g13562 | [
-0.02502942830324173,
0.033369049429893494,
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0.06966409087181091,
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0.042417582124471664,
0.025956152006983757,
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-0.014177176170051098,
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0.005739424377679825,
0.06317294389009476,
-0... |
<p>I've been studying Fluid Mechanics recently and on the book <em>Fundamentals of Fluid Mechanics 7e, Munson et al.</em> on page 456, the book states</p>
<blockquote>
<p>Another common multiple pipe system contains pipes in parallel ... However, by writing the energy equation between points A and B it is found that head losses experienced by any fluid particle traveling between these two locations is the same, independent of the path taken.</p>
</blockquote>
<p>Can someone please clarify this for me. How is it possible that two pipes different in diameter have the same losses?</p>
<p>I thought,</p>
<p>$$h_L = f\frac{l}{d_i}\frac{v^2}{2g}$$</p>
<p>Edit 1:</p>
<p>I'm sorry that I wasn't clear enough. Here's a diagram I sketched on the problem at hand. As you can see the pipes are parallel, and the flow is unidirectional, that is from A to B.</p>
<p><img src="http://i.stack.imgur.com/DEAgd.png" alt="enter image description here"></p>
<p>However they all have different diameters, but are equal in length.</p>
<p>Note: Regarding the name and nomenclature. These aren't heat losses, they're actually called <a href="http://en.wikipedia.org/wiki/Hydraulic_head" rel="nofollow">head losses</a>.</p>
<p>The equation is called the major head loss during a viscous flow in a pipe. According to this equation, the losses experienced by the fluid are proportional to the velocity squared and to a roughness factor f. The rest is also self-explanatory I believe. What I can't seem to grasp is how this is equal to the three pipes in this configuration.</p> | g13563 | [
0.0517146959900856,
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0.0150... |
<p>Suppose we have some inclined plane, and there is some chain of balls of length $l$ and mass $m$ lying on it. No friction at all in the system.</p>
<p>1) What is $x_0$ (the vertical hanging part of the chain) needed for the chain to be in equilibrium? </p>
<p><em>Answer</em>: $l/3$</p>
<p>2) If we push the chain a little bit to the right, what is the acceleration of the chain, at instant when the vertical part of the chain is $x$ long ($x > x_0$)?</p>
<p><em>Answer</em>: $a(x)=\frac{g}{l}(\frac{3}{2}x-\frac{l}{2})$</p>
<p>3) What is the velocity of the chain at instant when all of it is vertical (e.g. all the left part on the inclined plane "became vertical")? (<em>no answer</em>)</p>
<p><img src="http://i.stack.imgur.com/jydqH.png" alt="enter image description here"></p>
<p>1) I do not understand, why the component of the weight of the left part should be equal to the weight of the right hanging part. Their vectors are not along the same line, so why should this condition be necessary for equilibrium? Also, the left part is being pulled by the right, so there should be another force along the incline.</p>
<p>2) Based on the first question, this one should be:</p>
<p>$(1-\frac{x_0}{l})mg \sin 30^{\circ}-\frac{x_0}{l}mg=ma$</p>
<p>However, this leads to a wrong $a$, according to the answer.</p>
<p>3) Based on the book's answer of 2), is this right?</p>
<p>From Torricelli's equation:</p>
<p>$v^2=v_0^2+2a \Delta x$</p>
<p>$v(x)=\sqrt{v_0^2+2 \int_{l/3}^{x} a(x) dx}$</p>
<p>Therefore:</p>
<p>$v(l)=\sqrt{\frac{20}{3}l}$</p> | g13564 | [
0.06763982772827148,
0.024657269939780235,
0.0034098776523023844,
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0.0718918964266777,
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0.03565812110900879,
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0.017583008855581284,
-0.049562375992536545,
-0.0024... |
<p>This has been <a href="http://physics.stackexchange.com/questions/57481/the-bizarre-behaviour-of-superfluids-climbing-up-walls-and-geting-out-of-glass">asked </a> but I couldn't find a good answer why does super-fluid climb up the walls of container? What if the walls were too high? What forces are involved?</p>
<p><img src="http://i.stack.imgur.com/rgYNn.jpg" alt="enter image description here"></p> | g13565 | [
0.04375988617539406,
0.11629550904035568,
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-0.03196614980697632,
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0.005174398887902498,
0.025835847482085228,
0.028... |
<p>This question is the continuation of <a href="http://physics.stackexchange.com/questions/89367/how-to-find-proper-speed-relate-to-homogeneous-cosmic-background-of-the-galaxy">this one</a>. I came up with solution, but I'm not sure that it is correct. Can someone check it?</p>
<p>Let's introduce transverse (to the observer) proper speed $v_{\perp}$ of the galaxy. The galaxy travels distance $\Delta D$ in a time $\Delta t_{0}$:
$$
\Delta D = v_{\perp}\Delta t = v_{\perp}\Delta t_{0}\frac{a(t)}{a_{0}},
$$
where $dt_{0}$ refers to the time interval of observation of the galaxy, $dt$ refers to the time interval of light emission.</p>
<p>So
$$
d\theta = \frac{dD}{a(t) r(t)} = \frac{v_{\perp}dt_{0}}{a_{0}r(t)},
$$
where $r(t)$ is the galaxy position, </p>
<p>and finally
$$
\frac{d \theta }{dt_{0}} = \frac{v_{\perp}}{a_{0}r(t)}.
$$
Is this method correct? Also, can I identify the left side of this equation with the observing angular velocity? And how to find $r(t)$? To consider the FLRW interval for the light?
$$
ds^2 = dt^2 - a(t)^2\frac{dr^2}{1 - kr^2} = 0 \Rightarrow f(r) = \int \limits_{0}^{z} \frac{dz}{H(z)} \Rightarrow r = f^{-1}\left[ \int \limits_{0}^{z} \frac{dz}{H(z)}\right]?
$$</p> | g13566 | [
0.03090534918010235,
0.014569687657058239,
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0.01774861104786396,
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0.08512505143880844,
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-0.0002722606877796352,
0.04368593543767929,
0.07489761710166931,
0.028142649680376053,
0.... |
<p>I have an object I can rotate with a given torque. I would like to stop applying torque once I've reached a defined maximum rotational speed. The maximum rotational speed should be defined so that applying maximum torque will stop the rotation of the object within one rotation. If I know my torque and moment of inertia, how can I find the maximum rotational velocity to allow me to stop the object in one rotation?</p>
<p>Time is whatever is needed.</p>
<p>I've tried finding the angular acceleration required to stop the object, but that leaves me with the time variable. Of the equations I've tried, I'm left with a time variable as well as the maximum angular velocity.</p> | g13567 | [
0.034079283475875854,
-0.0457962341606617,
0.008219031617045403,
0.0032882948871701956,
0.011206484399735928,
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0.01710369810461998,
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-0.05656401440501213,
-0.025143280625343323,
0.00... |
<p>While studying Srednicki's book on quantum field theory, I encountered a particular identity that is of interest to me (equation 36.40):
$$\mathcal{C}^{-1}\gamma^\mu\mathcal{C}=-(\gamma^\mu)^T$$
where $\mathcal{C}$ is the charge conjugation operator, and $\gamma^\mu$ the well-known gamma matrices. This identity is shown to be true using the chiral/Weyl representation. However, I would like to be able to show it to be true without choosing a representation. Is something like this possible? If yes, could someone outline the procedure for me? Any help would be much appreciated.</p> | g13568 | [
-0.0035799711477011442,
-0.06543083488941193,
-0.014791380614042282,
-0.03591134399175644,
0.051603030413389206,
-0.04480234161019325,
0.05669103562831879,
-0.0026470532175153494,
-0.052250150591135025,
0.04439113289117813,
-0.036205753684043884,
-0.016336524859070778,
-0.0020268834196031094... |
<p>I've been trying to wrap my mind around the concept of <a href="http://www.google.com/search?q=anti-time" rel="nofollow">anti-time</a> and wondered what it is. If there is anti-matter and anti-gravity, does time have its negative? Your help is appreciated.</p> | g13569 | [
0.020841745659708977,
0.049395084381103516,
-0.005417222157120705,
-0.034115832298994064,
0.045888859778642654,
0.026835834607481956,
0.01583203300833702,
-0.03617539629340172,
-0.06821572780609131,
0.005171134136617184,
0.04702584445476532,
0.02282780595123768,
0.03494247421622276,
0.0417... |
<p>In thermodynamics the total energy of a system consists of kinetic energy of motion of the system as a whole, potential energy of the system as a whole due to <em>external</em> force fields, and energy contained within the system known as internal energy,
$$
E = E_{\mathrm{k}} + E_{\mathrm{p}} + U \, . \tag{1}
$$</p>
<p>That is the way it is said in many books, lecture notes and online source. For instance, the first paragraph of <a href="http://en.wikipedia.org/wiki/Internal_energy" rel="nofollow">Wikipedia article on internal energy</a> says:</p>
<blockquote>
<p>In thermodynamics, the <em>internal energy</em> is one of the two cardinal
state functions of the state variables of a thermodynamic system. It
<em>refers to energy contained within the system, and excludes kinetic
energy of motion of the system as a whole, and the potential energy of
the system as a whole due to external force fields</em>. It keeps account
of the gains and losses of energy of the system.</p>
</blockquote>
<p>Well, if a system is just one macroscopic body, I have no problems with these definition. But what if we have more than one body in our system?</p>
<p>Consider, for instance, an isolated system composed of two bodies of mass $m_{1}$ and $m_{2}$. According to classical mechanics, between two masses there always always exists a gravitational force
$$
F = \frac{G m_{1} m_{2}}{r_{12}^2} \, ,
$$
and there exist a gravitational potential energy
$$
V = - \frac{G m_{1} m_{2}}{r_{12}} \, ,
$$
due to this interaction.</p>
<p>Now, this potential energy $V$ is not a part of $E_{\mathrm{p}}$ in (1), since it is not due to external, but rather internal force field.
Clearly, it is also not a part of $E_{\mathrm{k}}$.</p>
<p>Where is it then? <strong>Is it included into internal energy $U$ or it is just an additional term for the total energy that has nothing to do with internal energy $U$?</strong></p>
<p>In other words, <strong>the increase in which quantity (according to the 1st law of thermodynamics) is equal to the heat supplied to the system plus the work done on it: internal energy counted with or without this potential energy $V$ due to gravitational interaction?</strong></p> | g13570 | [
0.0796269029378891,
0.05087551474571228,
0.009270750917494297,
0.016549546271562576,
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0.007131138816475868,
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0.062443967908620834,
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-0.009777143597602844,
-0.028453638777136803,
-0.027358273044228554,
-0.00001884829907794483,
... |
<p>From the maths governing an LC circuit (eg. $E_B=\frac{LI^2}{2}$) we can deduce, that the current through the inductor will have a maximum value, when there's no energy stored in the capacitor, or else $E_B = max \iff I=max$. But how to explain it intuitively?
Suppose we have a fully charged capacitor and we connect it to a inductor. As the voltage between the capacitor's plates decreases, so should the current flowing through the circuit. Yet, we observe the opposite, as the current increases. I suppose it's due to the EMF induced in the inductor, but shouldn't it merely decrease the rate with which the current is decreasing?</p> | g13571 | [
0.06565786153078079,
0.007977234199643135,
-0.0065575591288506985,
-0.004401904996484518,
0.09700128436088562,
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0.061579518020153046,
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-0.0569276288151741,
-0.06566690653562546,
0.012922735884785652,
0.02151651121675968,
0.040... |
<p>In <a href="http://arxiv.org/abs/1308.4055" rel="nofollow"><em>Why decoherence solves the measurement problem</em></a> by Art Hobson:</p>
<p>$|\psi \rangle _{SA} = c_1|s_1 \rangle |a_1 \rangle + c_2 |s_2\rangle |a_2 \rangle$
which is a wavefunction that describes non-local entangled state of system $S$ with measuring apparatus $A$ and reduced density matrix that describes subsystem is
$\rho_S = (|s_1 \rangle |c_1|^2 \langle s_1|\,\,+\,\,|s_2 \rangle |c_2|^2 \langle s_2| )/2$ and
$\rho_A = (|a_1 \rangle |c_1|^2 \langle a_1|\,\,+\,\,|a_2 \rangle |c_2|^2 \langle a_2| )/2$.</p>
<p>Now then paper says that when $c_1 = c_2$, reduced density matrices have non-unique basis, but have unique basis when $c_1 \neq c_2$. Can anyone present the reason why this is the case when $c_1 \neq c_2$? (So I do get that $c_1 = c_2$ case.)</p>
<p>Add: $\langle s_1 | s_2 \rangle = 0$ and $\langle a_1 | a_2 \rangle = 0$ is assumed. </p> | g13572 | [
0.006427641026675701,
-0.007425040937960148,
0.015261905267834663,
-0.04964156076312065,
0.05814647674560547,
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0.07620136439800262,
0.047328777611255646,
0.01665753312408924,
0.009312883950769901,
-0.0338515043258667,
-0.021433958783745766,
-0.01872326247394085,
0.024... |
<p>Firstly, I understand and apologize that this is more of a physics question than a math question.</p>
<p>I noticed that when I pulled a book out from under a pack of gum, the gum stayed largely in place (it did not move with the book). This confused me, so I decided to draw a diagram of the situation, assuming that my answer would be apparent once I could represent all of the forces in play. Of course (as the book was orthogonal to the ground) gravitational force and normal force could be ignored. The only other force that I see that can be in play is the friction between the book and the gum, which should make the gum move along with the book. There must, then, be some sort of force acting opposite and with a greater magnitude than friction. Is this correct, and if so, what is that force and how can it be calculated?</p> | g13573 | [
0.024791788309812546,
0.02865925431251526,
0.007756555452942848,
-0.05911197140812874,
0.005057380069047213,
0.032443005591630936,
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0.013163643889129162,
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-0.01211458444595337,
0.011936837807297707,
-0.05962671339511871,
-0.002467083279043436,
-0.... |
<p><a href="http://www.cheniere.org/books/aids/ch4.htm" rel="nofollow">This page</a> claims that original Maxwell's equations, when formulated by Maxwell himself in quaternion form, had some special scalar part of electromagnetic field, which somehow appeared to describe gravitation. The author says that further development of this is called "scalar electromagnetics" or, as Soviets are claimed to have called it, "energetics".</p>
<p>While I read that page, my gut feeling tells me this is all nonsense. But am I right? I've tried googling for this term, and found some antiscientific sites, and nothing like that in any respectable sources like science journals or wikipedia. So, is this really some real science, or is it antiscientific trash? If it's for real, are there any credible sources to read more about this?</p> | g13574 | [
0.06491295248270035,
0.05212537199258804,
-0.02969929948449135,
-0.01066016498953104,
0.0533272847533226,
0.048231229186058044,
0.021789399906992912,
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-0.039652105420827866,
0.05242981016635895,
-0.01503293402493,
0.06950334459543228,
-0.01517234... |
<p>Certain "whitening" toothbrushes are sold and I was wondering about the mechanisms behind the tooth whitening process. I suspect this is related to the shape and arrangement of the fibres, probably somewhat similar to how a microfiber cleaning cloth works, but couldn't find any authoritative confirmation.</p>
<p>So how does a whitening toothbrush work? I'm only interested in the physical effects - whitening toothpastes rely on their chemical properties so they're a completely different story.</p> | g13575 | [
0.013037833385169506,
0.01771322637796402,
0.019826743751764297,
0.013085859827697277,
0.07884598523378372,
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0.00460156099870801,
0.012577134184539318,
0.039052098989486694,
-0.04558494687080383,
-0.0008336285827681422,
-0.02227373607456684,
0.05155250430107117,
-0.00... |
<p>I understand that playing a square wave from speakers cannot produce a PERFECTLY sharp division between compression and rarefaction. But it's sharp enough to sound distinctly different from a sine wave. As it travels, does the wave "smoosh out" even further as it travels, changing from a square wave into something closer to a sine wave?</p> | g13576 | [
0.0012557992013171315,
0.04010898992419243,
0.00493680639192462,
-0.001667897100560367,
0.048314712941646576,
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0.03042614832520485,
0.01532017719000578,
0.028410479426383972,
-0.07189030945301056,
-0.07439720630645752,
0.031535763293504715,
0.05626513436436653,
0.0067... |
<p>Internet providers try to sell us the more and faster "fast internet" - 15Mb, 40Mb, 100Mb, and so on. But it's well known that the bandwidth the channel (in the most cases it's the telephone wire) restricted by the nature law. And this law is so fundamental as the light speed. (see, e.g., V.A.Kotetlnikov theorem). The bandwidth of a telephone wire is significantly less than providers propose us.</p>
<p>Can someone explain what is the matter here?</p> | g13577 | [
-0.017035841941833496,
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<p>I was wondering if there exist a particle analogous to the Higgs boson that gives rise to energy, I´m sorry it´s not the big question but I feel confused about how the universe works, also I have been searching and I couldn't find anything</p> | g13578 | [
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<p>I'm a third year physics undergrad with a very cursory knowledge of quantum mechanics and the formalism involved. For instance, I understand roughly how tensors work and what it means for a tensor to be irreducible, though it would take me a lot of work to apply this knowledge to a problem/extend it past what I've already seen.</p>
<p>As part of a project, I'm studying atomic nuclei in electric and magnetic fields. I'm trying to understand the energy of a nuclear quadrupole's interaction with an electric field gradient. The equation for this is</p>
<p>$E_Q = \sum_{\alpha,\beta} V_{\alpha\beta} Q_{\alpha\beta}$</p>
<p>where $\alpha$ and $\beta$ each iterate over $x, y, z$.</p>
<p>$Q$, the electric quadrupole moment, is given by</p>
<p>$Q_{\alpha\beta} = [\frac{3}{2}(I_{\alpha} I_{\beta} + I_{\beta} I_{\alpha}) - \delta_{\alpha\beta}I^2] * constant$</p>
<p>(taken from <a href="https://www.uni-muenster.de/imperia/md/content/physikalische_chemie/eckert/quadtut.pdf" rel="nofollow">this powerpoint</a>.) An electric quadrupole moment should have nothing to do with nuclear spin... or so I thought, until I ran across the idea of "spin coordinates" and the <a href="http://en.wikipedia.org/wiki/Wigner%E2%80%93Eckart_theorem" rel="nofollow">Wigner-Eckart theorem</a>. This is roughly all I know about the theorem -- that it exists and that it can somehow convert between Cartesian and spin coordinates in quantum systems -- and I'd like to understand it better.</p>
<p>THE SHORT VERSION: I do not need a detailed mathematical understanding of the Wigner-Eckart theorem, but I'm very curious as to the general idea of it. Can anyone think of a plain-English (or rather, minimal-math) explanation of the theorem that would make sense to a beginning quantum physics student?</p> | g13579 | [
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<p>Assume that we have a particle with weight m and initial speed v0, that follows a roller coaster path y(x).
<img src="http://i.stack.imgur.com/kyUeA.png" alt="Roller Coaster Path"></p>
<p>Assuming no energy loss to friction or air resistance, the total energy in the system is </p>
<p>$$E0 = m g y(x0) + 0.5 m vo^2$$</p>
<p>then the speed at each point $x_f$ is</p>
<p><img src="http://i.stack.imgur.com/jMCyQ.png" alt="enter image description here"></p>
<p>So, using the energy conservation principle, we can derive the speed at each point of the curve.</p>
<p>It gets tricky though, to try to figure out at what time the particle reaches a specific point of the curve.</p>
<p>Turning our attention to dynamics, should help us achieve the goal.</p>
<p>$$dS/dt = v(x)$$</p>
<p>Is the approach followed correct?</p>
<p><img src="http://i.stack.imgur.com/hz3U7.png" alt="enter image description here"></p> | g13580 | [
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<p>I know that this is a homework type question and I'm not asking a particular physics question, but I'm really desperate for help.</p>
<p>Here's the question:</p>
<p><img src="http://i.stack.imgur.com/Ob5xP.png" alt="enter image description here"></p>
<p>I tried to divide the string to 2 parts with $O$ as the mid-point of $AB$. </p>
<p>Let $AO$=$T_{1}$ and $OB$=$T_{2}$, then $T_{2}-T_{1}=m\ddot x $. I don't know what to do next.</p>
<p>Here's the marking scheme:
<img src="http://i.stack.imgur.com/qtU0o.png" alt="enter image description here"></p> | g13581 | [
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<p>I'm trying to calculate Stoke's drag constant using the equation found <a href="http://en.wikipedia.org/wiki/Drag_%28physics%29#Very_low_Reynolds_numbers_.E2.80.94_Stokes.27_drag" rel="nofollow">here</a>.</p>
<p>The system I wish to calculate it for is a mass oscillating vertically on a spring through air. The temperature is 25 degrees celsius. The area of the base of the mass is 4.9x10^-4 square metres.</p>
<p>I'm not sure how to find the 'fluid viscosity' in the linked equation, or what 'Stoke's radius' is.</p> | g13582 | [
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<p>Calculating the transition amplitude in Euclidean spacetime is useful because from it we can extract the ground state energy and ground state wave-functions values.</p>
<p>For example, let's assume we are calculating:
$\left<x=b\left.\right|e^{-\hat{H}T}\left.\right|x=a\right>$. Assume we can calculate this quantity via the path-integral formalism and we have found it to be equal to $f(T)$.</p>
<ul>
<li>We insert a complete set of energy eigenstates into the transition amplitude:
$$ \left<x=b\left.\right|e^{-\hat{H}T}\left.\right|x=a\right> = \left<x=b\left.\right|e^{-\hat{H}T}\sum_n\left|n\right>\left<n\right|\left.\right|x=a\right> = \sum_n e^{-E_nT}\left<x=b\right|\left.n\right>\left<n\right|\left.x=a\right> = f\left(T\right) $$</li>
</ul>
<p>The usual trick now is to take the limit $T\to\infty$ of the above equation and say that the most important term is the lowest energy eigenvalue, and so:
$$ \lim_{T\to\infty} \sum_n e^{-E_nT}\left<x=b\right|\left.n\right>\left<n\right|\left.x=a\right> \stackrel{?}{=} \lim_{T\to\infty} e^{-E_0T}\left<x=b\right|\left.0\right>\left<0\right|\left.x=a\right> = \lim_{T\to\infty} f\left(T\right)$$</p>
<p>$f\left(T\right)$ usually is of the form $A\times e^{- \varepsilon T} $ and so we say $E_0 = \varepsilon$.</p>
<p>I feel funny about this procedure because taking this limit, if $E_0$ is positive then this term should go to zero <em>as well</em>. In this sense, is the equality with the question mark merely an estimate, and not a true equality? If so $E_0$, which we obtain in this way, is just an approximation? Why is it then that for the SHO we get the exact result in this way $\frac{\omega}{2}$?</p>
<p>Even worse, when $f\left(T\right)$ is of the form $f\left(T\right)=A\times e^{- \varepsilon_0 T}+B\times e^{- \varepsilon_1 T}$, then I have seen (if I understand correctly) that the conclusion is then that $E_0=\varepsilon_0$ and $E_1=\varepsilon_1$ (i.e. the 2nd lowest energy eigenvalue is extracted <em>as well</em>) (for example, see Coleman "Aspects of Symmetry" page 274 equation 2.31).</p>
<p>Can anyone shed some light at the mathematical background of this "trick"? Is it not the same limit as the epsilon delta limit? Can I extract the whole spectrum in this way, just from knowledge of $f\left(T\right)$? If I can calculate the path-integral for various different values (not just $x=a$ and $x=b$) then could I, in principle, extract in this way also the whole set of energy eigenstates at all points? Is the information obtained in this way always an approximation? How can I find out the margin of error on this approximation then?</p> | g13583 | [
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0.05148... |
<p>This question may seem odd, but I can't think of anything better. So I'll go straight to the point.</p>
<p>Let's say there's a projectile in air going east, shot at a certain angle, with a certain speed. Then there's the wind blowing, for let's say 5 meters per second in the same direction as the projectile.</p>
<p>So how will the wind affect the projectile? Will it accelerate for 5 meters per second every second it lasts in the air, or will the speed just increase by 5 meters per second all through out? And what if the wind goes exactly the opposite direction? Will it have a negative effect? Should I also take into consideration the drag the object makes, the mass, the terminal velocity, or if there are other things I've missed?</p>
<p>I don't mind if you give formulas. It would also help. But I just wanted to know, in simple terms because I'm not really that inclined with terms used in physics, the effects of a blowing wind to a projectile motion.</p>
<p>Thanks in advance and sorry if I made some errors or misunderstanding with this post or if I used the wrong tags. Feel free to edit it. </p>
<p>Thanks again,<br>
Vincent :)</p> | g13584 | [
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0.009074... |
<p>Which cosmologies consistent with physics as we currently know it is consistent with Eternal Life lasting forever starting from here on Earth while preserving the memories of human life? With computers and robots colonizing the universe and growing without bound?</p>
<p>Tipler had suggested an Omega Point associated with a big crunch in a closed universe, but unfortunately, scales below the Planck length do not exist.</p>
<p>Dyson had performed an analysis in the article "TIME WITHOUT END: PHYSICS AND BIOLOGY IN AN OPEN UNIVERSE".</p> | g13585 | [
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0.02... |
<p>Why zeta regularization only valid at one-loop? </p>
<p>I mean there are zeta regularizations for multiple zeta sums.
Also we could use the zeta regularization iteratively on each variable
to obtain finite corrections to multiple loop diagrams.</p> | g13586 | [
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<p>AFAIK radio waves can be influenced by magnetic fields (when not traveling through a vacuum). Electrical wires create a magnetic field perpendicular to the length of the wire, as a function of the current running through it.</p>
<p>In air, water, or other medium, would radio waves be influenced by this magnetic field (or conversely by the electric field)?</p>
<p>Say for this purpose I have a radar which scan through walls, and I am interested in knowing wether the wires in the wall are currently "on" or "off". Would this be possible? How weak, or strong magnetic field (conversley electric field) is needed to influence radio waves (when not in a vacuum)?</p>
<p>Or have I completely misunderstood something here :) ?</p>
<p>Thanks alot!</p> | g13587 | [
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<p>Considering Einstein equations, suppose, for instance, that the RHS, the stress-energy tensor, is uniquely due to the electromagnetic field. Now, if we imagine a quantized version of these Einstein equations, we have a quantum field theory in $D$ dimensions (here the quantum electromagnetic field) as "source" of a "quantum gravity" theory in $D$ dimensions, so we may consider these equations as a kind of "dictionnary" between these two theories.</p>
<p>On an other way, there are some holographic dualities, which relates some quantum theory of gravity in a $D$ dimensional space with boundary, with some quantum field theory on the boundary ($D-1$ dimensions)</p>
<p>So, the question is, if, "skipping gravity", it is possible or not, and how, to directly relate the QFT in $D$ dimensions (source of gravity), and the other QFT (on the boundary) in $D-1$ dimensions. </p> | g13588 | [
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-0.0... |
<p>Any <a href="http://en.wikipedia.org/wiki/Free_and_open-source_software" rel="nofollow">FLOSS</a> Monte-Carlo package for reactor physics? Are there any Free and Open Source software packages for nuclear reactor processes simulation? Maybe, something similar to <a href="http://mcnp.lanl.gov/" rel="nofollow">MCNP</a>?</p> | g13589 | [
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-0.051700983196496964,
0.0012818804243579507,
0.02251148410141468,
0.056583963334560394,
0.... |
<p>Are electrons of any conductor really free ? I mean are they always already moving or do they move only when electrostatic field of some sort is applied across them. I suppose if they were always moving each and every conductor must have some varying magnetic field around it at all times which though negligible musy be detected. Is that really so ? Or are the so called free electrons not really free ?</p>
<p>Also is there some other experiment which i do not know about by which we have already proven that they are always moving ? does it take into account the earths and other electric fields which may be causing that movement ?</p>
<p>Addendum : the question is not duplicate of <a href="http://physics.stackexchange.com/q/80932/">Are free electrons in a metal really free</a> as that post talks about ease of electrons to interact with external fields, my question is about the nature of motion of electrons in absense of external field interference as in are electrons in free motion even when they are not under the influence of any electromagnetic field.</p> | g424 | [
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0.02344915084540844,
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0.002... |
<p>The <em>no hair</em> theorem says that black holes rapidly converge to a state that is completely described just by their mass, spin and charge. Black hole thermodynamics says that the black hole entropy is proportional to the surface area of the event horizon. As I understand it in information theoretic terms the black hole entropy is 1 bit per planck unit of area, which should then be the amount of information required to fully describe a black hole. These two statements seem to be incompatible. It seems that the thermodynamics says that if we fix the macroscopic no hair parameters there still remain all the surface bits to be fixed. Is there any real conflict here or is somehow illusory? Is it a quantum vs classical issue? Does the entropic information not count in some sense? If not why, can 2 equal mass Schwartzchild black holes be distinguished by their "surface information"? Is it that the surface information is just not observable because the surface is considered <em>in</em> the black hole? Or is this apparent discrepancy part of the black hole information paradox?</p>
<p>There is a very similar question with a detailed answer <a href="http://physics.stackexchange.com/questions/27922/black-hole-no-hair-theorems-vs-entropy-and-surface-area">here</a>, but I believe I am actually asking something different. The question and excellent answer there focus on the objects as they fall into a black hole. I am more interested in how to think about the total information in a steady state black hole and the current status of the no hair theorem wrt black hole entropy and the information paradox.</p> | g13590 | [
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<p>As the title asks, how do you represent an equation with four variables? Is there a practical way of representing them? (I've thought of one, but I don't think I can explain it clearly. This question has got me really curious.) Additionally, is there any practical way of solving these equations?</p> | g13591 | [
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0.004391126800328493,
... |
<p>I can turn-the-crank and show that $\frac{1}{2}\otimes \frac{1}{2} = 1\oplus 0$ etc, but what would be a strategy to proving the general statement for spin representations that $j\otimes s =\bigoplus_{l=|s-j|}^{|s+j|} l$. </p> | g13592 | [
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0... |
<p>In quantum mechanics, particles are described by wave functions, which describe probability amplitudes. In quantum field theory, particles are described by excitations of quantum fields. What is the analog of the quantum mechanical wave function? Is it a spectrum of field configurations (in analogy with QM wave functions' spectrum of particle observables), where each field configuration can be associated with a probability amplitude? Or is the field just essentially a superposition of infinitely many wave functions for each point along the field (as if you quantized a continuous mattress of infinitesimal coupled particles)? </p> | g13593 | [
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0.016... |
<p>As I've said elsewhere, I've not had the opportunity to take a class in general relativity. Nonetheless, I understand that two major aspects of the standard cosmological model are the <a href="http://en.wikipedia.org/wiki/Cosmological_principle" rel="nofollow">cosmological principle</a> and the observation of a <a href="http://en.wikipedia.org/wiki/Shape_of_the_Universe" rel="nofollow">flat space</a>. To get where I'm coming from, I'll try to give a brief description of my understanding of these concepts:</p>
<ul>
<li><p>cosmological principle - This principle states that there is no privileged position within the universe. In other words, wherever any observer is located, s/he will observe approximately the same thing. Obviously the specific celestial bodies observed will change, but the expansion of the universe will be judged the same and the universe will essentially appear isotropic.</p></li>
<li><p>flat space - This observation, tested and largely verified by the WMAP satellite, shows that the large scale universe is not curved.</p></li>
</ul>
<p>My natural inclination is that these two things cannot be simultaneously true. The reason it seems this way to me is that if any observer can see roughly the same amount of the universe in any direction, and the universe is of finite size, the observable portions must overlap somewhere. If the observable portions overlap, it must be possible to continue traveling in one direction and eventually end up where you started. To me, this seems to be what curvature is.</p>
<p>How do we reconcile these two concepts?</p>
<p>$\dagger$ I have read some of the articles on the subject such as those on <a href="http://en.wikipedia.org/wiki/Minkowski_space" rel="nofollow">Minkowski space</a> and <a href="http://en.wikipedia.org/wiki/Torus#n-dimensional_torus" rel="nofollow">multidimensional toruses</a>. I believe I can reconcile the two concepts and imagine a higher dimensional flat torus, but the concept is still a difficult one for me and I would love some clarification.</p> | g13594 | [
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0.018... |
<p>Few years ago I read some papers about Free Energy, written by Bruce de Palma, a physicist who is said to be the inventor of the N-Machine, which is an device that works with free energy latent in the space around us. There are several informal references to him and <a href="http://www.brucedepalma.com/" rel="nofollow">his</a> <a href="http://depalma.pair.com/" rel="nofollow">work</a>. However, I tried to find papers of him several times in Scielo, Science Direct, IEEE, Physical Letters, Nature and several other scientific databases and found no references to Dr. Bruce de Palma. Personally I find quite strange that a research of such importance do not have a formal paper in an journal of big impact. </p>
<p>Does his work make sense?</p> | g13595 | [
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<p>I) I know that virtual-photons are known to be the force-carriers for the Electromagnetic force, and that they are called "virtual" because the Energy-Time-inequality version of the Heisenberg Uncertainty Principle allows for particles that are high enough energy that they are very difficult to observe (because higher energy means a smaller possible time-scale for observation). </p>
<p>But I also know that photons are the quanta of EM radiation; i.e. they emitted from atoms at some point in space, and absorbed at other points in space as a means of transmitting radiation energy.</p>
<p>My question is this: are the photons that act as the force carrier of the Electromagnetic force the "same" photons (i.e. the exact same particle) as the photons that act as the quanta of EM radiation? </p>
<p>Is it just that the photons emitted as virtual particles have high enough energy that they act as a force carrier? If so, what causes charged particles to emit photons of such high energy?</p>
<p>II) As an add-on question: I'm being introduced loosely to Electro-weak Unification and the idea that at high enough energy, the EM- and Weak forces become indistinguishable from one another (and, I believe, that the difference between the EM-force and the Weak force, at low energy, is that the W and Z bosons that mediate the Weak force are massive, and therefor act at low range, whereas photons are massless and therefor act at long ranges). And subsequently, that the Higgs Boson helps to explain what gives W and Z bosons mass. </p>
<p>But what is the difference between the W and Z bosons and the photon that makes them interact with the Higgs mechanism, and the photon remain unaffected?</p>
<p>I hope these questions make sense.</p> | g13596 | [
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<p>Goldstein pg 151 says "it is clear that an inversion of a right-handed system into a left-handed one cannot be accomplished by any rigid change in the coordinate axis..." I am trying to understand what he means by a rigid change... is he saying that an inversion is a discontinuous jump that is impossible for an object to achieve? why can't it?</p>
<p>I can see clearly that the inversion (improper rotation) will be associated with a sort of jump(discontinuity) upon the mirror reflection... but I'm a little confused on the definition of a "rigid change". maybe the problem isn't the discontinuity of a mirror reflection but has to do with the change of handedness upon reflection??</p>
<p>goldstein also writes: " An inversion never corresponds to a physical displacement of a rigid body."</p>
<p>i'm a little confused as to what is the problem with inverting the z-axis??? how does that change the physics?</p>
<p>also, please do not talk about the quantum tunnelling aspect, I am having a problem understanding this classically and I don't want to get into all that ...</p>
<p>( let's say you take the vector r = (1,0,1) in a right handed cartesian coordinate system, then you rotate it 180 degrees you get the vector r' = (-1,0,1) in the new coordinate system, now if you "invert" the z-axis what is the problem with that in terms of "rigid change". why is that not a rigid change????)</p>
<p>as a further note in the example I am working with I think it's important to keep the transformations passive ( rotate the coordinate system 180 degrees counterclockwise and then do the inversion).</p> | g13597 | [
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<p>Based on my limited knowledge of nuclear physics, it seems that one day it may/will be possible to synthesize whatever elements we may need, given enough energy. Is this accurate?</p>
<p>Is there a table that lists the most efficient ways to create certain elements from more abundant ones via fusion or fission?</p>
<p>I daresay this has rather large implications for precious metals such as gold/silver which are used as stores of wealth, provided the energy requirements are not exorbitant.</p> | g13598 | [
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<p>I made comparison between Doppler effect in light and sound and one interesting thing that I saw was that in the case of sound there are different formulas to find the apparent frequency in different situation (like observer moving,source moving,both moving etc) due to Doppler effect but in the case of light there is only one formula necessary to describe these situations.Why is it so?</p>
<p>My thoughts:I thinks it's a consequence of constancy of light speed in any reference frame. </p> | g13599 | [
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