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<p>In discussions around a recent <a href="http://physics.stackexchange.com/questions/4172/what-does-john-conway-and-simon-kochens-free-will-theorem-mean/4227#4227"> Stack answer</a> which covered axiomatic quantum mechanics, Bell's Theorem and Random Fields (related to axiomatic QFT) the phrase "Heisenberg Cut" was used. The basic question is what does this mean?</p>
<p>Having reviewed <a href="http://www.phys.tue.nl/ktn/Wim/qm1.htm#Heis_cut" rel="nofollow">this discussion</a> I can provide some background to set a context for the question. In (Von Neumann) QM a distinction is made between : OBSERVER [Cut] QUANTUM OBJECT</p>
<p>This simplistic distinction has been critized later in that article and elsewhere such that the term "Heisenberg Cut" has fallen into disuse. If one wishes to make distinctions in a QM experiment then here is a larger proposal:</p>
<p>ENVIRONMENT [Cut1] QUANTUM OBJECT [Cut2] CLASSICAL INSTRUMENT [Cut3] OBSERVER [Cut4] O-O</p>
<p>here O-O is any hypothetical observer-observer as discussed in the "Wigner's Friend" concept.</p>
<p>So has the concept of "Heisenberg Cut" been re-introduced in modern axiomatic QM/QFT and if so what is its formalisation (ie how can one make experimental or Bell Theorem-like deductions from it?)</p>
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<p>How do you go about creating a stream of single file atoms?</p>
<p>The aim is to fire a stream of single file atoms (hydrogen, helium) down a vacuum and detect there arrival on the opposite end. Any tips/papers would be a great help. </p>
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<p>How do we measure mean part or time average of a (known) velocity field?</p>
<p>In other words, if I know velocity field how can I measure its time average or mean part?</p>
<hr>
<p>What is time average in general?</p>
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] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/12175/book-recommendations">Book recommendations</a> </p>
</blockquote>
<p>So I'm a Junior level math major. I've seen some abstract algebra, some differential geometry, and some lie theory. I'm currently working through some standard topology. I don't at all claim to be an "expert" in any of the above, but I'll attest that I have some decent mathematical maturity.</p>
<p>I've always had a soft spot for physics, and I wanted to develop my knowledge of it much more formally. Particularly things like general relativity and quantum mechanics seem very cool, but I'm lamentably pretty ignorant of them. Given my somewhat okay math background, is there a good starting point for someone like me?</p>
| 98 |
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<p>I was reviewing a paper of coupling to vector field and tensor field. I have got stuck with the term $$A_k \varepsilon^{kmn}\partial_mV_n=V^{T}.(\nabla\times A^{T})-\nabla.(A^{T}\times V^{T})+V^{T}.(\nabla\times A^{L})-\nabla.(A^{L}\times V^{T})$$ Where $A^T$ and $V^T$ are the transverse part of vector $A$ and $V$ respectively. And $A^L$ is the longitudinal part of $A$ . According to the paper, after calculation the only term that survives is this one-$$A_k \varepsilon^{kmn}\partial_mV_n=V^{T}.(\nabla\times A^{T})$$ other vanishes. Well we can use $$\nabla .V^T=0=\nabla \times V^L$$. That vanishes the term $V^T.(\nabla\times A^L)$. But still there are 2 more term left. How can I solve this? Does integration by parts can do any help?</p>
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<p>How could electric fields in these waves propagate through space although in space there's no electrons for the electric field to be formed? is there another type of charged particles that carry the electric field?</p>
<p>How could the electric field exist without charges?</p>
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<p>It is well known that in special relativity observers can disagree on the time ordering of two events.</p>
<p>It is also well known that entangled particles exhibit so called spooky action at a distance.</p>
<p>Today I read in the <a href="http://www.newscientist.com/article/mg21528834.700-new-maths-triggers-a-call-to-iron-out-quantum-world.html" rel="nofollow">New Scientist</a> and on the <a href="http://arxiv.org/abs/1208.3841" rel="nofollow">arXiv</a> that although the order of two events can be arbitrary, this is not so for multiple events. As the number of events increase the number of combinations of possible orders increase but not every one of these combinations will actually be possible to always observe.</p>
<p>According to the NS article it is possible to entangle three particles a,b and c and then have them in such a way that the collaspe of c cannot be observed to precede the collapse of both a and b by any observer even though c spookily causes the collapse of a and b.</p>
<p>Is this an outright contradiction between relativity and quantum mechanics or just a paradox ? What is the explantion ?</p>
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<blockquote>
<p><em>A racing car driver drives his car on a flat circular track of radius $\frac{25}3 m$ and a coefficient of friction $0.5$. Find the magnitude of its tangential acceleration (in $ms^{-2}$) at an instant when car starts slipping at a speed of $5 ms^{-1}$.</em> </p>
</blockquote>
<p>I found the centripetal acceleration to be $3ms^{-2}$ and thought about setting the resultant acceleration (vector sum of centripetal acceleration + tangential acceleration) = $\mu$$g$ where $\mu$ = 0.5 but I don't think it is correct. If it is, then can somebody please explain why?</p>
<p>By the way, I am getting the correct answer (=$5ms^{-2}$) by this method. </p>
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<p>Is it possible for a particle trapped in a 1D finite potential well to evolve from a even state to an odd state and vice-versa? Why?</p>
| 8,894 |
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] |
<p>How could the potential difference be constant across all the resistors of parallel connecting resistors although each resistor has a specific resistance?</p>
| 8,895 |
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<p>In the first SuSy lecture last week following theory of two real scalar fields has been considered as a first example: </p>
<p>$$\mathcal{L}=(\partial_\mu \phi_1)^2/2+(\partial_\mu \phi_2)^2/2-m^2(\phi_1^2+\phi_2^2)/2$$</p>
<p>which has the usual equation of motion $$(\Box+m^2)\phi_i=0;\quad i=1,2$$ Then the professor has written down following conserved currents for this theory:</p>
<p>$$J^{(n)}_{\mu_1\dots\mu_n}=\partial_{\mu_1}\phi_2\partial_{\mu_2}\dots\partial_{\mu_n}\phi_1-\phi_2\partial_{\mu_1}\dots\partial_{\mu_n}\phi_1$$</p>
<p>Using the equation of motion, it is easy to show that these currents are indeed conserved for all $n$.</p>
<p>As far as I can see, these are no Noether currents, at least I cannot see how to get something with arbitrary many indices using the standard formula for Noether currents; furthermore I don't see which symmetry of the Lagrangian they could reflect.</p>
<p>My questions now are:</p>
<ol>
<li><p>Are there really no symmetries corresponding to these currents or do I overlook something? If there are no such symmetries and the formula for Noether's currents doesn't apply, is there any way to get such currents or is it rather an educated guess?</p></li>
<li><p>Is there any way to intuitively visualize such currents with many indices? Can anything be said about their physical meaning (if there is some)?</p></li>
</ol>
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<p>What is a good example of a simple, physically useful <em>nonlinear</em> symplectomorphism $\kappa: \mathbb{R}^{2n} \rightarrow \mathbb{R}^{2n}$? I'm not much of a physicist, and all the examples I've worked have been purely mathematical and not connected to any physical problems. Obviously linear examples are well known and useful. </p>
<p>Actually, it would suffice if I could see some nice example of a nonlinear diffeomorphism (i.e. change of coordinates) $\varphi: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ given by $x \mapsto y$, as one can then lift this diffeomorphism to a symplectomorphism by transforming the momenta via $p_y := (d\varphi^{-1})^{*}p_x$.</p>
<p>Thanks in advance.</p>
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<p>I'm having a hard time to find a good (and modern) classification scheme for phase transitions and related universality classes. Can someone recommend a paper/book/site? Detailed mathematical aspects are very much welcome.</p>
| 8,898 |
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] |
<p>Is it correct to visualize operators existing as matrices parameterized by spacetime coordinates in the context of QFT?</p>
| 8,899 |
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<p>During discussion on another question, the question of singularties in modern physical theories arose. The big-bang is an obvious singularity in modern conceptions of the cosmos. Is it a goal of modern theories to find a way to remove the big bang singularity from theory, and how is that accomplished in theories being proposed today?</p>
| 8,900 |
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<p>In a semiconductor diode. There is a depletion region formed, it is formed when electrons from n type side migrate to p type side, now which electrons transfer? Valence band ones present at the boundary or the conduction band ones? If the conduction band ones only migrate, then are there enough present on the boundary such that they can create a field at the boundary that they can stop this diffusion process? </p>
<p>By boundary i mean the border of n type and p type material.</p>
| 8,901 |
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<p>When beginning my education, I regarded nearly everything as continuous and analog in nature: </p>
<ul>
<li>Physical objects could have any mass on a continuous scale</li>
<li>Light sources could emit any intensity of light on a continuous scale</li>
</ul>
<p>The more I learn, the more I find what I regarded as continuous is actually discrete:</p>
<ul>
<li>Physical objects are composed of discrete numbers of atomic and subatomic particles</li>
<li>Light sources emit a discrete number of photons</li>
</ul>
<p>This trend of finding that things are actually discrete seems to be part of unraveling the properties of nature. The further you dig into something, the more you find the basic elements that comprise it. </p>
<p>It seems strange to me that anything could be truly continuous in nature since such a thing could potentially store infinite information. Is there anything in the universe that we know with relative certainty is not discrete? </p>
<p><strong>Edit:</strong> This isn't really a duplicate of the question that is linked. That question is essentially asking, "does the Planck scale imply that space is discrete?" This is not the same as "is everything in the universe discrete?" I did not find the answer to my question there as the answers are addressing a different question.</p>
| 114 |
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<p>The Feynman-Kikuchi Partition function is given as</p>
<p>$$Z_{FK}=K_\beta \int dx \eta(x) \exp \left(-\frac{x}{\beta}\right) $$</p>
<p>where $K_\beta$ is a normalization constant and </p>
<p>$$\eta(x)=\frac{1}{N!}\sum_P \delta\left(x-(R_0-PR_0)^2/4\lambda^* \right)$$</p>
<p>where $R_0$ is a set of particle coordinates for a perfect cubic lattice, the sum over P means over all perturbations, and $\lambda^*$ is defined as</p>
<p>$$\lambda^*=\frac{\hbar}{2m^*}$$</p>
<p>where $m^*$ is the reduced mass. My questions is this: in Ceperley's notes "Path Integrals in the theory of condensed helium", he states that, if we differentiate the partition function above with respect to $\beta$, we obtain the energy, in the form</p>
<p>$$\epsilon=\epsilon_0+\frac{3T}{2}-\frac{T^2 \langle x\rangle}{N}$$</p>
<p>I can't see how he would get that--I know that I have to calculate</p>
<p>$$\epsilon=-\frac{1}{Z}\frac{\partial Z}{\partial \beta}$$</p>
<p>But wouldn't that just give me</p>
<p>$$\epsilon=-\frac{1}{\beta^2}\frac{\sum_P (R-PR)^2\exp\left(-\frac{1}{\beta}(R-PR)^2 \right)}{\sum_P \exp\left(-\frac{1}{\beta}(R-PR)^2 \right)}$$</p>
<p>I just don't see how that would give me Ceperley's results. Thank you in advance.</p>
| 8,902 |
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<p>The planck length is defined as $l_P = \sqrt{\frac{\hbar G}{c^3}}$. So it is a combination of the constants $c, h, G$ which I believe are all Lorentz invariants. So I think the Planck length should also be a Lorentz invariant!
But there seem to be some confusion about that, see e.g. the following paper
<a href="http://arxiv.org/abs/hep-th/0112090">Magueijo 2001: Lorentz invariance with an invariant energy scale</a>:</p>
<blockquote>
<p>The combination of gravity $G$, the
quantum $h$ and relativity $c$ gives rise
to the Planck length, $l_p$ or its
inverse, the Planck energy $E_p$ . These
scales mark thresholds beyond which
the old description of spacetime
breaks down and qualitatively new
phenomena are expected to appear. ...
This gives rise immediately to a
simple question: in whose reference
frame are $l_P$ and $E_P$ the thresholds for
new phenomena?</p>
</blockquote>
<p>But if $l_P$ is a Lorentz invariant their is no question about that. $l_P$ is the same in all reference frames! Another confusing issue is that the Planck mass (from which the Planck length is derived) is often derived by setting equal the Compton length $\lambda_C = \frac{h}{m_0 c}$ ( a Lorentz invariant 4-length) and the Schwarzschild length $r_{s} = \frac{2Gm}{c^2}$ (which I believe is not a Lorentz invariant, since in the derivation of the Schwarzschild metric it is assumed to be a 3-length, measuring a space distance). But since Compton wavelength and Schwarzschild radius are not lengths of the same kind I think such a derivation is not valid.
So my question is: </p>
<p>Is the Planck length a Lorentz invariant and if so, how to derive it then without using the Compton wave length and the Schwarzschild radius ?</p>
| 8,903 |
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<p>Can two electrons be in the <em>same state,</em> when they belong to two different atoms, which are "far enough" (whatever that means) apart from each other?
With "same state" I mean that (as far as specifiable) the states are really identical, except for the position of the electrons.</p>
<p>More specifically:<br>
I am still not clear of how the separation of particles is taken into account for the Pauli exclusion principle. E.g. in a crystal the electrons seem close enough for the exclusion principle to become meaningful, for particles "a universe apart" from each other, it seems that it is kind of redundant (is there specific maths to that?), but what about everything in between? </p>
<p>(This is closely related to the talk Brian Cox gave, see this question: physics.stackexchange.com/q/18527/16689 )</p>
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<p>Let's imagine a molecule and put it in a 3D space. Let's also imagine an electronic transition for this molecule.
I know how an electronic transition works, how to value if it is possible (using the rules derived from the symmetry of the molecule and so on). My question is: how do I understand how the electron moves during the transition WITHOUT using the symmetry of the molecule? Can I "see" in which direction the electron moves in the 3D space without using the symmetry?</p>
<p>(I hope I've been clear enough to understand the question! Sorry for my mistakes)</p>
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<p>I was studying <a href="http://en.wikipedia.org/wiki/Black-body_radiation" rel="nofollow">black body radiation</a> and how quantization of energy solves the problem of ultraviolet catastrophe. But I have a very fundamental doubt. A black body can be assumed as a cavity with a small hole with radiation leaking out of it. As the temperature of the black body is increased we can assume the the charge particles, electrons, on the metal surface will behave as harmonic oscillators and the energy of the harmonic oscillation will be equal to the energy density of the radiation inside the cavity at thermal equilibrium.</p>
<p>My doubt is that at thermal equilibrium, the cavity(assuming it to be uniform) will have a uniform temperature. Since the oscillations of the charged particles is due to the thermal agitation, how can the charge particles radiate all over the frequency range? The temperature is uniform over the cavity, wont they all be experiencing same thermal agitation and oscillate at same frequency</p>
| 8,906 |
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] |
<p>Can any red coloured transparent paper be used as an optical filter that only allows red colours through it?</p>
| 8,907 |
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<p>Consider a relativistic train of weight $W_t$ in its rest frame.
Force transformation equations say that in the planet's frame its weight is reduced to $W_p=\frac{W}{\gamma}$.</p>
<p>My question is: what is the reaction force experienced by the ground?
We cannot say that in every frame the reaction force is equal to the weight of the train, because these forces are applied to objects of different velocities, and so transform differently under Lorentz transformation.</p>
<p>In this particular case - if in planet's frame $R_p=W_p=\frac{W}{\gamma}$, then Lorentz transformation of reaction force to train's frame gives $R_t=\frac{R}{\gamma}=\frac{W}{\gamma^2}$, which is different to $W_t$</p>
| 8,908 |
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<p>In the physics tutorial topic on current electricty it defines the positive terminal as the high potential terminal and the negative as the low potential. When talking about positive test charges this analogy makes sense, the charge moves from the +ve to the -ve where it loses potential till it has to be "topped" up by the cell. </p>
<p>What confuses me when they begin talking electrons. Using this analogy would mean that the electrons move from the -ve to the +ve but this means it would work again the electric field so the potential energy increases till it reaches +ve terminal. </p>
<p>My question is how does this analogy,if it does, change to accommodate electrons? Does the electric field reverse so the -ve terminal is the high potential and the +ve the low potential? </p>
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<p>In the Zeeman effect, when we observe along the $B$ field, the polarization of light should be circular polarized. It can be understood by the conservation of angular momentum. $\Delta m=0$ can not be observed and $\Delta m=\pm1$ can be observed and thus circular polarization. </p>
<p>However, I can't understand what we observe perpendicular to $B$ field. It should be linear polarized light. So the state of the photon should be something like $|\mathrm{linear~polarized}\rangle=\frac{1}{\sqrt{2}}|x_+\rangle+\frac{1}{\sqrt{2}}|x_-\rangle$($|x_\pm\rangle$ are circular polarized states in $x$ direction. We assume $B$ is parallel to $z$ axis) ,depends on $\Delta m$. How could it be like this? Why the light is linear polarized and can't be circular polarized? I am really confused. </p>
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<p>I'm making a little UV exposure box and I'm looking for a way to evenly spread out the UV light.</p>
<p>I've used Fresnel lenses to do just this in the past, but that was for visible light. But from what I've read, not all things work at all wavelengths and some materials will block UV.</p>
<p>So my first question, would a Fresnel lens still work and evenly spread out UV light?</p>
<p>What material should I look for? The lens I've seen are PVC and from what I've seen elsewhere, PVC has good UV resistance, but I don't know if that means it will just hold up to UV or if it will block UV all together.</p>
<p>Any tips or suggestions would be great thank you </p>
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<p>I just read about how LCD displays were based only on black&white contrasts, and only colour filters on each subpixel generated the colour of a pixel. However, how does that happen for a <a href="http://en.wikipedia.org/wiki/Cathode_ray_tube" rel="nofollow">CRT</a>? </p>
<p>Is it the same process? If not, during the screen sweep, is there one beam modulated differently during each third of a pixel period that react in some way with the screen? Or three identical beams targeted at each subpixel coated with a different reactor? Or even three different beams targeted at each subpixel made of the same reactor?</p>
<p>Bonus question: how does the screen glow upon photons hitting its surface?</p>
| 8,912 |
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<p><img src="http://i.stack.imgur.com/fqcvC.png" alt="enter image description here"></p>
<p>Hi, I was just reviewing some slides from my thermodynamics class, and in one of the slides the professor asks what is the "physical meaning of the slopes" of the isobaric line in a T-v diagram. Can anyone help me understand this?</p>
<p>I know what I am looking at is the constant pressure line from a T-v diagram, and that the slope of the line would be $m = \frac{P_2 - P_1}{v_2 - v_1} = \frac{\Delta P}{\Delta v}$</p>
<p>I haven't been able to find anything on the internet or in my book that can tell me what the physical meaning is. Can anyone help me with some insight?? Thx! </p>
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<p>Firstly, most definitions of angular momentum assume a point about which you define angular momentum. I realize that you can consider the angular momentum about any point, and have many angular momentums, and that if they are all useful and all conserved then maybe it doesn't matter if there are lots of different ones. But it does make me wonder how fundamental it is, or even whether it always makes sense, or whether the term has the same meaning in every branch of physics.</p>
<p>I'm used to momentum being frame dependent, but conserved. Its conservation just looks like three of the free components of $0 = T^{\mu \nu}_{,\nu}$ from Special Relativity.</p>
<p>I'm also familiar with the fact that in Newtonian Mechanics, forces that act in the direction between two particles conserve angular momentum about any point.</p>
<p>I'm also familiar with the fact that for any variable that the Lagrangian doesn't depend on, there is a corresponding momentum conjugate to that variable that is conserved (so if a variable deserves the name angular, then the corresponding conjugate momentum is both conserved and equally deserves to be called an angular momentum).</p>
<p>I've also seen conservation of angular momentum from Special Relativity in the form $0 = (x^{\alpha} T^{\mu \nu} - x^{\mu} T^{\alpha \nu})_{,\nu},$ where this is the divergence of a rank 3 tensor. Though to be fair, this is usually derived from the symmetry of the stress-energy tensor $T^{\mu \nu}$ which itself is usually derived from considerations that angular momentum doesn't go crazy at fine scales. So it does make me wonder which ideas come first, conservation of angular momentum or the symmetry of the stress-energy tensor.</p>
<p>Also, you can have angular momentum in electromagnetic fields (or in electromagnetic potentials, which depend on gauge this is even more than just depending on a point). An example is the angular momentum set up by having a linearly charged wire inside a solenoid inside a charged cylindrical shell. But if you turn the current off from the solenoid, it begins to rotate so it seems like mechanical angular momentum is only conserved when coupled to field (or potential) angular momentum.</p>
<p>And in quantum theories you have intrinsic spin angular momentum as well as the regular angular momentum, and the regular one again depends on your origin or potentially also on the electromagnetic potentials (but here I'm less bothered by the apparent gauge dependence).</p>
<p>With so many potentially (pardon the pun) different momentums, and so many derivations of special cases where some of them are conserved. The question is whether they are the same thing in these very different theories, and whether they are always conserved or just some of them or just in some situations, and in particular how this relates to General Relativity.</p>
<p>For instance, a charged rotating black hole is often parameterized by a total angular momentum per unit mass. So it's common in General Relativity to talk about a total angular momentum. But does a total angular momentum make sense in General Relativity and what if anything from other theories does it correspond to (field angular momentum, potential angular momentum, mechanical angular momentum, intrinsic spin, combination of all or just some of those)?</p>
<p>I'm not even aware of a general differential conservation law for angular momentum in General Relativity. And knowing whether it is stored in the fields or in mechanical angular momentums seems relevant to knowing how much is inside a region if we want to get a total for a region.</p>
<p>As an example of how common the assumption of conservation of angular momentum is, a quick google search came up with </p>
<p><a href="http://csep10.phys.utk.edu/astr161/lect/solarsys/angmom.html" rel="nofollow">http://csep10.phys.utk.edu/astr161/lect/solarsys/angmom.html</a></p>
<p>as the second link and it says "all experimental evidence indicates that angular momentum is rigorously conserved in our Universe." The course is an Astronomy course, not a Cosmology or General Relativity course, but I'd still expect instructors and students in an Astronomy course to have some awareness of General Relativity and so wonder which things continue to hold in General Relativity.</p>
<p>The first link from a quick google search is to the wikipedia article on angular momentum, which cites the Newtonian mechanical versions, the gauge dependent electromagnetic case, the quantum case, and no mention of General Relativity except to say that angular momentum is not, in general, conserved in General Relativity, but it is missing a citation for that. It also just assumes at the beginning that no net external torque means conservation of angular momentum, even though the proofs used requires that forces act along the line between the particles even for Newtonian Mechanics and the article itself admits that angular momentum (however it is defined) is not consider, in general, in General Relativity.</p>
<p>I want to point out that one reason I express skepticism about the definition of angular momentum in General Relativity is because it does not appear to be conserved. If you had a quantity with a differential conservation law, then there are grounds to say we have something legitimate. If you define something and then see that it isn't conserved, then it begs the question about whether a different definition would have been conserved. And it seems strange to have a non-conserved thing exist in a theory that is supposed to be an experimentally verified limit of a quantum theory where thing you are supposed to correspond to is generally assumed to be conserved. In particular if every star is made up of ions and fields and you expect angular momentum to be conserved by them, then a definition that is supposed to correspond to angular momentum but isn't a conserved thing should be suspect. But the tensors I see for angular momentum in Special Relativity seem to generalize mechanical momentum, so don't include any intrinsic spin. So when a parameter refers to the total angular momentum of a system in General Relativity, it's not clear what is does or is supposed to correspond to. And I don't know if we are happy with our definitions as they are (say from a Lagrangian formulation of General Relativity), or whether this is an area of active research that goes by a name I'm not familiar with.</p>
<p>In case this helps anyone answer, there are classical electromagnetic forces besides the Lorentz force law for objects with intrinsic magnetic moments, e.g. $\vec{F}=\vec{\nabla}(\vec{\mu}\cdot \vec{B})$. So the usual angular momentum tensors might simply be ignoring the stress-energy associated with this kind of work (which unfortunately is non conservative, so I'm not immediately aware of how to get a stress-energy tensor from those kinds of forces). I also am not looking just for a pointer to Einstein-Cartan theory (or any other alternative to General Relativity) without a discussion about whether current General Relativity is considered to be confused, wrong, or deficient or whether these are just two theories that appear to be equally valid and functional at this juncture in our studies of Physics.</p>
<p>P.S. I wanted my fifth tag to be correspondence-principle but can't make a new tag.</p>
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<p>I was pondering this question after I read this review:</p>
<blockquote>
<p>M. Zahid Hasan and Charles L. Kane. “<a href="http://dx.doi.org/10.1103/RevModPhys.82.3045" rel="nofollow">Colloquium: topological insulators</a>.” <em>Reviews of Modern Physics</em> <strong>82</strong>, no. 4 (2010): 3045. (<a href="http://arxiv.org/abs/1002.3895" rel="nofollow">arXiv</a>)</p>
</blockquote>
<p>How do the edge modes on the interface between two domains with spin-Chern number n=1/-1 of a 2D system differ from the edge modes of the system with "n=2/0" interface?
Specifically in the two cases, spin-Chern numbers differ by 2 across the interface; according to the bulk-boundary correspondence, there should be 2 edge modes of the same spin in each case. However, in Z2 classification of TI, case 1 is non-trivial in both domains (n=1 and n=-1), yet case 2 is trivial (n=2 and n=0).</p>
<p>I'm guessing in case 1, we do have edge modes that are against impurity and do not backscatter, but in case 2, that is not the case.
Am I thinking in the right path? Is there any materials that discuss about this question?</p>
<p>Many thanks. </p>
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<p><strong>Context</strong>: The question refers to computational physics of non linear systems with <em>Mathematica</em>.</p>
<p><strong>Excercise</strong>:
Given the system $\{f_1: \dot{x} = a x + y + x^3, f_2: \dot{y} = x - y \}$:</p>
<ol>
<li>Find the equilibrium points and classify them.</li>
<li>What kind of bifurcation is there and for what value of $a=a^*$ does it happen ?</li>
<li>Draw the phase portrait for one $a<a^*$ and for one $a>a^*$.</li>
</ol>
<p><strong>Solution</strong>:
I calculate the equilibrium points by solving the system of equations $\{\dot{x} = 0, \dot{y} = 0\}$. I get three solutions: $(0,0), (-\sqrt{-1-a},-\sqrt{-1-a}), (\sqrt{-1-a}, \sqrt{-1-a})$.</p>
<p>My lecture notes mention that in order to classify an equilibrium point, I first need to find out the topology near the equilibrium points. This is done by calculating the eigenvalues of the following matrix: </p>
<p>\begin{equation}
A=
\begin{pmatrix}\frac{\partial f_1}{\partial x} & \frac{\partial f_1}{\partial y}\\\frac{\partial f_2}{\partial x} & \frac{\partial f_2}{\partial y}\end{pmatrix}_{(x_0^*, y_0^*)}
\end{equation}</p>
<p>As can be seen from the following screenshot (L1 are the eigenvalues of matrix A calculated at the 1st equilibrium point, at (0,0)), we can see that:</p>
<ol>
<li>for $a <-1$, it is $\lambda_1 < 0, \lambda_2 < 0$, therefore it is stable node.</li>
<li>for $a>-1$, it is $\lambda_1 < 0 < \lambda_2$, therefore it is saddle.</li>
</ol>
<p><strong>My 1st question is</strong>: What does it happen for $a = -1$, where the eigenvalues become (-2, 0) ? My closest guess is to use the <em>Hartman-Grobman theorem</em> and say that the equilibrium point is 'linearly stable'. Is there anything I am missing here ?</p>
<p><strong>My 2nd questions is</strong>: Regarding the bifurcation point, by looking at the equilibrium points of the system, we deduce that at value $a=-1$ they change (the stable node becomes saddle and vice versa). Does that suffice to say that there is a bifurcation point at $a=-1$ ? Also for $a=-1$ the three equilibrium points collide to just one. How does that this fact fit with everything else ?</p>
<p><img src="http://i.stack.imgur.com/HX4Xl.png" alt="Eigenvalues of matrix for equilibrium point (0,0)"></p>
<p><strong>Update:</strong></p>
<p>These are the phase portraits for $a<a^*, a>a^*$ with $a^*=-1$ being the bifurcation point:</p>
<p><img src="http://i.stack.imgur.com/ijkzF.png" alt="enter image description here"></p>
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] |
<p>Assume you're talking to someone ignorant of the basic facts of astronomy. </p>
<p>How would you prove to them that the Earth orbits the Sun? Similarly, how would you prove to them that the Moon orbits the Earth?</p>
| 8,917 |
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<p>In other words, could there be higher dimensional entanglements between entanglements? For instance, this could allow us to entangle two entangled-far-away pairs to create a system of four entangled particles.</p>
<p>I am sorry if this sounds like a silly question.</p>
| 8,918 |
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<p>In a paramagnetic system, where $N = N_\uparrow + N_\downarrow$ is fixed, how does one calculate the average number of spin-up particles $\langle N_\uparrow \rangle$?</p>
<p>You can assume we have the canonical partition function. The Hamiltonian for this system is:</p>
<p>$$ H = \sum_{i=1}^N {\frac{(p_i - b s_i)^2}{2m} - h s_i} $$</p>
<p>where $s_i = +1$ for spin-up and $s_i = -1$ for spin-down.</p>
<p>How do I actually go about calculating this?</p>
<p>I know, in general for an operator $O$:</p>
<p>$$\langle O \rangle = \sum_{\mu} P_\mu O_\mu = \frac{1}{Z} \sum_{\mu} O_\mu e^{-\beta E_\mu}$$</p>
<p>Can someone show me how to explicitly use the Hamiltonian to evaluate this? Also, can we use $\langle N_\uparrow \rangle$ to evaluate $\langle N_\uparrow - N_\downarrow \rangle$? Can you just say $\langle N_\uparrow - N_\downarrow \rangle = 2\langle N_\uparrow \rangle - \langle N \rangle = 2\langle N_\uparrow \rangle - N$ since $N$ is fixed?</p>
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<p>A <a href="http://www.cencophysics.com/planar-diode/p/IG0044534/" rel="nofollow">planar diode</a> in a vacuum bulb can support current in only one direction. To even get current flowing, you have to heat up the cathode filament to excite the electrons. However, once current is flowing, there is a certain limit imposed on it, making the resulting graph of current versus voltage look like this: </p>
<p><img src="http://i.stack.imgur.com/y6yS0.png" alt="Graph of Current vs Vooltage"></p>
<p>You can observe an inflection point about half way through the graph, and you'll notice the curve slowly flattening out. </p>
<p>What is the formal theory and terminology behind this limit? Is it because of the build up of space charge (slow moving electrons, in this case) in between the diodes, which would repel the electrons in the cathode and keep them from escaping across the diode, thus imposing a certain limit on current? </p>
| 8,920 |
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] |
<p>What are the typical power densities in conventional boiling water nuclear reactor per cubic centimeter of fission material?</p>
| 8,921 |
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<p>Consider the gauge covariant derivative defined by
$$
D_z = d_z + \Delta_z
$$
or explicitly
$$
(D_z)^a{}_c = \delta^a_c d_z + (\Delta_z)^a{}_c = \delta^a_c d_z + f_{bc}{}^a A_z^b
$$
Here, $d_z$ is the covariant derivative w.r.t. to the metric
$$
ds^2 = \gamma_{z{\bar z}} \left( dz \otimes d{\bar z} + d {\bar z} \otimes d z \right)
$$
$f_{ab}{}^c$ are the structure constants of a Lie algebra satisfying
$$
[T_a, T_b] = f_{ab}{}^c T_c
$$
Let us assume that $d_z^{-1}$ is a well-defined operator on the background. Let us also assume that the gauge field satisfies
$$
F^a_{z{\bar z}} = d_z A^a_{\bar z} - d_{\bar z} A^a_z + f_{bc}{}^a A_z^b A_{\bar z}^c = 0
$$
In matrix notation, we can write this equation as
\begin{equation}
\begin{split}
D_z A_{\bar z} = d_{\bar z} A_z,~~ D_{\bar z} A_z = d_z A_{\bar z}
\end{split}
\end{equation}
Under these conditions, I wish to write the inverse of the gauge covariant derivative $D_z^{-1}$ in terms of $d_z^{-1}$. Is this possible?</p>
| 8,922 |
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<p>So, I have been having a hard time understanding why there is even a complex phase for EM waves:</p>
<p>$$\phi=\exp[i\omega t]=\cos(\omega t)+i\sin(\omega t)$$</p>
<p>Don't understand why it is there? Any one have an explanation?</p>
| 295 |
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<p><a href="http://proj-cngs.web.cern.ch/proj-cngs/Download/CNGSDGVE/cngsdgve.pdf" rel="nofollow">http://proj-cngs.web.cern.ch/proj-cngs/Download/CNGSDGVE/cngsdgve.pdf</a></p>
<p>on page 13 I read that "the present plan is to provide nu_mu neutrinos with an energy between 5 and 30 GeV."</p>
<p>Wikipedia neutrino article <a href="https://en.wikipedia.org/wiki/Neutrino" rel="nofollow">https://en.wikipedia.org/wiki/Neutrino</a> says that neutrinos are electrically neutral.</p>
<p>What is the justification of giving a non-electrical particle the units of electricity?</p>
| 8,923 |
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<p>For some reason this question is giving me a hard time :(</p>
<p>The vector $r$ points from $P'(x',y',z')$ to $P(x,y,z)$.</p>
<p>(a) Show that if $P$ is fixed and $P'$ is allowed to move, then $\nabla'(\frac{1}{r})=\frac{\hat{r}}{r^2}$ </p>
<p>(b) (a) Show that if $P'$ is fixed and $P$ is allowed to move, then $\nabla(\frac{1}{r})=-\frac{\hat{r}}{r^2}$ </p>
<p>I don't really understand the notation $\nabla'(\frac{1}{r})$ What is the prime? what exactly am I applying the gradient operator to? and how can I show this and answer the question proposed? </p>
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<p>I am looking at a 2D harmonic oscillator
$$H=\frac{1}{2m}(p_x^2+p_y^2)+\frac 12m(\omega_x^2x^2+\omega_y^2y^2)$$
Where $\omega_x=5\omega_y$. I am told that the oscillator is prepared in a coherent state with the following qualities:
$$\langle x(0)\rangle=x_0$$
$$\langle p_x(0)\rangle=0$$
$$\langle y(0)\rangle=0$$
$$\langle p_y(0)\rangle=p_0$$
I am looking for the time dependent state of the system. My approach:</p>
<p>Seeing as this is a coherent state, the expectation values act as classical variables, this means that the position and momentum will be given as
$$q(t)=q(0)\cos(\omega t)+\frac{1}{m\omega}p(0)sin(\omega t)$$
$$p(t)=p(0)\cos(\omega t)-m\omega x(0)\sin(\omega t)$$
Additionally, the coherent state is given as:
$$\alpha (t)=\frac{1}{\sqrt{2m\omega\hbar}}(ip(t)+m\omega x(t))$$
So if I want to find the state as a function of time, do I find the alpha for both x and y and add them together?</p>
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<p>With respect to special relativity, I was wondering how the spatial dimensions would differ between the rest and LAB frame of an electron beam.</p>
<p>System: Electron bunch/beam traveling in linear motion. How large/long would the bunch appear in the point of view of an electron (rest frame). How large/long would the bunch look in the lab frame?</p>
<p>How would the answers change if the electron bunch/beam was accelerating?</p>
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<p>First of all many here will might say that it is Chemistry question.If you think so then read <a href="http://web2.physics.miami.edu/~zuo/class/spr_14/Chemical%20potential.pdf" rel="nofollow">this article</a> and then answer question.</p>
<p>Question is --- We know chemical potential is defined as $\mu_i =\mu_i^{standard}+RTln(a_i)$ .Here $a_i$ is activity of $i^{th}$ component of solution.In case of gases instead of $a_i$ it is $f_i$ that is fugacity of $i^{th}$ gas out of mixture of gases.Activity is here nothing but activity coefficient multiplied by concentration or in case of fugacity it is product of fugacity coefficient multiplied by partial pressure of gas.</p>
<p>But now this is not the only definition of Chemical potential.Chemical potential also means <strong>partial molar gibbs free energy</strong> when pressure and temperature of system are constant.We know that Gibbs free energy of system at constant temperature and pressure also represents Non-PV work done by system.Now how can the term $RTln(a_i)$ can be correlated to Non-PV work done by system in order both two definitions will be equivalent.</p>
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<p>In relativity, the symmetric energy-momentum tensor is given by
$$
T^{ij},
$$
where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus:
$$ \left(\frac{1}{c}T^{00}dV, \frac{1}{c}T^{10}dV\right)^{T}$$
is the 4-momentum.
Under a Lorentz transformation, this should transform like 4-vectors where
$$ \frac{1}{c}T^{00}dV= \left[\frac{1}{c}T'^{00}dV'+\frac{v}{c^2}T'^{10}dV'\right] \left( 1-\frac{v^2}{c^2}\right)^{-1/2}\\dV=dV'\sqrt{1-\frac{v^2}{c^2}}.$$
After simplifications, we have:
$$ T^{00}= \left[T'^{00}+\frac{v}{c}T'^{10} \right] \left( 1-\frac{v^2}{c^2}\right)^{-1}$$
But if we apply the Lorentz transformation to the tensor directly we get
$$ T^{00}= \left[T'^{00}+\frac{v}{c}T'^{10}+\frac{v^2}{c^2}T\
^{11} \right]\left( 1-\frac{v^2}{c^2}\right)^{-1}$$
What accounts for the difference? I think the first is wrong but have no idea why. </p>
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<p>I'm working on a problem in which a star of mass M1, radius R1 is surrounded by a thin shell of mass M2, , radius R2. I want to find the solutions to the gravitational potential h in the region in between the star and the shell and region outside both. </p>
<p>Can we assume the mass is stationary, and not too large, and thus use the analogous Poisson's equation (Laplacian of potential = 4*pi*G*rho)?</p>
<p>Or is there some physical reason that we should use the potential equation in the Hilbert gauge (d'Alembertian of tensor potential = 4*pi*G*(energy momentum tensor)/(c^2)?</p>
<p>My thinking is that Poisson's is totally appropriate for this simple situation of a stationary star with a shell mass around it. </p>
<p>Now, I don't see how to use Poisson's equation. I'm getting tripped up with how to consider the two masses. What if, for example, it's a very dense shell which is in fact more massive than the star. That would give a potential radially outward. How do I find a solution to the Laplacian?</p>
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] |
<p>This is a quite simple question: quarks do mix (through the CKM matrix), neutrinos do mix (through the PMNS matrix).</p>
<p>Then <strong>why do charged leptons not mix?</strong></p>
| 8,930 |
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] |
<p>Can anyone provide me with a rigorous mathematical definition of the <a href="http://en.wikipedia.org/wiki/Standard_Model" rel="nofollow">fundamental particles</a> (all fundamental bosons and fermions), reflecting the analogy of action of groups with interaction of particles, isospin and mediating forces? An answer would be preferable, but a link of an appropriate source would also suffice.</p>
| 8,931 |
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] |
<p>Precision is usually understood as the number or significant figures in some experiment.
Accuracy is the difference between the best measurement and the real value. </p>
<p>How are <a href="http://en.wikipedia.org/wiki/Accuracy_and_precision" rel="nofollow">precision and accuracy</a> determined from a given experiment? Or equivalently, how are systematical errors and statistical errors calculated. Statistical errors are usually treated approaching "the normal distribution". But I am not sure how systematics are determined...Perhaps making some "pattern" measurements?</p>
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<p>There are two Casimirs of the Poincare group:</p>
<p>$$ C_1 = P^\mu P_\mu, \quad C_2 = W^\mu W_\mu $$</p>
<p>with the Pauli-Lubanski vector $W_\mu$. This implies the Poincare group has rank 2. </p>
<p>Is there a way to show that there really are no other Casimir operators other than trying to build all possible combinations of generators and seeing them fail? </p>
<p>To state it differently: Can one determine the rank of the Poincare group without explicit construction of the Casimir operators?</p>
| 8,933 |
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<p>Consider an ideal steam turbine.</p>
<p>The power generated by a steam turbine comes down to the torque and the angular velocity, which is ultimately dependent on the velocity at which the flow enters the turbine (and turbine factors, but will only consider the flow properties). Similarly, the power needed by a turbopump is dependent only upon the velocity at which we want the fluid to leave the pump. The velocity of the flow can be determined as such:</p>
<p>$$
v = \dot{V}/A
$$
$$
\dot{V} = \dot{m}/\rho
$$</p>
<p>Now suppose I make a fluid loop, with a turbopump in series with a turbine of identical size and design. Continuity of the fluid loop gives us this equation:</p>
<p>$$
\dot{m} = \rho_1v_1A_1 = \rho_2v_2A_2
$$</p>
<p>Assuming no loss to friction or anything else, you will get exactly as much power from the turbine as you put into the turbopump. Okay so far.</p>
<p>However, then I simply make the turbine have a smaller cross section area. Since mass flow is constant through the fluid loop, $v$ increases, and you end up getting more power out of the loop than you put in. Since this is thermodynamically impossible, does this mean the flow density must decrease proportionally to assure that the power in and power out is the same? However, what if this was a liquid-only fluid loop, where the density remains roughly the same?</p>
<p>Ok, now suppose we turn this into a Closed Brayton Cycle. In between the turbopump and turbine we add in a boiler which adds an amount of heat energy to the fluid. Is it correct to use the ideal gas law to determine the density of the flow?</p>
<p>$$
P = \rho R'T
$$</p>
<p>In this way, while $\dot{m}$ remains constant, $\rho$ would decrease based on the temperature, which would ultimately increase $v$. Is that correct, or does the addition of heat alter the flow velocity differently in order to convert heat energy into work?</p>
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<p>I the following (american) test</p>
<blockquote>
<p>Vacuum testing consists of placing samples from the packiging operation into a jar filled with water. A lid is placed over the samples to fully immerse them in the water. A container lid is applied to create a seal effective enough to create approximately <strong>25 cm of vacuum</strong>. The vacuum pump is set, and the samples are tested for approximately 1 minute...</p>
</blockquote>
<p>Is 25 cm of vacuum equal to 333 or -667 mbar (or are the +- opposite)? </p>
<p>or </p>
<p>does it just mean that there has to be 25 cm distance from the water front to the container lid <strong>__</strong>?</p>
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<p>If photon is an elementary particle, how can different photons have different energy, if <a href="http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence" rel="nofollow">$E=mc^2$</a> and all photons have (or don't have) the same mass and the speed of photon is constant shouldn't it mean all photons have the same amount of energy?</p>
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<p>While reading the amazing things that the <a href="http://en.wikipedia.org/wiki/Mantis_shrimp" rel="nofollow">mantis shrimp</a> can do, such as moving two of their limbs so quickly that the water around them <a href="http://en.wikipedia.org/wiki/Supercavitation" rel="nofollow">'supercavitates'</a>, a friend of mine told me that those limbs were creating vacuum, in the water. Does this creation of vacuum happen? Or is it something else? If so, am I creating vacuum when boiling water?</p>
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<p>The baryon number B or lepton number L violation in the standard model arise from triangle anomaly. Right? Triangle diagrams are perturbative diagrams. Then why the B or L violation in Standard model is said to be a non-perturbative effect? I'm confused.</p>
| 8,938 |
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<p>For example in the models for holographic superconductors we can calculate the conductivity. Also there is an energy gap. I can understand that it describes a superconductor. However I have also heard people talk about superfluidity in holographic QCD. I believe they are talking about the condensates such as the pion or the chiral condensate. Where is the superfluid in holographic QCD (quark gluon plasma maybe?) and how do I know that it is a superfluid?</p>
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<p>What is the correct definition of the energy of a string ?</p>
<p>I suddenly get confused with the definition of the energy of a string. Considering, for instance, a bosonic open string in the light-cone gauge, We have $H = p^-=p_+$, the hamiltonian, and we have $p^0$, which appears in the expansion of the string in light-cone gauge $X^o(\sigma, \tau) = x^0 + \frac{p^0}{p^+}\tau + ...$. </p>
<p>a) In Zwiebach's First course in string theory (<a href="http://cdn.preterhuman.net/texts/science_and_technology/physics/String_Theory/A%20First%20Course%20in%20String%20Theory%20-%20B.Zwiebach.pdf" rel="nofollow">1</a>), there is a calculus of the entropy of a string, which begins (Chapter $16.2$ p $354$) by a function partition for a non relativistic string with fixed points (the quantum violin string). For a given energy $E = N \hbar w_0$, where $N$ is the level, the entropy is computed (this is direcly linked to the number of <a href="http://en.wikipedia.org/wiki/Partition_%28number_theory%29#Approximation_formulas" rel="nofollow">partitions</a> p(n)). More precisely, an expression for the entropy, $\sim T$, and the energy ,$\sim T^2$, are obtained, se we get a $S \sim \sqrt{E}$, and plugin the $E \sim N$ expression, we get a $S \sim \sqrt{N}$.</p>
<p>"Suddenly", in chapter $16.3$ page $361$, it is said that "we now return to relativist strings that carry no spatial momentum, and this happens if the open string endpoints end on a D-0 brane, so the energy levels are given by the rest mass of its quantum states". Of course, we have $m^2 \sim N$ (for large $N$), so $m\sim \sqrt{N}$, so if the energy ($p^0 ?$) is identified with $m$, we have $S \sim E$
Now, if we take the hamiltonian $H$, for large $N$, we have $H \sim N$, so $S \sim \sqrt{H}$</p>
<p>So, this confused me, because I have $2$ law expressions for the entropy, depending on the definition of the energy.</p>
<p>b) An other problem, is saying that the energy of the string is proportionnal to its length. If we look at $H$, we have $H=p^- \sim \frac{1}{l}$ (with zero trans verse momenta $p^i$), while $p^+ \sim \frac{l}{\alpha'}$. So, may I write that the correct energy is $p^o \sim (p^+ + p^-)?$</p>
| 8,940 |
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<p>When looking at a Schwarzschild black hole, for instance, we know that we may apply <a href="http://en.wikipedia.org/wiki/Black_hole_thermodynamics" rel="nofollow">black hole thermodynamics</a>. We may define a entropy of the black hole which scales like the area of the horizon : $$S \sim R_s^2$$. </p>
<p>It is understood in the more general context of the <a href="http://en.wikipedia.org/wiki/Holographic_principle" rel="nofollow">holographic principle</a> which states that " the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon"</p>
<p>Now, the non-gravitationnal energy $E_{ng}$, so the mass $M$ for the Schwarzschild black hole, has a different scaling :
$$E_{ng} \sim R_s$$</p>
<p>So, does that mean that the energy is encoded in a one-dimensional object (perimeter, loop, string, radius), and is it a different "holographic" principle ?</p>
| 8,941 |
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<p>So I was introduced to this "perpetual motion" riddle a few weeks ago. The problem goes like this: we all know perpetual motion machines are not possible, but this riddle <em>seems</em> like it should work as a perpetual motion machine - the problem is to explain <em>why it doesn't work</em>.</p>
<p><strong>Here's the situation:</strong></p>
<p>(1) You take a room, and put a wall down the middle of the room - splitting it in to two equal half-rooms. </p>
<p>(2) Take a perfectly cylindrical log whose length is the same as the length of the wall we just put in to make two half-sized rooms, and cut out a place halfway up the wall so that the log slips right in, length wise (if you were looking at the middle wall from the inside of one of the rooms, you would not see the ends of the log at all, you would a half-cylinder running the length of the wall - if you looked from the other room, you would see the other side of the cylinders length).</p>
<p>(3) Make sure the space between the log and the wall is air-tight (the log is treated to absorb no water, there is no friction between it and the wall, etc), and fill one of the half-sized rooms all the way to the top with water. Now you have one side of the log exposed to air, and one side totally surrounded by water.</p>
<p>The idea is that, since everyone has experience that logs rise in water, the side exposed to the water should "rise" and the log should spin, creating a perpetual motion machine.</p>
<p>Now, I have two explanations of why it <em>doesn't</em> work. One I came up with myself, and one that is proposed in the solution on the page in which I found the problem.</p>
<p><strong>My Solution:</strong></p>
<p>Water pressure increases as you increase in depth, so the water molecules hitting the log deeper in the water would have more force that the water molecules hitting the log less deep, but at each infinitesimal depth increase, the water is hitting the log at all angles, and the force from the molecules coming on from all directions would cancel out to leave a force pointing toward the center, at every place the log is exposed to water. Since all of the net forces from the water at each point exposed to water is pointing toward the center, there can be no net torque and the log cannot spin. The <strong>net</strong> force would be a slight force directly upwards (due to the difference in size of the force vectors pointing inwards between the less dense water up top and the more dense water on the bottom), but since the log is held in place, it cant move upwards.</p>
<p><strong>The Proposed Solution</strong></p>
<p>"To understand why this would not work, we need to look at how buoyancy itself works. </p>
<p>When a lighter than water object (lets say a hollow ball) is submerged it is pushed up by the water apparently in spite of gravity. In fact the opposite is true. It is gravity pulling down on the water that pushes the ball up. The kinetic energy to lift the ball comes from an equal volume of water falling to occupy the space where the ball just was. As the ball moves up, the evacuated area is filled with water from above it; therefore, this water is falling. When the water was above the ball it had potential energy that is exchanged for kinetic as it falls to fill the void left by the ball thus providing energy to lift the ball. </p>
<p>The opposite is true for a heavier than water object (lets say a brick), but it's still the same principle. As the brick falls through the water, it is filling space that was once filled by water. As the brick falls, it is providing energy to lift the water to fill the space it just evacuated.</p>
<p>Now back to our spinning log example. If the log were to spin, it would not be evacuating any space for the water to fill. Even though a different part of the log would be filling that space, it would still be the same space it was filling before. There would be not downward movement (falling) of water to convert potential energy into kinetic, so there is no energy to cause the log to spin."</p>
<p><strong>Here's my problem</strong></p>
<p>I've never understood this explanation of buoyancy. Why, just because an object is less dense than water, is the water "rushing below it" to fill the space evacuated by the object as it rises? Why doesn't the object just stay where it is? It seems like you're using buoyancy to explain buoyancy - the less dense object floats upward due to buoyancy and the water rushes in below to fill the evacuated space, which causes the buoyant force upwards... what?</p>
<p>Why is the water rushing below less dense objects, and not rushing below more dense objects? Am I missing something in the explanation?</p>
<p>I understand that when you submerge an object in water, it displaces an equal volume of water, and the weight of the water displaced equals the bouyant force upwards, but I just don't understand why the water is "rushing underneath and pushing the object up".</p>
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<p>In a newtonian universe, one can talk of a "time slice", that is, the state of the universe at a given point in (global) time. In a "typical" classical universe, a time slice would contain enough information to fully compute the state of the universe at any other point in time, backwards or forwards.</p>
<p>So, disregarding what we know of quantum effects and talking purely of a general-relativistic universe, which concept is closest to a time slice?</p>
| 8,943 |
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<p>A few years ago, when i studied the casimir effect interpretation as the filtering out of vacuum modes with appropiate boundary conditions, i had the following dilemma; supposedly the derivation of the force between the walls was <strong>entirely</strong> equivalent to just calculating Van der Waals forces. This, as it was argued, compelled us to not take too seriously the idea of a negative energy density of the space between the walls.</p>
<p>However, i was left wondering what would happen if one would take the interpretation based on vacuum modes a bit further, and we could somehow switch on and off the permitivity $\epsilon$ of the conductor; what sort of long range radiation we would expect to see?
A possible experimental implementation would be if the layers where superconductive, and then a magnetic field would be switched on just to break the superconductive phase.</p>
<p>We probably need to use the Dirac-Heisenberg-Wigner formalism for these sort of dynamic quantum systems, but what would be intuitively expected to be detected?</p>
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<p>I've variously heard the shape of the universe being described as multi-dimensional, like a helix or mobius strip, and super string theorem seems to say there are lots of universes all piled up next to each other in vibrating planes.</p>
<p>My question is, can the edges of our universe ever join up? Are they already all joined up? as in is our universe really in the shape of a giant donut (yum). or is this shear lunacy?</p>
<p>I guess I am assuming a model of the universe where the "edge" is not necessarily expanding constantly "out" into infinite amounts of empty vacuum, but rather one where the edges are the boundaries to that expansion (so that it seems from an observable position that the universe is expanding, when really its flexing inside these boundaries). As indicated in the comments no doubt an inaccurate description, but I was imagining it like a balloon.</p>
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<p>I've been reading <a href="http://en.wikipedia.org/wiki/Electrolysis_of_water" rel="nofollow">http://en.wikipedia.org/wiki/Electrolysis_of_water</a> and other related questions on physics.stackexchange, but I fear I don't have a decent enough understanding of math and science to understand and decipher into laymen terms.</p>
<p>I basically just want to know how much energy in watts or joules it takes, taking efficiency out of the equation (assuming the perfect, yet realistically possible method / voltage / etc), it takes to convert 1 liter of water into hydrogen and oxygen (electrolysis).</p>
| 8,946 |
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<p>What prevents a static black hole from accumulating more charge than its maximum? Is it just simple Coulomb repulsion?</p>
<p>Is the answer the same for rotating black holes?</p>
<h3>Edit</h3>
<p>What I understand from the answers given so far, is that <strong>maximum charge</strong> is a <strong>moving target</strong>. You can add charge to a black hole but Coulomb repulsion guarantees that you will do so in a manner than will increase "maximum charge value". Is this correct? </p>
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<p>I am reading an optics book (<em>Physics of Light and Optics</em> by Peatross and Ware) that asserts this:</p>
<blockquote>
<p>A beam of light can always be considered as an intensity sum
of completely unpolarized light and perfectly polarized light:</p>
<p>$$I=I_{Pol}+I_{Un}$$</p>
</blockquote>
<p>How does this marry with the superposition principle? Why can we just add the intensities?</p>
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<p>If a neutrino has mass then it travels less than the speed of light. Suppose I boost myself to the rest frame; i.e. bring it to rest in the laboratory. Now if it oscillates between different states and masses sitting there, where does the oscillating excess/loss energy and mass reside? In some internal state? I have a very limited knowledge of QM but in SR it would seem strange that "mass" would move into another place. A pointer to where I should start studying would (I hope) be sufficient.</p>
| 8,949 |
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<p><img src="http://i.stack.imgur.com/7GRZp.png" alt="enter image description here"></p>
<p>Is the nyquist plot of the open control loop. The starting point (not shown in the figure) is in the negative infinity of the imaginary axis.</p>
<p>What is the order of the process ?</p>
<p>What is the maximum gain of the controller, so that the control loop is still stable.</p>
| 8,950 |
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<p>In differential geometry, the differential forms are anti-symmetric tensors. </p>
<p>So, why is the anti-symmetric tensor like
$ d x_1 \otimes dx_2 - d x_2 \otimes d x_1 $, more important than the symmetric tensor like $ d x_1 \otimes dx_2 + d x_2 \otimes d x_1 $ for the theory?</p>
<p>Why do we need anti-symmetric tensors for the exterior algebra, the wedge?</p>
<p>In quantum mechanics, we have fermionic wave functions and bosonic wave functions. Is the former more fundamental than the latter in a certain sense?</p>
| 8,951 |
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<p>The density matrix $\hat{\rho}$ is often introduced in textbooks as a mathematical convenience that allows us to describe quantum systems in which there is some level of missing information.</p>
<p>$\hat{\rho} = \sum_{i=1}^N c_i \rvert\psi_i\rangle \langle \psi_i \rvert$</p>
<p>I have two questions regarding density matrices.</p>
<p>First, it is clear that a generic pure state $\rvert \psi \rangle$ belongs to some Hilbert space $\mathcal{H}$. But what mathematical space do density matrices belong to? It is clear that the expression $\hat{\rho} \in \mathcal{H}$ is incorrect, as a mixed state cannot possibly be described in terms of a state in a Hilbert space. Can we think of the space of all possible density matrices (of a given dimension) as a metric space? Does this space have the topological properties of a manifold?</p>
<p>Secondly, can the density matrix be considered 'physical'? For example, if we take a single photon described in the Fock basis (neglecting polarization), can the fundamental description of that photon ever be the completely mixed state $\frac{1}{2}(\rvert 0 \rangle \langle 0 \rvert+\rvert 1 \rangle \langle 1 \rvert)$? Or is this only a reflection of some ignorance on the part of the experimentalist, and in reality the photon must be described by a pure state?</p>
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] |
<p>In a couple weeks, I will conduct a lab experiment where I measure the lifetime of the muons from the secondary cosmic radiation. For that, we have two detectors above each other, one will give a start signal, the other will give a stop signal, assuming the muon came to rest in the second detector and decayed.</p>
<p>There is a preparation question that says:</p>
<blockquote>
<p>Muons as well as anti muons arrive at the surface of earth. Which nuclear process is possible for muons but not for anti muons? How does this qualitatively affect the measured lifetime?</p>
</blockquote>
<p>As far as I know, the decay of the muon goes like this:
$$ \mu^- \to \nu_\mu + \bar \nu_e + \mathrm e^-$$
And for the anti muon, it goes like this:
$$ \mu^+ \to \bar \nu_\mu + \nu_e + \mathrm e^+$$</p>
<p>The <a href="https://en.wikipedia.org/wiki/Muon#Muon_decay" rel="nofollow">Wikipedia page</a> says:</p>
<blockquote>
<p>The mean lifetime of the (positive) muon is 2.1969811±0.0000022 µs.[1] The equality of the muon and antimuon lifetimes has been established to better than one part in 104.</p>
</blockquote>
<p>What is that difference that they are asking about in the lab course manual?</p>
| 8,953 |
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<p>Suppose that a someone decided to calculate, for a given amount of heat added into a planet's atmosphere(<strong>an ideal gas</strong>), how much is the corresponding temperature rising of the atmosphere, $\Delta T$. Assuming that the whole heat transforms into the internal energy of the gas and distributes uniformly (s)he got $\Delta T=1K$. </p>
<p>A question rises: actually, some of the heat is transformed into gravitational potential energy of the atmosphere(we ignore kinetic energy of the atmosphere). If we take also this into account then how much is the temperature rising of the atmosphere, $\Delta T$ now? Maybe the effect due to the gravity is negligible? </p>
<p>For simplicity let's assume that the pressure change is approximately exponential with height, $h$ </p>
<p>$$P=P_0e^{-\frac{h}{H}}$$ where $P_0$ is pressure at $h=0$ and $H$ is called the scale height for pressure. </p>
<p>For definiteness, let's take the Earth's atmosphere. In this case $P_0=101$ $kPa$ is average sea-level pressure. $H$ is about $8$ $km$.</p>
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<p>Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also invariant under proper conformal transformations is seldom straightforward. Integration by parts, introducing Weyl connections and so on and so forth are needed, but yet at the end of the day, it can almost always be done. Why is that?</p>
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<p>I'm looking for something to supplement my Physics II class. Last year I started using <a href="http://www.teach12.com/tgc/courses/course_detail.aspx?cid=1007" rel="nofollow">these video lectures</a> to supplement my Calculus class and it helped tremendously.</p>
<p>I also turned to <a href="http://www.thinkwell.com/student/product/physics" rel="nofollow">this educational software</a> when I was stuck in Physics I.</p>
<p>I can't seem to turn up anything similar that deals with Physics II.</p>
<p>I'm pretty much looking for something that I can watch repeatedly until it sinks in. Perhaps you know of something?</p>
<p>Thanks</p>
| 8,955 |
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] |
<p>I stumbled onto this page</p>
<p><a href="http://mylifeisaverage.com/story/1364811/" rel="nofollow">http://mylifeisaverage.com/story/1364811/</a></p>
<p>and the post states that they were</p>
<blockquote>
<p>all making strings and shapes with
these sets of 216 really small
spherical earth magnets. What did I
do? I strung them together and found
the string's resonant frequency. It
was 15 Hz</p>
</blockquote>
<p>so I'm wondering how the poster could have figured this out?</p>
| 8,956 |
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<p>Let's have a definition of massive particle as an irreucible representation of the Poincare group. Then, let's have a spinor field $\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}}$, which is equal to $\left( \frac{m}{2}, \frac{n}{2}\right)$ representation of the Lorentz group. There is the hard provable theorem: </p>
<p>$\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}}$ realizes irreducible representation of the Poincare group, if
$$
(\partial^{2} - m^{2})\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}} = 0,
$$
$$
\partial^{\alpha \dot {\beta}}\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}} = 0.
$$
Can this theorem be interpreted as connection between fields and particles?</p>
| 8,957 |
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<p>How can we force a particle (let's say that we know this particle has spin up) to be in a superposition of spin up and down?</p>
<p>Wouldn't literally any interaction of it with anything cause it to be in superposition, since we can never know the exact position/speed of the thing it is interacting with, so surely the outcome is unknown?</p>
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<p>The other day in class the professor was explaining non-inertial reference frames. We were working out how to find the acceleration of a point as measured from the non-inertial reference frame, and one problem was finding the time derivatives of the unit vectors as measured from the non-inertial reference frame.</p>
<p>To explain how to do it, he drew a nice diagram that showed that, if $\mathbf{\Omega}$ is the vector representing angular velocity of the rotation of $\hat{\imath}$ (that is, its direction is the axis of rotation), then $\frac{\mathrm{d}\hat{\imath}}{\mathrm{d}t} = \mathbf{\Omega} \times \hat{\imath}$. This makes sense. Next, he said that we can use the same argument for the other unit vectors: $\frac{\mathrm{d}\hat{\jmath}}{\mathrm{d}t} = \mathbf{\Omega} \times \hat{\jmath}$ and $\frac{\mathrm{d}\hat{k}}{\mathrm{d}t} = \mathbf{\Omega} \times \hat{k}$. I don't understand why we use the same $\mathbf{\Omega}$ for all of them. Since their axes of rotation are different, shouldn't we use different angular velocity vectors?</p>
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<p>Person A is on Earth and a train (or whatever you want to imagine) travels past him at near the speed of light. How would person A perceive movement on the ship? If time is slowed on the ship from the perspective of Person A, then if Person B were washing the windows or something (moving his hands up and down), would they look like they were going really fast, slow, or normal? If time is slowed from the perspective of Person A, then Person B's hands would be moving a certain distance (let's say the window is a meter) in a really short amount of time, no? And that would mean it looks like it is going fast. But then since Person A is perceiving the time as moving slower, it would look slower, no? Would they cancel and movement on the ship looks normal?</p>
<p>I tried to see if the Wikipedia page could help, but it didn't seem to say anything about a stationary observer and a fast-moving vessel.</p>
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<p>Permutation for classical particle
$$\Omega=\frac{N!}{\Pi n_i!}$$
By using Lagrange method of undetermined multiplier, we get
$$n_i=Ae^{\frac{-E}{kT}}$$
Probability, $$p=\frac{n_i} {Z}$$
where we define $Z$ as
$$Z_{classical}≡∑e^{\frac{-E}{kT}}$$</p>
<p>But for fermion, $$n_i=(Ae^{\frac{E}{kT}}+1)^{-1}$$
My question is: why do we have the same partition formula for classical and quantum particle? If possible, please tell me how to define the partition function for fermion. Thanks</p>
| 8,961 |
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<p>I heard that neon signs contain plasma, why aren't they hot?
is it because the electrons and ions do not hit the lamp's wall?
Is it because it is non thermal plasma and electrons and ions are not in thermal equilibrium?
If that is the case do the electrons and ions and neutral atoms (all of them) hit the lamps wall?</p>
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] |
<p>I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with the axis of the world, then its orientation matrix is :</p>
<pre><code>1 0 0
0 1 0
0 0 1
</code></pre>
<p>Now we store the angular velocity as a vector that contains values in rad/s around each of the world's axis. For example if the object should rotate around the world's y axis at 20 rad/s, then the angular velocity is</p>
<pre><code>0 20 0
</code></pre>
<p>My question is then, say we want to apply this velocity over 1 second to the orientation matrix, how would we do this?</p>
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<p>I read that all bosons contribute to the casimir effect with an attractive force.</p>
<p><a href="http://math.ucr.edu/home/baez/physics/Quantum/casimir.html" rel="nofollow">http://math.ucr.edu/home/baez/physics/Quantum/casimir.html</a></p>
<p>Does the Higgs boson contribute to the Casimir effect? Could it be the missing 5%?</p>
| 8,964 |
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<p>A commercial airplane travels at a speed which is 85% of the speed of sound. The wings of the
airplane are designed such that the bottoms of the wings are flat and the tops of the wings are
curved so that air travelling above the wings follows a path which is 15% longer than the straight
path of the air below the wings. The wings are approximately rectangular in shape with a length
of 35 m and a width of 8 m. The thickness of the wings is negligible. What is the maximum mass
that the airplane can have and still maintain enough lift to fly? </p>
| 8,965 |
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<p>I thought for a long time that the Boltzmann formula for entropy, $S = k_B \ln W$, was a universally true statement, or rather <em>the</em> definition of entropy from the perspective of statistical mechanics. However, I have since come to understand that it is only applicable for an isolated system (i.e. the microcanonical ensemble) for which all microstates of the system are equally likely. The more general statement is the Gibbs entropy</p>
<p>$$S = -k_B \sum_i P_i \ln P_i \,.$$</p>
<p>However, I have seen a derivation of the Boltzmann formula such that I can't quite see <em>why</em> said formula doesn't always apply. I was hoping somebody could point out the error in the following reasoning.</p>
<p>From classical thermodynamics we know that</p>
<p>$$T = \left(\frac{\partial U}{\partial S}\right)_V \,.$$</p>
<p>Now let us consider two systems in thermal contact, allowed to exchange energy. If we suppose that all microstates of the <em>joint</em> system are equally likely, we argue that equilibrium will be attained for a division of energy that maximises the number of possible corresponding microstates. So we have</p>
<p>$$ \frac{d}{dE_1}\big(W_1(E_1)W_2(E_2)\big) = 0 \,. $$</p>
<p>Working through this, we get to the condition that</p>
<p>$$ \frac{d \, \ln W_1(E_1)}{E_1} = \frac{d\, \ln W_2(E_2)}{E_2} \,,$$</p>
<p>but since equilibrium corresponds to equal temperatures, we make the natural definition that</p>
<p>$$\frac{1}{k_B T} = \frac{d \, \ln W(E)}{d E}\,,$$
where we choose this particular form of the expression on the left since it results in energy flowing in the right direction (hot to cold) for two systems with very similar temperatures. </p>
<p>Putting this together with the above result, identifying $U =E$, we must have that</p>
<p>$$ S = k_B \ln W \,.$$</p>
<p><strong>Question:</strong> where in this argument have I made any assumptions or mistakes, such that this formula applies only to a specific class of systems? Why can I not use this formula to determine the entropy of (say) one of the two systems I placed in thermal contact (in the discussion above of temperature)? Why is the Gibbs formula the correct one for systems allowed to exchange energy? We also use, I believe, this definition of temperature in the derivation of the canonical/Boltzmann distribution (see e.g. <a href="http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics#Derivation_from_canonical_ensemble">here</a>), and yet in this case the reservoir is not an isolated system, and so I would have thought that this expression would not apply. Thank you.</p>
| 8,966 |
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<p>I have recently read an article about <a href="http://en.wikipedia.org/wiki/Gravity_assist" rel="nofollow">gravitation slingshot assist</a> used by <a href="http://blogs.discovermagazine.com/sciencenotfiction/2010/06/22/traversing-the-cosmos-with-a-little-help-from-my-friends-pt-ii/#.U9VLXvldUX8" rel="nofollow">Voyagers 1-2</a>, and was thinking on why this hasn't been used for travel between solar and other systems.<br>
I mean sligshot can be done as many times as it is necessary to get speed of lets say half the speed of light that would allow to travel to <a href="http://en.wikipedia.org/wiki/Alpha_Centauri" rel="nofollow">Alpha Centauri in ~10-20 years</a> can it not? There must be a flaw in my thinking that 3 or 4 planets can be re-used to get to necessary speed otherwise it would already have been done (drawing below). Even if planets would align differently I should always be able 'find' the planet that would allow me to jump to one that is closer to the sun, and repeat the acceleration again and again.
<img src="http://i.stack.imgur.com/t52Vs.png" alt="enter image description here"></p>
<p><strong>What maximum (theoretical) speed could be achieved using planets of solar system as sligshot and how much would this speed wary from planetary alignment and what realistic speed could be achieved?</strong></p>
<p>UPDATE: To be more specific on the second part of the question Lets say craft weight's 500kg at starting speed of 30,000 km/h initially it slings around Mercury (<code>radius 2440km</code>), Venus (<code>radius 6052 - 300 (atmosphere) = 5750 km</code>), and Earth (<code>radius 6378 - 300(atmosphere) = 6050km</code>) until diameter of planets is to wide to not to crash craft on surface. Then it flies to the moons of Saturn - Titan (<code>radius 5150km</code>), Rhea (<code>1527km</code>), Lapetus (<code>1470km</code>), Dione (<code>1123km</code>), Tethys (<code>1062km</code>), Enceladus(<code>504km</code>), Mimas (<code>396km</code>) and starts slinging there until diameter is to wide too. What approximate maximum speed could it get to leave the solar system?</p>
| 8,967 |
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<p>I heard some theory, such as technicolor, predicts the Higgs-like particle discovered at LHC should be a composite particle (correct me if I am wrong). Has this possible been completely excluded already?</p>
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<p>In episode 7 season 5 of Through the Wormhole, they say that gravity could just be a manifestation of the strong nuclear force and that the force carrier are a pair of Gluons. Is this valid in anyway? </p>
| 296 |
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<p>Lets say you build a steam boiler and then you connect several turbines to the boiler in series. What limits the number of turbines that you can connect to the boiler in this way? In my mind, it seems that the steam still has to escape, so no matter how many turbines are in the way, the steam will still turn all of them in its attempt to escape the boiler.</p>
| 8,969 |
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<p>Lets say that we made a glove, shirt, pants and a hat out of the most effective thermocouple material available today. How much electricity would be generated by each, by a healthy person, on a cool day (98 degrees F vrs 79 degrees F?)</p>
| 8,970 |
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] |
<p>How do magnets work on the atomic level? Is there current inside the magnet?</p>
| 297 |
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] |
<p>If electrons form a crystal in the Wigner crystal what is the structure of that crystal? cubic, bcc, fcc,...?</p>
| 8,971 |
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<p>I try to understand two principles formulated by Leonard Susskind in his book <em>The Black Hole War</em>:</p>
<p>1, To any observer who remains outside a black hole, the stretched horizon appears to be a hot layer of horizon-atoms that absorb, scramble, and eventually emit (in the form of Hawking radiation) every bit of information that falls onto the black hole.</p>
<p>2, To a freely falling observer, the horizon appears to be absolutely empty space. [...] </p>
<p>Now, in reaction to (an unanswered) <a href="http://physics.stackexchange.com/questions/22498/from-where-in-space-time-does-hawking-radiation-originate/22874#comment130473_22874">question</a> by Nathaniel, let us suppose that a distant observer A sees (according to the principle #1) Hawking radiation from a black hole (with Planck spectrum and say measurable temperature). Now suppose there is a freely falling gas somewhere between the event horizon and the observer. According to the principle #2, to the gas (considered an observer B) the horizon is empty space so there is no light coming from it to absorp.</p>
<p>Would the observer A detect absorption lines in the black hole spectrum? How does it change with distance of the gas (or the observer) from the black hole? Will the distant observer see the lines if he is free falling?</p>
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<p>I was watching a Scott Manley video on youtube and he mentioned that the Sun was loosing 4 million tons of mass a second as it converts to energy. </p>
<p>With a few trillion trillion stars also converting mass to energy, I wonder if that would be a component to the missing "dark matter" mass?</p>
<p>I'm a complete layperson here, just very interested in astronomy and the physics involved.</p>
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<p>I would like to know why two forces (of different magnitudes but same direction) that we'd use sequentially on an object to move it by the same amount twice, will produce two different values for the work quantity. </p>
<p>Why is there a mismatch between the maths and the observed physical change?</p>
<p>What exactly is the <a href="http://en.wikipedia.org/wiki/Work_%28physics%29" rel="nofollow">work</a> of a force? (If possible, please avoid circular definitions like "work is the energy produced by a force" and "energy is the ability to do work".)</p>
| 8,974 |
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<p>The quark mass term in the Standard Model Lagrangian looks like this:</p>
<p>$$ L = - \lambda_d \bar{Q}\phi d_R - \lambda_u \bar{Q} i \tau_2 \phi^* u_R $$</p>
<p>What is the reason for the $ i \tau_2 $ - factor? What keeps me from writing undesirable things like $$\lambda_u \bar{Q} \phi u_R $$ ?</p>
| 8,975 |
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] |
<p>Mass and spin of the particle are used in classification of elementary particles. The mass is defined to be a Lorentz invariant quantity. On the other hand, the spin is a spacelike 4-vector and cannot be defined as an invariant quantity.</p>
<p>My question is, what would be a convenient definition of a relativistic spin 3-vector? As is known, 3-vectors get contracted/dilated under Lorentz transformations. So, is the 3-spin defined to be equal to the rest frame 3-spin, or do we allow it to contract/dilate? It seems to me that the first option is generally used, especially when considering Thomas precession and similar effects. Although, I haven't seen any relevant discussion in textbooks on this topic.</p>
| 8,976 |
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<p>Two resistors are joined as shown. The top resistor receives a current of 3 A. What is the current in the other resistor? What is the current that enters at junction A? I'm confused on how the two currents are 3A and 1A because I thought in a series circuit all the currents are the same. Why is the answer to the current entering junction A 4 A and not 1 A?
<img src="http://i.stack.imgur.com/XviUa.jpg" alt=""></p>
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] |
<p>Also, is it possible to have electronic displays on the walls of a home? Is there anything in physics that prevents that?
I guess I'm trying to ask if something like this is possible:
<a href="http://www.techcrates.com/transparent-smartphones-our-new-reality/" rel="nofollow">http://www.techcrates.com/transparent-smartphones-our-new-reality/</a>
<a href="http://www.whistleout.com.au/MobilePhones/News/CES-LG-steals-display-glory-with-futuristic-mirror-and-window-TVs" rel="nofollow">http://www.whistleout.com.au/MobilePhones/News/CES-LG-steals-display-glory-with-futuristic-mirror-and-window-TVs</a></p>
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<p>Since synchrotron radiation is created when charged particles are radially accelerated and electrons are definitely orbiting a nucleus (assuming a Bohr model), electron should then logically emit synchrotron radiation. However, if it does, then it lose energy and would unfortunately spiral into the nucleus, which we know doesn't happens. So, is it that atoms doesn't produce synchrotron radiation or other mechanisms are compensating the synchrotron radiation effect?</p>
| 8,979 |
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<p>I remember reading in an introductory text to phase transition (sorry I don't remember the name) that at a second order phase transition the specific heat and the magnetic susceptibility become infinite and that this implies fluctuations on all length scales.</p>
<p>I understand how this implies strong fluctuations as they are respectively linked to the variance of the energy and of the magnetization, or that being infinite it's not possible to construct a preferred length scale with them; but I'm not sure to understand why it forces the fluctuation to happen at ALL the scales.</p>
<p>Do you have an intuitive argument or example for that?</p>
<p>Thank you in advance.</p>
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