# Tag Info

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You are right, the planetary model of the atom does not make sense when one considers the electromagnetic forces involved. The electron in an orbit is accelerating continuously and would thus radiate away its energy and fall into the nucleus. One of the reasons for "inventing" quantum mechanics was exactly this conundrum. The Bohr model was proposed to ...

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I can tell you why I don't believe in it. I think my reasons are different from most physicists' reasons, however. Regular quantum mechanics implies the existence of quantum computation. If you believe in the difficulty of factoring (and a number of other classical problems), then a deterministic underpinning for quantum mechanics would seem to imply one of ...

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Let us try to rewrite the equation in approximate form of finite differences: $$\frac{A(x,t+\Delta t)-A(x,t)}{\Delta t} = C_3\frac{A(x+h,t)+A(x-h,t)-2A(x,t)}{h^2} +$$ $$+ C_2 \frac{v(x+h,t)A(x+h,t)-v(x-h,t)A(x-h,t)}{2h} + C_1 A(x,t)+C_0$$ Where $\Delta t$ -- is a time step, and $h$ -- space step. The expression becomes your PDE, in the limit $\Delta t\to0, ... 10 There were many models overturned throughout history, I will list some of the most salient ones. I will ignore the ones that predate modern science, the most prominent one being the geocentric model of the solar system, and I will confine myself to wrong ideas that were scientifically accepted as probably true at some point in history. Phlogiston: This is ... 10 Theoretically, yes it should be possible to derive the boiling point of diatomic nitrogen from fundamental forces. In fact, you don't even need to involve the strong force or weak force (or the strong nuclear force, which is sort of different). The strong forces bind the quarks together into nucleons and the nucleons together into nuclei, but they have ... 9 Apologies in advance if the first part of this comes off a bit argumentative, but I think there is an important point about physical theory that should be made. This point is also implicit in David Zaslavsky's answer as well. Rant on effective theories Actually trying to calculate macroscopic properties like "chemistry" from fundamental theories like QCD ... 9 Actually a paper recently came out, and highlighted in Popular Science, discussing using fermionic field concepts to model crowd avoidance at Netflix. You can imagine that the same concept could be used to consider in any situation where there are large numbers of people competing for limited preferred items. Update Now that we have a few minutes, ... 8 There are thousands of such examples, it is basically all situations in condensed matter physics. You see a lot of regularities that have no explanation. Here's one of the most annoying ones for me: Moseley's law--- you can knock out one of the two electrons most tightly bound to a heavy atom (in the K-shell). This leaves a hole orbiting the nucleus. The ... 7 Check out Mark Smith's PhD thesis titled Cellular automata methods in mathematical physics, specifically Chapter 4: Lorentz Invariance in Cellular Automata. The conclusion part of the chapter: Symmetry is an important aspect of physical laws, and it is therefore desirable to identify analogous symmetry in CA rules. Furthermore, the most important ... 7 This could have been a comment, but as it actually anwers the question asked in the title, I'll post it as such: As far as I can tell there's no rational reason to dismiss these models out of hand - it's just that quantum mechanics (QM) has set the bar awfully high: So far, there's no experimental evidence that QM is wrong, and no one has come up with a ... 5 This is an example from hydrodynamics. When the effects of viscosity can be ignored (inviscid flow), a uniform incident flow can exert on immersed bodies only lift forces perpendicular to the asymptotic flow velocity. However, there exist an infinite number of solutions of the flow equations of motion satisfying the asymptotic conditions at infinity and the ... 5 Classically emission is continuous and the electron would need to occupy a "in between" energy level for a while, and that is forbidden in Bohr's scheme, so the emission can't be allowed to happen. This doesn't really explain why it can't happen, but that's phenomenology for you: you line keep lining up facts until your kludge (1) gets the right answer and ... 4 You can estimate that someone swimming in water has a Reynolds number of about$10^6 - 10^7$; what counts is that this number is$\gg 1.$In that case, you're dealing with the drag equation: http://en.wikipedia.org/wiki/Drag_(physics). If we assume that our swimmer has the same power$P$on the moon and on Jupiter, his velocity$v$scales as$$v \propto ... 4 In general, if you construct a manifold out of a combinatorial graph, or out of patches, then you're not finding anything "more fundamental". You're just describing the most straightforward and most superficial definition of the concept of topology. I realize that this very modest sentence contradicts the whole philosophy of Stephen Wolfram's book, and the ... 4 In cellular automata I do know there is explicit dependence on step/time. In quantum mechanics (and other many other theories) it is natural to write local evolution with respect to time. On the contrary, in 'pure' relativity, time is not that different from position. And thus there is no such natural interpretation like 'the next step is the next time'. ... 4 Briefly, The Bohr--planetary model doesn't really address these issues. Bohr, a genius, just asserted that the phenomena at the atomic level were a combination of stationarity while being in an orbit, and discrete quantum jumps between the orbits. It was a postulate that yielded some agreement with experiment and was very helpful for the future ... 4 As an alternative to Christian Blatter's heat interpretation,$A$might describe the concentration of particles adsorbed onto a one-dimensional substrate surface (or a two-dimensional one, where we ignore one of the dimensions). New particles are adsorbed at rate$C_0$per unit length. Adsorbed particles detach from the surface at rate$-C_1$per particle. ... 3 There are many physical intuitions often presented in various texts on fluid dynamics. I won't mention those here. I will, however, mention that mathematically the passage from a particle point of view to a continuum point of view is still a largely un-resolved problem. (With suitable interpretation, this problem was already posed by Hilbert as his 6th of 23 ... 3 The theory of fluids introduces material parameters in the stress tensor, which help model the substance. "The viscosity coefficient is the proportionality constant relating a velocity gradient in a fluid to the force required to maintain that gradient. The thermal conductivity is the proportionality constant relating the temperature gradient across a fluid ... 3 I asked this very same question at mathoverflow, too (do the policies of PSE have anything against this?), and got one further answer, which I leave to your attention: There are no "non-trivial" finite sub-groups of$O(3,1)$. 3 Space_cadet mentioned already work about deriving spacetime as a smooth Lorentzian manifold from more "fundamental" concepts, there are a lot of others -like causal sets, but the motivation for the question was: The reason for my interest in this regards one of the mysteries of quantum mechanics, that of quantum entanglement and action at distance. I ... 3 Unfortunately, nobody reads Bohr nowadays so Bohr's arguments are not understood and transmitted. Modern quantum mechanics is more complete and superior as a physical theory to the old quantum mechanics, so the omission is perhaps understandable, but it is not forgivable. Bohr's ideas explain the stability of H-atoms in a reasonable way, which is also ... 3 There are two questions here: Why criticize your models? And are there better ideas? I will try to answer the second question in a separate answer. Here I only give some comments of a general nature to adress the first question. I personally agree with you, and I think most people who care about this stuff do too, that it is disconcerting to have a theory ... 2 I assume that what you're asking is about the signal to noise ratio. Clearly the noise will not depend on distance; the problem is that the signal drops below the noise floor. Suppose you're transmitting with frequency$\lambda\$. As the distance increases the intensity drops but the relationship is not so simple as is suggested in the comments. For the ...

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The radiative portion is actually pretty straightforward. For the absorption of sunlight you multiply the strength of the sun (usually taken as 1000 watt/meter**2 at sea level by 1 minus the albedo, and multiply by the cosine of the angle. For IR, you need to know the emissivity (but for most surfaces .95 to 1 can be assumed), and use the Stefan Bolzmann ...

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The Hartree potential is typically calculated not through the integral you're giving, but by solving Poisson's equation. Look here or there for details about this calculation applied to DFT, and here for what I found to be a good lower-level introduction to Poisson solvers in general. Good luck for your quest, it's really a nontrivial thing to do! As an ...

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I can't see how a negatively charged electron can stay in "orbit" around a positively charged nucleus. Even if the electron actually orbits the nucleus, wouldn't that orbit eventually decay? Yes. What you've given is a proof that the classical, planetary model of the atom fails. I can't reconcile the rapidly moving electrons required by the ...

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As Ron noted, there are many, many examples within condensed matter; they often share a very similar story where the microscopic laws are known well (exactly, for the case of simulations), but the macroscopic laws are derived by symmetry concerns. Take for example, liquid crystals. We could simulate a collection of hard rods or ellipsoids - this is our ...

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