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81

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 ...


43

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 ...


22

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 ...


22

None of the interesting equations in physics can be derived from simpler principles, because if they could they wouldn't give any new information. That is, those simpler principles would already fully describe the system. Any new equation, whether it's the Navier-Stokes equations, Einstein's equations, the Schrodinger equation, or whatever, must be ...


21

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 ...


19

They are derivable from classical mechanics using either the continuum or molecular points of view. Starting with a continuum view, one applies conservation of mass, momentum, and energy to a control volume and the result is the Navier Stokes equations. The Navier Stokes equations, in the usual form, apply to Newtonian fluids, that is fluids whose stress ...


19

There is a great paper from the group of Howard Stone on this subject: Wetting of flexible fibre arrays (freely available here) They specifically study when 2 closely positioned parallel fibers (i.e. hairs) clump together due to the water droplets on the fibers. They quantatively determine when the volume of liquid is sufficiently small to cause ...


15

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, ...


14

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 ...


12

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, ...


12

The treatment of electrons as waves has combined with spherical harmonics (below image) to form the foundation for a modern understanding of how electrons "orbit." Tweaks to the spherical harmonic differential equations yields the Schrodinger equation, which yields the accepted models of electron orbital structures: The only element for which the ...


12

I once asked Putterman after a similar colloquium what he meant by this statement, and his answer was "long time tails". Long time tails are fractional powers that appear in the long time behavior of correlation functions, see, for example, here and here. These fractional powers are seen in molecular dynamics (they are more difficult to see experimentally), ...


11

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 ...


10

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 ...


10

[ text I had put here is moved to the original question, but I prefer not to erase the comments that were posted here. ]


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 ...


8

At present, the Navier-Stokes equations for the dynamics of water haven't yet been derived from microscopic principles.


7

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 ...


7

This is what I think the first bit of the calculation does. Suppose you start with a spherical eye with a hole in it (e.g. the pupil in the human eye): The radius of the eye is $ER$ and the radius of the hole is $AR$, and with the length $DA$ these form a right angled triangle. Pythagoras' theorem tells us: $$ DA^2 + AR^2 = ER^2 $$ so: $$ DA = ...


7

No. There is nothing wrong with perturbation theory, or with theories with known, restricted accuracy. The point of theory is to explain the results of observation from as simple an initial theoretical standpoint as possible. Therefore: Since experiment always has a finite uncertainty, one can only ask that theory match the experimental value within its ...


6

Yes. Ordinary quantum field theory is as wrong as Newtonian gravity for not including GR effects. That is to say, it is a perfectly fine theory inside its domain of validity, which in this case means pretty much everything below the Planck scale, just as Newtonian mechanics is valid for speed much less than the relativistic scale (the speed of light). ...


6

Foundational discussions are indeed somewhat like discussions about religious convictions, as one cannot prove or disprove assumptions and approaches at the foundational level. Moreover, it is in the nature of discussions on the internet that one is likely to get responses mainly from those who either disagree strongly (the case here) or who can add ...


6

Short answer: that depends on your definition of sound theory. For instance, it is possible to find peer-reviewed papers considering such possibilities. The idea that antimatter can be gravitationally repulsed from ordinary matter is definitely not the most popular one. Nevertheless, some people do try to apply it in astrophysical context. Let us have a ...


6

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 ...


5

Ok, I'm still not sure on what level you want to do this, but I will start you off with some basics. The most important factor is probably the solar elevation angle, $\theta$. As described on the wiki-page it can be calculated using this formula: $$\sin\theta=\cos h\cos\delta\cos\Phi+\sin\delta\sin\Phi$$ where $h$ is the hour angle, $\delta$ is the solar ...


5

Here's my quantitative attempt at $4.$ and $1.$: The Coandă effect here is the tendency of the airflow to adhere to the surface of the ball. This means that near the surface of the ball, the streamlines are curved with a radius of curvature approximately equal to the radius of the ball $R$; this curvature results in a pressure gradient just as it does in ...


5

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 ...



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