# Tag Info

## Hot answers tagged models

89

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 ...

71

Ever since the time of Newton physics is about observing nature, quantifying observations with measurements and finding a mathematical model that not only describes/maps the measurements but, most important, it is predictive. To attain this, physics uses a rigorous self-consistent mathematical model, imposing extra postulates as axioms to relate the ...

44

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 ...

36

@annav's answer already describes well how physical theories work and how they require self-consistency. I'd like to add some comments from a different perspective to that. TL;DR Physical theories have to be self-consistent AND consistent with observation. Mathematical self-consistency Firstly if we treat a physical theory as a mathematical axiom system ...

24

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 planetary ...

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

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 ...

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 ...

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, h\... 15 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 ... 14 If theories were only used to describe what we already know and observe, maybe they would not need to be self-consistent; they could even just degenerate into big lists of observed phenomena. This is what science looked like in Sumer, 5000 years ago. If we want physical theories to be predictive, they have to be self-consistent in the sense that they have to ... 14 If the only mathematical statements admitted in a physical theory were those having immediate empirical content (i.e. they can be tested by an unambiguous experiment), then you would have a very good case to make. Why? Because the consistency of the world of experience would guarantee the consistency of the mathematical formalism. End of story. In reality, ... 13 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 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 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 ... 11 [ text I had put here is moved to the original question, but I prefer not to erase the comments that were posted here. ] 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 ... 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 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 ... 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 = \sqrt{ER^...

7

Physics is the art of compressing our knowledge of the universe. As it happens, whenever we stick two massive bodies near each other (or notice them near each other), they seem to move towards each other. Now, we could simply record the fact that every massive body (individually) is moving towards every other massive body (individually). This is a large ...

7

Mathematical theories which are not consistent prove contradictory things (this is just a statement about mathematics and what it means to be inconsistent, not to do with physics in particular). We do not want theories of physics that predict contradictory things. Ideally we don't want theories that make any wrong predictions, but if our theory makes two or ...

7

Physical theories are not a collection of mathematical axioms, they are attempts at describing nature. Not only that. Physical theories are also supposed to make predictions. This is part of the Scientific Method. One does not expect to predict new phenomena - that can later be veryfied - using a non self-consistent theory. We cannot cheat. Following ...

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 (...

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