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According to a simplified quantum mechanics theory where electrons and nuclei are point charges and there's no nuclear chemistry, and the gravitational constant and cosmological constant are zero, with all physical constants derivable only from the following constants: speed of light; Planch's constant; proton charge; Coulomb's constant; electron mass; and proton mass; has anyone ever determined the exact formula for the density of water in its liquid phase at 1 atm in terms of temperature and those 6 physical constants? The atmosphere unit and the exact celsius scale itself are defined in terms of the triple point of water which in turn can be computed in terms of those 6 physical constants. Is it also true that the density of supercooled water and superheated water can't be determined exactly because they're not infinitely stable and will eventually undergo homogenous nucleation of the stable phase? Is it true that the less supercooled water is, the lower the space-time probability density of homogenous nucleation so the more accurately its density can be determined but its density can only be determined exactly from its freezing point to its boiling point? However, the reciprocal of the space-time probability density of homogenous nucleation probably varies superexponentially as the reciprocal of the amount supercooled the water is. Is it even true that the function that determines the density of water in terms of temperature is analytic at all temperatures above the freezing point and below the boiling point but not analytic at the freezing point or boiling point?

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No. That's not possible. What about neutron mass? What about the mass decrease due to the binding of nucleons through the residual strong force?

Beyond that, for even something as simple as $\ce{H_2}$, as considered using the non-relativistic Schrodinger equation, there is no exact solution for even the wavefunction of one molecule.

What NIST uses is this: http://nvlpubs.nist.gov/nistpubs/jres/097/jresv97n3p335_A1b.pdf

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  • $\begingroup$ A neutron can be made by fusing a proton and an electron together. Can it still not be done because the loss of nuclear potential energy reduces the total mass of a proton and electron and the reduction in nuclear potential energy wasn't given? $\endgroup$ – Timothy Nov 30 '15 at 22:17
  • $\begingroup$ @Timothy no, you would need an electron anti-neutrino as well. Also, the neutron mass is not the sum of the electron mass and proton mass. $\endgroup$ – DavePhD Nov 30 '15 at 22:21
  • $\begingroup$ A better answer would be if you wrote an answer that starts off with supposing the constants I gave as well as the mass of an oxygen nucleus was given and then answers the question of whether it has been determined in terms of those 7 constants or researchers have the resources that they would immediately be able to figure out how to do so. $\endgroup$ – Timothy Nov 30 '15 at 22:26
  • $\begingroup$ @Timothy Then you would have the issue of calculating an infinite number of Feynman diagrams to determine anything physics.stackexchange.com/questions/111400/… or even if you stuck with the Schrodinger equation, the three-body-problem prevents calculating even the wavefunction for H2 exactly en.wikipedia.org/wiki/Three-body_problem $\endgroup$ – DavePhD Nov 30 '15 at 22:33
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    $\begingroup$ @Timothy - you appear to be using a lot of techno-babble. Various things actually can't be done, not because they are hard to do, but that it is actually not possible to do. $\endgroup$ – Jon Custer Nov 30 '15 at 23:33

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