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I heard my friend, a researcher, say that we can, in theory, explain every event happening in the universe using the Conservation of momentum and energy. He added that we may not be able to do that "now" as we do not have all the variables required to describe the Universe completely.

My question is: 1) Is it possible to explain everything(including emotions of humans) if we are given all the variables, laws of conservation of momentum and energy and a computer that perform calculations at incredible speeds? (Note: the governing equations of system dynamics is not known, only the states and the conserved quantities)

Give a simple example, if the answer is "No".

Give a reference to a valid proof if the answer is "Yes".

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  • $\begingroup$ This is not known. Even in physics where the search for a simplified formulation of all the systems is a long searched "holy goal", there is no scientific conclusive evidence that this can be achieved. Although the fact that momentum-energy conservation seems to withstand test after test certainly seems to support there universality. But still you need more quantities to describe systems than just these two. For biological systems is even worse, not even a rigorous line between alive and inanimate systems can be clearly set without having gray areas. $\endgroup$ – rmhleo Sep 19 '14 at 9:39
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No. Consider the radioactive decay of an atom. The energy and momentum is conserved but the direction of emission is not known. We do know that on average, i.e. if we take many identical atoms and observe their decay, that the direction of emission is isotropic. However, for a single event we just can't seem to predict this direction beforehand! These kinds of quantum processes complicate any simulation, such that we could only ever describe a Universe on average (i.e. we would need to describe many versions of the universe).

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  • $\begingroup$ Does this mean we need some other quantities(other than Energy& momentum) to find the direction of emission or, going to another level, the process of radioactive decay is not deterministic with respect to the direction of emission? $\endgroup$ – Sathish Sep 19 '14 at 10:56
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    $\begingroup$ Current consensus says that the theory does not allow the prediction of these individual events. It is better to take the view that we simply do not know how to describe individual processes,except on average. In principle, you could try to construct a hidden variable theory, i.e. add possible things we do not know or observe to the theory, however, these theories become increasingly complicated (e.g. non-local, contextual, etc.). Pragmatic physicists tend to say our description is probabilistic, without thinking about how nature "is". Only time will tell if we can bypass this description. $\endgroup$ – Jasper Sep 20 '14 at 12:50
  • $\begingroup$ Also as mentioned above there are many more conserved quantities than energy and momentum. Most conserved quantities are related to symmetries. Examples: time translation: energy conservation; space translation: momentum conservation; rotation: angular momentum conservation; gauge invariance of EM-field: charge conservation; etc. Knowing all symmetries and all measurable initial conditions is apparently not enough to describe individual events. $\endgroup$ – Jasper Sep 20 '14 at 13:09
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No. There are more conservation laws: conservation of angular momentum, electric charge, color charge, weak isospin.

Without the charge conservation you cannot explain why electrons do not decay into neutrinos.

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I don't think energy conservation and momentum conservation can explain charge conservation in particle physics.

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