Experiments are showing that larger and larger objects can be entangled whereby proving that this quantum feature has no upper limit. Assuming this is true, does entangled celestial bodies mean even the 2-Body and not just N-body problems are also unsolvable?

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    $\begingroup$ The quantum two body problem can be done just fine (look up the Hydrogen atom). $\endgroup$ – Michael Brown Mar 28 '13 at 4:45

Quantum mechanics it the underlying layer of Nature at the microscopic level, its effect mainly constrained to small dimensions because of the small value of the Planck constant h_bar.

There exist large dimension quantum mechanical effects, effects that can only be described by quantum mechanical equations and experiments validate the predictions.

Superconductivity is one of them where there exist kilometers of superconducting wire at the LHC

The existence of crystals is another matter phase that requires quantum mechanical solutions.

In these, and other, examples of macroscopic manifestation of quantum effects, of which entanglement is one , the phases of the microscopic components of matter build up coherently to large dimensions. The general effect on matter as we know it is that the phases are lost: an incoherent statistical ensemble treatable with classical mechanics and electromagnetism is the usual state of matter.

When one reaches celestial dimensions it is hard to see any phases surviving in the interaction between two celestial bodies, which will be gravitational. We do not have a quantum gravity solution at the moment of the type of the Schroedinger equation so as to even imagine calculating the phases between two elementary particles under gravitation nor statistical ensembles of them, which are the celestial bodies.

Even as a thought experiment, it is not possible to check whether phases could survive on a celestial body and a quantum mechanical gravitational interaction retain its phases over celestial distances.

So no, at the moment the two body problem can be safely solved with classical theories of gravity.

That said, quantum entanglement effects are an active research for the first moments of the Big Bang where all forces are equally strong . The cosmic microwave background radiation is studied to see this effect,

if small thermal variations, generated by quantum fluctuations of matter in a very tiny space, had expanded to the size of the observable universe we see today. This is a very active field of study,

but these were not celestial bodies interacting but a primordial plasma/soup.

  • $\begingroup$ Schrodinger’s equation sets no limit on the size of wave functions so celestial dimensions are included. 2-Body problems such as DI Herculis and other binary stars are not solved with classical theories of gravity. With this in mind, why would quantum phenomena distinguish a star from a plasma ball or soup at any scale and during any time. It does not and it can be tested. $\endgroup$ – user4884 Mar 28 '13 at 15:04
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    $\begingroup$ Because of decoherence. Quantum mechanical solutions of the three other forces need coherence to display quantum mechanical phenomena at long distances. There is no coherence in the wave functions of the total earth, which is composed out of more than 10^30 individual wavefunctions. ( crystals have long range quantum mechanical attributes but the earth is incoherent). Plasma in space displays quantum mechanical attributes but it is not a single body , it is an ensemble so the two body concept is moot. $\endgroup$ – anna v Mar 28 '13 at 15:33
  • $\begingroup$ ", why would quantum phenomena distinguish a star from a plasma ball or soup at any scale and during any time" because plasma is a different state of matter, and the primordial soup where all forces are strong is another. Stars are incoherent to each other with respect to the three forces and we do not have a quantum theory of gravity at the level of computing phases between large bodies, even if it is conceptually possible. $\endgroup$ – anna v Mar 28 '13 at 15:40
  • $\begingroup$ Wave functions act on orbits (Debroglie) and indirectly effects the motion of objects on those orbits (electrons). Binary stars are two body systems whose orbits and motion is described by a large scale wave function which synchronizes a gravitational and electromagnetic field with quantum mechanical structures. That is officially how the DI Herculis and other binary star systems motion was solved. Those stars are not moot but very significant in completing Einstein's work. $\endgroup$ – user4884 Mar 28 '13 at 15:48
  • $\begingroup$ I find no such solution here : en.wikipedia.org/wiki/DI_Herculis , so could you give a link? $\endgroup$ – anna v Mar 28 '13 at 15:56

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