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I look forward to the answer on the next show. I hope that whatever the solution it also might address the possible temperature of a singularity or even the big bang as there must have been a fair amount of kinetic energy stored up in that little spec of mass just before it all started to rip space time apart! If there is a maximum then it must have been pre bang?I just read an article about the 4 trillion degrees achieved by a team in 2010, they state that the predicted temperature for photons and protons to melt is 2 trillion degrees.The LHC got to 10 trillion degrees at the end of 2010 and they have stated that at these temperatures the stuff of mater breaks down into what is called a " quark-gluon plasma" in this state apparantly they are freed of their attraction to eachother. Further reading shows that the maximum theoretical temp is the Planck temerature which is 1.41679 x 1032 Kelvins. I have no idea why there is a max. and I hope this is addressed in the answer on Sunday.It seems things can get a lot hotter then they are right now but not much colder in comparison.
Current cosmological models posit that the highest possible temperature is the Planck temperature, which has the value 1.416785(71)◊1032 kelvin. The Planck temperature is assumed to be the highest temperature in conventional physics because conventional physics breaks down at that temperature. Above ~1032K, particle energies become so large that there is no existing scientific theory for the behavior of matter at these energies. Gravitational forces between them would become as strong as other fundamental forces, requiring a hypothetical theory of everything for description.