A virtual creation with total mass-energy = $E$ is allowed as long as that virtual creation doesn’t last longer than $E/h$. Can the uncertainty principle also be used to estimate the mass-energy in the spontaneous creation of a universe - a spontaneous creation that has now lasted $13.6$ billion years? If so, the principle would require that universe to have a mass-energy less than $1.54\times 10^{-51}$ Joules. Is there a flaw in this?
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$\begingroup$ Duplicate of physics.stackexchange.com/q/2838/4552 $\endgroup$– user4552May 24, 2013 at 3:53
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$\begingroup$ Mike, the link Ben posted may not be an obvious duplicate. The point is that the net energy of our universe may be zero (or infinitesimally small) and that's why our universe can last so long. The idea is that the gravitational energy balances the matter energy and the lot adds up to zero. $\endgroup$– John RennieMay 24, 2013 at 6:31
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$\begingroup$ Thank's John. But that seems like the great mystery to me. How, from within the universe, it can look so real and massive - seemingly completely devoid of any quantum mechanical weirdness - yet from outside, from the viewpoint of other universes, its near zero mass-energy allows coherence and other quantum mechanical weirdness in its interactions with other universes of near zero mass-energy? How is that illusion created? From outside it behaves quantum mechanically like almost nothing is here. From inside its appears solid, huge and overwhelmingly massive. $\endgroup$– Mike McdonaldMay 24, 2013 at 15:09
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$\begingroup$ @JohnRennie: "The point is that the net energy of our universe may be zero[...]" LM's answer physics.stackexchange.com/a/2856/4552 to the earlier question explains why it doesn't make sense to talk about the net energy of the universe. $\endgroup$– user4552May 25, 2013 at 19:09
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$\begingroup$ @BenCrowell: it's an old idea and has been discussed by physicists far more accomplished than me. See my answer to physics.stackexchange.com/questions/46337/… for some links. NB I'm not commenting on the validity of these ideas, since that's beyond me. I'm just reporting that they exist. $\endgroup$– John RennieMay 29, 2013 at 6:10
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Well , the mass of the visible universe 6e51 kg contradicts this simplification .
The HUP is an inequality. It tells you that the mass must be at least this small number you give, it does not put bounds from above, that is why it is immaterial for our classical existence.
In addition the existing universe is not in a quantum mechanical virtual state, since it has undergone decoherence billions of years ago.
Edit in response to comments:
At the time of the Big Bang General Relativity holds. Unification of GR with the other three forces in a consistent with all data quantum mechanical theory is under research. We can only hand wave extrapolating our laboratory and observational knowledge to the first seconds of the creation of the universe.
The assumption is that the system will be following quantum mechanical laws and therefore a form of the HUP should apply.
The problem is in assuming the HUP for the virtual states of the first instants of the creation of the universe as an equality, assuming energy conservation, i.e. that the total observed energy existed at that instant. This is not valid, as conservation of energy is not well defined in General Relativity. Therefore at that small interval where the whole universe was coherent it is the inequality bounds that could have a meaning, and those are not violated. As time starts flowing decoherence appears and matter as we know it.
Conclusion: The current universe is not in a coherent quantum mechanical state where one could apply the HUP, so taking current time numbers and applying HUP for energy has little meaning except as a lower bound, if at that.
Applying the HUP at the first instants of the creation has little meaning because energy is not conserved where GR is dominant.
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$\begingroup$ The web page in the first link discusses the mass of the observable universe, which isn't what's relevant here. $\endgroup$– user4552May 24, 2013 at 3:50
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$\begingroup$ "The HUP is an inequality. It tells you that the mass must be at least this small number you give, it does not put bounds from above[...]" No, the OP has the inequality the right way around. In the traditional hand-wavy application of the energy-time uncertainty relation to the creation of pairs of virtual particles, the logic is that the energy of the pair has to be less than a certain amount, because if it were more than that, the violation of conservation of energy would be detectable despite the HUP. $\endgroup$– user4552May 24, 2013 at 4:02
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$\begingroup$ @BenCrowell conservation of energy does not apply to General Relativity which is the state of the creation of the universe, which is when coherent quantum states could exist and one could talk of virtual creation. $\endgroup$– anna vMay 24, 2013 at 4:06
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$\begingroup$ @BenCrowell by the way, you say " the OP has the inequality the right way around", but the OP is treating the inequality as an equality. It is OK to find the order of magnitude limits but it still is an inequality, setting a lower bound to the product. $\endgroup$– anna vMay 24, 2013 at 4:20