What is the difference between a quantum fluctuation and a singularity in the beginning universe?

I am sure this is a naive question that shows my lack of sophistication in physics but I keep reading "the early universe was a "singularity", on the other hand ..... I also see quantum fluctuation come up a lot.

Now I remember reading Tryon was the first to use "quantum fluctuation" for beginning the universe back in the 60's and I think as the story goes during the lecture he was attending; people laughed at him because he just blurted it out loud and they thought he was joking. But then warmed up to it.

I also read Guth came up with the "inflaton" field to cause the inflation. But I assume the inflation came after the original singularity and that before the singularity came the quantum fluctuation.

This is way I am asking what is the difference between the quantum fluctuation and a singularity. Thank you.

P.S. I did not mention "eternal inflation" but I assume this is the third element run amok?

• Rather than asking what it the difference, it would seem more natural to me to ask in what way they're similar. There is no obvious way in which they're similar, and we don't have any physical theory in which they're similar. Tryon was making a huge conceptual leap. – Ben Crowell Mar 21 '18 at 17:54
• So one difference is that quantum fluctuations are extended, $\delta E \delta t>\hbar$ and $\delta p \delta x>\hbar$, whereas a physical energy singularity (rather than just the mathematical meaning) (if such a thing exists, which is questionable) would occur at a literal physical point. That's incompatible with QM theory. – JMLCarter Mar 22 '18 at 5:48

Singularities exist in mathematical functions and appear when there is a division by zero. In particular classical theories which have the 1/r potentials theoretically have a singularity at r=0. Quantum mechanics turns these singularities either to fuzzy locuses, or forbids attaining the r=0 by the structure of the mathematical model, as happens with the solutions of Schrodinger equation even with a 1/r potential. When close to r, bound states take over, and discrete energy levels which forbid the r=0 ppoint.

The original Big Bang model was a classical model of General Relativity where singularities mathematically are allowed. In a similar way that a classical spherically symmetric explosion can be extrapolated to a point where all the mass is supposedly concentrated at r=0 ( a fictious theoretical point since in classical mechanics mass cannot be reduced to a point, it needs a volume), a General Relativiy model was built to fit the cosmological observations, and this model had a singularity at the beginning of time.

Before a time classified as a Planck time, 10^-43 seconds, all of the four fundamental forces are presumed to have been unified into one force. All matter, energy, space and time are presumed to have exploded outward from the original, General relativity singularity. Nothing is known of this period.

It was fairly successful originally, but then new observations demanded a quantum mechanical model for the very beginning of the Big Bang universe.

The current Big Bang model.: Quantum mechanics had to enter because the homogeneity of the cosmic microwave background radiation cannot be modeled with classical thermodynamics, and an effective gravitational quantization theory for the beginning of time had to be used.

This also gives the quantum mechanical fuzziness at the beginning of the universe which diffuses the classical singularity at the origin.

What is the difference between a quantum fluctuation and a singularity in the beginning universe?

The quantum fluctuation sits/takes-over where the classical singularity would be, creating the fuzziness due to the quantum mechanical probabilistic uncertainty at that point. There are no infinities, as there are in the classical singularity.

• This answer doesn't address the question, and the content is also wrong. The question is about the concept that the big bang itself might be describable as a quantum fluctuation, and this answer doesn't address that. The answer is also wrong because it claims that there is some relationship between the necessity of describing matter fields as quantum-mechanical and the idea of developing a theory of quantum gravity. There is no such relationship. – Ben Crowell Mar 21 '18 at 17:51
• OK anna and Ben...but cosmologists can't have their cake and eat it too. Quantum field theory which we know is correct assumes there are fields already there so a fluctuation can take place. Additionally how does the inflaton measure into this? Is it not yet another field? But does the inflaton field then not presume the existence of some other group of fields ? So inflation works fine as long as there is something already there to turn it on. You can't bootstrap from non existence. – Sedumjoy Mar 21 '18 at 20:41
• This is a theoretical research field. It is true that conservation of energy has been validated over and over again in physics experiments, and morphs to "you cant have something out of nothing" . It is only in General Relativity which fits cosmological observations, that energy is not necessarily conserved, and thus can fit a big bang model on the data. This old blog post by Lubos explores the problem and the solutions motls.blogspot.gr/2010/08/… , extra assumptions needed. – anna v Mar 22 '18 at 4:13
• as for the inflaton, if you look at the model, it is postulated for after the planck time, 10^-43 seconds. The original fluctuation we know nothing about at the moment, except speculative models. – anna v Mar 22 '18 at 4:16
• @Sedumjoy yes, cosmology is close to science fiction in one sense, a lot of speculation about the very early universe – anna v Mar 22 '18 at 17:07