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I've heard a few times in my 5+ decades that we can only calculate the "state of the universe" (loosely speaking, I don't know any math close to that high) back to very close, but not right to t=0.

As "Philip Gibbs - inactive" says on the How can the big bang occur mathematically? question page:

We do not have a complete mathematical description of the big bang. That would require a theory of quantum gravity because effects of both gravity and quantum mechanics become relevant when you want to describe what happens under the physical conditions that we think were important in the big bang...

Basically, to my layman's brain - the universe gets small enough that you need to use both quantum mechanics and gravity and we have no such math. That being the quantum gravity, again, I assume.

I believe I even heard someone say a number that may have just been off the top of his head, because it was something like 16 zero's after the decimal and then 1. As in one zillionth of a second after the big bang. Then we can't calculate any further back. The number may be just 8 zeros or something it was some years ago, and I've searched for the number multiple times over the last several years, just finally found a place where someone might know. (a related bit (hope that's ok) - I wondered if time came in quanta as well, and that this particular length after the big bang is how long a hypothetical quanta of time is.. remotely possible? Does the length of a time quanta even make sense?)

I hope I explained myself well enough.. I would love to know the math, but guessing I should ask a separate question on how to get from Calculus to Quantum Physics (& QED?) and the like. Thanks!

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The number you are looking for, often stated as the time Quantum Gravitational effects become important, is the Plank Time: $5.39×10^{−44}$ seconds after the Big Bang.

What you should know is that this time is only an order-of-magnitude estimate, not an exact time. It is also commonly thought of as "the smallest unit of time" possible, but that also is not exactly true. All we know for sure is that without a theory of Quantum Gravity, we can't make any claims about what happens in timescales shorter than the Planck Time, or what happened in our universe during the first Planck Time. That is all.

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    $\begingroup$ Additionally, we aren't even sure what happened before $10^{-32}$ seconds, because we don't have a Grand Unified Theory (which combines the Strong Nuclear force with the Electroweak one) or a fully formed theory of Inflation yet, and there's still a lot of questions about things before $10^{-12}$ seconds as well, because we don't know the specifics of how quark-gluon plasmas behaved in the Electroweak era. We only really begin to understand what's going on at Nucleosynthesis, around 2 minutes after the Big Bang. $\endgroup$ – Anthony Khodanian Nov 29 '20 at 2:14

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