According to the article on Wikipedia:
The Planck time is the length of time at which no smaller meaningful length can be validly measured due to the indeterminacy expressed in Werner Heisenberg’s uncertainty principle. Theoretically, this is the shortest time measurement that is possible.[1] Planck time is roughly 10−43 seconds. However, to date, the smallest time interval that has been measured is 10−21 seconds, a “zeptosecond”.[2][3][4] One Planck time is the time it would take a photon travelling at the speed of light to cross a distance equal to one Planck length. ( Planck time - Simple English Wikipedia, the free encyclopedia )
a Planck length is
about 10−20 times the size of a proton ( Planck length - Simple English Wikipedia, the free encyclopedia )
Time becomes immeasurable beyond this, thus Planck time is more-or-less a hard physical constraint on time measurement in the physical universe.
So the question posed was how long can someone go without sinning. I would argue that a single unit of Plank time is still an unreachable state of impeccability which no human being has ever attained.
It is, of course, possible to not do specific sins. There are a good many specific sins which I have never committed. And, thus, it is also reasonable to assert that a person can go a good amount of time between specific sins as well.
But the problem is that sinning isn’t just the act of committing very specific sinful actions. Sinning happens “behind the scenes” as it were–it happens in the subconscious as much as in the conscious–it’s not merely our deliberate thoughts, but even our implicit thoughts. It’s found not only in our explicit acts, but in our implicit ones. It occurs not only in actions, but also inactions. It is in our attitudes, our feelings, our thoughts, our way of doing things. It runs top to bottom and bottom to top, it is found in the deepest core of myself.
The answer, then, if I am to be honest before the Law, is that there isn’t a single moment of my mortal existence that goes without sin. For I am, in Adam, altogether dead and at enmity toward God.
The Apostle St. Paul declares, with full honesty about his own sinful condition:
“What a wretched man am I! Who can save me from this body of death?!”
The point here isn’t, of course, to be a pessimist or a cynic about being human. As though the goal is to view oneself with such low self esteem as to be given over to endless and incurable despair. And, more importantly, it is not to look at your fellow man and deny the intrinsic goodness of the Image of God in which all human beings were created, as though I can look at my neighbor with scorn, like the Pharisee who beheld the Publican with contempt. Rather the point is to bear sincere realism about the human condition apart from Divine Grace. Apart from Christ.
That in my flesh, the old Man in me, is a sinner. Every moment of every day, waking or sleeping.
Therefore we can confess, as in this Penitential Prayer:
Most merciful God, we confess that we have sinned against You in thought, word, and deed, by what we have done, and by what we have left undone. We have not loved You with our whole heart; we have not loved our neighbors as ourselves. We are truly sorry and we humbly repent. For the sake of Your Son Jesus Christ, have mercy on us and forgive us; that we may delight in Your will, and walk in Your ways, to the glory of Your Name. Amen.
As Dr. Luther wrote in his letter to Philip Melancthon,
“If you preach grace, then preach real grace not pretend grace; if grace is real then you bear real sin, not pretend sin.”
“Sin boldly” is not a call to sin. But a reminder that you, me, all of us, are actually quite sinful. We have real sin, and we can’t pretend otherwise. Because to pretend otherwise is to deny real grace. Because God has real grace for real sinners. Thus be fully honest with yourself: You are a sinner; and here now trust in Christ who has conquered sin, death, and the world.
God doesn’t want fake saints.
He saves real sinners. For
Christ came to save sinners, and I am the chief of sinners.