Q&A: Regarding "Wages Accrue from Beginning to End" and Planck Time
Regarding "Wages Accrue from Beginning to End" and Planck Time
Question
Good evening,
In the Talmudic discussion of hiring a worker (and other rentals as well), we find a view that the wage for the work is divided among each and every moment of the duration of the work. One practical consequence is that one cannot betroth a woman with payment for work, because at every moment the worker earns wages; that wage is not worth a perutah, becomes a loan, and one cannot effect betrothal with a loan.
My question is theoretical, but I would be happy to gain some understanding of the matter.
If it were imagined that units of time were each worth a perutah of wage, then it would be possible to betroth even according to the view that wages accrue from beginning to end; that would be no worse than the opinion that wages are paid only upon completion of the entire job.
From a mathematical standpoint, time, like number, can be divided infinitely, and therefore even if the fee is very high, there are still infinitely many units of time, so no single unit of time is worth a perutah, because every unit of time can be divided again and again.
But from a physical standpoint, the smallest unit of time is Planck time; that is, there is a unit of time that cannot be divided. It therefore follows that if the wage payment were high enough that, when divided into units of Planck time, each unit would be worth a perutah, then even according to the view that wages accrue from beginning to end it would be possible to betroth a woman with payment for work.
Does the view that wages accrue from beginning to end hold that time is mathematically infinite, such that betrothal with payment for work is impossible even theoretically, or is it simply that Planck time is so tiny that it is inconceivable that the wage for one unit of Planck time would be worth a perutah, though theoretically it could happen?
Many thanks!
Answer
Are you really asking me this? It sounds like a question for an article by Torah-observant scientists from fifty years ago.
Discussion on Answer
First, Planck time is theoretical hairsplitting with no importance. The fact that it is the shortest measurable time does not mean that the time axis is not continuous. Second, we're talking about 10 to the power of minus 44 seconds, meaning all the money in the universe over a billion billion years for one transaction would not give you an amount that even comes close to a perutah's worth. Third: do you really think that even if the time axis were discrete, that would change the laws of hiring in Jewish law, or in any other legal system on earth? If anything, I would isolate units on the time axis according to a perutah's worth and not according to Planck time (a legal discretization, not a physical one). That even makes sense, since a debt of less than a perutah's worth does not exist, so it makes sense to accumulate the debt in quanta of a perutah.
In short, what is improper in the question is its unfounded assumptions. Forgive me, but there's nothing to apologize for, because this isn't about offending me but about offending intelligence. 🙂
Thank you very much for the answer. The first point answers my question—that there is no difference between a mathematical and a physical way of looking at the time axis; it's only a way of measuring, but there is no unit of time that cannot be be divided.
I already wrote that this is a theoretical question.
As for isolating units according to the value of a perutah, that is what Rashi writes in Kiddushin 48a at the end of the page. But if so, why according to the view that wages accrue from beginning to end can one not betroth with the wages themselves? After all, the first unit of time worth a perutah would be the betrothal money and the rest would be completion of the payment (and this would not be betrothal with a loan), just as we find on 8a that if one betroths with a maneh, if he gave a dinar she is betrothed and he will complete the rest.
Therefore, the explanation that units of wages are measured by the value of a perutah is difficult, and Rashi's view needs to be reconciled. I would be glad if you have an explanation.
Sabbath peace!
Correction: Rashi 48a (s.v. "rather, where he betroths").
That was exactly my point. If you're already discretizing the time axis and raising the difficulty that betrothal should take effect, then do it on the basis of a perutah's worth and not on the basis of Planck time.
So it's clear that we do not discuss the effectiveness of betrothal on the basis of discrete time. As for Rashi, I don't have time right now to look into it.
Yes—if I asked here on the site, that means I really am asking the honorable Rabbi. If there was something improper in the question, I sincerely apologize and ask forgiveness, but in my poverty of understanding I do not see what wrong I committed.