- #1
Mickey1
- 27
- 0
I am considering the following question and I want you to agree (but perhaps you don’t):Rutherford wrote a letter to Bohr, as an answer to a previous letter from Bohr containing one of the first of Bohr’s descriptions of the atomic model, saying that he understood the atom model Bohr advocated. He commented further that there was a question he understood that Bohr had no doubt considered himself: when does an electron “know how to jump?”.
From this exchange, it is obvious that the issue of determinism was something that accompanied quantum mechanics from its very first formulation. It was not “discovered” later as a separate entity.
Although not versed in history, I now offer what I believe to be a historical equivalence, regarding set theory and the real numbers. Cantor discussed the fact that real numbers was unaccountable as opposed to rational. The rational was constructible, and easily understood as the solution to simple integer equations such as x*b=a, but the real numbers cannot be defined in a similar simple way, being were more easily defined as a collection of numbers such as (intuitively) all numbers on a number line or all limits of Cauchy sequences.
Playing the role of Rutherford, I would have written to Cantor that I easily understand many mechanisms from rational numbers, but the real numbers cannot be defined as easily. In lieu of an simple general point-wise definition such as a/b above, the question pops naturally up: what can we say about the whole “collection” of the real numbers?
I propose that set theory was a companion of - the recently more rigorously defined - real numbers, just the way as problems of determinism was for quantum physics. Observe that this is not the way it is being portrayed today. (In fact nobody agrees with me on MATH.SE).
From this exchange, it is obvious that the issue of determinism was something that accompanied quantum mechanics from its very first formulation. It was not “discovered” later as a separate entity.
Although not versed in history, I now offer what I believe to be a historical equivalence, regarding set theory and the real numbers. Cantor discussed the fact that real numbers was unaccountable as opposed to rational. The rational was constructible, and easily understood as the solution to simple integer equations such as x*b=a, but the real numbers cannot be defined in a similar simple way, being were more easily defined as a collection of numbers such as (intuitively) all numbers on a number line or all limits of Cauchy sequences.
Playing the role of Rutherford, I would have written to Cantor that I easily understand many mechanisms from rational numbers, but the real numbers cannot be defined as easily. In lieu of an simple general point-wise definition such as a/b above, the question pops naturally up: what can we say about the whole “collection” of the real numbers?
I propose that set theory was a companion of - the recently more rigorously defined - real numbers, just the way as problems of determinism was for quantum physics. Observe that this is not the way it is being portrayed today. (In fact nobody agrees with me on MATH.SE).