Originally Posted by
Mario F.
As chance decided, a couple of months ago I finished reading The complete Road to Reality, by Roger Penrose (ISBN 0224044478). There's an important chapter in the book that addresses your concerns, that I would I'd like to put here:
He then proceeds to give examples in the context of the real-number system. A few paragraphs later he briefly discusses this thought in the context of quantum mechanics:
Finally, I would like to expose you to an Einstein quote, since you seem so eager to refer to him in this discussion:
"One can give good reasons why reality cannot be represented as a continuous field. Quantum phenomena must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory."
...
Your argument against an unknown mathematical construct or property isn't acceptable, Sebastiani. No one since Heisenberg or before him, for whom science has been their cradle, will ever attribute to magic or little goblins the unknowns they tend to discover along their path. Your faith in mathematics should, it too, be tempered. We have been expanding our mathematical knowledge along our history exactly because we have been faced with realities that forced us to create new formal systems that better describe the physical world. Other times (and more often) we just "stumble" upon a new formal system naturally as a consequence of new discoveries.
To think that Heisenberg left to small mathematical goblins his discoveries is wrong. Quantum physics emerged almost entirely out of purely mathematical extrapolations, as there was little in the way of technology to produce empirical evidence. He was first and foremost a mathematician. And he stumbled upon a problem that even his contemporaries, among them Einstein, clearly understood to be something new and potentially changing in the mathematical field. He was awarded much more respect by physicists to this day than what you have done here. Even on the matter of the observation effect.
And even though our understanding of quantum mechanics has evolved in the 90 years since, there's still much left to do that does not remove the idea that indeed we may need a new formal system to describe reality at the quantum level. Heisenberg mathematical goblins haven't been discarded. And it is this thought, this way to look at science, this complete refusal to close our eyes to new thoughts and ideas that makes science move forward. Not close our eyes and mock the past. Your beloved Einstein would agree to this.