Imaginary Numbers May Be Essential for Describing Reality
Charlie Wood
Quote:In quantum mechanics, the behavior of a particle or group of particles is encapsulated by a wavelike entity known as the wave function, or ψ. The wave function forecasts possible outcomes of measurements, such as an electron’s possible position or momentum. The so-called Schrödinger equation describes how the wave function changes in time — and this equation features an i.
Quote:No real-number description, however, can replicate the pattern of correlations that the three physicists will measure. The new paper shows that treating the system as real requires introducing extra information that usually resides in the imaginary part of the wave function. Alice’s, Bob’s, and Charlie’s particles must all share this information in order to reproduce the same correlations as standard quantum mechanics. And the only way to accommodate this sharing is for all of their particles to be entangled with one another.
Quote:Even without recruiting an Alice, a Bob and a Charlie to actually perform the experiment that the new paper imagines, most researchers feel extremely confident that standard quantum mechanics is correct and that the experiment would therefore find the expected correlations. If so, then real numbers alone cannot fully describe nature.
[url=https://www.quantamagazine.org/imaginary-numbers-may-be-essential-for-describing-reality-20210303/?utm_source=pocket-newtab#comments][/url]
The word 'imaginary' may be somewhat emotive in this context, as though it conveys some sort of mystical significance. It's probably fairer to regard it just as a tool in the mathematician's toolkit. In some contexts for example an imaginary number is no more exotic than 2D geometry, it can be quite mundane.
(2021-03-05, 05:30 AM)Sciborg_S_Patel Wrote: [ -> ]Imaginary Numbers May Be Essential for Describing Reality
Charlie Wood
This certainly seems to show the presence of Mind as being basic to the structure of the Universe. Another example is Euler's Equation, where the use of i or the square root of -1 indicates the presence of Mind behind the structure of mathematics:
e>[i(pi)] = 0
where
e is Euler's number, the base of natural logarithms,
i is the imaginary unit, which by definition satisfies i2 = −1, and
pi is the ratio of the circumference of a circle to its diameter.
Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics. (Wiki)
(2021-03-05, 11:50 AM)nbtruthman Wrote: [ -> ]Another example is Euler's Equation, where the use of i or the square root of -1 indicates the presence of Mind behind the structure of mathematics:
e>[i(pi)] = 0
Hmm. To me this takes us to the question of whether mathematics is invented or discovered. If we take the position that we discovered a particular thing in mathematics, is that because we can't conceive of it being invented? That is to say, not even invented by
Mind. On the other hand, if we invented it, then we take credit ourselves. Either way it seems problematic.
(2021-03-05, 05:30 AM)Sciborg_S_Patel Wrote: [ -> ]Imaginary Numbers May Be Essential for Describing Reality
Charlie Wood
There is no issue in the framework of Informational Realism. Quantities like e and i are discovered in an epistemological context. The discovery of imaginary numbers is formed by minds importing mutual information from the natural world.
These values, when used in simulations, "work" because they are natural data, formed as informational relationships, corresponding to the ontological structures underlying model realty. When any information object with dispositional uses is uncovered and applied by minds -- real world processes are happening. The mutual information structured into an useful algorithm can change real-world probabilities in predicting and understanding physical events.
(2021-03-05, 09:57 AM)Typoz Wrote: [ -> ]The word 'imaginary' may be somewhat emotive in this context, as though it conveys some sort of mystical significance. It's probably fairer to regard it just as a tool in the mathematician's toolkit. In some contexts for example an imaginary number is no more exotic than 2D geometry, it can be quite mundane.
Oh I don't think it's some sort of proof that Imagination is Reality...but it does open the question as to what the imaginary numbers are supposed to correspond to.
A new dimensional axis? The reality of possibilities being actualized? My guess is those physicists with a philosophical bent will be take interest in this, we just have to wait to see what comes out of [the thought experiment] if this claim is strengthened by experimentation.
It's interesting that a number of great mathematicians have felt that their inexplicable creativity in math discoveries was divinely inspired. Georg Cantor and Srinivasa Ramanujan are examples. It’s really hard explain where all those new ideas came from.
Quote:"Georg Cantor (1845–1918) is best remembered for being “perhaps the first mathematician to really understand the meaning of infinity and to give it mathematical precision… Cantor coined the new word “transfinite” in an attempt to distinguish these various levels of infinite numbers from an absolute infinity, which the religious Cantor effectively equated with God (he saw no contradiction between his mathematics and the traditional concept of God).
Cantor also believed that his theory of transfinite numbers ran counter to both materialism and determinism — and was shocked when he realized that he was the only faculty member at Halle who did not hold to deterministic philosophical beliefs.
Ramanujan is another example like that. He didn’t have a formal education in math. And he said that there was a Hindu goddess that would tell him mathematics while he slept.
That seems to be the most reasonable explanation I can think of for how he did that or how the incredible Euler did his seemingly endless and sourceless creative generations, unless we work out a complete artificial intelligence and it can do what Cantor or Ramanujan or Euler did. For now, I think the best explanation is the one that Ramanujan gave."
(From
https://uncommondescent.com/intelligent-...stand-out/ )