Sabine Hossenfelder asks, Do complex numbers exist?

_{Denyse O'Leary

March 6, 2021

Intelligent Design, Mathematics}

Share: Facebook; Twitter; LinkedIn; Flipboard; Print; Email

Complex numbers have a real component, say 6, and an imaginary component, say √-1. So it is 6+√-1. In a recent math flap, someone claimed that complex numbers don’t really exist and others claim, yes, they do.

Sabine Hossenfelder thinks they do exist, at least for quantum physics. Discussing the “yes, they do” camp, she explains:

The question which they look at in the new paper is then whether there are ways to entangle particles in the normal, complex quantum mechanics that you cannot build up from particles that are described entirely by real valued functions. Previous calculation showed that this could always be done if the particles came from a single source. But in the new paper they look at particles from two independent sources, and claim that there are cases which you cannot reproduce with real numbers only. They also propose a way to experimentally measure this specific entanglement.
I have to warn you that this paper has not yet been peer reviewed, so maybe someone finds a flaw in their proof. But assuming their result holds up, this means if the experiment which they propose finds the specific entanglement predicted by complex quantum mechanics, then you know you can’t describe observations with real numbers. It would then be fair to say that complex numbers exist. So, this is why it’s cool. They’ve figured out a way to experimentally test if complex numbers exist!
Sabine Hossenfelder, “Do Complex Numbers Exist?” at BackRe(Action)

But, she warns, if they are right,

This conclusion only applies if you want the purely real-valued theory to work the same way as normal quantum mechanics. If you are willing to alter quantum mechanics, so that it becomes even more non-local than it already is, then you can still create the necessary entanglement with real valued numbers.
Sabine Hossenfelder, “Do Complex Numbers Exist?” at BackRe(Action)

The people who don’t think complex numbers really exist would probably not be happy with quantum mechanics being even more non-local without them. But of course, if complex numbers really do exist, then immaterial things really exist. Not a good time to be a hard core materialist.

Comments

Whatever VL. I wasn't even talking to you.. My comment was in regards to the character of the debate between real and imaginary in the naturalism in general and mathematics in particular and my comment stands on its own merits in regards to that topic, (as I made clear in my comment). i.e. The main point is simply that the 'unnatural' mathematics that ended up describing this universe is unexpected given naturalistic premises, and that our mathematical descriptions of the universe fit far better with a Theistic presupposition and conception of nature. Given that Theism holds that there is life after death, then that is, or should be, VERY good news for you. And In so far as my comment even concerned you personally, that fairly straight forward conclusion that I drew should have made you feel happy instead of defensive.bornagain77_{March 7, 2021
March
03
Mar
7
07
2021
06:26 PM
6
06
26
PM
PDT}

BA, I don't think anyone in this conversation is "debating whether complex numbers should be regarded as real or should be regarded as imaginary." Hossenfelder has offered what I called an idiosyncratic definition of what "exists" means in terms of numbers, but everyone else that has commented understands that the nature of imaginary numbers is no different than that of those we call real numbers. It's interesting how a comment can send you down your own self-motivated anti-naturalist rabbit hole without really engaging the conversation at hand.Viola Lee_{March 7, 2021
March
03
Mar
7
07
2021
06:03 PM
6
06
03
PM
PDT}

Given the naturalistic premises that dominate science nowadays, the whole controversy over whether the square root of negative 1 is real or imaginary is fairly humorous. In the naturalist's and/or materialist's denial of the primacy of conscious for any conception of reality that we may have for the universe,
“The principal argument against materialism is not that illustrated in the last two sections: that it is incompatible with quantum theory. The principal argument is that thought processes and consciousness are the primary concepts, that our knowledge of the external world is the content of our consciousness and that the consciousness, therefore, cannot be denied. On the contrary, logically, the external world could be denied—though it is not very practical to do so. In the words of Niels Bohr, “The word consciousness, applied to ourselves as well as to others, is indispensable when dealing with the human situation.” In view of all this, one may well wonder how materialism, the doctrine that “life could be explained by sophisticated combinations of physical and chemical laws,” could so long be accepted by the majority of scientists." – Eugene Wigner, Remarks on the Mind-Body Question, pp 167-177. “No, I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness.” - Max Planck (1858–1947), one of the primary founders of quantum theory, The Observer, London, January 25, 1931 “Consciousness cannot be accounted for in physical terms. For consciousness is absolutely fundamental. It cannot be accounted for in terms of anything else.” - Schroedinger, Erwin. 1984. “General Scientific and Popular Papers,” in Collected Papers, Vol. 4. Vienna: Austrian Academy of Sciences. Friedr. Vieweg & Sohn, Braunschweig/Wiesbaden. p. 334.?
In the naturalist's and/or materialist's denial of the primacy of conscious for any conception of reality that we may have for the universe, the entire naturalist's and/or materialist's conception of reality collapses into self-refuting incoherency.
Basically, because of reductive materialism (and/or methodological naturalism), the atheistic materialist (who believes Darwinian evolution to be true) is forced to claim that he is merely a ‘neuronal illusion’ (Coyne, Dennett, etc..), who has the illusion of free will (Harris), who has unreliable, (i.e. illusory), beliefs about reality (Plantinga), who has illusory perceptions of reality (Hoffman), who, since he has no real time empirical evidence substantiating his grandiose claims, must make up illusory “just so stories” with the illusory, and impotent, ‘designer substitute’ of natural selection (Behe, Gould, Sternberg), so as to ‘explain away’ the appearance (i.e. the illusion) of design (Crick, Dawkins), and who also must make up illusory meanings and purposes for his life since the hopelessness of the nihilism inherent in his atheistic worldview is simply too much for him to bear (Weikart), and who must also hold morality to be subjective and illusory since he has rejected God (Craig, Kreeft). Who, since beauty cannot be grounded within his materialistic worldview, must also hold beauty itself to be illusory (Darwin). Bottom line, nothing is truly real in the atheist’s worldview, least of all, beauty, morality, meaning and purposes for life.,,, Darwinian Materialism and/or Methodological Naturalism vs. Reality – video https://www.youtube.com/watch?v=CaksmYceRXM
Thus, given that the methodological naturalists end up claiming that practically everything, (that everyone, (including atheists themselves), regard as being real), is merely illusory, then it is quite humorous that people who are, (I assume), by and large committed to a naturalistic conception of reality, are debating whether complex numbers should be regarded as real or should be regarded as imaginary. As Viola lee pointed out, exactly the same kind of arguments were made about negative numbers, and even zero, at other points in time. It seems that there is an underlying naturalistic bias in mathematics to regard the counting numbers, which can be assigned to things we see, as real, and to regard any other numbers as merely imaginary. But alas, as Shakespeare once quipped, "There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy."
"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy." - Hamlet (1.5.167-8), Hamlet to Horatio
And so it is with mathematics, i.e. "There are more things in mathematics, Horatio, Than are dreamt of in your naturalistic philosophy." Naturalists, by their continual dismissing of certain 'unnatural' concepts in mathematics as being merely imaginary, simply do not expect 'unnatural' mathematical descriptions to be forthcoming for the universe. Yet, 'unnatural' mathematics underly our most 'perfect' theories in science. Our best theories in science are all based on 'unnatural' higher dimensional mathematics and geometry, instead of being based on 'natural' Euclidian geometry and 'classical' mathematics, (as would be presupposed by naturalists who hold that this 3-D physical realm is the only realm of existence),
Why do you need imaginary numbers (the square root of negative one) to describe Quantum Mechanics? “Quantum theory needs existence of an x such that x^2= -1. The reason for this is that orthogonal function spaces, of dimension greater than 2, cannot exist otherwise. In fact the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement. Even the Canonical Commutation Relation doesn’t need it. And nor do the eigenvalue equations. In those, any general scalar will do. But in the wave packet, you need an i.” – Steve Faulkner – Philosophy of Science, Logic, Epistemology https://www.researchgate.net/post/Why_do_you_need_imaginary_numbers_to_describe_Quantum_Mechanics2 Of note: In mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. The Applicability of Mathematics as a Philosophical Problem - Mark Steiner - (page 44) Excerpt: Let us now recapitulate: beginning with the concept of a Hilbert space, a certain kind of (usually infinite-dimensional) vector space, and the formal requirement that a unit vector on the space represents all possible information can be gleaned. First, the space cannot be a real vector space; the usual formalism is, therefore, based on a complex Hilbert space. With this formalism the Heisenberg uncertainty principle follows directly. So does the quantization of angular momentum, including the so called "space quantization". So does the prediction that "electron spin" cannot be due to spatial rotation. And so do the selection rules for the spectrum of hydrogen, based on the "nonphysical" concept of parity. The role of Hilbert spaces in quantum mechanics, then, is much more profound than the descriptive role of a single concept. An entire formalism-the Hilbert space formalism-is matched with nature. Information about nature is being "read off" the details of the formalism. (Imagine reading off details about elementary particles from the rules of chess-castling. en passant-a la Lewis Carro;; in Through the Looking Glass.) No physicist today understands why this is possible.. https://books.google.com/books?id=GKBwKCma1HsC&pg=PA44 Four-dimensional space - with 4-D animation: Excerpt: The idea of adding a fourth dimension began with Joseph-Louis Lagrange in the mid 1700s and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann.,,, Higher dimensional spaces have since become one of the foundations for formally expressing modern mathematics and physics. Large parts of these topics could not exist in their current forms without the use of such spaces.,,, Einstein's concept of spacetime uses such a 4D space, though it has a Minkowski structure that is a bit more complicated than Euclidean 4D space. https://en.wikipedia.org/wiki/Four-dimensional_space Spacetime Excerpt: In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the definition of a spacetime interval that combines distance and time. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded. Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed that spacetime becomes curved in the presence of mass or energy.,,, Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[10]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime. https://en.wikipedia.org/wiki/Spacetime also see the higher dimensional 'amplituhedron" that lies behind Quantum Electrodynamics
Of related interest, up until a few years ago, Anton Zeilinger featured this following video on his outreach page,
Dr. Quantum (in) Flatland - video https://www.youtube.com/watch?v=sEVEKL1Fbx0
Now if anything should be considered 'unnatural' by an atheistic naturalist that video is it :) It is also interesting to note that, whereas atheists have no observational evidence whatsoever that the Multiverses that they have postulated to try to ‘explain. away’ the fine tuning of the universe are real, (nor do Atheists have any evidence whatsoever that the ‘parallel universes’ that they postulated to try to ‘explain away’ quantum wave collapse are real), Christians, on the other hand, can appeal directly to Special Relativity, General Relativity, and Quantum Mechanics, (i.e. our most precisely tested theories ever in the history of science), to support their belief that God upholds this universe in its continual existence, as well as to support their belief in a heavenly dimension and in a hellish dimension.” https://uncommondescent.com/intelligent-design/closer-to-truth-are-there-really-extra-dimensions/#comment-722947 So in conclusion, it is humorous to see naturalists debating what is real and what is imaginary in mathematics since their own worldview can't even properly distinguish between what is real and what is illusory in real life. And since their naturalistic worldview certainly didn't anticipate the 'unnatural' higher dimensional mathematics that ended up accurately describing this universe To repeat Shakespeare,
"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy." - Hamlet (1.5.167-8), Hamlet to Horatio
Verse:
John 3:12 I have spoken to you of earthly things and you do not believe; how then will you believe if I speak of heavenly things?
bornagain77_{March 7, 2021
March
03
Mar
7
07
2021
05:30 PM
5
05
30
PM
PDT}

This raises the obvious question of what it means to say something "exists". If all that is required for something to exist is that a conscious mind perceives or is aware of it then numbers - real or imaginary - or London or the United States or the Earth or the Sun all exist. But the so does Middle Earth or Gandalf or the Star Wars galaxy or Narnia. On the other hand, is there a Universe of phenomena out there which exist whether or not there is a conscious mind to be aware of them? Is there an objective reality as well as a subjective reality and where is the boundary between the two? As WJM correctly points out, all our experience of anything happens in our conscious mind. There seems to be no way for us to step "outside" of our mental world to see if there is actually anything beyond. I believe in a mental model theory in which our conscious world is an imperfect model of what is actually out there built from data abstracted from that external reality through our physical sensory systems. The problem is that, as far as I can see, there is no way to prove it. As he says, by Occam's Razor, his theory is preferable on the grounds that it is more parsimonious. All I can say is that I prefer mine because it fits better with what I experience. But I could be completely wrong.Seversky_{March 7, 2021
March
03
Mar
7
07
2021
04:29 PM
4
04
29
PM
PDT}

re 7: I hope you know that imaginary numbers exist in exactly the same way that all other kinds of numbers exist. The word "imaginary" was coined by a skeptic when they first were developed, and the name stuck, but exactly the same kind of negative arguments (see what I did there?) were made about negative numbers, and even zero, at other points in time.Viola Lee_{March 7, 2021
March
03
Mar
7
07
2021
01:22 PM
1
01
22
PM
PDT}

Complex numbers are combinations of real numbers and imaginary numbers. I wonder how many in this discussion want imaginary numbers to really "exist" for ideological reasons? E.g. if imaginary numbers exist then other imaginary things might also exist, like unicorns, fairies, magic, macroevolution, and so on.Fasteddious_{March 7, 2021
March
03
Mar
7
07
2021
01:01 PM
1
01
01
PM
PDT}

People had this same debate about whether negative numbers were real: some major mathematicians rejected them as nonsense, and it took about a century for them to get fully accepted. But, as Hossenfelder herself point out, complex numbers have been accepted and used for a very long time. That is not the way she is using "exists", which in the quote I clipped in #1 she puts in quotation marks.Viola Lee_{March 7, 2021
March
03
Mar
7
07
2021
05:26 AM
5
05
26
AM
PDT}

Moreover, regardless of whatever the Atheistic Naturalist's definition of 'real' may be in regards to any mathematics that may describe this universe, Godel, with his incompleteness theorem, has proven that mathematics is necessarily incomplete, and therefore mathematics cannot function as a 'God substitute' (as Atheistic Naturalists are apparently falsely presupposing in their arguments,,,, falsely presupposing in their arguments whether or not complex numbers are found to be 'real' or "imaginary'.)
THE GOD OF THE MATHEMATICIANS – DAVID P. GOLDMAN – August 2010 Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel’s critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes. http://www.firstthings.com/article/2010/08/the-god-of-the-mathematicians Taking God Out of the Equation – Biblical Worldview – by Ron Tagliapietra – January 1, 2012 Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties. 1. Validity … all conclusions are reached by valid reasoning. 2. Consistency … no conclusions contradict any other conclusions. 3. Completeness … all statements made in the system are either true or false. The details filled a book, but the basic concept was simple and elegant. He (Godel) summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem. Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation. Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3). https://uncommondescent.com/philosophy/why-god-appears-to-be-a-mathematician/#comment-703707
Mathematics, contrary to what the vast majority of theoretical physicists apparently believe today, simply never will have the capacity within itself to function as a God substitute. As Dr. Bruce Gordon explains, “The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,, Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.”
BRUCE GORDON: Hawking’s irrational arguments – October 2010 Excerpt: ,,,The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,, Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality.,,, Universes do not “spontaneously create” on the basis of abstract mathematical descriptions, nor does the fantasy of a limitless multiverse trump the explanatory power of transcendent intelligent design. What Mr. Hawking’s contrary assertions show is that mathematical savants can sometimes be metaphysical simpletons. Caveat emptor. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/
Of supplemental note:
KEEP IT SIMPLE - Edward Feser - April 2020 Excerpt: Mathematics appears to describe a realm of entities with quasi-divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our experience lack. Mathematical objects seem immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order. How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect.,,, https://www.firstthings.com/article/2020/04/keep-it-simple March 2020 This view the mathematics exists “because they are God’s thoughts” and the Christian view that God created the universe, (i.e. that the universe is contingent upon God), and that the universe has not always existed, (as Aristotle had held), were presuppositions that were necessary for modern science to finally take root in Medieval Christian Europe. https://uncommondescent.com/philosophy/edward-feser-on-mathematics-and-the-sense-of-the-divine/#comment-695391
Verse and Quote;
John 1:1 “In the beginning was the Word, and the Word was with God, and the Word was God” What is the Logos? Logos is a Greek word literally translated as “word, speech, or utterance.” However, in Greek philosophy, Logos refers to divine reason or the power that puts sense into the world making order instead of chaos.,,, In the Gospel of John, John writes “In the beginning was the Word (Logos), and the Word was with God, and the Word was God” (John 1:1). John appealed to his readers by saying in essence, “You’ve been thinking, talking, and writing about the Word (divine reason) for centuries and now I will tell you who He is.” https://www.compellingtruth.org/what-is-the-Logos.html ‘the Word’ in John1:1 is translated from ‘Logos’ in Greek. Logos is also the root word from which we derive our modern word logic http://etymonline.com/?term=logic
bornagain77_{March 7, 2021
March
03
Mar
7
07
2021
04:22 AM
4
04
22
AM
PDT}

Of related note, The argument over whether complex numbers are real or imaginary goes back a long way. Carl Friedrich Gauss was the mathematician who first explained the 'dimensional extension' of complex numbers over and above the real number line,,,
The Mathematics Of Higher Dimensionality - Gauss & Riemann - video https://www.youtube.com/watch?v=mxy3JhPRlV0
In response to complex numbers, "Descartes had rejected complex roots and coined the derogatory term "imaginary" to describe the square root of negative one," Yet both Leibniz and Gauss rejected the notion that complex numbers were 'imaginary'. Leibniz stated that ""The divine spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and non-being, which we call the imaginary root of negative unity." And Gauss went so far as to say that complex magnitudes should be awarded "full civil rights."
Complex Magnitudes Excerpt: Descartes had rejected complex roots and coined the derogatory term "imaginary" to describe the square root of negative one, , but Leibniz thought that "The divine spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and non-being, which we call the imaginary root of negative unity." Gauss invented the "complex plane" (shown below) to represent these quantities. He suggested that complex magnitudes be called "lateral" instead of "imaginary" magnitudes since they represent a dimensional extension of the continuum. Gauss also proposed that complex magnitudes be awarded "full civil rights." In the language of Plato's allegory of the cave, complex numbers represent "forms" from a higher dimension casting "shadows" on the real number line. http://www.keplersdiscovery.com/ComplexNum.html
Of note, both Leibniz and Gauss were devout Christians.
Christian Mathematicians – Leibniz - January 30, 2012 By Steve Bishop Excerpt: Leibniz believed in the God of Christianity and he also had an extraordinarily high esteem for reason and its capabilities. ... In 1709 he attempted to improve the ontological argument for God and in 1710 His Theodicy, or “Vindication of the Justice of God“, was published. https://godandmath.com/2012/01/30/christian-mathematicians-leibniz/ Carl Friedrich Gauss Excerpt: Carl Friedrich Gauss was a devout Christian who supported monarchy and opposed Napoleon, whom he saw as an outgrowth of the revolution.,,, http://www.conservapedia.com/Carl_Friedrich_Gauss
Gauss's work on complex numbers, like the square root of negative one, extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part. In this way the complex numbers contain the ordinary real numbers while extending them in order to solve problems that would be impossible with only real numbers. This 'higher dimensional number line', particularly this understanding gained for the 'higher dimensionality' of the square root of negative one (i), is essential for understanding the 'wave packet' in quantum mechanics prior to measurement:
Why do you need imaginary numbers (the square root of negative one) to describe Quantum Mechanics? “Quantum theory needs existence of an x such that x^2= -1. The reason for this is that orthogonal function spaces, of dimension greater than 2, cannot exist otherwise. In fact the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement. Even the Canonical Commutation Relation doesn't need it. And nor do the eigenvalue equations. In those, any general scalar will do. But in the wave packet, you need an i.” - Steve Faulkner - Philosophy of Science, Logic, Epistemology https://www.researchgate.net/post/Why_do_you_need_imaginary_numbers_to_describe_Quantum_Mechanics2
In Hossenfelder's article the argument appears to be that we presently don't really need complex numbers in order to do our calculations for quantum mechanics,
However, you can of course take the wave-function and this equation apart into a real and an imaginary part. Indeed, one often does that, if one solves the equation numerically. And I remind you, that both the real and the imaginary part of a complex number are real numbers. Now, if we calculate a prediction for a measurement outcome in quantum mechanics, then that measurement outcome will also always be a real number. So, it looks like you can get rid of the complex numbers in quantum mechanics, by splitting the equation into a real and imaginary part, and that’ll never make a difference for the result of the calculation.
,,, And the argument in her article continues with the fact that this proposed experiment will prove that complex numbers are not just a 'mathematical convenience' but are irreducibly necessary for our calculations in quantum mechanics, and are therefore to be considered 'real'.
in the new paper they look at particles from two independent sources, and claim that there are cases which you cannot reproduce with real numbers only.,,, ,,, if the experiment which they propose finds the specific entanglement predicted by complex quantum mechanics, then you know you can’t describe observations with real numbers. It would then be fair to say that complex numbers exist. So, this is why it’s cool. They’ve figured out a way to experimentally test if complex numbers exist! ,,, If you, on the other hand, are in the camp of people who think there’s something wrong with quantum mechanics because it uses complex numbers that we can never measure, then you are now caught between a rock and a hard place. Either embrace complex numbers, or accept that nature is even more non-local than quantum mechanics.
First off, let me state that I firmly believe that the proposed experiment will be successful. Quantum Mechanics has a very long history of shattering 'naturalistic' assumptions about locality and realism. Secondly, let me bluntly state the fact that Atheistic Naturalists have no clue why mathematics, ('real' numbers or otherwise), should even be able to describe the universe in the first place. Both Wigner and Einstein are on record as to regarding the applicability of mathematics to the universe to be a 'miracle'. Einstein even went so far as to chastise 'professional atheists' in the process of calling it a 'miracle':
The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.,,, It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind's capacity to divine them.,,, The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html On the Rational Order of the World: a Letter to Maurice Solovine – Albert Einstein – March 30, 1952 Excerpt: “You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton’s theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the ‘miracle’ which is constantly reinforced as our knowledge expands. There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles.” -Albert Einstein http://inters.org/Einstein-Letter-Solovine
bornagain77_{March 7, 2021
March
03
Mar
7
07
2021
04:21 AM
4
04
21
AM
PDT}

This is only mysterious if you're starting from the Platonic nonsense that mathematics exists outside the human mind. If you start from reality, complex numbers are just a highly useful notation. It's like asking if plural endings on nouns exist. Suffixes and Inflections are not an intrinsic part of the universe, but they're a highly useful way of symbolizing a type of numerical relationship.polistra_{March 7, 2021
March
03
Mar
7
07
2021
12:58 AM
12
12
58
AM
PDT}

In electrical engineering, for example, complex numbers are used in dealing with with vector rotation and phase relationships. There is absolutely nothing mysterious about them at all.Concealed Citizen_{March 6, 2021
March
03
Mar
6
06
2021
11:36 PM
11
11
36
PM
PDT}

I didn't think this post made sense. Then I looked at the paper and see that she says, " it’s only if a mathematical structure is actually necessary to describe observations that we can say they “exist” in a scientifically meaningful way." That is certainly different than what the question of whether complex numbers exist usually means. I wonder if what she says is a widely accepted use of "“exist” in a scientifically meaningful way," or whether this is an idiosyncratic meaning of her own.Viola Lee_{March 6, 2021
March
03
Mar
6
06
2021
08:22 PM
8
08
22
PM
PDT}

Prev 1 2 3

You must be logged in to post a comment.

Leave a Reply