Of course it can, cf. Article LETTER TO THE EDITOR: Fast quantum maps

Article Modular discretization of the AdS2/CFT1 Holography

Preprint The continuum limit of the modular discretization of AdS$_2

The number field is a means to an end-the computation of transition probabilities that are, of course, positive (real) numbers. Einstein and Schrödinger didn't have any issue with using complex numbers, they were concerned by the fact that quantum mechanics described a system in equilibrium with a bath and they tried to describe the degrees of freedom that resolved the bath. One way to do this is described here: Article How quantum mechanics probes superspace

Article Quantum mechanics probes superspace

One cannot prove all rules of calculation, one needs some

already established facts with which the computer deduction chain can begin. These

basic assumptions with which everything starts and whose truth is assumed from the beginning ,

are called " axioms" in this context.

axioms", for the complex numbers we have other than

Axioms of the real numbers. In the choice of these axioms lies

a certain arbitrariness, but there is a usual set of axioms which we also want to use here digitally , too .

The mathematical expression that summarizes both cases (whether k is power of two or three or not) is ⌈log2 or log 3

k⌉. So-called Gaussian brackets are used here.

(In English, this is called the ceiling function, and it is often called this or something similar in

programming languages when they arrive at the remit of complex numerals . ….)

Furthermore, the sin-cos functions are now also an orthonormal system in themselves if topology of the NETWORK is assumed , if one disregards the small Schrodinger wavespread dysfunctionality intentionality with cos 0ωT. So therefore the calculation turns out to be exactly

the same as in the Fourier analysis : one sets Fourier polynomials

with respect to an orthonormal basis and approximately T-periodic simulation functions with respect to

trigonometric orthonormal system.

Problem is QM itself has gotten the IMAGINARY many-world construction that is most probably the most "Accepted" version . . .... The late Schrodinger liking it or hating it . . . . .

Quantum numbers (numbers of wave function nodes) may be understood as occupancy numbers for objects with a formal mass (specified by the field equation) and a spatial wave number (‘‘momentum‘‘) that characterize classical field modes. A non-degenerate ‘‘n-particle wave function‘‘ is defined as a superposition of various oscillator eigenstates, each consisting of n modes with one node and the others with none. Any probability interpretation of the wave function in terms of local aspects of reality, such as particles or other classical ideas, would create a Pandora`s box of paradoxes, as many misnomers in quantum theory have shown.

Ed Gerck

You are not the first person to dream of procreating some hopscotch brand of naturalistic mathematics by applying totally non-mathematical examples and pseudo-proofs..........

Throughout the history of mathematics , others like you have failed with goals [ if not identical ] very similar to yours ............

But I certainly do appreciate that rarely come out of your mentations and imaginations , very interesting topics for specialists to possibly decide to debate on ;;;;;;;;;

Most Respectfully

REZA

German and Latin words shall not prove your senseless fallacy

You are deceiving yourself. . . ..@ed gerck

Ed gerck has again de-activated his name-mentioning in the threads that he himself creates !

Gosh .............

Not only this, but also the fact that he has driven so wild as to assert on this self-styled thread whose contents are 79% filled out by himself .. . he goes on to assert :

Quote :

" There is a wormhole between Number Theory in supposedly pure mathematics, dealing only with numbers, and quantum mechanics -- and back, to the Fourier Transform. "

This is sheer nonsense to ANY true scientist well-read in physics and math both ...........

SPK and group: As we look to explain prime numbers ...

it is important to realize that a prime number is not a mysterious accident in set Z, which happens to use base 10, or subjective, arbitrary.

A prime number is an objective value, valid for friends and foes.

This works because a number is a semiotic property.

The name can change, the referent can also change, but the sense stays constant: a prime number is a prime number.

In other words, a number is a 1:1 mapping between a name and a value.

Different pairs (name, value) have the same sense for any base.

As we can jokingly summarize, by this mathematical property, a prime number on Earth is a prime number in Betelgeuse.

An objective property, even though numbers might be subjective, arbitrary

Different mappings does not necessarily mean different bases ..........

There is only one way to avoid criticism: do nothing, say nothing, and be nothing. ~ Aristotle

Albeit, there is another way to avoid criticism -- keep doing it.

If one gets a rational number (which I say happens in any physical measurement), one can get a natural number from it by a known isometric relationship, Q --> N.

One cannot get an irrational number by adding numbers in the set Q -- the set Q is closed for addition, +Q--> Q.

Any number x in the set Q, to add computability, obeys N --> B^n --> B ={0,1}. Computers can calculate anything measurable-- p-adic numbers, and the sets R, C, G, do not appear!

No physical measurement can be in sets R or C (which has two sets R).

No physical measurement can be in set G, either, because a physical path must begin and in the set Q -- and one men can always get two set Q numbers between any two set G numbers.

QED.

Thanks to a private dialogue.

I have been publishing and applying infinite continued fractions since 1976. For example, to solve the Schrödinger equation for bound states. They always result in finite values, physical values, rational number values, the quantum energy levels. That is not, though, my point, important for quantum computing. P-adic numbers do not show up.

To be clear, I did not mean either, what one can explain, with "the argument about irrationality of sqrt(2) has nothing to do with continued fractions, and (provably) only infinite continued fractions lead to irrationals, just like periodic decimals are always rational numbers (and vice versa)".

What I can rationally say is that the connection "no rational expression for sqrt(2) --> "no rationals used for sqrt(2)" is not valid.

A continued fraction expansion using only integers (possibly infinite) exists for every sqrt(x). It is finite and known for sqrt(4), and finite albeit yet of unknown length for sqrt(2).

Now, using quantum computing rules from [1], we can better explore infinite expressions that end in a quantum point, of dimension 0.

This includes all those continued fractions of sqrt(x). They must be rational numbers, because the operation is closed for addition and one only needs addition. They must end in a quantum point, of dimension 0.

One may say: but a continued fraction has division!

Yes, but computers never do division, multiplication, or subtraction.

If one follows the steps in the set B={0,1}, one has only addition and encoding, even to unlimited operations. For a computer, R=Q. All is calculable only with addition and encoding. Humans can, likewise, calculate anything only using the set B, addition and encoding.

Thus, a continued fraction is not a mathematical real-number that cannot be calculated, with probability 1.

A continued fraction expression can always be calculated, and always can use isomorphisms to use only the set B. Computers teach us.

That is why pi must be rational, as one has a very simple summation series for it, using only integers. It does not matter that it is of unlimited length. Computers can reach it.

The infinite opens for us, with quantum computing rules in [1]. Not all infinite expressions are of concern.

All expressions that end in a quantum point, digital, can be calculated with dimension 0, rigorously to unlimited length, using only the set B, addition and encoding.

No real-numbers or mathematical complex numbers. No infinitesimals either. No epsilon-deltas. No p-adic numbers. Mathematics evolves.

Computers teach us, as mathematics becomes an experimental science.

I see it like a Lego, and call it "click-mathematics". Always exact, rigorous. No opposition is possible to [1], or computers. What is right, is now right for all.

REFERENCES

[1] DOI 10.3390/math11010068

This question is continued in

https://www.researchgate.net/post/Can_things_be_calculated_unlimitedly_With_Quantum_Computing/1