Importantly for quantum computing [1], software can use only the set Q, while the hardware can use the sets N or B for better results. Computers do not find imaginary numbers in the Boolean set of {0,1}; only 0 and 1, and yet can calculate a reactive current! Imaginary numbers have no physical meaning [2], so we can discard "non-abelian anyons" in attempts for quantum computing.
The numbers to use in all sciences must be based on Boolean numbers (set B), natural numbers (set N), integer numbers (set Z), and rational numbers (set Q). Other sets can be added, for human benefit, such as set Q*, but are not needed by computers -- that use only set B.
There is no reason to use the set ℂ in mathematics, physics, or engineering, because there is no physical meaning [2] -- and hides physical meaning.
One can totally avoid using the set ℂ and can calculate, numerically and in algebra, all that one needs [2]. We, thus, proved a negative -- the set ℂ is not needed in mathematics, physics, or engineering [2].
We just have to enlarge our view of the set Q, with a possible rotation included (i.e., not added) for each number, and resulting expressions using arithmetic. This new set, to be published elsewhere, is still called by the same letter Q in the set Q*, but the letter now stands for "Quantum".
We have a new terminology in the 21st century. Are we aware of more dimensions? We propose at least 6 dimensions.
Nature seems holographic, providing the connectedness of disjoint regularities -- i.e., connecting Number Theory In "pure" mathematics with quantum physics, continued fraction with the Schrödinger equation for bound states in quantum computing [1].
Regularities such as amplitude and phase can be taken naturally into account together, not just amplitude. The well-known double-slit experiment], the laser effect on targets, and holograms, e.g., depend on this (in publication).
In addition, as in the FFT and now in the FT, one does not need to calculate trigonometric functions (in publication).
Then, using the cartesian construction, the new set Q* applies to higher-dimensional spaces nD, where n is in N, such as 4D and spacetime.
In a next publication, we will show that the reality we live in is described by at least 6 dimensions, including the Euler-Lagrange equation and the Calabi-Yau manifold, but also using the set Q*. This proposal also includes SR and QM. A preview is available in [3].
As a consequence, reality becomes quantum ontically, as evidenced by the new set Q* using amplitude and phase as part of a number to describe the dimension nD, where n>=6.
What is your qualified opinion?
REFERENCES
[1] https://www.researchgate.net/publication/370063125/
[2] https://www.researchgate.net/publication/370755777/
[3] https://www.researchgate.net/publication/333677283/
We all know about phase space already. (and live in only 3D), cant understand any more of those remarks.
Many people may have a misconception that we live in a 3D world, but that is not actually correct.
We live in a 4D world, 3 spatial dimension and 1 Time dimension. However, we travel 3 dimensionally.
Let's say I have to meet my friend, so for that I need to mention him two things - Where and When both, absence of any one of these would result in the failure of our meeting.
Where - is the 3 coordinates, 3 dimensions.
When - is the 4th coordinate, time.
Me and my friend could be at same location but at a different time, or we could be at same time but different locations.
To help people who can't understand those remarks. Please read on.
First, abandon the set C. Computers do not find imaginary numbers in the Boolean set of {0,1}; only 0 and 1, and yet can calculate a reactive current! Imaginary numbers have no physical meaning [2], so we can discard "non-abelian anyons" in attempts for quantum computing.
HRHAD:
You wrote: "it is not clear how this number was determined or what empirical evidence supports it. Therefore, it is premature to conclude definitively that we live in at least 6 dimensions based on the available."
But the question cites 3 references and discusses! The first comment also says:
According to ref.[3],
"The state of a system of n particles is then represented, statically, by a point in 6n-dimensional space."
It is all given there, what is the question?
In describing the reality we live in as at least 6D, we open new vistas, e.g., to the spacetime -- no longer as an approximation, but as what we can calculate, and how to do it using the well-known Euler-Lagrange equations. In Einstein's words:
". . . creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up."
As Heisenberg wrote:
"What we observe is not nature itself, but nature exposed to our method of questioning ." We cannot observe neither mathematically nor physically any dimensions more than 3, neither numerically nor algebraically. But now can take into account position and momentum for 3 directions in space -- and that includes time ... and spacetime.
In describing the reality we live in as at least 6D, we break the mold of only reaching to 4D. One needs 6D to represent changes in time and space. One can even make a theory how to travel in time, which our consciousness can do -- and explains how to defeat grief, PTSDs, and normal aging. We can use the "pharmacy of the mind" studied by Ellen Langer of Harvard.
- Badges
- Science method