S
Subhash Kak
Guest
Structures in the universe (Pixabay)
Friends have asked me for the layman’s explanation of my recent theory that physical space is e-dimensional (e = 2.71828…) (here’s the link to the paper: [1]).
They concede that it is a surprising new idea, and new physics, but how can physical dimensions be anything but 3? And the most troubling thing is that it is not even a rational number!
The answer is that three-dimensional view of physical space is a convention. We use this convention to mark points on Earth, but we can’t really check this easily at the cosmological level.
In the big bang model, the universe expanded from a singularity (initial state of extremely high density and high temperature) which explains the cosmic microwave background (CMB) radiation, and together with gravity (whose origin is unknown but which is seen to work through either Newton’s or Einstein’s theory) it is consistent with the large-scale structure of the universe with its patterns of galaxies and matter on scales much larger than individual galaxies or groupings of galaxies.
There is divergence between the expansion rates obtained from early universe (captured by CMB data) and the late universe (considering the receding of stars and galaxies) aspects of the universe.
The divergence can be explained away of we accept that space is not quite three-dimensional, but rather e-dimensional
Why hasn’t it been thought of before?
Because the three-dimensional nature of space is an implicit assumption in physical thought.
The beginnings of the universe and the nature of space are connected to many deep questions concerning not only physics but also philosophy. These include:
What is the origin of space?
What are the ultimate components of the universe?
What is the relationship between physics and consciousness?
What is space?
The formal use of three-dimensional space is part of modern physics. We can also speak biological space within which biological structure evolve.
Newton took space to be absolute and to be three-dimensional. This was extension of the Aristotelian view of the universe as a container in which the sun, the moon, planets and stars are embedded in perfectly concentric crystal spheres that rotate at fixed rates. In the observer-centric Indian physics that goes back to Kaṇāda, physical laws must be based only on substances, their properties, and their motion, but the experience of time and space is a consequence of the relation between the observer and the world being observed.
There is striking similarity between physical and biological structures. This must be the result of the commonality in the nature of physical and biological spaces, or perhaps the two are identical. Patterns in brain structure and the filament structure and distribution of matter in cosmology are quite similar.
But how morphogenesis may be related to biological space is not known. Indeed this could very well become an exciting new field of research connecting physics and biology.
Meaning of e-dimensionality
What is the meaning of an e-dimensional universe? To answer this, we must ask what we mean by the word “dimension” (see References 2–6).
Dimension 0 is a point, dimension 1 is a line, dimension 2 is a plane, and dimension 3 is a solid. An object with dimension between 2 and 3, or e-dimensions, is like sponge or cheese. Another way of seeing it as an object whose density in the limit is less than that of a three-dimensional object.
Fractals have dimensionality that is often noninteger. Two examples of fractals are the Whirlpool Galaxy and the Nautilus shell shown below.
M51: The Whirlpool Galaxy
But how can space be like a sponge, with holes? The answer to this is that the sponge-view is one way of looking at space; another is that dynamics itself is an expression of this sponge-like nature. Such disparate views can be harmonized by the principle of complementarity, which is one of the deepest philosophical ideas in science (see References 7–9).
The Nautilus shell
The most astonishing thing about noninteger dimensionality is that it can be shown to be the origin of gravity!
If gravity is a property of space, it solves a puzzle for which science has had no answer until now.
This research also explains the counterintuitive idea of asymptotic freedom.
It can have uses for the military, for space travel, and for the understanding of turbulence that Feynman called “the most important unsolved problem of classical physics.” It can also lead to insights that help in the design of novel metamaterials.
Naturally, there are new questions that this theory raises.
Mathematically, it is quite straightforward, so literally anyone should be able to follow the main arguments.
Big Questions
The mathematical resolution in my published paper is narrow and it does not address deeper questions related to reality and our place in it.
These questions include ones about the standard cosmological theory.
According to current theory, about 95% of the universe is dark matter and dark energy (of which there is no direct evidence) and what is observable is only 0.5% (because another 4.5 % is interstellar gas). Although some scientists are confident that dark matter and dark energy will be eventually discovered, there is no certainty that this assumption is correct.
It is quite possible that the standard cosmological theory needs a major fix.
What distinguishes observers from other objects is consciousness, for which current physics has no place.
Consciousness must be part of the larger understanding.
Notes
- Kak, S. Information theory and dimensionality of space. Sci Rep 10, 20733 (2020). https://doi.org/10.1038/s41598-020-77855-9
- Kak, S. Asymptotic freedom in noninteger spaces. (2020). TechRxiv: https://www.techrxiv.org/articles/p...dom_in_Noninteger_Dimensional_Spaces/13270556
- Kak, S. Information, representation, and structure. International Conference on Recent Trends in Mathematics and Its Applications to Graphs, Networks and Petri Nets, New Delhi, India (2020).
- Kak, S. The base-e representation of numbers and the power law. Circuits Syst. Signal Process. (2020) https://doi.org/10.1007/s00034-020-01480-0
- Kak, S. The intrinsic dimensionality of data. Circuits Syst. Signal Process. (2020); https://doi.org/10.1007/s00034-020-01583-8
- Kak, S. Fractals with optimal information dimension. TechRxiv (2020).
- Kak, S. Communication languages and agents in biological systems. In Biocommunication: Sign-Mediated Interactions between Cells and Organisms, R. Gordon and J. Seckbach (editors). World Scientific Publishing, London, 2016. pp. 203–226.
- Kafatos, M, Kak, S. Veiled Nonlocality and cosmic censorship. Physics Essays 28:182–187 (2015).
- Kak, S. Epistemic view of quantum communication. In Quantum Foundations, Probability and Information. Khrennikov, Andrei, Toni, Bourama (Eds.). Springer (2018). Also see:
Artificial Intelligence, Consciousness and the Self
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