A Categorical View on the Principle of Relativity

Gaio, L. M.; Rizzuti, B. F.

doi:10.48550/arxiv.2205.15408

Cited by 1 publication

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References 14 publications

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“…where − → v , − → x represents the scalar product in R 3 . The transformation has linearity [52]. Then, the Lorentz category is defined as the category whose objects are inertial frames of reference and morphism are Lorentz transformations [52].…”

Section: Lorentz Transformationmentioning

confidence: 99%

General Formulation of Topos Many-Node Theory

Simchi¹

2023

New Frontiers in Physical Science Research Vol. 9

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Among the various existing theories, we show how the concept of the space-time network has entered the physics of quantum gravity by reviewing the theories of loop quantum gravity and causal sets. Assuming that the first creatures of creation create a network, it is shown that how the network can be mapped to a topos discrete quantum manifold which is equipped with both the discrete calculus and the Alexandrov's algebra. We assign a locale to each nodes of the space-time network and show that in general, invariance under Lorentz transformations is no longer true. it is shown that the cosmological constant is non-zero and is proportional to the second power of the Hubble radius. By considering a population (set), including newly born timid children and non-timid children who survive until the birth of the new network, it is shown that the entropy of the space-time network is quantized and increases as the network grows. In consequence the inflation of the world is expected phenomenon. Also, we show that how world inflation can be described based on the concept of truth object and truth value belong to the topos theory. Although, the temperature and pressure are both high in the early moments of the creation of the world, it is shown that the quanta of vibrations, called netons, can be attributed to the vibration of space-time network, and it is expected that they will be observed in the future experiments related to cosmic background radiation. Finally, it is shown that the root of noncommutative geometry Topos Many-Node Theory: Roots, Foundations and Predictions 2 is in attributing the locale to the nodes of the space-time network instead of a point. This theory, which is quantum-relativistic from the beginning, has not the problem of a point particle, the concept of probability is an emergent concept, it does not include the problem of the measurement theory, it is not a universal Lorentz invariant, its cosmological constant is non-zero and is proportional to the second power of the Hubble radius, it describes the inflation of the universe and it has a non-commutative geometry, is called the many-node theory.

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Section: Lorentz Transformationmentioning

confidence: 99%

General Formulation of Topos Many-Node Theory

Simchi¹

2023

New Frontiers in Physical Science Research Vol. 9

View full text Add to dashboard Cite

show abstract

A Categorical View on the Principle of Relativity

Cited by 1 publication

References 14 publications

General Formulation of Topos Many-Node Theory

General Formulation of Topos Many-Node Theory

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