Causality and the Arrow of Time in the Branch-Cut Cosmology

Jan 27, 2020
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Having just read and enjoyed the 'Quantum time flip' makes light move simultaneously forward and backward in time, article here by Ben Turner, let me offer the following paper on 'Causality and the Arrow of Time in the Branch-Cut Cosmology', which was released yesterday.

By Benno Bodmann1 | César A. Zen Vasconcellos*2,3 | José de Freitas Pacheco4 | Peter O. Hess5,6 | Dimiter Hadjimichef2

1Universidade Federal de Santa Maria (UFSM), Santa Maria, Brazil
2Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil
3International Center for Relativistic Astrophysics Network (ICRANet), Pescara, Italy
4 Observatoire de la Côte d’Azur, Nice, France
5Universidad Nacional Autónoma de Mexico (UNAM), México City, México
6Frankfurt Institute for Advanced Studies (FIAS), Hessen, Germany
Correspondence
*César A. Zen Vasconcellos. Email: cesarzen@cesarzen.com

We basis our initial analysis of the arrow of time on a relationship between the time evolution operator of quantum system and the time-independent density operator which describes the equilibrium state of a many-particle system at temperature 𝑇 . We highlight through this analysis the identifica- tion of the imaginary temporal component of the branch-cut complex cosmic form factor with the direction in which the time-parameter flows globally, or the arrow of time. As a novelty, in this work we calculate the number of branches in the branch-cut universe to achieve causality involving the global time of evolution of the universe and the local time of travel of the light around each Hubble horizon. The preliminary result obtained is comparable to 60 e-folds of contraction in the FLRW cosmic scale factor 𝑎(𝑡) to overcome causality achieved in the bouncing model.

INTRODUCTION
The arrow of time problem, the unidirectional flow of time embodied in the second law of thermodynamics, represents one of the main fundamental problems of physics, since the macroscopic time-asymmetry emerges from a symmetrical-time micro-physics (Eddington, 1928; Ellis, 2013).

The meaning of time and the direction and passage of time, is a mystery that has challenged our understand- ing and imagination since the dawn of our civilization, which become strikingly illustrated in a thought of St. Augustine of Hippo, a known philosopher and theolo- gian: “If nobody asks me, I know what time is, but if I am asked then I am at a loss what to say”. In a brief synthesis on the philosophical journey of human- ity regarding the meaning of time, Parmenides denied
time’s existence, Plato imagined a world of ideas out- side it and Hegel spoke of the moment in the spirit transcends temporality (Reichenbach, 1999).

Albert Einstein, presumably inspired by Parmenides1 , 2 , by conceiving the ‘Einstein Uni- verse’ (Einstein, 1917), paved his view about the universe, a four-dimensional space-time ball with fixed radius, in which time has no beginning, being infinite in both directions, an universe that has always existed and will always exist, known nowadays as the ‘Block Universe’ (BU).

In Einstein’s conception, the universe was assumed to be a continuous, immutable, four-dimensional space- time block that contains all moments of time, without attributing to them any special particularity, in which the past, the present and the future are equivalent and indistinguishable attributes. In this sense, there is no ‘now’ that can be uniquely called the present, no flow of time and not even evolution of space-time. This rep- resentation implicitly embodies the idea that time is just an illusion (Barbour, 2000), emphasized once by Albert Einstein that the true reality is timeless3

In contrast to the BU view, George Ellis (2013, 2014) advocates that the true nature of spacetime is best represented as an Emergent Block Universe (EBU). The main feature of the EBU is an indefinite spacetime, “which grows and incorporates ever more events, ‘concreting’ as time evolves along each world line, with quantum uncertainty continually changing to classical definiteness”. In this view, the present represents a boundary that separates the past, which once existed, from the future and is indeterminate because of quantum uncertainties and the arrow of time is distinguished from the direction of time, which is non-locally defined in the evolving block universe concept.

Abstract
We basis our initial analysis of the arrow of time on a relationship between the time evolution operator of quantum system and the time-independent density operator which describes the equilibrium state of a many-particle system at temperature 𝑇 . We highlight through this analysis the identifica- tion of the imaginary temporal component of the branch-cut complex cosmic form factor with the direction in which the time-parameter flows globally, or the arrow of time. As a novelty, in this work we calculate the number of branches in the branch-cut universe to achieve causality involving the global time of evolution of the universe and the local time of travel of the light around each Hubble horizon. The preliminary result obtained is comparable to 60 e-folds of contraction in the FLRW cosmic scale factor 𝑎(𝑡) to overcome causality achieved in the bouncing model.

THE ARROW OF TIME IN BRANCH-CUT COSMOLOGY
The arrow of time, a term coined by Arthur Stan- ley Eddington (1928) and identified as the macroscopic unidirectional flow of time, is one of the most enig- matic features of the evolutionary universe, challenging our understanding about. Encapsulated in the second law of thermodynamics5 , the asymmetrical thermody- namic macroscopic arrow of time emerges from a micro- physics symmetrical in time. This is the crucial aspect where the difficulty of understanding its origin resides.

KEYWORDS:
Arrow of time; Causality; Bekenstein criterion; Branch-cut cosmology
time’s existence, Plato imagined a world of ideas out- side it and Hegel spoke of the moment in the spirit transcends temporality (Reichenbach, 1999).

Albert Einstein, presumably inspired by Parmenides1 , 2 , by conceiving the ‘Einstein Uni verse’ (Einstein, 1917), paved his view about the universe, a four-dimensional space-time ball with fixed radius, in which time has no beginning, being infinite in both directions, an universe that has always existed and will always exist, known nowadays as the ‘Block Universe’ (BU).

See: https://arxiv.org/pdf/2212.02670.pdf

This study, dated December 6, 2022, offers the latest ideas on the arrow of time and the quantum forces underlying it.

Throughout human history, in the writings of essayists, philosophers, or scientists, there is a recurring question about their ideas and conceptions about time, the flow of time and even, in a more philosophical sense, about eternity. In this particular, the word ‘mystery’ as a qualifier of a difficulty inherent to the elucidation of this recurring theme is perpetuated over time. Branch-cut cosmology, in turn, lacks, despite some sketches made in the past, a formulation that addresses another mystery, a quantum mechanical approach required for physics at the Planck Scale, in which spacetime geometry is a quantum variable, through generalizations of usual quantum theory that incorporates spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time (see Hartle, 1995).

Hartle's work. 'Quantum Mechanics at the Planck Scale' may be viewed at: arXiv:gr-qc/9508023
Hartmann352
 
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