Parallel Universes in Non-Equilibrium Dynamics: Negative Initial Velocity, Past Contraction, and the Coexistence of Expanding and Contracting Solutions
Abstract
We show that the exact solution of Non-Equilibrium Dynamics (NED),
2R
3 − 3ℓpR
2 = 3Kt2 + 12ℓ
2
p
v0 t + 4ℓ
3
p
,
admits two branches for any radius R:
t±(R) =
−2ℓ
2
p
v0 ±
√
4ℓ
4
p
v
2
0 −
Kc
3
K
,
where c = 4ℓ
3
p − 2R3 + 3ℓpR2
. For v0 < 0, one branch describes an expanding universe (t+)
and the other a contracting universe (t−). Both branches originate from the same initial
condition R = 2ℓp, R˙ = v0 < 0. We propose the following hypothesis:
Parallel Universe Hypothesis. The expanding and contracting branches are
two parallel universes that coexist, sharing the same initial condition v0 < 0.
The negative initial velocity v0 < 0 implies that the universe was contracting in the
past. We identify v0 as the contraction velocity near R = 2ℓp. The two branches are dual
to each other: t+ increases with R (expansion), while t− decreases with R (contraction).
The return to R = 2ℓp occurs at t = 0 and t = −4ℓ
2
p
v0/K. We present the hypothesis, its
physical interpretation, and its observational consequences.
Related
- Anisotropic speed discrimination sensitivity for expanding and contracting optic flow
- The Breathing Twin Universes (Interconnected Expansion-Contraction and the Single Knock as Inter-Universal Contact).
- Cyclic Cosmic Expansion in Non-Equilibrium Dynamics: Identification of the Initial Velocity v0 as the Contraction Velocity near R = 2ℓp, Past Contraction, Future Turning Points, Cosmic Age, and Repeated Cycles
- Cyclic Cosmic Expansion in Non-Equilibrium Dynamics: Identification of the Initial Velocity v0 as the Contraction Velocity near R = 2ℓp, Turning Points, Return to R = 2ℓp, Cosmic Age, and Repeated Cycles
- Non-equilibrium thermodynamics of an expanding Swiss-Cheese braneworld cosmology with a matter bounce
BibTeX
@misc{ueda2026parallel,
title = {{Parallel Universes in Non-Equilibrium Dynamics: Negative Initial Velocity, Past Contraction, and the Coexistence of Expanding and Contracting Solutions}},
author = {takashi ueda},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23478386},
url = {https://zenodo.org/records/23478386},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Parallel Universes in Non-Equilibrium Dynamics: Negative Initial Velocity, Past Contraction, and the Coexistence of Expanding and Contracting Solutions
AU - takashi ueda
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23478386
UR - https://zenodo.org/records/23478386
AB - We show that the exact solution of Non-Equilibrium Dynamics (NED), 2R 3 − 3ℓpR 2 = 3Kt2 + 12ℓ 2 p v0 t + 4ℓ 3 p , admits two branches for any radius R: t±(R) = −2ℓ 2 p v0 ± √ 4ℓ 4 p v 2 0 − Kc 3 K , where c = 4ℓ 3 p − 2R3 + 3ℓpR2 . For v0 < 0, one branch describes an expanding universe (t+) and the other a contracting universe (t−). Both branches originate from the same initial condition R = 2ℓp, R˙ = v0 < 0. We propose the following hypothesis: Parallel Universe Hypothesis. The expanding and contracting branches are two parallel universes that coexist, sharing the same initial condition v0 < 0. The negative initial velocity v0 < 0 implies that the universe was contracting in the past. We identify v0 as the contraction velocity near R = 2ℓp. The two branches are dual to each other: t+ increases with R (expansion), while t− decreases with R (contraction). The return to R = 2ℓp occurs at t = 0 and t = −4ℓ 2 p v0/K. We present the hypothesis, its physical interpretation, and its observational consequences.
ER -