TheDark Energy and Entropy Paradox in Relativistic Frames of reference.pdf

Relativistic length contraction leads to a puzzling consequence when applied to the Large Hadron Collider (LHC). From the proton’s rest frame, the ring circumference contracts from 26.7 km to only a few meters, implying a drastic reduction in enclosed volume, vacuum energy, and holographic entropy. If interpreted literally, this suggests an observer-dependent loss of energy and information, apparently violating conservation principles. In this paper, we propose a resolution based on a staggered quantized spacetime framework. Each relativistic observer is embedded in a distinct but adjacent layer of a higher-dimensional grid, preserving global conservation laws while permitting observer-dependent geometries. In this view, contraction does not erase energy or entropy but redistributes their encoding across the grid. This construction synthesizes special relativity, Planck-scale quantization, holographic entropy bounds, and entanglement-based emergent spacetime. By embedding relativistic frames in staggered layers of an entangled grid, we reconcile Lorentz invariance with information conservation and provide a new conceptual tool for exploring the emergence of spacetime.

1. The Dark Energy and Entropy Paradox in
Relativistic Frames
Author: Eran Sinbar
Affiliation: Independent Researcher, Misgav, Israel
Date: September 27, 2025
ORCID number: 0000-0003-4803-0498
Abstract
Relativistic length contraction leads to a puzzling consequence when applied to the Large
Hadron Collider (LHC). From the proton’s rest frame, the ring circumference contracts from
26.7 km to only a few meters, implying a drastic reduction in enclosed volume, vacuum
energy, and holographic entropy. If interpreted literally, this suggests an observer-
dependent loss of energy and information, apparently violating conservation principles. In
this paper, we propose a resolution based on a staggered quantized spacetime framework.
Each relativistic observer is embedded in a distinct but adjacent layer of a higher-
dimensional grid, preserving global conservation laws while permitting observer-
dependent geometries. In this view, contraction does not erase energy or entropy but
redistributes their encoding across the grid. This construction synthesizes special relativity,
Planck-scale quantization, holographic entropy bounds, and entanglement-based emergent
spacetime. By embedding relativistic frames in staggered layers of an entangled grid, we
reconcile Lorentz invariance with information conservation and provide a new conceptual
tool for exploring the emergence of spacetime.
1. Introduction
The unification of relativity, quantum theory, and information remains one of the central
challenges of modern physics. Special relativity ensures consistency of physical laws across
inertial frames, yet it was formulated without reference to quantum entanglement, Planck-
scale discreteness, or the holographic principle. Conversely, quantum gravity programs
such as the AdS/CFT correspondence suggest that spacetime geometry itself emerge from
entanglement. Reconciling these perspectives requires reexamining how relativistic
observers encode energy and information.

A concrete paradox arises in the context of the Large Hadron Collider (LHC). A proton
accelerated to 6.5 TeV experiences a Lorentz factor of nearly γ ≈ 7000. From the proton’s
perspective, the L= 26.7 km ring contracts to only L’~3.85 m. The corresponding volume
and surface area contract by the same factor, implying a proportional reduction in both
vacuum energy E = ρΛV and holographic entropy S = A / l
p
2
. If taken literally, this suggests
that the proton inhabits a world with vastly less dark energy and entropy than the

2. laboratory frame, contradicting the principle that conservation laws and entropy bounds
should be held in every inertial frame.

We argue that this apparent loss signals a deeper structural issue. Standard relativity
explains contraction geometrically, but it does not address how vacuum energy or entropy
bounds transform between frames. To resolve this, we introduce a staggered quantized
spacetime framework, in which each observer inhabits a distinct geometric layer of a
higher-dimensional grid. These staggered layers preserve internal consistency within each
frame while ensuring global conservation across the grid. In this picture, contraction is not a
physical loss but a re-localization of information between layers.
2. Relativistic Contraction and the Paradox
According to special relativity, the contracted length L′ is given by:
L′ = L / γ
where γ = 1 / √(1 − v²/c²). For a 6.5 TeV proton, γ ≈ 6929.5, leading to L′ ≈ 3.85 m. The
volume and surface area enclosing the LHC ring also contract accordingly. If the proton’s
frame truly contained less dark energy and entropy, this would violate conservation laws.
3. Energy and Entropy Conservation
In the laboratory frame, the vacuum energy is:
E (Lab) = ρΛ × V (Lab)
S (Lab) = A (Lab) / ??????
??????
??????

From the proton’s frame:
E (Proton) = ρΛ × V (Proton) = E (Lab) / γ
S (Proton) = S (Lab) / γ
This apparent reduction suggests missing energy and entropy. However, physical laws
require conservation across all frames.

3. 4. Staggered Quantized Spacetime Framework
We propose that each observer resides within a locally quantized three-dimensional world
matrix, which defines their unique frame of reference. These matrices—such as the "Geneva
LHC world" or the "proton world"—are adjacent yet distinct, and are embedded within a
broader, non-local and non-quantized three-dimensional structure known as the grid
dimension, or simply the grid. The grid acts as a connective substrate, enabling the non-
local correlations observed in quantum mechanics—such as quantum entanglement,
quantum tunneling, and the Feynman path integral—while linking otherwise isolated world
matrices without direct interaction. In this framework, phenomena like contraction are not
interpreted as losses, but rather as relocalizations of energy and entropy within each
matrix. Despite local variations, the global system remains conserved, with the grid
ensuring coherence across the staggered layers of quantized spacetime.
5. Mathematical Formulation
Let W_L and W_P denote the Geneva and proton worlds. Each has its own metric ??????
µν:
E (Lab) = ρΛ × V (Lab), S (Lab) = A (Lab) / ??????
??????
??????

E (Proton) = ρΛ × V (Proton) = E (Lab) / γ, S (Proton) = S (Lab) / γ
Global conservation across the grid requires:
E(total) = E (Lab) + E (Proton) + E (grid)
S(total) = S (Lab) + S (Proton) + S (grid)
6. Interpretation and Implications
This framework reframes relativistic contraction not as a physical loss but as a
redistribution of information. Each observer’s world remains consistent internally, while
the grid ensures global conservation. The model provides a possible bridge between
relativity, holography, and entanglement-based emergent spacetime.
7. Conclusion
The apparent loss of dark energy and entropy in relativistic frames challenges the
consistency of physical law. By embedding observers in staggered quantized spacetime
layers, global conservation is preserved while allowing observer-dependent geometries.
This model may offer a new perspective on the emergence of spacetime.
8. Numerical Calculations
8.1 Dark Energy Content
Lab Frame (Geneva): V ≈ 267,000 m³ → E ≈ 0.0001845 J

4. Proton Frame: V ≈ 38.53 m³ → E ≈ 2.66 × 10⁻⁸ J
8.2 Entropy Bound (Holographic Principle)
Lab Frame (Geneva): A ≈ 84,432.81 m² → S ≈ 3.23 × 10⁷⁴
Proton Frame: A ≈ 12.18 m² → S ≈ 4.66 × 10⁷⁰
Appendix: Notation Glossary
W_L: Laboratory frame ( LHC)
W_P: Proton frame
V: Enclosed volume
A: Surface area of the accelerator ring
ρΛ: Vacuum energy density
l
p
2
: Planck length
γ: Lorentz factor
E, S: Energy and entropy in each frame

2.1 Why Special Relativity Alone Cannot Resolve the Paradox
Special relativity guarantees the invariance of local physical laws across inertial frames.
However, this invariance applies to local conservation of energy-momentum, not to global
assignments of vacuum energy or entropy. In the standard formalism, different observers
may define hypersurfaces of simultaneity differently, leading to distinct notions of spatial
volume and enclosed energy. From the laboratory frame, the LHC ring encloses a volume of
V^(L) ≈ 2.67 × 10^5 m³, while in the proton’s frame this reduces to V^(P) ≈ 38.5 m³.
Multiplying by the Lorentz-invariant vacuum energy density ρΛ yields observer-dependent
total energies.

One might argue that this discrepancy is a trivial artifact of frame dependence. However,
when vacuum energy is linked to a cosmological constant, and entropy is constrained by
holographic bounds, these quantities are not arbitrary bookkeeping devices but
fundamental invariants of spacetime structure. In particular:
1. Vacuum energy: A cosmological constant acts as a Lorentz-invariant source in Einstein’s
equations. Its value cannot fluctuate between observers without breaking general
covariance [Weinberg 1989].
2. Entropy bounds: The Bekenstein-Hawking area law and its covariant generalization
[Bekenstein 1973; Bousso 1999] imply that entropy is tied to geometric surfaces in a way
that should not depend on observer slicing.
3. Quantum entanglement entropy: Modern results show that entanglement entropy across
causal horizons is observer-dependent (e.g. the Unruh effect [Unruh 1976]), but the global
entanglement structure remains invariant.

Thus, special relativity alone offers no mechanism to ensure simultaneous validity of

5. energy-momentum conservation and entropy bounds across all inertial frames. The
paradox at the LHC highlights this gap: if a relativistic observer can contract spacetime and
thereby reduce the total encoded vacuum energy and entropy, then global conservation
principles are violated.

This motivates the introduction of an additional structure — here modeled as a staggered
quantized spacetime grid — which preserves global conservation by embedding observer-
dependent worlds within a higher-dimensional entangled framework.
This approach resonates with the holographic paradigm introduced by Maldacena
[Maldacena 1998], in which spacetime geometry is dual to boundary entanglement
structure, and with the ER=EPR conjecture of Maldacena and Susskind [Maldacena &
Susskind 2013], suggesting that spacetime connectivity itself arises from quantum
entanglement.

References
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