Casimir Correlated Patterns as Probes of Emergent Spacetime.pdf

The black hole information paradox has led to the development of the holographic principle, which posits that all information within a volume of space is encoded on its boundary. This paper proposes a novel extension: that the scrambled holographic information on a boundary influences quantum vacuum fluctuations within the enclosed region. Specifically, we hypothesize that the popping in and out of existence of virtual particles encodes this boundary information in a scrambled form. We propose a testable prediction involving a kilometer-scale vector of Casimir plates placed at the CERN Large Hadron Collider (LHC), where a gradient in what we term the Casimir correlated pattern is expected due to varying information density. Crucially, we suggest that these correlated fluctuations may not merely reflect the structure of spacetime but could constitute its very emergence—offering a mechanism by which space, time, and even gravity arise from the statistical behavior of vacuum fluctuations modulated by holographic information. This framework offers a new perspective on the interplay between quantum information, spacetime geometry, and vacuum dynamics.

1. Holographic Modulation of Vacuum
Fluctuations: Casimir Correlated
Patterns as Probes of Emergent
Spacetime
Author: Eran Sinbar
Affiliation: Independent Researcher, Misgav, Israel
Email: [email protected]
ORCID: 0000-0003-4803-0498

Abstract
The black hole information paradox has led to the development of the holographic principle,
which posits that all information within a volume of space is encoded on its boundary. This
paper proposes a novel extension: that the scrambled holographic information on a
boundary influences quantum vacuum fluctuations within the enclosed region. Specifically,
we hypothesize that the popping in and out of existence of virtual particles encodes this
boundary information in a scrambled form. We propose a testable prediction involving a
kilometer-scale vector of Casimir plates placed at the CERN Large Hadron Collider (LHC),
where a gradient in what we term the Casimir correlated pattern is expected due to varying
information density. Crucially, we suggest that these correlated fluctuations may not merely
reflect the structure of spacetime but could constitute its very emergence—offering a
mechanism by which space, time, and even gravity arise from the statistical behavior of
vacuum fluctuations modulated by holographic information. This framework offers a new
perspective on the interplay between quantum information, spacetime geometry, and
vacuum dynamics.
1. Introduction
The black hole information paradox, first articulated by Hawking, challenges the
reconciliation of quantum mechanics with general relativity. Hawking radiation appears
thermal and devoid of information, suggesting a violation of unitarity. In response, the
holographic principle emerged, asserting that the information content of a volume is
encoded on its boundary, not in the bulk. This paper proposes that the vacuum fluctuations
within a region—manifested as virtual particles—are influenced by the scrambled
holographic information on the boundary. This leads to a new interpretation of vacuum
dynamics as an information-encoding process, observable through what we define as
Casimir correlated patterns.

2. 2. Background
2.1 The Black Hole Information Paradox
Hawking’s semiclassical analysis of black holes predicts thermal radiation, implying
information loss. However, developments such as the Page curve and quantum extremal
surfaces suggest that information is preserved.
2.2 The Holographic Principle
The AdS/CFT correspondence provides a concrete realization of the holographic principle,
where a gravitational theory in a bulk AdS space is dual to a conformal field theory on its
boundary.
2.3 Vacuum Fluctuations and the Casimir Effect
Quantum field theory predicts that the vacuum is filled with transient virtual particles. The
Casimir effect, a measurable phenomenon between closely spaced plates, arises from
modifications to vacuum energy due to boundary conditions. We reinterpret this effect not
merely as a force but as a Casimir correlated pattern—a spatially structured modulation of
vacuum fluctuations influenced by boundary-encoded information.
3. Refined Hypothesis: Holographic Modulation of Vacuum Fluctuations
We propose that the quantum vacuum is not a uniform stochastic background but a
dynamic medium modulated by the holographic information encoded on the boundary of a
region. In this framework:
- The scrambled information on the boundary—arising from black hole thermodynamics
and holographic entropy bounds—acts as a statistical source influencing the behavior of
virtual particles.
- These fluctuations are not random but statistically biased by the boundary’s information
content, similar to how thermal fluctuations are shaped by temperature gradients.
This hypothesis builds on the idea that entanglement entropy and boundary conditions in
quantum field theory can influence local observables, suggesting that virtual particle
dynamics may carry imprints of holographic data. We define the Casimir correlated pattern
as the spatially varying statistical signature of vacuum fluctuations between Casimir plates,
modulated by the density and structure of boundary-encoded information.
Mathematically, this could be modeled by introducing a boundary-dependent term in the
vacuum expectation value of the energy-momentum tensor, possibly linked to the
entanglement entropy across the boundary surface.

3. 4. Experimental Proposal: Casimir Correlated Pattern Gradient as a Probe
of Holographic Influence
4.1 Setup
We propose a linear array of Casimir plates, each nanometer scale in size, extending over
several kilometers. This array would be placed at the CERN Large Hadron Collider (LHC):
- Near end: Positioned as close as safely possible to the collision point, where particle
interactions generate high entropy and dense holographic information.
- Far end: Located kilometers away, in a region of low informational activity.
- Orientation: The Casimir plates are aligned perpendicular to the local gravitational vector
to minimize gravitational noise and mechanical deformation, ensuring that any measured
pattern gradient is attributable to informational effects rather than gravitational artifacts.
Figure 1: Experimental Prediction
A schematic of the proposed kilometer-scale vector of Casimir plates at CERN. The plates
are aligned from the high-information collision point to a distant low-information region.
The term 'Casimir correlated pattern' is annotated to indicate both the expected spatial
gradient and temporal modulation along the vector, correlated with the frequency and
entropy of particle collisions.

4. 4.2 Prediction
The Casimir correlated pattern is expected to exhibit a measurable gradient along the
vector, decreasing with distance from the collision point due to the reduced influence of
boundary-encoded information. This gradient would be detectable using high-precision
force sensors or fluctuation correlation analysis.
4.3 Theoretical Basis
The Casimir effect is sensitive to the local vacuum energy density, which in turn depends on
boundary conditions. If the holographic principle holds, then regions with higher
informational density (e.g., near collisions) should exhibit enhanced vacuum modulation,
leading to a more pronounced Casimir correlated pattern.
We model the pattern intensity as:
P(d) = P₀ / d²
where:
- P₀ is the pattern intensity near the collision,
- d is the distance from the collision point.
This inverse-square model reflects the geometric spreading of holographic information over
a spherical boundary surface.
4.4 Correlation with Collision Frequency and Entropy Flux
We further propose that the Casimir correlated pattern is dynamically responsive to the
collision frequency and entropy flux at the LHC. In this view:
- High-frequency collisions near the interaction point generate a dense flux of quantum
information, increasing the local holographic entropy density.
- This elevated information density modulates the vacuum fluctuations more strongly,
leading to a higher amplitude or complexity in the Casimir correlated pattern.
- As the collision frequency varies (e.g., during different operational phases of the LHC), the
pattern should exhibit temporal correlations with these changes.
This suggests a dual gradient:
- A spatial gradient in the pattern intensity as a function of distance from the collision point.
- A temporal modulation of the pattern correlated with the real-time collision rate.
By synchronizing the measurement of the Casimir correlated pattern with the collision log
data from the LHC, one could test for statistical correlations between:
- The pattern amplitude or structure on the plates.
- The collision frequency, energy, and entropy production rates.
This would provide a time-resolved probe of how quantum information flux influences
vacuum structure.
5. Implications
- Quantum Gravity: Suggests a deeper link between spacetime geometry and quantum field
behavior.
- Information Theory: Positions vacuum fluctuations as a medium for information encoding.

5. - Experimental Physics: Offers a new method to probe the holographic nature of spacetime
through measurable patterns in vacuum dynamics.
6. Conclusion
This paper proposes that the vacuum is not merely a passive stage but an active participant
in the encoding of holographic information. The predicted Casimir correlated pattern
gradient, both spatial and temporal, offers a testable signature of this hypothesis,
potentially bridging the gap between quantum information theory and observable quantum
field dynamics.
Appendix A: Rationale for Inverse-Square Modeling of Casimir Correlated
Pattern Gradient
The inverse-square model for the Casimir correlated pattern gradient is motivated by
fundamental principles of geometric spreading in three-dimensional space. In classical
physics, several forces and field intensities—such as gravitational force, electric field
strength, and radiative flux—obey an inverse-square law. This behavior arises because the
surface area of a sphere increases with the square of the radius, given by A = 4πr². As a
result, any conserved quantity emitted from a point source becomes diluted over a growing
spherical surface.
In the context of this paper, the collision point at the CERN LHC is treated as a source of high
entropy and holographic information. This information is encoded on a spherical boundary
surrounding the source. As the distance from the source increases, the density of boundary-
encoded information decreases proportionally to 1/d², where d is the radial distance.
If vacuum fluctuations are modulated by this holographic information density, then the
Casimir correlated pattern—sensitive to local vacuum energy—should also exhibit a spatial
gradient that follows an inverse-square law:
P(d) = P₀ / d²
Here, P₀ is the pattern intensity near the collision point, and d is the distance from that
point. This model reflects the geometric attenuation of holographic influence and aligns
with well-established physical laws.

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