Universal Critical Mass for Quantum Collapse ($M_c$): A Cosmological Limit to Unitarity

Douglas H. M. Fulber FEDERAL UNIVERSITY RIO DE JANEIRO • January 2026 DOI: 10.5281/zenodo.MC_MODEL_2026 (Proposal Ver. 1.1)

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Abstract We propose the existence of a fundamental mass scale, $M_c \approx 5.3 \times 10^{-16}$ kg, where quantum unitarity is spontaneously violated due to interaction with the cosmological acceleration horizon. Derived from a geometric constraint on the 8-dimensional phase space, $M_c = m_P (a_0/a_P)^{1/8}$, this hypothesis predicts that spatial superpositions of masses $M > M_c$ decay into statistical mixtures within a finite intrinsic time. This provides a clear, falsifiable target for next-generation levitated optomechanics experiments.

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1. Operational Definition

Standard Quantum Mechanics assumes that the coherence of a superposition can be maintained indefinitely if the system is perfectly isolated. We challenge this axiom by introducing an intrinsic decoherence scale linked to the information capacity of the universe.

We propose a critical mass $M_c$ such that for $M > M_c$, the intrinsic coherence time is finite:

$$ \tau_{intr}(M) < \infty \quad \text{for} \quad M > M_c $$

2. Theoretical Motivation: 8D Phase Space Geometry

Why the specific exponent $1/8$? This is not a random dimensional fit, but a consequence of the full covariant phase space geometry.

The quantum state of a relativistic particle lives in an 8-dimensional Phase Space Bundle $\mathcal{M}8$ consisting of 4 spacetime coordinates ($x^\mu$) and 4 momentum coordinates ($p\mu$):

$$ \dim(\mathcal{M}_8) = \dim(x^\mu) + \dim(p_\mu) = 4 + 4 = 8 $$

In the Entropic Gravity framework, the cosmological horizon $a_0$ imposes a fundamental information density limit. The resolution of a quantum state is bounded by the smallest resolvable hyper-volume element. The scaling relation arises from projecting this 8-dimensional constraint onto the 1-dimensional mass parameter.

Thus, the critical mass $M_c$ relates to the Planck mass $m_P$ via the 8-th root of the scale hierarchy:

$$ \frac{M_c}{m_P} \sim \left( \frac{a_0}{a_P} \right)^{1/8} $$

This implies that quantum coherence is a volume-preserving symmetry in $\mathcal{M}_8$ that breaks when the phase space volume of the superposition exceeds the holographic entropy bound determined by $a_0$.

3. The Number ($M_c$)

Using the derived relation:

$$ M_c = m_P \cdot \left( \frac{a_0}{a_P} \right)^{1/8} $$

With:

• $m_P \approx 2.17 \times 10^{-8}$ kg
• $a_0 \approx 6.8 \times 10^{-10}$ m/s$^2$ ($c H_0$)
• $a_P \approx 5.56 \times 10^{51}$ m/s$^2$

We calculate:

$$ \boxed{ M_c \approx 5.3 \times 10^{-16} \text{ kg} } $$

In atomic mass units: $3.2 \times 10^{11}$ amu. This places the transition zone squarely between current macromolecule interferometry ($10^4$ amu) and microscopic dust.

4. Direct Prediction ("The Guillotine")

The theory predicts a saturation in interference visibility scaling with mass. The total decoherence rate is:

$$ \Gamma_{total} = \Gamma_{env} + \Gamma_{intr}(M) $$

The experimental signature is a plateau in $\Gamma_{total}$ for $M &gt; M_c$ that does not decrease with vacuum or temperature improvements.

5. Experimental Scenario

We recommend testing this hypothesis using:

• Levitated Optomechanics: Silica nanospheres (radius 100-500 nm) cooled to the ground state.
• MAQRO Mission: Space-based interferometry for high-mass nanoparticles.

6. Falsifiability Criteria

The theory is falsified if stable quantum interference (visibility > 50%) is observed for a mass $M \geq 10^{-14}$ kg maintained for $t &gt; 1$ second.

7. Conclusion

We present a precise, zero-parameter prediction for the breakdown of quantum unitarity. The value $5.3 \times 10^{-16}$ kg serves as a definitive test for next-generation quantum experiments.