Momentum-space entanglement between low-energy states and higher dimensional Kaluza, Klein levels within five-dimensional systems has been quantified; this enables detailed description of system states beyond what’s possible using standard four-dimensional theories. The calculations reveal that while local effective theories accurately predict low-energy behaviour, they fail to fully capture the complete quantum state due to connections, entanglement, with these additional dimensions. Quantum connection exists between low-energy particles and higher dimensional states within five-dimensional systems; even when simplifying theories to fewer dimensions, information about those extra ones isn’t lost but remains encoded as entanglement.
Current methods accurately predict behaviour at lower energies, yet don’t fully describe the complete quantum state because of these connections. This suggests our understanding of complexity arising from simpler systems requires further refinement. Standard methods accurately predict behaviour at lower energies; however, these fail to fully describe the complete quantum state due to connections with additional dimensions.
Zero mode entanglement reveals corrections to low energy limits via compactification radius
Entanglement measures now reveal a factor of (μR)2/1024π^3 differentiates mutual information between zero modes and Kaluza-Klein levels from corrections observed at low energies, with μ representing resolution scale, and R denoting the compactification radius. Previously inaccessible detail is now available thanks to this finding; local four-dimensional theories alone could not achieve it. While effective theories accurately describe observable phenomena, they do not fully capture the complete quantum state due to entanglement with higher dimensional states, a connection that persists even when supersymmetry cancels vacuum energy.
Calculations demonstrate subtle differences in how dimensionality impacts quantum correlations by revealing momentum space correlation between lower and higher energy particles within five-dimensional systems. Mutual information between zero modes and individual Kaluza-Klein levels decreases proportionally to one divided by level mass, holding true even with interactions present.
This relationship features a coefficient of (μR)2/1024π^3 for cubic theories dependent on both resolution scale μ and extra dimension size R. However, additional quantum effects related to high energy states obscure this signal in quartic theories involving four interacting particles; these calculations reveal entanglement persists despite supersymmetry cancelling vacuum energy due to non-local correlations not captured by standard four-dimensional physics.
Dimensional reduction preserves entanglement revealing persistent extradimensional effects
Calculations illuminate how information about extra dimensions subtly persists as entanglement when simplifying to fewer dimensions, something previously hidden from standard techniques. Despite limitations stemming from initial approximations used for calculating interdimensional interactions, the work establishes a key principle: that information regarding hidden dimensions isn’t simply lost during model simplification. Extending these computations demands significant computational resources and may uncover modifications or corrections to their findings. The research shows even reducing dimensionality, a common technique for manageable calculations, doesn’t erase information about those hidden dimensions entirely; instead it lingers as subtle connections between observable and unobservable components, meaning standard four-dimensional theories describe what we observe but not the complete underlying state of the system.
This research demonstrated that entanglement persists between zero modes and higher dimensional Kaluza-Klein levels in five-dimensional scalar systems undergoing reduction to four dimensions. Mutual information between these states decreases with level mass, a relationship quantified by (μR)2/1024π3 in cubic theories where μ is resolution scale and R is compactification radius, but can be obscured by additional quantum effects in quartic interactions.
This finding indicates that simplifying physics to fewer dimensions, while common practice, does not fully eliminate information about those extra dimensions; instead it manifests as non-local correlations beyond what standard four-dimensional effective theory captures. The authors plan to extend these calculations with greater computational resources.
👉 More information
🗞 Momentum-space entanglement and mutual information in Kaluza-Klein reduction
✍️ Udaykrishna Thattarampilly and Yunlong Zheng (Yangzhou University)
🧠 ArXiv: https://arxiv.org/abs/2610.37009
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