Assuming faster-than-light (FTL) communication is possible via Bohm’s Quantum Potential, you’re entering a
non-local hidden variable interpretation of quantum mechanics. In that framework—Bohmian Mechanics—the
quantum potential acts instantaneously across spatial distances, coordinating entangled particles.

In such a universe, if FTL influence via the quantum potential exists, Lorentz invariance is broken or modified,
and a preferred foliation of spacetime (absolute simultaneity) must be assumed. Given that, we can explore what
symmetries might still be applicable to entangled states:

1. Permutation Symmetry of Entangled States

• Entangled states of identical particles are symmetric (bosons) or antisymmetric (fermions) under exchange.
• This symmetry is preserved even across large spatial separations.

Example:

|Ψ⟩ = (1/√2)(|↑⟩ₐ |↓⟩ᵦ − |↓⟩ₐ |↑⟩ᵦ)

2. Gauge Symmetry

• The global phase invariance of quantum states (a U(1) symmetry) still holds.
• The Bohmian wavefunction evolves under Schrödinger dynamics and remains gauge invariant.

3. Non-Relativistic Galilean Symmetry

• Bohmian mechanics typically violates Lorentz symmetry, but preserves Galilean invariance in the non-relativistic limit.
• The quantum potential is invariant under Galilean transformations.

4. Time-Reversal Symmetry

• Bohmian trajectories are deterministic and time-reversible.
• The Schrödinger equation is time-reversal symmetric (modulo complex conjugation), and so is Bohmian evolution.

5. Configuration Space Symmetry

• In Bohmian mechanics, the wave function lives in configuration space, not 3D physical space.
• Entangled states are non-factorizable and inherently nonlocal in this space.

Caveat: Breaking Lorentz Symmetry

• Allowing FTL interaction via the quantum potential violates Lorentz symmetry, unless a preferred reference frame is introduced.
• Spatial rotation symmetry (SO(3)) may be preserved, but boost symmetry is broken.

Summary Table

Symmetry	Preserved?	Notes
Permutation (Exchange)		Important for identical entangled particles
Gauge (U(1))		Global phase invariance
Galilean		Non-relativistic limit; Bohmian-compatible
Lorentz		Violated by non-local influences
Time-Reversal		Bohmian mechanics is deterministic and reversible
Configuration Space Symmetry		Fundamental in Bohmian interpretation

In Conclusion

If FTL communication via Bohm’s quantum potential exists, the entangled states still obey permutation, gauge, time-reversal, and
configuration-space symmetries, but Lorentz invariance must be relinquished. In its place, a hidden preferred frame
or foliation of spacetime is assumed. The overall coherence of entangled states is preserved through the nonlocal structure of the
wavefunction in configuration space, guided by a universal quantum potential.

The post Symmetries in Entangled States appeared first on Time Travel, Quantum Entanglement and Quantum Computing.