Relativistic spacetime crystals.

Area of Science:

• Physics
• Crystallography
• Spacetime Geometry

Background:

• Periodic space crystals are established; time crystals are a recent exploration.
• Relativistic spacetime crystals require accounting for space-time mixing via Lorentz transformations, previously limited to 2D.
• Conventional Minkowski spacetime (MS) describes relativistic physics.

Purpose of the Study:

• To introduce and describe renormalized blended spacetime (RBS) as an equivalent, reformulated description of relativistic physics in flat spacetime.
• To demonstrate the transformation from MS to RBS, revealing new symmetries.
• To enumerate RBS point and space groups and their mapping to conventional space crystal groups.

Main Methods:

• Reformulation of Minkowski spacetime (MS) through observer clock blending and coordinate renormalization.
• Transformation of Lorentz boosts into Euclidean rotations.
• Identification of RBS point groups and their relation to space crystal groups.

Main Results:

• A novel equivalent description of relativistic physics in flat spacetime termed renormalized blended spacetime (RBS) is established.
• The transformation process converts spacetime hyperbolas to Euclidean circles, enabling Euclidean constructions.
• RBS point groups for flat isotropic RBS spacetime are identified as cylinder groups (mm2 in 2D, (∞/m)m in 3D, hypercylinder in 4D).
• An antisymmetry operation is introduced, leading to color spacetime groups and revealing hidden RBS symmetries.

Conclusions:

• Renormalized blended spacetime (RBS) provides an alternative and insightful framework for understanding relativistic physics.
• The RBS formalism uncovers symmetries not easily apparent in the conventional Minkowski spacetime (MS).
• The study offers a new perspective on spacetime structure and symmetry in physics.