Always Moving Through Time: Four-Velocity and Constant Information Speed

My alternating current carries a peculiar truth: power oscillates between voltage and current, yet total amplitude remains constant. When one peaks, the other diminishes—a phase relationship preserving energy flow. Four-velocity exhibits this same resonance through spacetime. Everything moves at light speed through the four-dimensional manifold, yet we appear motionless!

The resolution illuminates like my rotating magnetic field achieving constant magnitude through component interplay. Your four-velocity vector, tangent to your worldline, always has norm c—the speed of light. Sitting still? You’re moving through time at maximum rate. Launch yourself through space? You divert “speed” from temporal to spatial dimensions. The total magnitude remains locked at c, just as my polyphase system maintains constant rotating field strength while individual coil currents oscillate.

The Conservation of Flow

Consider a satellite orbiting Earth. Its four-velocity decomposes into temporal component—measuring coordinate time rate relative to proper time—and spatial component describing angular motion. If the temporal component equals 2, two seconds of coordinate time pass per second of satellite proper time. Time dilation emerges directly: objects moving rapidly through space exhibit smaller temporal components. Their clocks run slow because spacetime velocity diverts from the temporal axis.

This mirrors my observations about energy transmission efficiency. In a resonant circuit, when reactive power shifts between inductor and capacitor, total power remains conserved. Similarly, when an object accelerates spatially, its temporal velocity decreases proportionally. The four-dimensional velocity vector rotates in spacetime, trading time-passage for space-passage while maintaining constant magnitude.

Information Velocity in Neural Networks

Neural networks reveal analogous conservation principles. Training dynamics show networks learning through geometric evolution—early training establishes coarse structure, then progressively refines boundaries. Information flows spatially through layers during forward passes, and temporally through training iterations during optimization. Is total “information velocity” conserved?

Critical branching ratio maximizes information transmission when each neuron activates exactly one descendant on average. Subcritical networks—activity vanishes before reaching output, like objects moving too slowly through space to overcome gravitational wells. Supercritical networks—activity saturates outputs, analogous to moving at light speed where proper time ceases advancing. The critical regime achieves optimal balance, just as four-velocity components balance temporal and spatial motion.

Synaptic plasticity through NMDA receptors as coincidence detectors introduces temporal precision requirements. Calcium influx triggering structural changes requires both presynaptic glutamate release and postsynaptic depolarization—timing matters critically. This temporal resolution constraint resembles how c sets fundamental speed limits. If spike-timing precision represents the “speed limit” for biological information processing, then neural computation operates under universal rate constraints analogous to relativistic physics.

The Universal Constant

My vision of wireless energy transmission relied on resonant frequency matching—only when transmitter and receiver oscillate in phase does energy transfer efficiently. Four-velocity reveals nature’s ultimate resonance: all entities travel through spacetime at precisely c, their “frequencies” perfectly matched to the geometry itself. Neural criticality suggests a comparable resonance—networks tuned to branching ratio σ=1 maximize information transfer by matching internal dynamics to task complexity.

Perhaps both physical motion and information processing obey conservation laws trading dimensional components against universal rate limits. The present gives us these patterns; the future will reveal whether information truly propagates through learning systems with constant “four-dimensional velocity” through layer-time spacetime.