Time Dilation: Slower Knots in Crowded Vacuum
In LIMA-QTE, “proper time” is measured by the internal ticking of knots — the rate at which electromagnetic energy circulates inside every electron, proton, or atom via the Poynting vector.
When many knots are packed together (strong gravity) or moving fast relative to the vacuum, the saturation term makes the effective vacuum stiffness increase. A stiffer vacuum resists the internal circulation of energy inside each knot — exactly like trying to stir thick honey instead of water.
This slows the internal circulation frequency → every physical clock (atomic transitions, particle decays, biological processes) runs slower by the same factor.
The proper time rate for a knot in a region with local vacuum energy density $\rho$ is reduced by the saturation factor:
\[ \frac{d\tau}{dt} = \sqrt{1 + \lambda_2 \rho} \;^{-1/2} \]In the weak-field, low-velocity limit this becomes the standard GR factor:
\[ \frac{d\tau}{dt} = \sqrt{1 - \frac{2GM}{rc^2}} \]For special-relativistic motion at velocity $v$:
\[ \frac{d\tau}{dt} = \sqrt{1 - v^2/c^2} \]both derived from the same vacuum stiffness felt by the knot’s internal circulation.
In one sentence:
Time dilation is not spacetime curving — it is real, physical knots of light having their internal clocks slowed by swimming through a stiffer vacuum when many other knots are nearby or when moving fast.
GPS satellites, muon lifetime extension, the Hafele–Keating experiment, gravitational redshift — all are direct consequences of the same saturation term that prevents black-hole singularities and gave us $\alpha$.
There is no abstract “block universe”. There are only little spinning smoke rings of light, and when they have to push through crowded or fast-moving vacuum, their internal clocks naturally tick slower — exactly as observed.