Redshifted civilizations, galactic empires, and the Fermi paradox

Abstract

Given the vast distances between stars in the Milky way and the long timescales required for interstellar travel, we consider how a civilization might overcome the constraints arising from finite lifespans and the speed of light without invoking exotic or novel physics. We consider several scenarios in which a civilization can migrate to a time-dilated frame within the scope of classical general relativity and without incurring a biologically intolerable level of acceleration. Remarkably, the power requirements are lower than one might expect; biologically tolerable orbits near the photon radius of Sgr A* can be maintained by a civilization well below the Type II threshold, and a single Type II civilization can establish a galaxy-spanning civilization with a time dilation factor of $10^4$, enabling trips spanning the diameter of the Milky way within a human lifetime in the civilizational reference frame. We also find that isotropic monochromatic signals from orbits near the photon radius of a black hole exhibit a downward frequency drift. The vulnerability of ultrarelativistic vessels to destruction, combined with the relatively short timescales on which adversarial civilizations can arise, provides a strong motivating element for the ``dark forest'' hypothesis.

Figures (7)

• Figure 1: Spacetime diagram illustrating the so called "twin paradox" in one spatial dimension and in units where $c=1$, so that light travels on $45^\circ$ lines. The numbers indicate the elapsed proper time along each trajectory, and the dots indicate clock ticks for the identical clocks carried by each twin.
• Figure 2: Time dilation factor $\Gamma$ for an unstable circular orbit (near the photon radius) versus mass for a tidal acceleration $a_\mathrm{tidal}=1~\mathrm{m/s}^2$ across a distance of $\chi\sim2~\mathrm{m}$.
• Figure 3: Frequency ratio $\nu_\mathrm{o}/\nu_\mathrm{s}$ versus angular position of a distant observer $\phi_\mathrm{o}$, given a source in a circular orbit with time dilation factor $\Gamma=10^4$ with $l>0$ emitting a signal isotropically with frequency $\nu_\mathrm{o}$. Since $l>0$, the source moves in the positive $\phi$ direction. As the source moves, the curve shifts to the right; an observer at a fixed angular position will see $\nu_\mathrm{o}/\nu_\mathrm{s}$ decrease as the source continues to move in the positive $\phi$ direction.
• Figure 4: An illustration of a civilization based around a network of linear paths and nodes. Vessels accelerate and decelerate along each path, such that multiple vessels simultaneously arrive at each node when the civilizational frame coincides with that of the Milky way.
• Figure 5: Plots of distance and proper time required to accelerate a vessel to a peak time dilation factor $\gamma_\mathrm{p}$, assuming a uniform proper acceleration of $10~\mathrm{m/s}^2$. The top subplot corresponds to Eq. \ref{['Eq:PropTravelTime']} and the bottom corresponds to Eq. \ref{['Eq:DistanceTraveled']}.