Heat Dissipation Is the Main Constraint in Interstellar Travel

Writing truly hard science fiction, such as Will of the Stars means contending with the laws of physics as they actually are, rather than as we would like them to be. In particular, I am going to assume that the speed of light is a real constraint and that the various tropes about FTL (wormholes, warp drives, and so on) are not feasible. Given this assumption, some futurists have modeled the speed of interstellar expansion as approaching the speed of light. The idea is that sufficiently advanced technology, intelligence, and engineering could eventually allow humanity, or another species, to colonize worlds almost as quickly as light can travel between them. However, if we look at the laws of physics as well as the economic and physical incentives that govern expansion across the stars, there are many constraints on interstellar travel that appear long before we reach the speed of light. Why is this important? Correctly estimating the speed at which a high-tech civilization can spread across the stars changes our perspective on the Fermi paradox. If we don’t see other civilizations because they are confined to individual star systems, or because they expand at only a small fraction of the speed of light, then interstellar expansion itself may be a very difficult but ultimately conquerable “Late Filter.” It also changes how we should search for alien civilizations and what kinds of technological signatures we should expect them to produce. Understanding the physical constraints on interstellar travel, colonization, and expansion also changes our perspective on what our own civilization could look like in an optimistic future. Given how much visions of the future inform the present, it is worth making those visions more physically precise. There are three broad ways of accelerating a spacecraft through interstellar space: pushing off against an external megastructure, using light or beams of particles from a large source, and carrying reaction mass in a rocket. It is worth distinguishing between two types of interstellar travel: travel between two already established star systems, and travel from an established system to a completely new one. In both cases, a spacecraft needs to accelerate to its cruising velocity and then decelerate at the destination. But unless the destination already has infrastructure capable of braking the spacecraft, such as a laser sail or a magnetic megastructure, the final deceleration has to be performed by the spacecraft itself. This makes the use of rockets inevitable for the sake of expansion from one previously settled system into a new one. Relativistic Rockets At relativistic velocities of either the rocket or the exhaust velocities, we need to use the relativistic rocket equation. For a rocket with initial rest mass m_0, final rest mass m_1, and exhaust velocity v_e, it is: mjx-container[jax="CHTML"] { line-height: 0; } mjx-container [space="1"] { margin-left: .111em; } mjx-container [space="2"] { margin-left: .167em; } mjx-container [space="3"] { margin-left: .222em; } mjx-container [space="4"] { margin-left: .278em; } mjx-container [space="5"] { margin-left: .333em; } mjx-container [rspace="1"] { margin-right: .111em; } mjx-container [rspace="2"] { margin-right: .167em; } mjx-container [rspace="3"] { margin-right: .222em; } mjx-container [rspace="4"] { margin-right: .278em; } mjx-container [rspace="5"] { margin-right: .333em; } mjx-container [size="s"] { font-size: 70.7%; } mjx-container [size="ss"] { font-size: 50%; } mjx-container [size="Tn"] { font-size: 60%; } mjx-container [size="sm"] { font-size: 85%; } mjx-container [size="lg"] { font-size: 120%; } mjx-container [size="Lg"] { font-size: 144%; } mjx-container [size="LG"] { font-size: 173%; } mjx-container [size="hg"] { font-size: 207%; } mjx-container [size="HG"] { font-size: 249%; } mjx-container [width="full"] { width: 100%; } mjx-box { display: inline-block; } mjx-block { display: block; } mjx-itable { display: inline-table; } mjx-row { display: table-row; } mjx-row > * { display: table-cell; } mjx-mtext { display: inline-block; } mjx-mstyle { display: inline-block; } mjx-merror { display: inline-block; color: red; background-color: yellow; } mjx-mphantom { visibility: hidden; } _::-webkit-full-page-media, _:future, :root mjx-container { will-change: opacity; } mjx-math { display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0; } mjx-container[jax="CHTML"][display="true"] { display: block; text-align: center; margin: 1em 0; } mjx-container[jax="CHTML"][display="true"][width="full"] { display: flex; } mjx-container[jax="CHTML"][display="t