One of the things the paper does is make the overall determination that power available >> power needed. So as part of assessing that, I identified all the components which contributed to each and examined how realistic/sensitive to assumptions they are.
To begin with, here are the factors from the paper which impact the energy required for colonizing the galaxy.
The mass of each payload / self-replicating probe to be sent.
Mass of the payload is a linear factor in the energy required.
The travel speed.
Well understood physics. It is non-linear factor in the energy required.
The efficiency of the fuel mass.
This is well understood physics. From ashallow investigation, this seems to be a highly sensitive point in the paper since 1) we have not yet constructed rockets/fuel source combinations with sufficient specific impulse values required by the paper, and 2) the specific impulse is part of an exponential factor in energy required.
The number of probes to be sent as function of number of destinations and probes sent per destination as redundancy against loss of probes due collision or other issues.
1. I outsourced checking the paper’s work to calculate the number of reachable stars at different speeds. Physics contacts reported that the calculations made in the paper all appeared correct.
2. I did not examine the redundancy requirements in depth since wasn’t easy to reconstruct how they derived the result, my intuition is this is not a crucial aspect of the paper, especially a lower speeds which are my main interest.
Launch system feasibility and efficiency.
Note that some of these variables directly the per-probe energy costs and others (specifically redundancy due to expected collisions and travel speed hence stars reachable) affect the total energy required.
In comments to this answer, I’ll examine each in further depth.
To travel between the stars it is necessary to be able to accelerate an interstellar probe to some very fast speed, let it travel through space (without friction, it will keep going due to energy), and then decelerate it once it arrives at the target destination. Space is insanely large and to get most places you really want to be traveling at a significant fraction of the speed of light; however, this requires enormous amounts of energy since by special relativity, the faster you are travelling, the more energy is required to accelerate further. This enforces the limit that you cannot go faster than the speed of light since this would require infinite energy.)
This formula is linear in mass (m) and considerably superlinear in velocity (v) approaching infinity as velocity approaches the speed of light (c).
The y-axis is incremented in units of 100 million gigajoules (=10^17 joules). Even accelerating a 1kg mass to 10% the speed of light requires 4.5*10^14 joules. 50% of c requires 1.4*10^16 joules.
For comparison, world energy consumption in 2013 was estimated by the International Energy Association to be 5.67x10^20 joules. In other words, accelerating a single 5 tonne probe to 10% c would require ~1% of Earth’s entire energy consumption. Accelerating to 80% could required 100% of 2013’s energy consumption. Now consider that to colonize the universe, we need to send upwards of 100 million (10^8) probes.
Since we need to both accelerate and decelerate a probe, this energy is required twice over. Doubling the mass of the probe doubles the energy required, but doubling the target speed multiplies the energy required many times over even at very small fractions of the speed of light.
Specific Impulse and the Fuel Component of the Probe’s Mass
Importantly, part of what we need accelerate is the fuel required to decelerate the probe once it arrives at its destination. The greater the fuel we send along with a probe, the greater the initial launch energy required. We want fuel which is highly efficient by its mass, i.e, it has high specific impulse.
The amount of fuel mass required to decelerate a probe is extremely sensitive to the specific impulse (Isp) of the fuel used. Oliver Habryka noticed that Eternity in Six Hours may be making unreasonable assumptions about achievable specific impulses attainable. Further investigation revealed that which specific impulses are attainable may determine whether or not space colonization is affordable at all. To me, it is a major sensitivity in the paper.
Transformed to isolate initial mass, the relativistic rocket equation gives:
m0: initial mass
m1: final mass
c: speed of light
Isp: specific impulse
Δv: change in velocity
This formula for the initial mass is linear in final mass and exponential in specific impulse. For a fixed mass of 1kg, the initial fuel mass required to accelerate to different fractions of the speed of light are shown by:
Isp can be measured in m/s; the x-axis gives Isp as a fraction of the speed of light. The dotted lines correspond to 4% of c (the Isp for fission given by the paper) and half that value, 2% of c.
On page 11, Armstrong and Sandberg provide the following values of specific impulse (measured as a fraction of c).
Of these, we have only actually attained nuclear fission, however not in efficient rocket form. As Habryka pointed out, the paper makes the assumption that almost all of the energy released by nuclear fission is converted into kinetic energy, however that this may be unrealistic.
Habryka identified a nuclear rocket concept which may be capable of achieving an Isp of 3%-5% the speed of light. Fission fragment rockets, while not yet built, uses only existing materials. Habryka, who’s physics are stronger than mine, believes the the rockets simple design and mechanism should be feasible.
I’ll reiterate the importance of specific impulse by pointing out that to accelerate a mass of 1k to 50% requires 1.02 x 10^3 tonnes of fuel with Isp of 4%c (value given for fission) and 1.04 x 10^9 tonnes of fuel at 2% of c, i.e. half the value. A mere halving of the specific impulse of the fuel results in an increase of six orders of magnitude in the fuel mass required.
To give a sense of where we are at, the Falcon Heavy rocket has an Isp of only 0.001% of C (3110 m/s). Proven and prototyped propulsion systems are in this range too. Ion thrusters, an existing technology, may be able to achieve up to 3% (100,000 m/s), however these required a both source of electricity as well as propellant, likely requiring a nuclear reactor and nuclear fuel.
It seems to me that only by making innovations somewhere with rocket technology (fission, fusion, antimatter) or with something more exotic (light sails, Bussard ramjets, etc.) that space colonization to distances much beyond our immediate neighbors could be possible. What we have now would not be enough apart from perhaps some experimental ion thrusters, but those require both a source of electricity, e.g. nuclear reactor, as well as a propellant.
The mass of replicator, specific impulse of the fuel, and travel speed determine the energy required to launch a single probe.
The number of probes to be sent is determined by the number of destinations and the redundancy factor in number of probes sent to ensure that one probe arrives at each destination. Due to collisions with interstellar dust or other failures, we can imagine that not every self-replicating probe will arrive at its destinations.
The number of destinations is limited by one’s travel speed since increasing large regions of space are moving beyond our reach due to expansion of the universe. The faster one travels, the more distant stars one is able to reach before they get too far away.
The authors of Eternity in Six Hours (pg. 21) ``calculated that:
Travelling at 50% c, one could reach 1.16 x 10^8 galaxies
Travelling at 80%c, one could reach 7.62 x 10^8 galaxies
Travelling at 90%c, one could reach 4.13 x 10^9 galaxies
For reference, an average galaxy might have 10^8 stars.
The authors calculated travelling at 99%c, a redundancy factor of 40 is required, i.e. 40 probes for every destination. For 80%c and 50%x, the redundancy is less than 2. I did not prioritize looking into this calculation and am trusting the result that at lower speeds, the redundancy factor required is not very high.
To save on the mass which has to be launched (which requires squaring the rocket equation), the authors of Eternity in Six Hours favor an external fixed launch system which accelerates the replicating probe including both probe and fuel for its later deceleration.
In the paper, the authors briefly list coilguns, quenchguns, laser propulsion, and particle beam propulsion as potential means of accelerating the probes. They state even though the theoretical energy efficiency of these systems could approach 100%, since one never obtains the theoretical efficiency, they assume 50% efficiency.
The question here:
Is it possible to build a launch system which launches (possibly quite large) probes to significant fractions of the speed of light?
Looking back at our paper, I think the weakest points are (1) we handwave the accelerator a bit too much (I now think laser launching is the way to go) . . .
My shallow impression is that the proposed launch systems might only represent large engineering challenges more than difficult physics/designs breakthroughs. Coilguns have been constructed and laser propulsion has been demonstrated in the lab. What remains is a question of scale and efficiency. However, even a difference between 5% efficiency and 50% efficiency is only a single order of magnitude. Not a large difference in the overall picture here.
One of the things the paper does is make the overall determination that power available >> power needed. So as part of assessing that, I identified all the components which contributed to each and examined how realistic/sensitive to assumptions they are.
To begin with, here are the factors from the paper which impact the energy required for colonizing the galaxy.
The mass of each payload / self-replicating probe to be sent.
Mass of the payload is a linear factor in the energy required.
The travel speed.
Well understood physics. It is non-linear factor in the energy required.
The efficiency of the fuel mass.
This is well understood physics. From a shallow investigation, this seems to be a highly sensitive point in the paper since 1) we have not yet constructed rockets/fuel source combinations with sufficient specific impulse values required by the paper, and 2) the specific impulse is part of an exponential factor in energy required.
The number of probes to be sent as function of number of destinations and probes sent per destination as redundancy against loss of probes due collision or other issues.
1. I outsourced checking the paper’s work to calculate the number of reachable stars at different speeds. Physics contacts reported that the calculations made in the paper all appeared correct.
2. I did not examine the redundancy requirements in depth since wasn’t easy to reconstruct how they derived the result, my intuition is this is not a crucial aspect of the paper, especially a lower speeds which are my main interest.
Launch system feasibility and efficiency.
Note that some of these variables directly the per-probe energy costs and others (specifically redundancy due to expected collisions and travel speed hence stars reachable) affect the total energy required.
In comments to this answer, I’ll examine each in further depth.
Energy Required to Accelerate Mass
To travel between the stars it is necessary to be able to accelerate an interstellar probe to some very fast speed, let it travel through space (without friction, it will keep going due to energy), and then decelerate it once it arrives at the target destination. Space is insanely large and to get most places you really want to be traveling at a significant fraction of the speed of light; however, this requires enormous amounts of energy since by special relativity, the faster you are travelling, the more energy is required to accelerate further. This enforces the limit that you cannot go faster than the speed of light since this would require infinite energy.)
The relativistic kinetic energy of a rigid body is given by:
This formula is linear in mass (m) and considerably superlinear in velocity (v) approaching infinity as velocity approaches the speed of light (c).
The y-axis is incremented in units of 100 million gigajoules (=10^17 joules). Even accelerating a 1kg mass to 10% the speed of light requires 4.5*10^14 joules. 50% of c requires 1.4*10^16 joules.
For comparison, world energy consumption in 2013 was estimated by the International Energy Association to be 5.67x10^20 joules. In other words, accelerating a single 5 tonne probe to 10% c would require ~1% of Earth’s entire energy consumption. Accelerating to 80% could required 100% of 2013’s energy consumption. Now consider that to colonize the universe, we need to send upwards of 100 million (10^8) probes.
Since we need to both accelerate and decelerate a probe, this energy is required twice over. Doubling the mass of the probe doubles the energy required, but doubling the target speed multiplies the energy required many times over even at very small fractions of the speed of light.
Specific Impulse and the Fuel Component of the Probe’s Mass
Importantly, part of what we need accelerate is the fuel required to decelerate the probe once it arrives at its destination. The greater the fuel we send along with a probe, the greater the initial launch energy required. We want fuel which is highly efficient by its mass, i.e, it has high specific impulse.
The amount of fuel mass required to decelerate a probe is extremely sensitive to the specific impulse (Isp) of the fuel used. Oliver Habryka noticed that Eternity in Six Hours may be making unreasonable assumptions about achievable specific impulses attainable. Further investigation revealed that which specific impulses are attainable may determine whether or not space colonization is affordable at all. To me, it is a major sensitivity in the paper.
Transformed to isolate initial mass, the relativistic rocket equation gives:
m0: initial mass
m1: final mass
c: speed of light
Isp: specific impulse
Δv: change in velocity
This formula for the initial mass is linear in final mass and exponential in specific impulse. For a fixed mass of 1kg, the initial fuel mass required to accelerate to different fractions of the speed of light are shown by:
Isp can be measured in m/s; the x-axis gives Isp as a fraction of the speed of light. The dotted lines correspond to 4% of c (the Isp for fission given by the paper) and half that value, 2% of c.
On page 11, Armstrong and Sandberg provide the following values of specific impulse (measured as a fraction of c).
Of these, we have only actually attained nuclear fission, however not in efficient rocket form. As Habryka pointed out, the paper makes the assumption that almost all of the energy released by nuclear fission is converted into kinetic energy, however that this may be unrealistic.
Habryka identified a nuclear rocket concept which may be capable of achieving an Isp of 3%-5% the speed of light. Fission fragment rockets, while not yet built, uses only existing materials. Habryka, who’s physics are stronger than mine, believes the the rockets simple design and mechanism should be feasible.
I’ll reiterate the importance of specific impulse by pointing out that to accelerate a mass of 1k to 50% requires 1.02 x 10^3 tonnes of fuel with Isp of 4%c (value given for fission) and 1.04 x 10^9 tonnes of fuel at 2% of c, i.e. half the value. A mere halving of the specific impulse of the fuel results in an increase of six orders of magnitude in the fuel mass required.
To give a sense of where we are at, the Falcon Heavy rocket has an Isp of only 0.001% of C (3110 m/s). Proven and prototyped propulsion systems are in this range too. Ion thrusters, an existing technology, may be able to achieve up to 3% (100,000 m/s), however these required a both source of electricity as well as propellant, likely requiring a nuclear reactor and nuclear fuel.
It seems to me that only by making innovations somewhere with rocket technology (fission, fusion, antimatter) or with something more exotic (light sails, Bussard ramjets, etc.) that space colonization to distances much beyond our immediate neighbors could be possible. What we have now would not be enough apart from perhaps some experimental ion thrusters, but those require both a source of electricity, e.g. nuclear reactor, as well as a propellant.
Number of Probes to be Sent
The mass of replicator, specific impulse of the fuel, and travel speed determine the energy required to launch a single probe.
The number of probes to be sent is determined by the number of destinations and the redundancy factor in number of probes sent to ensure that one probe arrives at each destination. Due to collisions with interstellar dust or other failures, we can imagine that not every self-replicating probe will arrive at its destinations.
The number of destinations is limited by one’s travel speed since increasing large regions of space are moving beyond our reach due to expansion of the universe. The faster one travels, the more distant stars one is able to reach before they get too far away.
The authors of Eternity in Six Hours (pg. 21) ``calculated that:
Travelling at 50% c, one could reach 1.16 x 10^8 galaxies
Travelling at 80%c, one could reach 7.62 x 10^8 galaxies
Travelling at 90%c, one could reach 4.13 x 10^9 galaxies
For reference, an average galaxy might have 10^8 stars.
The authors calculated travelling at 99%c, a redundancy factor of 40 is required, i.e. 40 probes for every destination. For 80%c and 50%x, the redundancy is less than 2. I did not prioritize looking into this calculation and am trusting the result that at lower speeds, the redundancy factor required is not very high.
Launch System Feasibility Efficiency
To save on the mass which has to be launched (which requires squaring the rocket equation), the authors of Eternity in Six Hours favor an external fixed launch system which accelerates the replicating probe including both probe and fuel for its later deceleration.
In the paper, the authors briefly list coilguns, quenchguns, laser propulsion, and particle beam propulsion as potential means of accelerating the probes. They state even though the theoretical energy efficiency of these systems could approach 100%, since one never obtains the theoretical efficiency, they assume 50% efficiency.
The question here:
Is it possible to build a launch system which launches (possibly quite large) probes to significant fractions of the speed of light?
What efficiency is realistically achievable?
When contacted for comment, one of the authors, Anders Sandberg, stated:
Looking back at our paper, I think the weakest points are (1) we handwave the accelerator a bit too much (I now think laser launching is the way to go) . . .
My shallow impression is that the proposed launch systems might only represent large engineering challenges more than difficult physics/designs breakthroughs. Coilguns have been constructed and laser propulsion has been demonstrated in the lab. What remains is a question of scale and efficiency. However, even a difference between 5% efficiency and 50% efficiency is only a single order of magnitude. Not a large difference in the overall picture here.