3 ms·

> but interstellar travel would not be much of a challenge with that sort of energy abundance. I don't think I agree. 1) The extremely high (but still finite)

> but interstellar travel would not be much of a challenge with that sort of energy abundance. I don't think I agree. 1) The extremely high (but still finite) amount of energy required to evaporate the Pacific Ocean is still much less than the infinite energy you need to accelerate even one single space traveler to the speed of light. Infinity is weird. Of course we won't be trying to reach the speed of light but the energy (and fuel) required to move half the species (so that the other half can stay on Earth/Mars/…) will still be significant. 2) My second argument was that the Stefan-Boltzmann law is just the same on board the space ship. And if we live there for generations, chances are our energy consumption per capita will be similar as on the planet we left, and so we will be running into similar issues with Stefan-Boltzmann's law. Sure, we can split up the passengers across multiple space ships and make each ship much bigger (to increase surface size) but not only will this increase the total mass and thus fuel required for the trip but we would probably still not achieve the (rather high) surface area per capita ratio that we have on Earth.

codethief 5y ago
Addendum to 1): Thinking a bit further, just because we can produce a high amount of energy that doesn't necessarily mean we can automatically convert it into kinetic energy for a space ship very well. Most propulsion systems in space still require expelling a propellant and conservation of momentum means this is unlikely to change. (Sure, one could imagine solar sails but the little momentum exchanged there won't get half of humanity to Proxima Centauri very fast.) So while we might have unlimited energy we might still be constrained by momentum requirements. The only way I can see to solve this conundrum would be producing enough propellant on board the space ship, e.g. (lots of) photons, using a laser. Definitely not impossible (especially not at these energy levels) but it'll be interesting to see what these propulsion systems will look like exactly. :) Ideally, we would of course try to use the propellant to also get rid of the waste heat mentioned earlier but I'm not sure whether this would work entropy-wise.
Aeolun 5y ago
> The extremely high (but still finite) amount of energy required to evaporate the Pacific Ocean is still much less than the infinite energy you need to accelerate even one single space traveler to the speed of light. True, but how many tons of space junk can you accellerate to 95% of light speed for the same amount of energy?
- codethief 5y ago
  Quick back-of-the-envelope calculation: Approx. mass of Pacific Ocean[0]: m_ocean = 7.1×10²⁰kg Specific heat of water: c = 4.2kJ/(kg · K) Temperature of Pacific Ocean: T_1 ~ 293K Temperature at which water starts boiling: T_2 ~373K => Energy needed to make Pacific Ocean boil: E_heat = c m_ocean ΔT = c m_ocean (T_2 - T_1) ~ 3×10²⁶ J On the other hand, the relativistic kinetic energy formula is: E_kin = (γ-1) m c², where γ = 1/sqrt(1-v²/c²) = 1/sqrt(1-0.95²) and m is the space junk's mass. Setting E_kin = E_heat therefore yields: => m = E_heat / [(γ-1)c²) = 3×10²⁶ J / (2.2×10¹⁶ m²/s²)] = 10¹⁰ kg For comparison: The mass of all of humanity combined is somewhere between 10¹¹kg and 10¹²kg. Now those numbers do look somewhat comparable but: - We haven't taken into account the space ships required to transport everyone - E_heat was waste heat but since practically all energy will become waste heat at the end of the day, E_heat gives us a pretty good estimate of the total energy we will have (had) access to. All in all 0.95·c doesn't seem feasible for moving humanity to Proxima Centauri, given E_heat. For moving 10¹⁰ kg of space junk, sure, though I'm not sure what you were planning to do with all that space junk in the first place? [0]: https://en.wikipedia.org/wiki/Pacific_Ocean https://en.wikipedia.org/wiki/Pacific_Ocean
zo1 5y ago
Not quite sure I follow. On earth we're mostly limited to radiation to get rid of excess heat, I understand that part. But on a space-ship, can we not just expel the heat via mass? I.e. We super-heat some dense materials and just shoot them out.
- codethief 5y ago
  Where will you be getting all that mass from, though? > We super-heat some dense materials This won't work as you would need to put in additional work (leading to additional waste heat) in order for this process to lower ambient temperature. The only thing you could do is shoot stuff out that's precisely at ambient temperature, compare https://news.ycombinator.com/item?id=28471620 https://news.ycombinator.com/item?id=28471620 .

codethief 5y ago

Addendum to 1): Thinking a bit further, just because we can produce a high amount of energy that doesn't necessarily mean we can automatically convert it into kinetic energy for a space ship very well. Most propulsion systems in space still require expelling a propellant and conservation of momentum means this is unlikely to change. (Sure, one could imagine solar sails but the little momentum exchanged there won't get half of humanity to Proxima Centauri very fast.) So while we might have unlimited energy we might still be constrained by momentum requirements. The only way I can see to solve this conundrum would be producing enough propellant on board the space ship, e.g. (lots of) photons, using a laser. Definitely not impossible (especially not at these energy levels) but it'll be interesting to see what these propulsion systems will look like exactly. :) Ideally, we would of course try to use the propellant to also get rid of the waste heat mentioned earlier but I'm not sure whether this would work entropy-wise.

Aeolun 5y ago

> The extremely high (but still finite) amount of energy required to evaporate the Pacific Ocean is still much less than the infinite energy you need to accelerate even one single space traveler to the speed of light. True, but how many tons of space junk can you accellerate to 95% of light speed for the same amount of energy?

codethief 5y ago
Quick back-of-the-envelope calculation: Approx. mass of Pacific Ocean[0]: m_ocean = 7.1×10²⁰kg Specific heat of water: c = 4.2kJ/(kg · K) Temperature of Pacific Ocean: T_1 ~ 293K Temperature at which water starts boiling: T_2 ~373K => Energy needed to make Pacific Ocean boil: E_heat = c m_ocean ΔT = c m_ocean (T_2 - T_1) ~ 3×10²⁶ J On the other hand, the relativistic kinetic energy formula is: E_kin = (γ-1) m c², where γ = 1/sqrt(1-v²/c²) = 1/sqrt(1-0.95²) and m is the space junk's mass. Setting E_kin = E_heat therefore yields: => m = E_heat / [(γ-1)c²) = 3×10²⁶ J / (2.2×10¹⁶ m²/s²)] = 10¹⁰ kg For comparison: The mass of all of humanity combined is somewhere between 10¹¹kg and 10¹²kg. Now those numbers do look somewhat comparable but: - We haven't taken into account the space ships required to transport everyone - E_heat was waste heat but since practically all energy will become waste heat at the end of the day, E_heat gives us a pretty good estimate of the total energy we will have (had) access to. All in all 0.95·c doesn't seem feasible for moving humanity to Proxima Centauri, given E_heat. For moving 10¹⁰ kg of space junk, sure, though I'm not sure what you were planning to do with all that space junk in the first place? [0]: https://en.wikipedia.org/wiki/Pacific_Ocean https://en.wikipedia.org/wiki/Pacific_Ocean

zo1 5y ago

Not quite sure I follow. On earth we're mostly limited to radiation to get rid of excess heat, I understand that part. But on a space-ship, can we not just expel the heat via mass? I.e. We super-heat some dense materials and just shoot them out.

codethief 5y ago
Where will you be getting all that mass from, though? > We super-heat some dense materials This won't work as you would need to put in additional work (leading to additional waste heat) in order for this process to lower ambient temperature. The only thing you could do is shoot stuff out that's precisely at ambient temperature, compare https://news.ycombinator.com/item?id=28471620 https://news.ycombinator.com/item?id=28471620 .