Yeah. Well. That's a fun math game and not much more. Other view on "energy growth rate": https://dothemath.ucsd.edu/2011/07/galactic-scale-energy/

Energy growth is due to end sooner or later.

First, in the real world, any long term exponential growth is actually the upward branch of an S (that plateau at some point) or of a bell curve (that falls down after a peak).

Second, with such an energy growth rate we'll boil the ocean from heat dissipation long before we reach the stars.

There is also the problem that as you get away from the sun you receive less energy. Making your own portable mini sun with a fusion reactor is essential for interstellar travel.

Mostly I agree. But: we can keep our energy curve growing for a bit longer, if we branch out into the local space around us. No worries about boiling the ocean, when the energy stays in orbit.

Does that include slowing down and stopping, or would you be at max speed by the time you got there?

I always thought that was a very well thought out aspect of The Expanse: spend half the trip accelerating, then flip the ship around and spend the other half slowing down (aka accelerating in the opposite direction).

Disclaimer: Just an arm-chair Space Engineers player here.

> I always thought that was a very well thought out aspect of The Expanse: spend half the trip accelerating, then flip the ship around and spend the other half slowing down (aka accelerating in the opposite direction).

With current technology you would not do this, since that means using extra fuel that weighs a lot and thus increases the force required for the same amount of acceleration as you'd get with less fuel and less burn.

Of course that changes drastically if the fuel required for more acceleration (and its container) is very light-weight. I would assume fusion or fission based thrusters would be better in this regard, however I think currently those produce very little acceleration in a vacuum compared to combustion thrusters.

Any impulse / reaction engine is subject to the Tsiolkovsky rocket equation. It's just that with higher specific impulse and reactant velocity the total mass is reduced.

Since the rocket equation is a function of the effective velocity times the natural log of the wet/dry mass ratio, changes in exhaust velocity matter more than changes in propellant mass: you're better off with heavier propellant moving faster, than lighter propellant moving slower.

Ion drive engines tend to use xenon (a heavy nobel gas) for this reason. Unfortunately, xenon is rare even on Earth, and extraordinarily rare in space -- tanking up on a road trip would be difficult.

This completely dismisses any tangential factors, of course. Going earlier might be an advantage, as new ways to kill each other (or kill Terran ecosystems) emerge.

Going later to optimize for time is one aspect of deciding how to spread throughout the galaxy. Another question might ask, which is the most risk reducing strategy? And the answer might be completely different.

As a startup founder, I learned the hard way to not assume progress will ever be exponential.

As a guy who lives in a finite world where energy comes mainly from fossil fue in a way or another, I do not assume that any constant progress in energy supply is something achievable.

No, and traveling near lightspeed is likely hardly possible. However, fusion will likely become a reality within our lifetimes, and if we can build fusion powered spaceships, we could likely reach a fraction of the speed of light, say, 0.2c. I don't think it's that crazy to think we could do that a few centuries from now. That still means it would take over 1000 years to reach that planet.

Personally, I think that if humanity progresses that far technologically, without destroying itself, we probably won't care that much about habitable planets or planets with water. We'll just live in space and harvest the energy and resources that are available nearby. There are a lot of other planets much closer to us than K2-18b. We could just build bases in orbit around those stars, harvest asteroids for minerals and hydrogen for fusion power.

Alpha Centauri would "only" take 22 years to reach at 0.2c (plus some time for acceleration and deceleration). You could leave earth and live to see that solar system, and you could travel there on a ship that is basically a large city that will just park itself in orbit around the star on arrival, acquire resources, and start building something bigger.

Besides fusion I think hibernation will also become a reality within this century.

This will make the 22 year trip to Alpha Centauri more palatable.

1000 year trip in a single lifetime will require some life extension as well

Although it seems unlikely now, imagine if we could ever reach 0.9c or maybe even 99.9% of the speed of light.

Perhaps not ships containing humans, but some kind of other tiny ship containing a replicator machine and DNA for humans.

For 0.999c, it would only take around 71 days to reach Alpha Centauri from Earth (as seen from the ship). That's pretty mind boggling.

Besides the incredible amount of energy you would need for 0.999c, which is physically difficult (impossible?) to bring on a ship, there's other physical constraints that make this difficult, such as the fact that the vacuum is actually not that empty. The faster you go, the more you have small particles hitting your ship at near lightspeed, micrometeorites, etc.

As soon as you get fusion the game drastically changes. And fusion is only 30 years away.

Isn't it always 30 years away?

No. It's mostly a number of Euros away and we haven't been funding it very well.

Maybe we should update it to "always 30 billion Euros away".

Why do you think that no state put significant effort into fusion research? You would imagine the first country to figure it out would dominate the world for decades to come.

I don't think fusion power makes you dominate the world. It's not like building fusion plants is free.

Could you give some sources for that or explaing where exactly the problems in fusion technology lie and how it could be solved by throwing money at it?

ITER is planned to be completed in 2026 and it'll generate a net 0 of electricity at 300MW in/out.

It seems the issue with fusion is that it actually works much better at scale. But the same could be said about nuclear reactors - it obviously is much harder to build a compact one.

Does it work better at scale? The sun definitely produces a lot of energy in total. However, "the Sun's "power density" is "approximately 276.5 W/m3, a value that more nearly approximates that of reptile metabolism or a compost pile than of a thermonuclear bomb".

If, overlooking the details, we were able to build a cubic meter sized "fusion box" that outputs 276W, then it would take about 2 million of them to produce a reasonable output for a power plant of 600MW. And it would take up about half the volume of NASA's vehicle assembly building, ignoring any support structure needed. That's not unimaginably huge, but it's pretty large compared to other types of power plants, I would think.

So assuming we solve all the technical problems to capturing the power source of the stars using handwavium or perhaps generously donated alien widgets, I wonder if it might still be uneconomic.

This is already a few years old, but pretty informative:

https://hardware.slashdot.org/story/12/04/11/0435231/mit-fus...

Over any timeframe, the rate of progress between the beginning and ending of the timeframe can be phrased as exponential for some exponent. It's just a matter of accurately estimating what that exponent is.

I take your point though - hypergrowth cannot be sustained - and estimating that exponent is fairly valueless if volatility is too high. This is all just math fun that won't be valuable if we bump along for hundreds of years and then all of sudden make a massive discovery.

Thats true considering only two datapoints. It gets more interesting when more datapoints follow an exponential rule, say subsequent disruptions, no of transistors on processors or stock market indices.

That's a lot of hand-waving. Reminds me of Drake equation. Why not just admit we have no clue yet? Also the Parker Solar Probe speed is due to orbital mechanics of basically free-falling towards the sun and you'd have to do things very differently if you wanted to have that speed going out of the solar system.

As others have said, E=mv^2/2 only holds at very small fractions of the speed of light. I believe the equation you need is E=mc^2/sqrt(1-v^2/c^2)-mv^2.

https://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_ki...

Can you explain this further? It seems this is relevant more for something other than the Wait Calculation. The original Wait Calculation doesn't factor in mass at all. I'm having trouble understanding what this impacts. Is this more about relativistic time passage, like from the ship traveler versus the observer?

Most scenarios I've explored - low velocity growth rate, nearby planets/stars - the Wait Calculation tells you to stop researching and start launching long before your tech gets to significant fractions of light speed.

Honestly, I made that comment without fully thinking through how to implement my suggestion, and now I realize that I've stumped myself. However, let me explain what I meant anyway:

First of all, you're right that this won't really impact your answer at insignificant fractions of light speed. You mentioned that using the 4.72% growth rate, the equation tells you to wait until you've passed the speed of light, and I thought it might be interesting to more accurately model the energy required at relativistic speeds.

So the same way that you used the classical mechanics equation for kinetic energy, E=mv^2/2, ignoring mass and solving for v, to get v=sqrt(2E) and approximating to v=sqrt(E), I thought you could manipulate the relativistic equation similarly.

Now, having gotten a solution from WA, I'm starting to think that I overestimated the effect on accuracy that changing the equation would have. I want to approximate the solution by ignoring some terms or changing an nE to an E^2 or something, but I think that might negate any gain in accuracy.

So to answer your questions more directly, I was attempting to address the error you get when the calculation tells you to wait until you can travel above or near the speed of light, and I only included mass in my equation to try to communicate it to you more accurately, with the assumption that when actually using it you would ignore the mass.

Anyway, I hope I at least clarified my previous comment, even if it turned out not to be very useful! If anyone has a better understanding of how to better model relativistic speeds I'd love to hear their explanation.

Btw, if you measure the time as experienced by the traveller, the classic equation will give you exactly the right answer:

Pouring more energy into acceleration won't make you move faster (even subjectively) but it will shorten the way. (From the outside, it looks like time dilation.)

Progress in physics was much faster in the early 20th century when it wasn't so fascinated with deep space. Yes, you needed to observe eclipses to verify relativity, but that was a tool, not the end in itself.

Cosmology involves distances that are so great that it seems like it's pouring a whole bunch of smart people's efforts down the drain in an ultimately futile waste of brain power that will never amount to anything much at all. Besides, when we get faster than light travel we can just pick up exoplanet research where we left off and it will actually be practical and probably far more efficient with the computers and such we will have developed by then.

> Cosmology involves distances that are so great that it seems like it's pouring a whole bunch of smart people's efforts down the drain in an ultimately futile waste of brain power that will never amount to anything much at all.

I think it depends on what one wants to get out of the research. If the goal is a commercially realizable product on a shortish time horizon (say < 50 years), then cosmology may not be the best approach. But the justification for cosmology and much of astrophysics is typically that it is a probe of fundamental science and the acquisition of knowledge for its own sake. In which case whether we can ever travel to other planets or galaxies is moot, since it's the physical understanding and knowledge that's the goal.

Many before me have used the example of relativity, which when proposed, seemed to have little practical value. But GPS wouldn't work without relativistic corrections. 100-120 years ago one could've made a similar statement about fundamental physics and work on relativity. But if we'd abandoned it because of a lack of immediate relevance then we wouldn't have workable GPS today. The benefits of fundamental research (in many areas, not just astrophysics) are often quite difficult to forecast.

> when we get faster than light travel

FTL requires numerous things to be true about our universe, that all signs say are not.

The speed of light is just a compute constraint imposed on the physics simulation that is our universe. If we can just get the gods who are running that simulation to give us a little extra compute time in our neck of to woods then we can all be galactic explorers.

Just for the sake of argument, let's run with that.

If we're in a physics simulation, we don't experience at the rate that the simulation is processed. One "tick" of the simulation could be processed in one second of the host universe, or one hour: and we wouldn't feel the difference. We are processed at the same tickrate as the rest of the universe, so we experience the passage of time at the same rate that the simulation flows.

The speed of light isn't just the speed of light, it's the speed of causality. It just so happens that light moves pretty well at that "speed limit" (in a vacuum). We could ask our computational hosts to increase or decrease c, and we still wouldn't be able to travel any faster than it.

We could ask the host to update their algorithm to let c be a property of objects and then just do spaceship.c = 1000 * c.

Would probably be a heck of a refactor to get it working without bugs though.

Just leave the bugs in for the speedrunners to use.

speedrunners can restart the game if they crash it.

@mesid asked in a now dead comment:

> What does speed of causality mean? And how is light so close to that?

Take a look at this video by PBS Space Time on the topic:

https://www.youtube.com/watch?v=msVuCEs8Ydo

You may need to go down the rabbit hole and watch the earlier videos on relativity and related topics.

The short story “Dust” (1992) by Greg Egan explores these ideas in a pretty entertaining way.

Here, I found a copy: https://emperybooks.com/wp-content/uploads/2018/06/Greg-Egan...

Why would time outside of the simulation have any bearing on time within the simulation?

Only via side-channel attacks.

Maybe there are glitches possible.

...crushing all my dreams of being a starship captain, thanks.

IMHO we will still get a space opera-esque future, just within the Solar system, not outside of it. There is plenty of space, energy and material around for potentially trillions of people on billions of space stations and space ships.

And we can still spread out from there. It is a well-thought out element of the Hyperion Cantos (occult SciFi): They do have some kind of Stargate to insta-travel, but building those Stargates requires people to travel for decades if not hundreds of years. These guys are put into stasis for the duration of the trip, and get to go home every couple of decades to talk to their grandchildren/distant descendants.

Leaving SciFi aside, our communication technology will be up to the task of relaying information comparatively quickly (light speed or faster), and parallel societies could be built in neighboring solar systems.

I am reading big space operas right now.

What we know of this reality is so limiting compared to what we can imagine.

Good dreams. Many of us have them.

I also like to dream the knowable remains much larger than the currently understood too.

Funny thing is that the imaginary worlds in books are way less weirder compared to what reality has to offer. Apparently because it's harder to develop the story.

Any book in particular you'd recommend?

"reality is so limiting compared to what we can imagine"

This is actually a central theme of the Zones of Thought novels by Vernon Vinge where a character in the far future describes our current time as the "Age of Failed Dreams" (GAI, nanotech etc.) - turns out that he is wrong but for rather neat reasons....

https://en.wikipedia.org/wiki/A_Fire_Upon_the_Deep

https://en.wikipedia.org/wiki/A_Deepness_in_the_Sky

Anything in the Culture series by Iain M. Banks;

The Expanse series by James S. A. Corey;

The Commonwealth and Void trilogies by Peter F. Hamilton, and the Night’s Dawn trilogy also by Peter F. Hamilton;

The Dune saga by Frank Herbert.

I'll add the Ancillary (Imperial Radch) series by Ann Leckie to these good suggestions.

Hamilton’s The Reality Dysfunction was the stupidest book I’ve ever read and took hundreds of pages to expose itself. Are his others any more grounded (like your other suggestions)?

Yeah the Night’s dawn series was a bit out there compared to the genre average. The Commonwealth series is considerably closer to baseline, and his best books IMO. The void trilogy (and the newer trilogy whose name escapes me) follow on from the Commonwealth books, and while good, don’t hold up to the first three.

Thanks for the heads up! I liked his writing style so I’ll put them on the list.

did you read the same book as me.. it was pretty awesome

I'm a huge fan of Hamilton's books but I have to agree this one was.. different.

I think I liked it in the end, though not as much as his other books, but can absolutely understand people would dislike it.

The reincarnation of Al Capone?

Foundation Trilogy is not really an Opera, but definetely up there with the big guys. Also an incredibly quick read.

Neal Asher's Polity Series as well.

It's the culture with more detailed worlds and villains.

Is Pandoras Star worth the effort?

Definitely. I still have some series to read, especially the dark tower from Stephen King which I already started, but I think I'll re-read the whole commonwealth saga in the near future.

Yep, the Commonwealth series got solid 4s out of 5s from me, which is very good — I very rarely give a book a 5.

The Baen Free CD has always been a great source of free sci fi books for me

> Progress in physics was much faster in the early 20th century when it wasn't so fascinated with deep space.

I don't think measuring progress is tivial enough to make that assumption. It's also unfair to blame a fascination with deep space for any slower progress, things are more complicated than that.

Getting humans onto anther planet asap is one of the most important things one can pursuit for humanity. The earth is a giant single point of failure

> when we get faster than light travel we can just pick up exoplanet research where we left off

if we get FTL, we'll be able to pick up that research before we left off ...

> it seems like it's pouring a whole bunch of smart people's efforts down the drain in an ultimately futile waste of brain power that will never amount to anything much at all.

Well, at least they're not making people click ads ...

we might some day discover that we are roughly coaxially located between 2 civilizations exchanging knowledge, and get up to speed with their knowledge.

or observe civilizations broadcasting knowledge in a loop: motivation? perhaps the faster they can get others up to speed, the faster others might contribute knowledge back which may some day save their civilization.

Why is annual energy growth rate or industrial growth rate assumed to correlate to the speed of space travel?

Just because we build more power plants or sell more tractors doesn't imply a corresponding improvement in spacecraft technology.

The Wait Calculation seems to make even less sense than the Drake Equation - which is at least correct in theory even if the actual variables have so much uncertainty it is useless.

> taking the square root to get velocity growth rate

This is your mistake. It's an approximation that works well only at low speeds.

Why don't you stick to the energy growth rate (instead of the 4.72% velocity growth rate) and then use the relativistic formula of the kinetic energy (in which the relationship between energy and velocity is not quadratic — the quadratic approximation is valid only for small velocities)?

So our only hope to see a planet different from ours is that some advanced alien population comes to "see" us, with all the implications this has...

History does not favour the civilization which is visited.

Our history doesn't.

Given what we see in non-human nature, the tendency of visitees to get rekt by visitors is much, much more likely due to the dynamics of competition for life than to some human-specific variable.

> One common recommendation for annual energy growth rate is 1.4%

Where does this come from? Does it even hold water when compared to past data? Looking at some Wikipedia data for the past 20-30 years, it seems that the increase in speeds is much higher:

https://en.wikipedia.org/wiki/List_of_vehicle_speed_records#...

Does this take into consideration that your mass increases as you travel closer to the speed of light?

No, I'm not sure what that would suggest - how would that need to be accounted for? Maybe some fraction of light speed would need to be the upper bound, low enough that mass increase wouldn't have a material impact? I'm having trouble understanding what impact the mass increase would have in the first place.

It's a cool project! Just as others say, once you get to a notable fraction of the speed of light, you need to account for relativity.

does this take into consideration that you would need to start slowing down halfway there?

It wouldn't need to be halfway. At 3gs acceleration, it would take about 115 days to accelerate up to the speed of light. You'd then travel ballistically for the majority of the journey before having to decelerate for another 115 days.

Given the total journey would be ~40,000 days the 230 days of acceleration probably isn't going to impact things too much. Even if you brought it back to 1g acceleration, it's still only around 700days out of 40,000.

I just read somewhere in this thread that 'ship-time' at the speed up time is zero. So that would mean 230 consecutive days of acceleration.

No, it assumes you start and end at whatever that maximum velocity is that we've been able to achieve.

That'd be fun to add, though. I'm not really sure what human-safe acceleration is - people here assume it's in the 1g-3g range. (That seems like a lot to me though, particularly for a long period of time - I think anything more than a fraction of g would be wildly uncomfortable.)

1G would be great as it would remove any unexpected physiological impacts of living in zero or low gravity.

Having said that, the distance and duration means that only a small portion of this journey would be under acceleration, the rest would be in zero g.

Spending a century in zero g would probably have a bunch of strange side effects and almost certainly mean that the people alive when they arrived wouldn't be able to stand the planets gravity.

This exact topic is what about 80% of The Expanse is about.

Not quite true. You'd spend half of the travel time under 1g accelerating, then the ship does a 180 degree flip in 0g, and then you spend another half of the travel time under 1g decelerating.

Edit: Of course, at constant 1g acceleration, at day number 354 we reach 1c. Don't know if we should start coasting before we reach 1c or just the hell with it and see what happens if we keep accelerating.

So many people in this thread are acting like constant acceleration is possible. Unfortunately the faster you get, the more energy it takes to maintain constant acceleration.

> Don't know if we should start coasting before we reach 1c...

Don't worry about it. Your rocket would need to expend an infinite amount of energy to accelerate to c. The energy stored in your finite-sized rocket is finite. At a certain point it becomes futile to keep trying to accelerate -- though I suspect that the impacts of space dust will eventually cause a significant amount of drag

http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/r...

"Unfortunately the faster you get, the more energy it takes to maintain constant acceleration."

I'm not sure what you mean by this. You could also say "the slower you get, the more energy it takes to maintain constant acceleration". Constant means ongoing, so as long as it is constant, you are going to have to expend more energy.

Unless you mean that somehow, you could determine your absolute speed by how much you accelerate for a given expenditure of energy, but wouldn't that violate relativity?

Can you alternate accelerating and decelerating? I mean that's a heck of a lot more energy, but at least you're not risking reaching light speeds.

Wouldn't 1g be perfect? I've been enjoying it for a few years now on this planet.

I took it as 1g of acceleration. I don't know. Wouldn't plain old 1g mean no acceleration at all?

Edit: Oh... I guess not. :) I got confused with the extra g's we'd need to escape earth, but that's so short-term that it can be ignored. Yeah, I think 1g would be perfect.

When you sit in a car and it accelerates forward you can feel your back being pushed into the seat. When you lie in bed gravity will also push you into the bed. In both cases it's a force acting on your body. So being pushed in space in a ship accelerating at 1g will feel like normal gravity with the 'ground' being the back of the ship.