# How to get across the galaxy moving slower than light - in a single lifetime?

All the recent talk on Worldbuilding about the vast energies available to higher-level Kardashev civilizations, the need for 50,000 year message-systems, and so on, got me thinking. With enough energy, wonderful things might become possible in space travel.

The galaxy is 100,000 light years across. Humans live about a century under optimal conditions. The speed of light cannot be exceeded. How do I get a live human from point A to point B 40,000 light years away? Seems an insurmountable problem, no?

Before I get accused of duplicating a previous question on faster-than-light travel, let me clarify: at no point would the ship move faster than the speed of light from the perspective of observers on Earth, nor would this ship use Alcubierre-style drives to warp space.

What I'm talking about are time and space distortions caused by relativistic spaceflight. Not only does time pass more slowly for the ship-board explorer from the perspective of observers at home, but as she accelerates, distances in the direction parallel to the direction of movement appear to shrink. At some point (I think around 70%c from Earth's perspective), distance shrink will make the explorer estimate that she is going at 100%c if she where to assume that distances measured at Earth where correct. At the same time an person on earth would observe the explorer as aging less than one year for every light year she travels.

Recall that the formulas below must be true both from the perspective of a fixed observer and from the perspective of the explorer:
$L=L_0 \sqrt{1-\frac{v^2}{c^2}}$

$t=\frac{t_0}{\sqrt{1-(v/c)^2}}$

The energy requirements to accelerate a ship to this speed would be immense, of course, but a Type II civilization, having $10^{26}$ watts (joules/sec) at its disposal, should have no trouble with this at all.

Would it indeed be possible to travel across the Milky Way in a single lifetime, if you were willing to forsake friends and family?

How would the monstrous time-lag at the homeworld affect a society's willingness to send out explorers?

Where would such expeditions go? What would be a worthwhile destination?

• You are totally correct! From the traveler's frame, the distance appears to be length-contracted and so traversed more quickly. From the stationary frame, she appears to be aging more slowly and so spends less subjective time traveling. However, in either case she can never beat a light pulse traveling the same course, as it will appear faster in both frames. – 2012rcampion Jan 21 '15 at 2:44
• The problem is that from the perspective of anyone you left behind it still took you decades to reach the target. It's not really FTL if you can't go there and come back in a reasonable timeframe to the people you left behind... – Tim B Jan 21 '15 at 9:56
• @TimB, I know, hence the effective FTL, rather than actual. I still think it's exciting that one can travel across the Milky Way in only a few years of personal subjective time. Lots of story-writing options open up... – Serban Tanasa Jan 21 '15 at 12:37
• This question would be better asked at physics.stackexchange.com. However I think that you ignore the fact that from the explorer's perspective the velocity of the explorer is 0. The time dilitation formulae you quote is what is observed by a stationary observer affecting a moving object. Ie. from the explorers perspective it's the earths clock that is dilated. – Taemyr Jan 21 '15 at 13:04
• @Closers, so we have an ftl tag, but questions about effective ftl are off-topic. I am officially befuddled. – Serban Tanasa Jan 23 '15 at 21:03

Would it indeed be possible to travel across the Milky Way in a single lifetime, if you were willing to forsake friends and family?

This is straight forward math. We know that the speed needed will be quite close to 1c. So we need the length we are traveling to be one that light will cross in a single lifetime. The milky way is about 100000 light years across, we want it to be about 50 light years across. $$L=L_0 \sqrt{1-\frac{v^2}{c^2}}$$ $$L/L_0=50/100000=1/2 000=\sqrt{1-\frac{v^2}{c^2}}$$ $$1-\frac{v^2}{c^2}=\frac{1}{4000000}$$ $$\frac{v^2}{c^2}=\frac{3999999}{4000000}$$ $$v=c\times\sqrt{\frac{3999999}{4000000}}=(1-1.25*10^{-7})c$$

This requires $1.8*10^{20} J/kg$ and as such would be a huge, but arguably possible, undertaking for a type II civilization.

How would the monstrous time-lag at the homeworld affect a society's willingness to send out explorers?

It would mean that sending explorers would be of limited use. You send explorers to learn about the world (or universe in this case). So you require that they somehow send information back. This means that for sending explorers the time span on Earth is what is important, which means about 4 years to nearest star, plus 4 years to send information back. This is doable, the Rosetta mission took 10 years - however that also gathered some interesting data on the way. Assuming a limit of 20 years for how long we are prepared to wait for data means that we can only explore stars within 10ly. We know of 12 stars or stellar remnants in that sphere. More might be discovered, but it will be a fairly small set anyway. Interesting targets could be the stellar remnant Sirius B (to gather data on a stellar remnant), Barnard's Star (to gather data on a very old star) and the Sirius binary system (to gather data on a pair of very young stars). The Alpha Centauri system is also interesting, since it's the closest stars and because it's the only target within the 10ly sphere where earth like planets could exist. If a potentially Earth like planet did exist around Alpha Centauri A or B, then that would immediately jump it to the top of the list. (the current Earth-mass exoplanet has not been confirmed).

Where would such expeditions go? What would be a worthwhile destination?

Other than for science as described above there are no destinations that are worthwhile for people remaining on Earth.

Because of the long waiting time for people back on Earth there can be no destination that would be worthwhile for an investor on Earth. The combination of an enormous investment to send the expedition and a 10 through 1000+ year wait for a return would mean that the return on investment would be negligible.

That means that any expedition would need to have value for the people making the expedition. - Settling is the only reason I could imagine as potentially worthwhile. So a target would be a star system with a planet that is confirmed to be terraformable. - No such target exists today, but we are getting better at detecting planets.

• Depressingly accurate answer, in my view. – Serban Tanasa Mar 21 '15 at 17:41
• Could long-term exploration be worthwhile for a Type II civilization that's mastered immortality? – Dan Smolinske Apr 16 '15 at 15:55
• The equations on the relativistic rocket page are also relevant--if you're assuming the travelers are biological humans rather than mind uploads or some other form of AI, then you won't want to accelerate at a rate much greater than 1G, and you'd also want to start decelerating at 1G at the halfway point to arrive at your destination at low speed--the page indicates this means a 20 year journey to the center of the galaxy, and 28 years to the Andromeda galaxy. – Hypnosifl Apr 16 '15 at 16:47
• If we take it to the extreme, then settling planets around other stars may be necessary for the survival of life from Earth. Once the first have settled there, it is likely easy to cross-breed between humans at either end by sequencing DNA and sending the DNA as digital communication. Imagine what people left on Earth would be willing to pay to have a child of their own born in a colony at another star if ours is just about to burn out. – kasperd May 7 '15 at 16:52
• @Hypnosifl what if we put the humans into giant water-tanks or something to make the body withstand immense G-Forces ? Maybe we could freeze them solid to avoid damages? – Falco Jun 5 '15 at 12:53

Here are my R calculation results. The first two columns are fractions (and multiples!!!) of $c$.

Effect.Veloc.Astronaut  Starship.veloc.stationary   Joules.100000.kg.ship
0.01                    0.01                        4.50E+17
0.1                     0.0995                      4.50E+19
0.2                     0.196                       1.80E+20
0.5                     0.447                       1.10E+21
1                       0.707                       3.70E+21
2                       0.894                       1.10E+22
5                       0.981                       3.70E+22
10                      0.995                       8.10E+22
20                      0.9988                      1.70E+23
50                      0.9998                      4.40E+23
100                     0.99995                     8.90E+23
1000                    0.9999995                   9.00E+24
10000                   0.999999995                 9.00E+25
100000                  0.99999999995               9.00E+26


As you can see, humankind's energy output for a year early 21st century would barely suffice to accelerate a 100 ton craft to 0.2 c.

Source: Xenology: An Introduction to the Scientific Study of Extraterrestrial Life, Intelligence, and Civilization, 1975, R. Freitas

5e20 Joules are about 1.5e13 watts. A mature type I Kardashev (so by the chart above humanity cca 2300) could get 1e17 watts, so output of 3e24 Joules. Even for a type I, relativistic interstellar travel is difficult.

A type II, about 900 years at 3% growth rates after Type I is reached, have 10e26 watts to play with, or 3e33 J, so launching a small ship at relativistic speeds would take no more than a few seconds' worth of the civilization's power output, similar to a Saturn V launch for 20th century mankind.

That does still leave a few major difficulties.
1. Energy density of fuel.
2. Deceleration.
3. Shielding.

(1) Can be alleviated somewhat by beaming power to the ship.
(2) Remains open, and I have no idea how to get enough reaction mass to decelerate on board. Perhaps a payload consisting of a miniaturized AI with self-replicating machinery (a few grams), or a Bussard Ramjet could work as well.
(3) A lot of ablation mass will be needed since each dust particle in the way will strike my ship like a shaped charge. Perhaps a powerful laser to clear the path?

As to where I'd go, I would probably go to the nearest Earth-like world, see what or who is there. On the other hand, I'm not sure I would want to lose all those Earth centuries it would take...

PS: I know it's generally bad form to give an answer to your own question, and all this might hinge on some miscalculation, but I got too excited about the effective FTL drive!

• It's not bad form to answer your own question, not at all. It's explicitly encouraged. – Shokhet Jan 21 '15 at 2:43
• @Shokhet, oh, cool! – Serban Tanasa Jan 21 '15 at 2:48
• I do it all the time. There's even a dedicated check-box for it when you ask a question, so you can post the question and answer at the same time, if you want. – Shokhet Jan 21 '15 at 2:59
• Saturn V churned out equivalent power to 85 Hoover Dams. So, I'd say more than 1-3 seconds. But not 10,000-30,000 seconds worth of the world's power. – user3082 Jan 21 '15 at 8:12
• @user3082, Humankind, cca 1970 used up 2e17 BTU = 2e20 J per year so a rate of 6e12 Watts (J/sec). The Saturn V pumped out 1.3e11W for 150 seconds, so 1.95e13J. That's about 3 seconds of humanity's output. – Serban Tanasa Jan 21 '15 at 13:11

Your conclusion, that an explorer can travel a distance that in our reference frame is 4 ly, in a time span that he can messure as less than 4 years, is correct.

However;

"Not only does time pass more slowly for the ship-board explorer, but as she accelerates, distances in the direction parallel to the direction of movement appear to shrink."

This is not quite accurate.

Only length contraction will be visible to the traveller.

Both length contraction and time contraction is visible for an observer moving with zero speed relative to an inertial frame observing objects having a nonzero speed relative to that frame.

So for an observer on earth observing the explorer you would not see length contraction. - Because the sun and target star is not moving at relativistic speed relative to your reference frame.

While for the explorer, he will not see time dilation. - His speed is zero in his reference frame. However he will see length contraction, because the stars have relativistic speeds in comparison with his reference frame.

So the two effects will be visible to different observers. The observer on earth will see the clock of the explorer running slower while the length between the two stars remain constant, while the explorer will observer the length between the two stars as shorter - while of course seeing his clock as running at regular speed.

• I edited my question to take your very pertinent points into account. Let me know if the current formulation could be further improved. – Serban Tanasa Jan 23 '15 at 2:07
• @SerbanTanasa At no point would an explorer making accurate messurements estimate that he travels at 1c. To get at that value he would have to make some incorrect assumtion, like that the distances as measured on Earth where correct. I have proposed an edit to clarify this. – Taemyr Jan 23 '15 at 8:26
• Yeah, I suppose she'd have to use the original Earth-based distance estimates. – Serban Tanasa Jan 23 '15 at 11:49
• You seem to be comparing two distinct issues--it's true the traveler doesn't see his own time slowing, but then he doesn't see his own length contracting. If he measures external stars in his own instantaneous inertial frame at any given moment, he will measure both the fact that distances between stars have contracted and the fact that clocks on planets orbiting the stars have slowed down, in this frame (though if he uses an accelerating frame like Rindler coordinates he could measure external clocks running faster than his own). – Hypnosifl Apr 16 '15 at 16:41

Additional to the other answers pointing out the huge amount of energy needed to achieve significant time dilation.

If the civilisation had achieved really long term stability it could send out self-replicating robot probes. On arrival in nearby solar systems they would construct a high tech infrastructure including interstellar radio transmitters and matter assembly systems. They'd also send out more probes. So the technological infrastructure would expand on a spherical wavefront across the galaxy at a small fraction of the speed of light.

A number of millions of years later every solar system in the galaxy would be connected.

To travel you would upload your mind and transmit it, along with a body plan. At the other end a body would be built and your mind installed into it. Effectively you would travel at the speed of light plus a constant upload/download time. There would of course be no way to go home.