I'm sure it has been, but I'm mainly talking about popular sci-fi movies. I'm su...

eesmith · on Aug 10, 2021

I'm not much into visual media, so I can only come up with a few examples of 'sleep' devices:

Star Trek's "Space Seed" - 200 years in sublight stasis, no mention of speed or distance. Could be 0.5c for all we know. 100 ly at Enterprise's warp 6 cruising speed would take about 4 months, which seems not unreasonable.

The movie "Alien" - stasis, but seemingly with FTL given the times and distances involved. (https://avp.fandom.com/wiki/LV-223 says it was a 2 year voyage to the moon LV-223 in Prometheus.)

The TV series "Red Dwarf" - sublight, though it did break the light barrier once. Science in general is only relevant for comedic effect. https://www.ganymede.tv/2004/04/the-science-of-red-dwarf/ .

None of these seem to be characterized as "it takes you 150 years of travel at light speed to get to a place that is 150 light years away".

Which one am I missing?

edna314 · on Aug 10, 2021

What came to my mind immediately was 'Passengers'. But, reading up the plot on Wikipedia, it is possible that it never actually was mentioned how far away the destination was or how fast they were going. So, maybe it wasn't a misconception on the sci-fi side, but on my side. For sure, any light speed travel shouldn't take any time and infinite amount of time should pass for the rest of the universe.

eesmith · on Aug 10, 2021

From Wikipedia, 60 light years and "a journey lasting 120 years".

It doesn't say if that's 120 ship years or Earth years. I'll assume ship years as that makes the most sense in context.

Assuming constant acceleration to the 1/2-way point, flip, deceleration, and using http://www.projectrho.com/public_html/rocket/slowerlight3.ph... :

  T = (c/a) * ArcCosh[a*d/(c^2) + 1] (given acceleration and distance)

  60 years = (c / a) * arccos(a * 30 ly / (c^2) + 1)
  1893456000.0 = (3E8/a) * arccos(a * 3.15576 + 1)

Using Wolfram Alpha to solve - https://www.wolframalpha.com/input/?i=1893456000.0+%3D+%283E...

  a = 0.14748 m/s^2 or about 1.5% g

Time elapsed on Earth is only a bit longer than ship time:

  t = (c/a) * Sinh[a*T/c] = 1.15 * ship time ("proper time")

Final velocity at flip is:

  v = c * Tanh[a*T/c] = 0.73 * speed of light

simonh · on Aug 10, 2021

Having sleep pods and such isn't silly if the travel time really is many years.

philipswood · on Aug 10, 2021

Sleep pods are also not silly if you assume your speeds aren't going to be a significant fraction of the speed of light.

edna314 · on Aug 10, 2021

I mean yes, but there is a rather specific window where they make sense: at ~1-80% of c. Lower speeds it doesn't make sense to engage in interstellar travel at all, because even travelling 100s of years won't get you anywhere. At higher speeds it doesn't make sense because of time dilation.

rsynnott · on Aug 10, 2021

But that's a... pretty important window. There are not-completely-bonkers hypothetical spacecraft designs that could get to, say, 0.2c. There's nothing particularly plausible that could get to 0.99c.