Special Relativity for Dummies, I mean writers

So, practically everyone knows thanks to Albert Einstein that on a starship traveling close to the speed of light time will pass more slowly than in the rest of the universe, though it does seem that not everyone understands how that works.  For example, I recall reading a passage in The Andalite Chronicles where the narrator explained that they were traveling to earth at a sub-light speed that would take them about three days because if they went at maximum burn they might make it in a few hours but that would be years on earth.  That’s just wrong, relativity slows down time onboard the ship, it doesn’t speed up time outside or anything.

For example, Proxima Centauri is 4.2 lightyears from earth, if one were to travel that distance in a ship at 99.99% the speed of light (assuming instantaneous acceleration and deceleration) the trip would take over four years from the perspective of everyone outside the ship but just over 21 days would pass on board.

The casual writer can use relativistic time dilation realistically in their story with the help of either this equation:

The equation for relativistic time dilation.

Or this convenient table:

Velocity % c        Length (metres)               Mass (tonnes)   Ship hour (in minutes)

0                              100                                         100                         60

10                           99.50                                     100.50                   59.52

20                           95.39                                     104.83                   57.20

30                           95.39                                     104.83                   57.20

40                           91.65                                     109.11                   55.00

50                           86.60                                     115.47                   52.10

60                           80.00                                     125.00                   48.00

70                           71.41                                     140.03                   42.75

80                           60.00                                     166.67                   36.00

90                           43.59                                     229.42                   26.18

95                           31.22                                     320.26                   18.71

99                           14.11                                     708.88                   8.83

99.9                        4.47                                        2,236.63               2.78

99.99                     0.71                                        14,142.20             1.17

100                         zero                                       infinity                  zero

Now, you’re probably wondering why the table includes units of length and mass and why the former decreases with increased velocity and the latter increases.  The answer has to do with why traveling near the speed of light slows down time.  You see, according to Einstein’s theory of General relativity the passage of time varies with location, and the biggest factor determining time is gravity, we’ve observed this from GPS satellites whose clocks need to be adjusted by 38 microseconds every day because time passes faster up in orbit.  Now Einstein also maintains that as an object travels faster, its mass approaches infinity, which is why we can’t travel faster than the speed of light.   And what is it that produces gravity?  Mass, of course.   One can see the commonly used visual metaphor for how mass warps the “fabric” of space time, forming “depressions” where objects fall in, below.

So, to summarize, velocity increases mass which increases gravity which slows down time.

There are a couple final issues that makes incorporating special relativity into fiction complicated.  For example, accelerating to nearly the speed of light without incorporating some kind of inertial damping or killing a biological crew would take a fairly long time, say one year at a comfortable 1G (which could also provide a sort of artificial gravity for the crew if the decks were oriented in the right direction).  The other is that we have no ideas on how to bring a starship to relativistic speeds within a human lifetime, not even a nuclear or antimatter rocket, what with all the fuel it would need.  A bussard ramjet would bypass the fuel issue but would the ramscoop would produce too much drag to reach sufficient speeds, while a light-sail might be capable of reaching relativistic velocity if powered by a laser projected from earth, but considering the acceleration rate of a multi-kilometer sheet of reflective metal pushed by photons that would take centuries to reach relativistic.

On another note, a few authors have attempted to bypass the acceleration and propulsion problems with Phlebtonium.  Typically using gravity manipulation to cancel inertia or as a “reactionless drive”.  There are also some authors who think that if one manages to exceed the speed of light time dilation would reverse itself and shipboard time would run faster than external or even in the opposite direction, the truth, of course, is that we don’t know what would happen because we can’t travel faster than light.

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