## 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.

Thank you for the article! Definitely a help! The only question I would have is a related but different topic. In the case of the journey to Alpha Centauri, where the journey for the crew is 21 days and the journey for earth is 4ish years, would the speed of aging also differ? Assuming the same conditions as your journey, would a crew that went there and back without stopping be barely 2 days older while the residents of earth would be almost 9 years older?

If they went on a round-trip you’d be right about the people on earth, those on the ship would be more like 42 days older.

Your point about the outside world time frame remaining steady is spot on. However, I’ve never heard anyone try to explain the SR apparent mass increase in terms of GR gravity. I can’t imagine them being related. If you have a stationary observer A and a body B moving at near light constant speed, the relative SR mass will remain constant. However, the equivalent GR time dilation will depend on the distance between them (1/r^2), so the relative clock rate would vary with the distance, and therefore over time, ticking faster for the stationary object as it moves away. I’ll bet the two effects are an order of magnitude apart.

Excellent exposition of special relativity. Spot on about the acceleration times to get to near lightspeed velocities. Although, like Ray Virzi, I do feel uncomfortable about relativistic mass increase being due to GR effects to spacetime.

But I will take issue with “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.”

Not so, special relativity can be applied to objects moving at faster than light velocities. The physicist Robert T Jones did this in his paper “Relativistic Kinematics for Motion Faster than Light,” NASA Technical Memorandum, Feb. 1982. To be found at: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19820012323_1982012323.pdf

Using your Proxima Centauri example and assume at spaceship that travels from Earth to Proxima Centauri instantaneously (the mechanism is analogous to your instantaneous acceleration and deceleration mechanism). External observers, stationary with respect To Earth and Proxima Centauri, will report an instantaneous tarnsition, while inside the FTL vehicle roughly four years will have passed. Essentially the ship time approaches the distance travelled at FTL velocities.

Interestingly this gives a picture of time behaving differently in the three different velocity domains. With time stretching out as velocities that of light, time is stretched to infinity at lightspeed, so no time passes for a lightspeed observer, and time approaches that of the distance travelled for a superluminal observer (ie, someone in a FTL spaceship).

This doesn’t make FTL travel any easier. In fact, it has its own problems. Besides there would have to be a mechanism to go from one side of the lightspeed barrier to the other. To date, there’s no sign of any mechanism to do so. Im sure someone will say what about quantum tunnelling? I know, but there’s nothing about it that suggests it can jump above lightspeed.

One thing annoys me about SF writers who call relativistic time dilation time compression. This is wrong. The effect of time slowing down as velocity increases and approaches that of light, when expressed geometrically, is due to a stretching of the events, therefore it dilates. Above lightspeed, the events are closer together and this might be truly called ‘time compression’.

Ok,

Using the standard relativistic formula exactly as you have given, what is;

t when v = 0 stationary

t when v = c light speed

Answer

t = t0

t = 0

So where is the time dilation?

[…] excellent blog Science In My Fiction has an article on special relativity that describes some phenomena. It does, however, confuse special and general […]

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Special Relativity for Dummies, I mean writers <Loved it!

Jason Berkowitz SEOScience In My Fiction » Blog Archive » Special Relativity for Dummies, I mean writers

I do consider all of the ideas you’ve presented to your post.

They are really convincing and will definitely work. Still,

the posts are very short for beginners. Could you please extend them

a little from subsequent time? Thanks for the post.