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Murphy's Law

A Metamorphosis Alpha® play-by-post adventure run by ghost_of_warden

Time Dilation Interlude: How Long Has Warden Been Gone?

plutoniumblondenapecity

OOC

Does anyone know how much ship time would pass in 500 years relative to time for those not travelling at Warden's speed?

blaen_495

OOC

No, but if you hum a few bars I can fake it.

Seriously, what is the speed of the Warden? Plugging that into Einstein's time-space dilation equation should give the result. Note: I failed physics, so the answer in my game would be "a bloody long time."

zhaxier

OOC

A distillation of the time dilation equation for our purposes is:

t' = t * sqrt(1 - (v/c)²),

where "sqrt" is the square root function and

t' = time that passes in the base frame of reference,
t = time that passes in the moving frame of reference,
v = constant velocity of the moving frame of reference,
c = speed of light.

If we let the Sol system be the base frame and (Murphy's Law's) Warden the moving frame, and if we ignore the 3 years of acceleration/deceleration that occurred in 2290, 2331 and 2332, then people aboard Warden have so far traveled 40 years at c/2 (to get to 82 Eridani) and 447 years at c/10 relative to Sol.

However, to an Earth-bound observer, Warden would have been traveling only

t' = 40 * sqrt(1 - (0.5c/c)²) + 447 * sqrt(1 - (0.1c/c)²)

= 479 years or so,

not the Newtonian 487 s/he might expect.

Eight years' "savings" isn't a whole lot! In short, not even Warden's max speed of c/2 is enough to produce dramatic relativistic effects.

So blaen_495 was right after all when he wrote "a bloody long time"! (Who needs physics, anyway? ;)

For an excellent example of time dilation as it applies to spaceflight, look here.

Great question.

-Z.