# 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 - (0.5*c*/*c*)^{2}) + 447 * sqrt(1 - (0.1*c*/*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.

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