Time dilation

Time dilation, according to Albert Einstein's special theory of relativity, is the slowing-down of the passage of time as experienced by people or objects traveling at a substantial fraction of the speed of light. Gravitational time dilation is the general relativistic slowing down of the passage of time deep in the gravitational field of a large object.

Table of contents

1 Velocity time dilation 2 Gravitational time dilation 3 Time dilation and space flight

Velocity time dilation

When one accelerates towards the speed of light, time slows down with respect to the rest of the Universe. That is, a stationary observer would see the travelling objects slowing down their activity (while still travelling fast). For them, time passes slower.

It is important to note that this effect is extremely small at ordinary speeds, and can be safely ignored for all ordinary situations. It is only when an object approaches speeds on the order of 30,000 km/s (still 1/10 of the speed of light), that it becomes important.

The formula for determining time dilation factor is:

Where T₀ is the passage of time measured by a stationary observer and T₁ is this passage of time measured by an observer travelling at velocity v.

%c	Length contraction	Relativistic Mass	Time dilation
0	1.000	1.000	1.000
10	0.995	1.005	0.995
50	0.867	1.155	0.867
90	0.436	2.294	0.436
99	0.141	7.089	0.141
99.9	0.045	22.366	0.045

Taken to the extreme, an observer travelling at the speed of light (which, according to special relativity, is impossible for any object with a non-zero rest mass) would be all but frozen with respect to the outside world. Massless particles (which are forced by relativity to travel at the speed of light) include photons and gluons. Recently it was determined that neutrinos have a mass, unlike previously thought.

Gravitational time dilation

Gravitational time dilation is a verified effect of general relativity, and has been experimentally measured using atomic clocks on airplanes. The clocks that travelled aboard the airplanes were slightly fast with respect to clocks on the ground. The effect is significant enough that the Global Positioning System needs to correct for its effect on clocks aboard artificial satellites, providing a further experimental confirmation of the effect. Time dilation due to velocity is negligible in both cases.

An extreme example of gravitational time dilation occurs near a black hole. A clock falling towards the event horizon would appear (to observers far away) to slow down to a halt as it approached the horizon. A small and sturdy enough clock could conceivably cross the horizon without suffering adverse effects at the horizon, but to far away observers it would "freeze" and be flattened out on the horizon.

Time dilation and space flight

Time dilation could make it possible to travel "into the future": if we could accelerate a starship enough, one year aboard the ship might correspond to ten years outside. Indeed, a constant 1g acceleration would permit humans to circumnavigate the known Universe (with a radius of some 15 billion light years) in under a subjective lifetime. A more likely use of this effect would be to enable humans to travel to nearby stars without spending their entire lives aboard the ship. However, any such use of this effect would require an entirely new method of propulsion. A relativistically accelerated object also gains mass, so further acceleration would require increased amounts of fuel. A further problem with relativistic travel is that the interstellar medium would turn into a stream of cosmic rays that would fry the ship unless stark radiation protection measures were taken.