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Time dilation was used in the Doctor Who episodes "World Enough and Time" and "The Doctor Falls", which take place on a spaceship in the vicinity of a black hole. Due to the immense gravitational pull of the black hole and the ship's length (400 miles), time moves faster at one end than the other.
The speed of light in a locale is always equal to c according to the observer who is there. That is, every infinitesimal region of spacetime may be assigned its own proper time, and the speed of light according to the proper time at that region is always c. This is the case whether or not a given region is occupied by an observer.
That is, clocks at higher altitude tick faster than clocks on Earth's surface. This effect has been confirmed in many tests of general relativity, such as the Pound–Rebka experiment and Gravity Probe A. In the Hafele–Keating experiment, there was a slight increase in gravitational potential due to altitude that tended to speed the clocks ...
If you travelled a year at 95% the speed of light; you'd age one year, and people on Earth would age 3.2 years! But if you were going 50% the speed of light it would only be 1.15 years. The effect ...
This combines the effects of time dilation due to motion (by factor α = 0.6, five years on Earth are 3 years on ship) and the effect of increasing light-time-delay (which grows from 0 to 4 years). Of course, the observed frequency of the transmission is also 1 ⁄ 3 the frequency of the transmitter (a reduction in frequency; "red-shifted").
The orbits of these binary pulsars are decaying due to loss of energy in the form of gravitational radiation. The rate of this energy loss ("gravitational damping") can be measured, and since it depends on the speed of gravity, comparing the measured values to theory shows that the speed of gravity is equal to the speed of light to within 1%. [22]
Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula [2] [3] = = where: G is the universal gravitational constant (G ≈ 6.67 × 10 −11 m 3 ⋅kg −1 ⋅s −2 [4])
Now, by Liouville's theorem, time-reversal of all microscopic processes implies that the amount of information needed to describe the exact microstate of an isolated system (its information-theoretic joint entropy) is constant in time. This joint entropy is equal to the marginal entropy (entropy assuming no correlations) plus the entropy of ...