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This observer finds that time t passed between the front of the train passing the post, and the back of the train passing the post. Because the two events - the passing of each end of the train by the post - occurred in the same place in the ground observer's frame, the time this observer measured is the proper time. So:
The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the medieval sense of "reconciliation of a difference". The two times that differ are the apparent solar time , which directly tracks the diurnal motion of the Sun , and mean solar time , which tracks a theoretical mean Sun with uniform ...
where Δt is the time interval between two co-local events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on their clock), known as the proper time, Δt′ is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer ...
Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events, as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational ...
This is a different voyage than the one shown above, as both schemes take the same assumed total point-of-view time: T=12 (stay-at-home), resp τ=12 (ship), so the results of the calculated other-one's times must be different: τ=9.33 (ship), resp T=17.3 (stay at home). In the standard proper time formula
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In the equation given at the beginning, the cosine function on the left side gives results in the range [-1, 1], but the value of the expression on the right side is in the range [,]. An applicable expression for ω ∘ {\displaystyle \omega _{\circ }} in the format of Fortran 90 is as follows: