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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 ...
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 ...
The characteristic aspect of the machine's design is its automatic performance of elapsed-time calculations, as calculating the difference between two times manually is a tedious and error-prone process, and the machines quickly gained popularity. Abbott founded the Calculagraph Company in New York City, and later moved to New Jersey. The ...
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 ...
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The fundamental reason for merging space and time into spacetime is that space and time are separately not invariant, which is to say that, under the proper conditions, different observers will disagree on the length of time between two events (because of time dilation) or the distance between the two events (because of length contraction).
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