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The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. [1] The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line.
A different term, proper distance, provides an invariant measure whose value is the same for all observers. Proper distance is analogous to proper time. The difference is that the proper distance is defined between two spacelike-separated events (or along a spacelike path), while the proper time is defined between two timelike-separated events ...
On this usage, comoving and proper distances are numerically equal at the current age of the universe, but will differ in the past and in the future; if the comoving distance to a galaxy is denoted , the proper distance () at an arbitrary time is simply given by = where () is the scale factor (e.g. Davis & Lineweaver 2004). [2]
This is an accepted version of this page This is the latest accepted revision, reviewed on 12 January 2025. Directionality of traffic flow by jurisdiction Countries by direction of road traffic, c. 2020 ⇅ Left-hand traffic ⇵ Right-hand traffic No data Left-hand traffic (LHT) and right-hand traffic (RHT) are the practices, in bidirectional traffic, of keeping to the left side and to the ...
A synchronous frame is a reference frame in which the time coordinate defines proper time for all co-moving observers. It is built by choosing some constant time hypersurface as an origin, such that has in every point a normal along the time line and a light cone with an apex in that point can be constructed; all interval elements on this hypersurface are space-like.
The basic formula for DR is Distance = Speed x Time. An aircraft flying at 250 knots airspeed for 2 hours has flown 500 nautical miles through the air. The wind triangle is used to calculate the effects of wind on heading and airspeed to obtain a magnetic heading to steer and the speed over the ground (groundspeed).
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A fuller explanation of the concept of coordinate time arises from its relations with proper time and with clock synchronization. Synchronization, along with the related concept of simultaneity, has to receive careful definition in the framework of general relativity theory, because many of the assumptions inherent in classical mechanics and classical accounts of space and time had to be removed.
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