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In relativity, proper time (from Latin, meaning own time) along a timelike world line is defined as the time as measured by a clock following that line. 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 ]
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Proper length [1] or rest length [2] is the length of an object in the object's rest frame. The measurement of lengths is more complicated in the theory of relativity than in classical mechanics . In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously.
The arclength parameter is called proper time and usually denoted τ. The length of M is called the proper time of the particle. If the worldline M is a line segment, then the particle is said to be in free fall. [1]: 62–63 A world line traces out the path of a single point in spacetime.
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.
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]
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Parts of a driver's work day are defined in four terms: On-duty time, off-duty time, driving time, and sleeper berth time.. FMCSA regulation §395.2 states: [5]. On-duty time is all time from when a driver begins to work or is required to be in readiness to work until the driver is relieved from work and all responsibility for performing work.