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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]
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 ...
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 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.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true ...
Time: The interval between two events present on the worldline of a single clock is called proper time, an important invariant of special relativity. As the origin of the muon at A and the encounter with Earth at D is on the muon's worldline, only a clock comoving with the muon and thus resting in S′ can indicate the proper time T′ 0 =AD.
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