New Transformation Equations and the Electric Field Four-vector

Proper Time and Length

If the spacetime interval, , in either frame is between events that are separated, solely, by a time interval, i.e. , then , where is the proper time. Since the proper time is the only component in the interval, we have . Similarly, if the events are separated solely by a space interval, i.e. , then , where is the proper length, hence, . The proper time, , and the proper length, , are always the maximum measurements of time and length made between events in any frame. We put no primes on the proper time or length, since they are the same in all reference frames. If there are space and time components of the spacetime interval between events in a reference frame, then neither component is proper and both will be less than the proper value. However, an observer can always determine the proper values from his own components. In general, the proper value of any quantity, in this theory, will be its maximum value.

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