Proper Time

proper time [′präp·ər ′tīm]

(relativity)

The time measured by an ideal clock that is carried along with a specified particle, and is based on the invariant timelike space-time intervals between points along the particle's trajectory.

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Proper Time 

in the theory of relativity, the time measured by a clock in the proper frame of reference of a moving body. In other words, proper time is the time measured by a clock rigidly attached to the body—that is, a clock at rest with respect to the body and located in the same place as the body.

The duration of a process, as measured by an observer outside the body in which the process occurs, depends on the relative velocity of the observer and the body. In measurements far from attracting bodies, the special theory of relativity can be used (seeRELATIVITY, THEORY OF). Suppose the measurements are made in some inertial (laboratory) frame of reference and the body moves with the constant velocity v relative to the frame. The relation between the proper time interval Δτ and the observer’s time interval Δτ is then , where c is the speed of light in a vacuum. If v varies with time, then the proper time interval corresponding to the observer’s time interval between t₁ and t₂ is

When gravitational fields are present, the general theory of relativity must be used. The strength of a gravitational field is indicated by the absolute value of the gravitational potential φ. The potential is in fact negative; outside the field, φ is assumed to be equal to zero. The larger the absolute value of φ, the slower the flow of the proper time of a process in the gravitational field from the point of view of an observer outside the field. For fields that are sufficiently weak—that is, when ǀφǀ/c² << 1—the relation between the proper time interval Δτ according to a stationary clock at a point with the potential φ and the time interval Δt for a stationary observer outside the field is given by the equation Δτ = (1 – ǀφǀ/c²)Δt.

It can be seen from the above equations that the proper time interval is always shorter than the time interval measured in any other frame of reference.

I. IU. KOBZAREV