Standard clock

Standard clock

It is an important concept in special relativity. Its definition: if the time interval between two points on the world line of a clock is equal to the world line length of two points, then the clock is a standard clock.

General description

Clocks in daily life can be regarded as standard clocks, such as electronic clocks, hourglass or atomic clocks. When describing the speed of an object with respect to a specified reference frame, the speed can be expressed by the following formula: v = x / T, where the time or time interval T is measured by the standard clock of the specified reference frame. In particular, the world line of photons is always an optical geodesic line, and its line length is always zero, that is, the time measurement (also called fixed time) of its standard clock is always zero. Generally speaking, the time of photons does not pass.

Definition supplement

1. Because the system of geometric units is often used in the theory of relativity, taking the speed of light C = 1, the above definition can be expressed as: DT = DX / C under the international system of units

2. Travel time rate: the reading of any two points on the world line is equal to the line length

Clock synchronization of standard clock

definition

According to the standard clock definition, the observer's inherent time is equal to his world line length. As for which point on the line to choose as the zero point of the world line T, it only involves the initial setting, which is arbitrary when there is only one observer. However, if a reference frame is considered, the selection of the standard clock zero point of each observer must meet certain requirements. For example, if R is an inertial reference frame, G is one of the observers, and if P 0 belongs to G as the fixed time zero point of G, then Z 0 represents the hypersurface passing through P 0 and orthogonal to all observers' world lines, then any observer G1 in R system must choose the intersection of Z and his own world line as the zero point of inherent time. This requirement is the clock synchronization of standard clock

practice

At first glance, clock synchronization can be achieved by the following methods: G sets its standard clock to zero (event P0) and tells G1 "now set the clock to zero". However, since it takes time for the signal to propagate, if Q represents the event that G1 receives the notification, then q is not necessarily on the hypersurface Z0. If Z1 executes the command, that is, to set its own clock to zero in event Q, it will not reach the requirement of clock synchronization. Here is a clock synchronization method. Observer g told G1 in advance, "you have a mirror on your body. When the mirror receives my light, set your clock to zero." Then, observer g lights up to G1 at a certain time (event P1), and is reflected when it reaches G1 (event P2). P3 represents the event that G receives the reflected light. Let P4 be the end point of p1p3 on the G world line (measured by the length of the world line), then the observer g only needs to set his own clock to zero at this point to synchronize the G1 clock with his own clock. This approach uses the property that the speed of light is independent of direction (photons walk like optical geodesics)

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