What is a clock? it is a device that measures time, but what are the essentials of a clock? I submit these are the essentials of a clock:
(1) A clock requires a uniform motion. Because only the kinematics (not the dynamics) are significant, a uniform rotation is acceptable. But because the result will be represented as a line – a timeline or time axis – a linear uniform motion has a more direct connection with what is measured, so let us take the first essential as a uniform linear motion.
(2) In order for clocks to be measuring alike, it is necessary that there be a standard rate for all clocks. In addition, clocks should have a standardized beginning point, so that clocks are interchangeable.
(3) A clock requires a pointer which indicates the present time on a time scale as it moves at the standard uniform rate. This would be the hands and dial on a common analogue clock. On a linear clock it is a part whose position in motion is interpreted as the present value of time. The pointer and scale are essentials of a clock.
Furthermore, a clock must be interpreted as showing the present time of the observer’s rest frame.
All the essentials of a clock can be represented by a frame in standard uniform motion relative to the observer’s rest frame. In that case, a clock should be definable in terms of frames of reference: one rest frame and one frame in uniform motion relative to the observer’s rest frame, as in the following.
An observer is a body capable of use as a measurement apparatus. An observer makes measurements relative to a frame of reference. A frame of reference is a physical system relative to which motion and rest may be measured. An inertial frame is a frame in which Newton’s first law holds (a body either remains at rest or moves in uniform motion, unless acted upon by a force). A frame of reference here shall mean an inertial frame.
An observer basically is a rest frame since they are so closely associated. In classical physics there is a universal time, which can be associated with a clock defined by a frame always in motion relative to the observer’s rest frame. This is a universal clock.
A rest frame of observer P is a frame at rest relative to P. A motion frame of observer P is a frame in uniform motion relative to P. Each observer has at least one rest frame and at least one motion frame associated with it. In (3+1) only one dimension of an observer’s motion frame is used, so the other two dimensions are hidden. In (1+3) only one dimension of an observer’s rest frame is used, so the other two dimensions are hidden.
A motion frame with a standard rate of motion is a clock frame. Positions (chronations) on the dimension in relative motion of a clock frame provide the time for the observer. That time is assigned to the observer’s whole rest frame for (3+1) coordinates. Positions (locations) on the dimension of the rest frame in motion relative to the clock frame provide the stance for the observer. That stance is assigned to the observer’s who motion frame for (1+3) coordinates.
Space is the union of all rest frames. Accordingly, there is no single rest frame for all of space. However, each rest frame provides a sample of all of space that is just as good as any other rest frame. So we may take any rest frame as the frame for all of space.
Space is the geometry of locations in R3. A place point is a spatial point. The space origin is a reference place point. The location of a place point is the space vector to it from the space origin.
Chron (3D time) is the union of all motion frames. Accordingly, there is no single motion frame for all of time. However, each motion frame provides a sample of all of time that is just as good as any other motion frame. So we may take any motion frame as the frame for all of time.
Chron is the geometry of chronations in R3. A time point is an instant. The time origin is a temporal reference time point. The chronation of a time point is the chron vector to it from the time origin.
A frame of reference is unmarked if there are no units specified for its coordinates. A frame of reference is marked by specifying (1) units of either length or duration for its coordinates and (2) an origin point. A space frame of observer P is a rest frame of P that is marked with units of length. A time frame of observer P is a motion frame of P that is marked with units of duration.
A clock may be started and stopped at the will of the observer, as with a stopwatch. A clock measuring time as a dependent variable will have to stop or be continuously recorded. A clock measuring time as an independent variable will have a pre-set limit or continue uninterrupted, which is represented as a clock that runs continuously.
Speed, velocity, and acceleration require an independent motion frame. Pace, lenticity, and relentation require an independent rest frame, which measures not chronation on a timeline, but location on a placeline, which is measured by an odologe (see here).