iSoul In the beginning is reality.

Linear clocks and time frames

The idea of a linear clock was mentioned before here, here, and here.

One bar on top of anotherOne bar shifted on another

Consider two bars or rods, one on top of the other (left), each with a zero point aligned at first. The top one moves at a constant rate relative to the other, which is at rest. After a time T, the top bar has moved an interval measured by the difference between the zero points of the bars (right). The length that B moved relative to A measures the time of motion.

Side note: a 12-inch ruler turned into a circle would form the markings for a 12-hour clock. The hours of time would correspond to inches of length.

A time frame of reference (TFR), or time frame, is a frame of reference for time. Like a space frame of reference (SFR) it is composed of rigid bars or rods that can in principle be extended indefinitely.

Three contiguous barsTwo bars moving along another bar

Consider three contiguous rigid bars or rods: A, B and C, as above. A is at rest relative to B and C, B moves relative to A at a given reference rate, and C moves relative to A at a rate to be determined. All three bars are aligned with a zero point at the start (left). The positions of the bars indicate the length and duration of motion after B moves for a time T and C moves for a length L (right).

The length of C’s motion is measured by the interval L between the starting and ending positions of C projected onto A, that is, the zero point of C and the length L on A are simulstanceous. The duration of C’s motion is measured by the interval T between the starting and ending positions of B’s zero point in relation to A and simultaneous with C.

Thus the length of a motion is its measure relative to a bar at rest, and the duration of a motion is its measure relative to a bar in motion at a reference rate.

Imagine contiguous bars or rods such as A and B linked like a monorail that can be oriented in any direction. Then consider a network of such pairs of rods in three orthogonal directions. Call this network a time framework of reference (TFWR).

Note that both length and duration are measured in three dimensions, which are 3D space and 3D time respectively. Let there be an equivalence relation which defines a scalar time for all places in space. Let there be an equivalence relation which defines a scalar stance for all instants in time.

In this way 3D space with scalar time and 3D time with scalar stance are defined. These may be combined in a 6D manifold of 3D space and 3D time in which either space or time may contract into a scalar.

This shows how motion may be conceived in two ways: (1) as an entity in motion relative to a frame at rest, or (2) as an entity at rest relative to a frame in motion, i.e., a time frame. The entity is in 3D space if the frame is at rest. The entity is in 3D time if the frame is in motion.

For example, from the perspective of an observer in the frame of a landscape, a vehicle on the road is moving in a 3D space frame of the landscape at rest. From the perspective of an observer in the frame of a vehicle, the landscape appears to move but is actually at rest, and the vehicle is moving with a 3D time frame.

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