Figure 4 Space-time properties for a comparison of two inertial systems K’ and K. For example, when inertial system K’with a velocity of 3 m/s is compared with the inertial system K’with a velocity of 0, when observed from K, the time of K is lengthened and space is shortened. In contrast, when observed from K, the time of K’is shortened and space is elongated .
⑶ Velocity is two-dimensional, and there is an infinite but not instantaneous velocity. The inertial system principle and universal velocity invariant principle follow Axiom 1 and do not follow the relativity principle; in other words, a certain moment of the clock only corresponds to a specific distance in space and does not correspond to other distances. For example, infinite time only corresponds to infinite distance, not to a finite distance (such as a distance of 1 meter), and a finite clock scale only corresponds to a finite distance, not to infinite distance. Unlike ⑵, here the velocity of light is not the only basis for defining space and time, allowing for the existence of arbitrary values for velocity. Two implications arise from this arbitrary velocity, First, it is meaningful that the space-time is not equivalent. For example, although 1 second is equivalent to 300,000 kilometers, it is not equivalent to 3 meters at 3 m/s, but a velocity of 3 m/s is meaningful. Second, the magnitude of velocities can be compared. For example, the velocity of light has the same quantitative value as the unit of time for 3 m/s. The stationary state of it, unlike the Cartesian coordinates of relativity, should be given as 0/∞. The single-dimensional nature of Axiom 1 denies the correctness of this concept. The essence of (2) and ⑶ are still Axiom 2.
⑷ There is only one-dimensional space or time, and there is no concept of velocity, regardless of whether it is infinite or finite. Space and time are independent of each other here, with a certain moment of the clock only corresponding to the moment itself, not to other moments or any distance or position in space. Likewise, a certain distance in space corresponds only to its own distance, not to any other distance in space or any time of the clock. Therefore, the inertial system principle of Axiom 1 and the universal velocity invariant principle are followed here. Velocity has become single-dimensional space or time and Only the finite and infinite space, or finite and infinite time can be talked about.. If the concept of velocity is being referred to, the two values (distance in space and time in time) are neither equivalent nor dependent on each other. The essence of (4) is Axioms 1 and 3. For instance, for a velocity event moving to infinite distance in 1 second, it can be seen from the above definition that 1 second is not equivalent to infinite distance, because the concept of a single event of infinite speed being associated with time and space is meaningless. Rather, 1 second and infinity exist independently as two events: an event of infinitely great space in one dimension and another event of 1 second in time in one dimension.
6 Meaning of one-dimensional velocity
By comparing (3) and (4), we can outline their specific features. For feature (3), the velocity is determined by the ratio of the two dimensions. There is an infinitely great velocity, expressed by ∞/dl, where ∞ is infinitely great and dl is infinitesimally small. A state of zero velocity is denoted as dl/∞, and dl does not equal 0 here (due to the nature of Axiom 2). Feature (3) follows the inertial system principle of Axiom 1 and the universal velocity invariant principle ,but does not follow the relativity principle, so the Cartesian coordinate system does not apply to (3). For example, a Cartesian coordinate system with a velocity of 0 (i.e., static) does not exist. Motion is absolute and there is no static state, so a comparison of two inertial frames is a comparison of two specific states. For example, let the inertial system K' be the infinite velocity and the inertial system K velocity be 0. Figure 5 shows a comparison of the two inertial systems. Their spatiotemporal properties are determined by two points (a and b). When observed from K', the time lengthens and space shortens in K. In contrast, from the point of view of K, the time in K’ is shortened and the space is lengthened. Because Cartesian coordinates do not apply to (3), the Lorentz transformation does not make sense here. The transformation of the magnitude of space-time is a universal transformation, which is determined by the magnitude of a and b.