Quantized Spacetime

star field

7  Special Relativity

If mass particles are to average speeds slower than light in quantized spacetime, they must still make a mixture of pauses at zero speed and transfers at light speed to achieve the average speed. The transfers, however, require bosons, which are massless and ageless. How can fermions meet these restrictions? I assume they lose their mass and stop aging to make each transfer. In continuous spacetime, the reduction of aging with speed is computed by Einstein’s special relativity as time dilation, which has been confirmed experimentally.

In quantized spacetime, a reduction of aging arises when a particle enters a quantum in transfer state from one in a pause state, because aging can only occur  in the pause state. As speed goes up, pauses get fewer and there are fewer quantum intervals for aging. The process achievement of an average speed is illustrated in the figure below, where the progress of a particle moving at one quarter the speed of light is shown.

In the top horizontal string of quanta, the speed is controlled by a repeated group of four quanta, marked with a red underline under one yellow  (transfer) quantum and three blue (intrinsic) quanta. In every group of four quanta, a transfer of one Planck length takes place in four Planck seconds. In the three intrinsic quanta the particle simply moves through time steps alone, in a transfer quantum a particle moves through both space and and time, but its time does not increase aging.The sequence is as follows.

transfer and intrinsic quanta

Start with a blue quantum to the left of a yellow quantum. The particle dwells one Planck interval in that quantum then spends one Planck interval in transfering to the yellow transfer quantum. The particle then makes an intrinsic transfer in one planck interval into a blue quantum, moving through no distance. A transfer quantum provides only one transfer and after that changes its state in become an intrinsic quantum, unless it is followed by another transfer quantum. So the movement caused by the change of state is simply a movement in time. The particle then spend one more time interval in the quantum in its intrinsic state. Then the cycle repeats. There  are three intrinsic time intervals and one transfer time interval. In effect the particle moves one Planck length in four Planck time intervals, so its speed is one fourth of the speed of light.

The two-dimensional array that below the single line of quanta at the top provides an intrinsic time axis and a transfer time axis. The vertical line of blue intrinsic quanta on the left represents the aging taking place in a particle that is  not moving. The other two strings, at different speeds, show how movement slows aging by replacing intrinsic quanta with transfer quanta. In the bottom string, the three quanta interspersed with a transfer quantum have only aged by two blue quanta whereas the all-intrinsic line has aged by three quanta.


Mass Increase

In special relativity, mass is not predicted to decrease as speed goes up, but to increase, and this too is confirmed experimentally. The explanation in quantized spacetime is as follows. Particle mass is measured in the pause state, as is the radioactive lifetime of the particle. When a particle transfers between quanta, its mass is removed together with aging time. The latter is replaced by transfer time. To avoid breaking the law of conservation of energy (mass being energy) the mass in the remaining intrinsic quanta, after particles in transfer quanta have lost their mass, must increase. This is the increase experimentally observed. It is inversely proportional to the number of intrinsic quanta remaining. This is how quantized spacetime calculates the mass increase effect of special relativity, the answer being the same as the standard calculation.

It also provides the same values for relativistic mass and momentum, raising again the question of how a particle with mass can move at the speed of light. The answer may be that in one quantum interval the action of a transfer is below the Planck constant, and the energy borrowed for the transfer is returned after the transfer. If so, transfers at light speed become as acceptable in quantized spacetime as virtual particles are in continuous spacetime.  8/14/2020  5:54  7

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