A model, driven by the Einstein's theories of relativity, is suggested. This model tends to correlate the relativistic view on time dilation with the current models and conclusions on time perception. The model uses energy ratios instead of geometrical transformations to approach and express time dilation. Brain mechanisms like the arousal mechanism and the attention mechanism are interpreted and combined. Matrices of order two are generated to contain the time dilation between two observers, from the point of view of a third observer. The matrices are used to transform an observer time to another observer time. Correlations with the official time dilation equations are given in the appendix.
A mathematical demonstration is made to derive the inverse form of the Lorentz factor using as a tool the centripetal acceleration of a clock hand. When a resistance is applied against the motion of a clock hand, the centripetal acceleration decreases. The ratio between the final centripetal acceleration of the clock hand and its initial centripetal acceleration gives a ratio between two squared velocities. By squaring root this ratio, we obtain the equivalent form of the inverted Lorentz factor.
This paper shows how the time dilation due to motion, calculated normally using the Lorentz factor, can be encoded in the real part of a complex number by using the Euler's formula. The imaginary part of this complex number will contain the velocity. It also shows how the time dilation due to gravitational attraction can be encoded using the same formula. A combination of time dilation and gravitational time dilation is presented using this formula. The magnitude of this complex number represents the constancy of the speed of light.
In compliance with the principle of relativity, a time dilation equation expressed as an energy ratio is used to combine time dilation due to motion and due to gravitational attraction. To show the correlation with the time dilation equations, the Lorentz factor and the gravitational time dilation equations are derived from the equation. The equivalence between the time dilation due to motion and due to gravitational attraction emerges and a combination of both is made possible using the energy ratio equation.
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