Space time interval conservation in FER and its consequences. Tachions do not exist, acceleration to the speed interpreted as the speed of light is possible

In the Lorentzian space-time:

In the model of Euclidean Reality (FER):

The space-time interval is equal to the distance
in the Lorentzian space-time. This distance can be:

• positive
• equal to zero
• imaginary (square of the distance can be negative)

In the figure below is presented observation of object moving along the black trajectory, by observeres moving along trajectories green and blue (both observers have common space-axis which has to be perpendicular to the observed object's trajectory).

In the FER model the idea of the space-time interval is reduced to the cases of mutual observations.
The space-time interval is here equal to the proper time of observed object
Its properties:

• can be positive
• can't be equal to zero (if there no exists any non zero factors in the interval formula)
• can't be imaginary (square of the distance can not be negative)

CONCLUSIONS:

In the Lorentzian space-time:

In the model of Euclidean Reality (FER):

• The space-time interval can be imaginary then tachions (hypothetical superluminal particles - for which the space time interval is imaginary) can exist
• The space-time interval equal to zero is equivalent to existence singularities. It means that, for instance, any object, having non-zero mass, can not reach the speed of light (for motion with the speed of light the space-time interval is equal to zero)

• The space-time interval can NOT be imaginary then tachions can NOT exist             
         
• The space-time interval equal to zero is equivalent to moving of an object along trajectory being perpendicular to the trajectory of an observer. It does not mean that any singularity exists here. The object can be then accelerated to the trajectory perpendicular to trajectory of an observer (moving along this trajectory is interpreted as moving with the speed of light), however the observation of process of the acceleration will last to infinity. For instance - a rocket can be accelerate to such trajectory but astronauts will be able to observe themselves accelerating to the speed of light, even many years after their coming back from the interstellar journey