Let consider the following case:
Three particles moving with different velocities are hitting the probe positioned in the point x_{0}t_{0} of the observer's frame.
In the Lorentzian reality position of the probe can be described with one point x_{0}t_{0} The world lines of bodies hiting the probe are intersecting each other in the point x_{0}t_{0} Different angles of worldlines correspond to different velocities. The angles of the worldlines must be within the range +/ 45^{0}(in this picture) 
In the New Euclidean Reality (FER  Fourdimensional Euclidean Reality) the position of the probe is represented by the sphere
(in the picture it's the circle) with radius x_{0} and center in the point t_{0} on the time axis of the observer becuse:

In the FER, the representation of the point x_{0}t_{0} is a sphere with radius x_{0} and origin in point t_{0} on the observer's trajectory. All points on this sphere correspond to
one and the same moment of time t, and for particle moving from one point of the sphere to another, the flow of time is equal to zero. The sphere in the FER is a representation of the point in the xt spacetime, because for the observation of each of the bodies, a different direction in the FER has to be chosen as the space dimension. 