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Services for Science and Education – United Kingdom 120

European Journal of Applied Sciences (EJAS) Vol. 12, Issue 5, October-2024

• from them were made incorrect conclusions about physical unreality of discovered

400 years before creation of SRT by Scipione Del Ferro, Niccolo Fontana Tartaglia,

Gerolamo Cardano, Lodovico Ferrari and Rafael Bombelli2 [8] imaginary numbers and

the existence in nature of our only visible universe, in which all measurements are

carried out only using real numbers.

As can be seen from the graphs (see Fig. 1a, b,c) of relativistic formulas of this version of SRT

m = m0 / √1 − (

v

c

)]

2 (1)

Δt = Δt0√1 − (

v

c

)

2 (2)

l = l0√1 − (

v

c

)]

2 (3)

where

m0

is the rest mass of the moving body;

• m - relativistic mass of the moving body;

• 0 t - rest time of a moving body;

• t - relativistic time of a moving body;

• 0

l - rest length of a moving body;

• l - relativistic length of a moving body;

• v - the velocity of the moving body;

• c - speed of light;

in the range of pre-light speeds v<c all these quantities take values measured by real numbers,

in the range of superluminal speeds v>c takes values measured by imaginary numbers, and at

the speed equal to the speed of light v=c, the function

m( v )

has a gap. Therefore, in the pre- light speed v<c range formulas (1)-(3) have been explained. And in the superluminal range of

speeds v>c the results of calculations in the form of imaginary numbers the creators of SRT

could not explain. And in modern textbooks of physics they are not explained till now. After

all, what is 5 meters, 6 grams and 7 seconds is clear to everyone, but what is 5i meters, 6i

grams and 7i seconds, where

i = −1

, and now no one can explain. Moreover, as can be seen

from the graphs of formulas (1)-(3), in the superluminal range of velocities v>c (see Fig. 1a, b,

c) these formulas correspond to physically unstable processes that cannot exist in nature at

all.

Indeed, let us assume that the material body in the range

v  c

for some reason began to

move faster. Then its mass according to the function graph

m( v )

in Fig. 1a will decrease. But

2 And perhaps even before them imaginary numbers were discovered by Paolo Valmes [9], who was burned alive at

the stake by the Spanish Inquisitor Tomas de Torquemada.

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121

Antonov, A. A. (2024). Mathematical Sciences: From the Experimentally Proved Principle of the Physical Reality of Imaginary Numbers it Follows

that the Invisible Afterlife World, Mentioned in All Religions, Really Exists. European Journal of Applied Sciences, Vol - 12(5). 119-145.

URL: http://dx.doi.org/10.14738/aivp.125.17569

because of this lighter body will move faster. This, according to the graph of the function, will

lead to a further decrease in the mass

m( v )

of the moving body. And this will again lead to an

increase in the velocity v of the material body. And so on. Therefore, in the end this material

body with zero mass and infinitely high-speed flies to 'nowhere'.

And assuming that the material body on the graph of the function

m( v )

in the range

v  c

for

some reason began to move slower and reasoning in a similar way, we will come to the

conclusion that this material body moving slower and slower, will overcome the point of

astrophysical singularity v=c and, being in the range v<c will, stop.

So, at any point in the range

v  c

on the graph of the function

m( v )

the ongoing process will

indeed be unstable and therefore cannot exist.

And so, the fate of SRT hung in the balance. After all, no one would not need a theory that even

its authors could not explain. But SRT was saved by the fact that in it introduced a postulate

called the principle of non-exceeding the speed of light, the meaning of which is clear from its

name. And from this postulate followed that the formulas (1)-(3) in the superluminal range of

speeds

v  c

do not need to be explained, since imaginary numbers allegedly do not describe

any processes that do not exist in nature.

Fig. 1: Graphs of functions

m( v ), t( v )

and

l( v )

corresponding to the existing and the

corrected versions of the STR in the subluminal

v  c

and superluminal

v  c

ranges

Indeed, let us assume that the material body in the range for some reason began to move

faster. Then its mass according to the function graph in Fig. 1a will decrease. But because of

this lighter body will move faster. This, according to the graph of the function, will lead to a

further decrease in the mass of the moving body. And this will again lead to an increase in the