No, because statistical proof doesn't make sense. Nor is there any ``sphere of light''.

Special relativity describes the property that Maxwell's equations, in the absence of sources, are invariant under global Lorentz transformations, if the fields transform in a certain way under Lorentz transformations (the starting point is the remark that any solution of Maxwell's equations is a solution of the (in)homogeneous wave equation and the homogeneous wave equation is invariant under global Lorentz transformations). This then implies how the sources should transform, if they're present. And what matters are the quantities that are invariant under global Lorentz transformations. That's all there is to it.

Dear Ismail Abbas , Science is following speed light as constant phenomenon, while this light is not actual natural sunlight that it does not have constant speed with massive different frequencies, wavelength, and visible/invisible character. . Thus the whole SR , and E/m equation become obsolete. Article Title: Science is wrong on…Light & Photon

In his original thought experiment in 1905, Einstein came up with 5 hypotheses that led to some giant fundamental conclusions[1,2]:

First, it provided theoretical evidence for relativistic changes in time, length, and relative velocity previously known as imperial Lorentz transformations. Secondly, he also discovered the relativistic mass transformation which was eventually crowned by the most important equation in physics, namely the mass-energy equivalence E = mc^2.The original derivation of special relativity a century ago in a straight and understandable picture is simple and based on 5 consecutive irreducible assumptions, but it can be reformed as shown below in parentheses and in bold letters:

*I-the laws of physics are the same for all inertial frames of reference.

There is no preferred frame of reference, which is a valid universal law of physics.

[Obviously, this hypothesis is untouchable.]

**II - the speed of light in a vacuum is a universal constant regardless of the uniform motion of the observer. (In agreement with the Michelson-Morley interference experiment of 1887).

Keeping in mind that this is the upper speed limit of any object with rest mass or even massless photon.

Einstein said that this was also the maximum possible speed of information transfer.

[We have a reservation here, it is not c in itself which is a universal constant, but the mass-energy equivalence relation E0=m0c^2 which is the original universal law and therefore c^2 is constant. Thus c^2 is a universal constant for transforming energy and rest mass, just like Boltzmann's constant k, Planck's constant h, the gravitational constant G, etc. They are all defined by imperial laws which have no theoretical proof. The constancy of c is a consequence of the constancy of c^2.

Additionally, the way Einstein proves Lorentz transformations is based on the constancy of c but again we have reservations about this saying. We'd better assume that Lorentz transformations are also the universal law of physics and need no proof.]

***III-Einstein's third hypothesis is that there is no contraction in space perpendicular to the direction of movement x.

In other words, y1=y2 and z1= z2,

[Hypothesis III and the resulting equation 4 below are in full agreement with theory and experiment.]

However, the famous Noble Prize scientist R. Feynman disagreed with Hypothesis III and continued by assuming relativistic spatial variations normal to motion, i.e. in the y and z directions and arrived at its own special relativity which we consider to be inaccurate.]

Figure 1 shows the propagation of Einstein's light sphere as seen by two different observers, one is stationary at its center and the other is moving away in the x direction at a uniform speed v and, surprisingly enough, is always kept at the same center. It follows from hypotheses I and II that the two equations describing the same luminous sphere event should be identical and that their centers O1 and O2 coincide. Note again that both observers will also be at the same coincident centers of the same sphere.

The two propagation equations observed by the two inertial frames 1&2 can be written as follows:

x1^2+y1^2 +z1^2 =c^2 t1^2 . . . . . . . . . . . . (1). . .observed by the rest frame (Einstein station)

And,

(x2-vt2) ^2+y2^2 +z2^2 =c^2 t2^2 . . . (2). . .observed by moving reference (Einstein train).

Note again that Einstein assumed that both observers would continue to be at the center of the same sphere of light for the entire time t >0! Fig. 1.

Therefore, x1^2+y1^2 +z1^2 -c^2 t1^2 = (x2-vt2) ^2+y2^2 +z2^2 -c^2 t2^2 . . . . . . (3)

Now, using Einstein's third hypothesis, there is no change in space perpendicular to the direction of movement x. In other words, y1 = y2 and z1 = z2, so equation 3 reduces to:

x1^2+ +c^2 t1^2 = (x2-vt2)^2+c^2t2^2 . . . . . . (4)

For Einstein to solve Equation 4, he had to provide an additional forth hypothesis:

I****V-Einstein's fourth hypothesis starts from the proposition that relativistic transformations of space and time must be linear like mother nature itself and that space-time transformations preserve the constancy of the volumetric element of the invariant 4D unit space, for two inertial observers.

measure the length of the station.

x1t1(at the station) =x2t2 (in the train).

In mathematical language with Gamma as parameter,

x1=x2.Gamma and,t1=t2/Gamma

solving Eq,4 for Gamma you simply get,

Gamma=SQRT[1/(1-v^2/c^2)] . . . . . . (5)

which is the Lorentz transformation itself. In other words,

x2 (moving frame) = x1 (resting frame) / Gamma. (6) called spatial contraction,

and,

t2(moving frame) =t1(rest frame) * Gamma. (6). . called time dilation.

[Here again we must agree with Einstein's equations. 6 and 7 which perform Lorentz transformations resulting from the constant speed of light c. Alternatively, we can view Lorentz transformations as an imperial universal law of physics consistent with the claim of constancy of the speed of light c.

Only we assume that although the Einstein "proof" or more precisely the Einstein validation of the Lorentz transformations via his sphere of light  is rigorous but  it is the Lorenz transformations which is a universal law of physics that produce the Einstein sphere of light and not the opposite.

Therefore, x=x0/Gamma, . . . . (8 known as length contraction.

and,

t=t0 *Gamma, . . (9) known as time dilation.

Gamma >= 1 .

Again, in the above relationships of length contraction and time dilation, the notations x0, t0 replace x1 and t1 in Figure 1 and represent the observer's measurements in the marker fixed 1 (Einstein station) and x and t replace x2. , t2 and represent the measurements of the observer in the moving frame 2 (Einstein train).

Note that x0 and t0 are conveniently called true length and real time while x and t are called measured length and measured time which converge to x0 and t0 as v approaches zero.

*****V-Einstein's fifth hypothesis

Einstein used his Lorentz-derived transformations of time, length, and relative velocity to advance and ultimately find his revolutionary law of relativistic mass transformation,

m=m0/SQRT (1-v^2/c^ 2). . . . . . (10)

To arrive at eq. 10, he performed another thought experiment that considered two balls of the same mass m colliding vertically and applied the universal laws of conservation of energy and momentum before and after the collision, as observed in both in the rest frame and in the moving frame with uniform speed v.

He thus concludes the relativistic formula for mass transformation (10).

Next, Einstein considered Newton's second law of motion, in its general form, to be a universal relativistic invariant law and used it as follows:

F = d (mv)/d t,

where,

m=m0/SQRT (1-v^2/c^2)

It was simple to show that,

d (Work done W) = F. dx =Kinetic Energy EK =dm c^2d W=v . d p ​​​​=v d (Gamma m (0) v)= m(0).v^2 d Gamma +m(0) v d v .(11)

By integrating over both v and Gamma, we arrive at an increase relativistic of EK= m0 c^ 2 (Gamma-1).

Therefore, E(total)= (m0 +dm) c^2, that is,

the total energy E(total)=m c^2. . . . . . (12).

Equation 12 is the well-known mass-energy equivalence relation. This means that mass can be transformed into energy, called mass annihilation, and energy can be transformed into mass, called mass creation.

###

Let us now move on to the statistical derivation of Einstein's special relativity without using his sphere of light but relying on the statistical chains of matrix B:

There are two approaches to statistically deriving equation 3, both of which turn out to be the same.

Either to study the numerical values ​​of the time-dependent solution of the heat equation through the strings of the B matrix or via the geometry of the 4D x-t unit space.

1- In the 4D unitary statistical space x-t: the time t is orthogonal to x, y, z so we define the diagonal D as given by,

D^2=x1^2+y1^2 +z1^2 -c^2 t1^2 . . .B1

for the station reference frame,

And,

D^2 = (x2-vt2) ^2+y2^2 +z2^2 -c^2 t2^2. . . .B2

for the train frame of reference,

The two observers in the two benchmarks must have the same measurement, the same geometric diagonal D.

by substituting y1=y2 and z1=z2 in the two equations B1,B2 above, we arrive at equation 4, namely,

x1^2+ c^2 t1^2 = (x2-vt2)^2+c^2t2^2 . . B3

To solve equation B3, use the equality of the elements of 4D space, namely:

x1, t1 =x2. t2.

Or in mathematical language with Gamma as parameter,

x1=x2.Gamma and,t1=t2/Gamma

and solving for Gamma, we conclude that,

Gamma=SQRT[1/(1-v^2/c^2)] . . . B4

Equation B4 is identical to equation 5.

and using the relativistic mass transformation proven by Einstein's thought experiment,

m=m0/SQRT (1-v^2/c^2)

And applying Newton's second law of motion,

F = d (mv)/dt,

We can arrive at mass-energy equivalence.

E(total)=mc^2.

[As far as I know, there is no way to arrive at the mass-energy equivalence relation without going through Newton's second law of motion in its general form.]

As simple as that.

To be continued.

1-Relativity, special and general theory, by Albert Einstein, Ph.D. Professor of physics at the University of Berlin, translated by Robert W. Lawson, M.Sc., University of Sheffield, New York, Henry Holt and Company , 1920.

(PDF) A rigorous reformulation of Einstein's derivation of the special theory of relativity.

2- I. Abbas, A rigorous reformulation of Einstein's derivation of the special theory of relativity, Researchgate , IJISRT review, Feb 2022.