The STEMU Axiom – the Axiom of Unity - creates problems for modern scientists who ignore its existence. It is simple, clear and incontestably reveals errors based on mathematics models with incomplete relation to reality.
The main reason of crisis in theoretical physics is ignorance or rejection of the STEMU axiom. Its essence is that it is impossible to:
· separate existence of space, energy/matter and time
· separate energy/matter from space
· contemplate their separate existence.
· separate time from space or from energy/matter.
In reality space, energy/matter and time are primary and inseparable from each other as elements of the universe. Almost all modern physical theories contradict this axiom. STEMU must be reflected in all mathematical models describing a changing reality, to assure a foundation of the model in the real world. Motion of any objects in space are inseparable from time.
The Axiom of Unity has been broken by the modern transition to description of microcosm behavior. The result is an impassable jungle and many scientific fables that will need a lot of time to return to a classical and logical way of development. All experiments must proceed within the framework of the Axiom of Unity.
STEMU Axiom applied – Lorentz transformations.
The beginning of relativity was described by Galileo with the transformation from a rest frame F to frame F’, moving at speed V in Euclidean space.
x’ = x -Vt (1)
t’ = t (2)
Space and time represent absolute properties of the universe.
The corresponding Lorentz transformations for relative space and time that satisfy the special relativity premises are
x’ = (x-Vt)/(1-V2/C2).5 (3)
t’ = (t-Vx/C2)/(1-V2/C2).5 (4)
x’ = (x-Vt)/(1-V2/C2).5 (3)
t’ = (t-Vx/C2)/(1-V2/C2).5 (4)
From (3) it follows that as V=>C the size of a spatial interval x’ decreases, corresponding to relativity of space. From (4) when V=>C the size of t’ also decreases, corresponds to relativity of time. But experimental results contradicting the transformations of Lorentz and the special theory of relativity appeared…. The authoritative Sagnac experiment, largely overlooked by the world scientific community.
Conclusions based on the same mathematical model of SR vary widely, changing the physical sense it represents. In the Lorentz transformations (3) and (4) x’ and t’ are separate, contrary to reality. A changing spatial interval is always a function of time. Therefore the Lorentz transformations describe a false reality.
From STEMU it follows that space, time and matter cannot exist in an isolated condition, but only together.
In (3) and (4) changing the size of x’ in F’ is independent of time t’ in the same frame. To correct this erroneous interpretation equations (3) and (4) must be analyzed together. So we divide the first into the second,
x’/t’ = (x-Vt)/t-Vx/C2 (5)
This now reflects the dependence of coordinate x’ on time t’, consistent with the STEMU axiom. Energy/matter is present in (5) implicitly via the speeds V and C, since only material objects can have speed.
In fig. 1 x is a position coordinate for a light signal in F, equal to the product of C for a time t.
Substituting x = Ct in (5) yields x’ = Ct’, the position of a light signal in F’. This signal is located on the co-terminus axes OX and OX’, at a point K - the crossing point of light spheres with two axes OX and OX’ (fig. 1). The geometrical sense of the Lorentz transformation is simply to fix x’ of a point K in F’ and x in F(fig. 1).
Lorentz transformations must give all mathematical symbols x,x’,t,t’,V,C included in these transformations a precise geometrical and physical sense. But there is no information in these transformations that reflects any physical effects.
Lorentz transformations can carry out the role of a theoretical virus. At the origin of time, if a light source flashes at point O (fig. 1) then x=Ct. Substituting in (1),
Ct = Vt + x’ (6)
Squaring both sides and simplifying,
0 = C2t2 –(Vt+x’)2 = C2t2 –v2t2 – 2Vtx’-x’2 (7)
0 = C2t2 –(Vt+x’)2 = C2t2 –v2t2 – 2Vtx’-x’2 (7)
0 = C2{t(1-V2/C2).5 –Vx’/C2(1-V2/C2).5}2 – x’2/(1-V2/C2) (8)
Let
T’ = t(1-V2/C2).5 –Vx’/C2(1-V2/C2).5 (9)
Let
T’ = t(1-V2/C2).5 –Vx’/C2(1-V2/C2).5 (9)
and
X’ = x’/(1-V2/C2).5 (10)
Replace
X’ = x - Vt (11)
X’ = x - Vt (11)
The result is
T’ = (t-Vx/C2)/(1-V2/C2).5 (12)
X’ = (x-Vt)/(1-V2/C2).5 (13)
X’ = (x-Vt)/(1-V2/C2).5 (13)
Expressions (12) and (13), derived from the Galilean transformations, completely coincide with the Lorentz transformations (3) and (4). Once it was thought that Galilean transformations are a special case of Lorentz transformations, but careful analysis shows the reverse - Lorentz transformations are a special case of Galilean transformations, which are also contrary to the Unity Axiom.
In (8) x’ and t are interdependent variables. We have taken x’ and t from (8), and made them independent of each other, violating the Axiom of Unity and distorting reality.
STEMU Axiom applied – Minkowski space
Uncontrolled intrusion into physics by mathematicians – such as Minkowski’s four-dimensional geometry - has made mathematical knowledge primary and physical secondary. Advances in physical knowledge have been held back by interminable complex mathematical models and their transformations, many of which are erroneous.
To show this we call the mathematical models containing only geometrical parameters, mathematical, and the temporal we call physical and mathematical.
The equation of a sphere containing only geometrical parameters,
x2 + y2 + z2 = R2 (14)
x2 + y2 + z2 = R2 (14)
let's call mathematical. The same equation, but with a variable radius of sphere R=Ct, automatically becomes physical and mathematical by including time and a physical parameter, C.
x2 + y2 + z2 = C2t2 (15)
x2 + y2 + z2 = C2t2 (15)
By analyzing transformations we have made obvious the inept manipulation of the physical parameter time. The lesson is that maximal care must be taken in analyzing the consequences of mathematical models containing time.
Lorentz's transformations are said to follow from Minkowski geometry. (see Modern physics in applied sciences, B.Robertson).
In F the light sphere equation is
x2 + y2 + z2 = C2t2 (16)
x2 + y2 + z2 = C2t2 (16)
In F’
x’2 + y’2 + z’2 = C2t’2 (17)
Combining,
x2 + y2 + z2 - C2t2 = x’2 + y’2 + z’2 - C2t’2 (18)
x2 + y2 + z2 - C2t2 = x’2 + y’2 + z’2 - C2t’2 (18)
x’ and t’ are defined as in (3) and (4) and physical and mathematical equality is claimed from
x2 + y2 + z2 - C2t2 = 0 (19)
x’2 + y’2 + z’2 - C2t’2 = 0. (20)
x2 + y2 + z2 - C2t2 = 0 (19)
x’2 + y’2 + z’2 - C2t’2 = 0. (20)
Equating two zeroes is equating nothing. To bypass this difficulty, Minkowski uses
x2 + y2 + z2 - C2t2 = S2 (21)
x’2 + y’2 + z’2 - C2t’2 = S’2 S,S’ <> 0 (22)
x2 + y2 + z2 - C2t2 = S2 (21)
x’2 + y’2 + z’2 - C2t’2 = S’2 S,S’ <> 0 (22)
This is not Euclidean geometry because the 4-D Pythagorean theorem is invalid. The interval S has an invented physical sense of mixed dimensions – space-time. Physicists have surprisingly simply agreed with the absurdity of this interval.
We shall check on its conformity to the Axiom of Unity.
Comparing (19) and (21), we see that in the geometry of Euclid Ct = OM - a rectilinear diagonal of a rectangle(fig. 2); in the geometry of Minkowski this diagonal cannot be rectilinear, as this equation does not correspond to the Pythagorean theorem. The presence of S in (21) forms a diagonal – the curvilinear ОЕМ (fig. 2). This implies that parallel straight lines may cross (at M).
Fig. 2. Analysis of Minkowski geometry
The straight line diagonal Ct = OM in (19) corresponds to a photon moving rectilinearly in space. The curvilinear diagonal Ct = OEM in (21) contradicts this property. So we have no justification for putting photon speed C in Minkowski space to represent reality.
We test this statement by trying to define coordinates for a light signal in space at the moment of time t, when x = y = z. From (21) we have
x = y = z = {(S2+C2t2)/3}.5 (23)
x = y = z = {(S2+C2t2)/3}.5 (23)
The unknown spatial interval leaves undefined x = y = z. Equation (21) does not permit defining the photon position on a trajectory OEM during time t, breaking the STEMU axiom.
The length of a diagonal Ct = OM is measured with the help of the photon moving rectilinearly with speed C so, using (19), we can define the photon location on a diagonal Ct = OM at any moment, corresponding to the Axiom of Unity. At each point on a diagonal Ct = OM the photon (energy/matter), space and time have indissoluble unity. For example, for the special case x=y=z , (19) gives the result
x = y = z = Ct/3.5 (24)
For any t we can find corresponding coordinates x ,y ,z.
x = y = z = Ct/3.5 (24)
For any t we can find corresponding coordinates x ,y ,z.
Introduction of interval S in (21) automatically transforms a rectilinear trajectory Ct = OM into a curvilinear path Ct = OEM, forcing light to move on a curve. The curvature radius of this path is undetermined…
Imagine the chaos if light moved on a curved path. In fact from a distant star to Earth it is possible to have only one direct line. Physicists did not care to analyze the conformity of these transformations to reality. Note that Riemanian geometry, as a non-Euclidean geometry, is automatically inapplicable in all cases involving C.
STEMU Axiom applied – quantum mechanics
The Axiom of Unity will allow us to establish the reality of theories on which modern quantum physics is based. We shall start with the equation of a monochromatic DeBroglie wave .
Psi = A sin 2pi(ft – x/lambda) (26)
f = frequency, lambda = wavelength
Psi = A sin 2pi(ft – x/lambda) (26)
f = frequency, lambda = wavelength
In nature movement of any object in space is ultimately synchronized; the coordinate x always can be represented as a function of time t. In (26) x and t are considered independent variables. This does not happen in reality, since the coordinate x of varying position of any object in space is dependent on time t. Hence (26) contradicts the basic axiom of natural sciences – the STEMU Axiom. Therefore we exclude (26) from the arsenal of valid equations! The same is true for the Schroedinger equation in three-dimensional space, although solutions are more complex, and also for the Dirac equation.
Nevertheless the De Broglie equation (26) and Schroedinger are widely used now in quantum physics and in some cases describe results of experiments, though they are fictional. The wave function psi can have the same amplitude for different values of x, so solutions of these equations have the nature of probabilities, not allowing an exact solution. The reason is the violation of the Axiom of Unity.
Newton’s laws of mechanics do operate within the framework of the Axiom of Unity; the equation of Schroedinger contradicts this axiom.
Schroedinger’s equation has caused enormous harm to physics and, especially, chemistry.
Differential equations of partial derivatives violate the Axiom of Unity. Such equations usually include time, and the change of other parameters is considered independent of time, contradicting the Axiom of Unity.
The Maxwell equations also do not permit opening up the structure of electromagnetic radiation and, in particular, of a photon. The field theory developed by D. Landau and textbooks written by L.D. Landau and E.M. Lifshitz are ideal, lacking contradictions.
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