Question one: What's the meaning of Lorentz transformation? What's the meaning underlining it? (The matrix form). Is there is any mathematic proof or relationship to explain and conduct its general form(The matrix form)? (means: What's the meaning of it's general form?)
Question two: (This is a mad one.) First, start with special relativity. The special relativity in Minkowski space has four variable. However, since the time can be calculated out by differential equation through c, there are only three fundamental variable(x,y,z), and several quantities(like mass).
Here is the tricky part: If we use the idea from general relativity (just the idea and not the equation), and if we use curvature as the "property of the space itself" (as there is no absolute direction of it), the whole space can be described with just 2 fundamental variables(space and curvature) with several measured quantities.
Thus, even the space is three dimension or more(like mass or whatever), can we express all the law of physics with only two fundamental variables?
Yours Sincerely
Dear Yocong,
Speaking in general and in one abstract form, the Lorentz transformations are the one which keep invariant the 2-tensor Minkowski's pseudometric. The whole continous group is the special orthogonal group
SO(3,1)
of dimension 6. Thus the distance of light ray is always constant and independent of the source or observer on the 4-dimensional space-time.
Question 2.
In this question you mix geneal relativity ( Riemann curvature different to cero) and also basic concepts as the number of coordinates independent. Frankly I do not understand what is your intention.
I hope that this can help.
Please read the paper, may be helpful for you.
A new approach to the correction of
Galilean transformation.
www.researchgate.net/profile/Sheng_Liu37
A logical contradiction has been found hidden in the Lorentz transformation ,which is demonstrated in the paper. And a new space-time transformation is proposed to eliminate the contradiction, which accordingly proves that the special theory of relativity is invalid..
The Lorentz (L-) group SO(3,1) from mathematical viewpoint is an artificial construction in ~1892-95 evoked to preserve validity of Maxwell equations of electrodynamics. in 1905 Einstein came across another math object invariant under the L-group, it was a scalar, square of 4D space-time interval. This gave birth to the theory of relativity
But pure mathematically the L-group SO(3,1) has its much more symmetric and beautiful 1:1 isomorphic (close to be identical) image, it is the special linear group of 3D rotations over compex number field, SL(3,C); it has same 6 parameters of rotations though is represented by 3D square orthogonal matrices. This group gives birth to my Quaternion (or Rotational) theory of relativity (see my papers of 2007, 2008).
Another partner of L-group is the 1:2 isomorphic special linear group of reflextions over compex number field, SL(2,С), represented by 2D square matrices. This "spinor" group has as well 6 parameters but covers twivce SO(3,1) and SO(3,C). It gives birth to my "General theory of mechanics arising from a fractal surface" of 2015.
YC: The special relativity in Minkowski space has four variable. However, since the time can be calculated out by differential equation through c, there are only three fundamental variable(x,y,z)
That is not correct. Two events in Minkowski spacetime have coordinates (x1,y1,z1,t1) and (x2,y2,z2,t2) and separation (dx,dy,dz,dt). To connect them with a worldline having a differential of value c means you are requiring each to lie on the light cone of the other, for example dx=cdt, but that is not true for independent events which may be spacelike or timelike separated.
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