Masterov doesn't understand special relativity, the Lorentz transform or symmetry. It is not about actual (real) coordinates versus "visible" (apparent but not real) coordinates. All coordinates are man-made inventions to name places and times because nothing in nature comes pre-labeled with coordinates.
REMINDER:
Master Theory identifies two types of coordinates: actual (real) and visible.
In this topic discussed visual coordinates only.
It for visual coordinates only.
We see a stars and galaxies in the visual coordinates.
Real coordinates of the stars and galaxies differ from the visual coordinates.
Real coordinates obey Galilean transformations.
If you're talking about relativity, then no. The coordinates related by Lorentz transforms are those that clocks and rulers measure. They are not visual coordinates. They do not take into account the time it takes for light from whatever you are seeing takes to reach you.
The assumption made with Cartesian coordinates in space and time is that each of the four directions is at right angles to the other, such that the directions of place (conventionally: x,y,z) are distinct from the direction of time (conventionally: t). That space and time need at least 4 dimensions for a full description of events is physically obvious since we test this hypothesis on a daily basis every time we arrange a rendezvous. Being late means we got x, y and z right and made a mistake with t.
Both Galilean and Lorentzian relativity assume that any inertial object can be the origin of our x,y,z coordinate system. Therefore the origin of x,y and z in one coordinate system may be in motion relative to the origin of x', y' and z' in the other. Both Galilean and Lorentzian relativity assume any object in inertial motion in a coordinate system has constant velocity, and so are a suitable framework for Newton's first law of motion.
Newton said:
Всякое тело продолжает удерживаться в состоянии покоя или равномерного и прямолинейного движения, пока и поскольку оно не понуждается приложенными силами изменить это состояние.
Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
Russian Wikipedia: Newton's Laws of Motion
So if a body is in inertia motion, in every admissible coordinate system, it will have constant velocity $$(u_x,u_y,u_z)$$ and since any body in inertial motion may be an origin of such an admissible coordinate system, it follows that some other coordinate system will assign a potentially different (but still constant) velocity to the same object, $$(u_x',u_y',u_z')$$.
SRT:
$$\Delta x'=\Delta x/\gamma$$
$$\Delta y'=\Delta y$$
$$\Delta z'=\Delta z$$
$$\Delta t'=\Delta t\gamma$$
This is NOT the Lorentz transform. This is NOT a good summary of physics.
The Galilean transform $$G(v) = \Lambda_0(v) = \tiny \begin{pmatrix} 1 & 0 & 0 & 0 \\ v & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}$$ and the Lorentz transform $$\Lambda(v) = \Lambda_{c^{-2}}(v) = \tiny \begin{pmatrix} \cosh \tanh^{-1} \frac{v}{c} & \frac{1}{c} \sinh \tanh^{-1} \frac{v}{c} & 0 & 0 \\ c \sinh \tanh^{-1} \frac{v}{c} & \cosh \tanh^{-1} \frac{v}{c} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}$$ are both transforms of Cartesian coordinates of time and space. They both take motionless worldlines and convert them to worldlines with velocity v in the x direction. They both take worldlines moving at -v in the x direction and convert them to motionless world lines. They both commute with translations in space and/or time and as they are linear, they work equally well on Cartesian coordinates and differences of Cartesian coordinates. Both transforms are parametrized the same way, such that if an object has velocity $$(u_x = -v, \; u_y = 0, \; u_z = 0)$$ then in the other coordinate system it be at rest: $$(u_x = 0, \; u_y = 0, \; u_z = 0)$$.
The two transforms say different things, however about the structure of space-time, which is illustrated in that the Galilean transform has eigenvectors of space-only, while the eigenvectors of the Lorentz transform mix up time and space in exactly the same way that world-lines of light moving in the x direction do.
So if you want to test if Newton and Galileo are right about absolute time or if Lorentz and Einstein are right, you need a single model which can be used to calculate both outcomes based on varying a single parameter and see what value of the parameter is consistent with physical experiment. Thus, I introduced the generalized Galilean transform (following von Ignatowsky).
$${\huge \Lambda_K (v)} = \begin{pmatrix} \frac{1}{\sqrt{1 - K v^2}} & \frac{K v}{\sqrt{1 - K v^2}} & 0 & 0 \\ \frac{v}{\sqrt{1 - K v^2}} & \frac{1}{\sqrt{1 - K v^2}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}$$
Fan's pet theory set $$ K < 0 $$ but his results were more consistent with $$K > 0$$.
Newton, Galileo and Masterov assumed $$K = 0$$ but only Masterov rejects evidence that K is closer to $$c^{\tiny -2}$$ -- Newton and Galileo didn't have access to that level of precision experiment.
That is not the only difference. The earliest definition of SRT defines it as satisfying two postulates:
- The laws of physics are the same in all inertial coordinate systems.
- The speed of light is invariant.
You have addressed the second postulate but not the first. The first postulate is basically saying that the transformation between inertial coordinate systems must be a symmetry that leaves the laws of physics unchanged. It comes from the fact that SRT was intended as a replacement for Galilean relativity, which is based on a similar principle.
With any symmetry, applying one symmetry and then another is still a symmetry. If $$S_{1}$$ is a symmetry and $$S_{2}$$ is a symmetry, then $$S_{1} S_{2}$$ is a symmetry.
Examples:
- If $$R_{1}$$ is a rotation and $$R_{2}$$ is a rotation, then $$R_{1} R_{2}$$ is still a rotation.
- If $$T_{1}$$ is a translation and $$T_{2}$$ is a translation, then $$T_{1} T_{2}$$ is still a translation.
- If $$G_{1}$$ is a Galilean transform (of velocity $$\bar{u}$$) and $$G_{2}$$ is a Galilean transform (of velocity $$\bar{v}$$), then $$G_{1} G_{2}$$ is still a Galilean transform (of velocity $$\bar{u} \,+\, \bar{v}$$).
- If $$\Lambda_{1}$$ is a Lorentz transform and $$\Lambda_{2}$$ is a Lorentz transform, then $$\Lambda_{1} \Lambda_{2}$$ is still a Lorentz transform.
But if $$M_{1}$$ is a "Masterov transform" and $$M_{2}$$ is another "Masterov transform", you will find that $$M_{1} M_{2}$$ is generally
not a "Masterov transform".
MT:
$$\Delta x'=\Delta x/\gamma^2$$
$$\Delta y'=\Delta y/\gamma$$
$$\Delta z'=\Delta z/\gamma$$
$$\Delta t'=\Delta t$$
While Galileo has a velocity composition law of $$w = u + v$$ (because $$G(u)G(v) = G(v)G(u) = G(w)$$) and Einstein had a velocity composition law of $$w = \frac{u + v}{1 + c^{-2} u v}$$ (because $$\Lambda(u)\Lambda(v) = \Lambda(v)\Lambda(u) = \Lambda(w)$$) there is no sensible formula for the composition of velocities in Masterov's transform because the closest you can come is $$w^2 = u^2 + v^2 - \frac{u^2v^2}{c^2}$$. (But this doesn't generalize to motion in other directions as it is not a symmetry.)
Example 1: $$u = \frac{c}{3 \times 10^6} \approx 360 \; \textrm{kph}, v = \frac{c}{9\times10^6} \approx 120 \; \textrm{kph}$$
Galileo: $$w = \frac{4 c}{9 \times 10^6} \approx 480 \; \textrm{kph}$$
Lorentz: $$w = \frac{12\times 10^6}{27\times 10^{12} + 1}c \approx 480 \; \textrm{kph}$$
Masterov: $$|w| = \frac{\sqrt{90 \times 10^{12} -1}}{27 \times 10^{12}} \approx 380 \; \textrm{kph}$$ (inconsistent with experiment)
Example 2: $$u = \frac{c}{3 \times 10^6} \approx 360 \; \textrm{kph}, v = -\frac{c}{9\times 10^6} \approx -120 \; \textrm{kph}$$
Galileo: $$w = \frac{2 c}{9 \times 10^6} \approx 240 \; \textrm{kph}$$
Lorentz: $$w = \frac{6\times 10^6}{27\times 10^{12} - 1} c \approx 240 \; \textrm{kph}$$
Masterov: $$|w| = \frac{\sqrt{90 \times 10^{12} - 1}}{27 \times 10^{12}} \approx 380 \; \textrm{kph}$$ (inconsistent with experiment)
Example 3: $$u = \frac{c}{3 \times 10^6} \approx 360 \; \textrm{kph}, v = -\frac{c}{3\times 10^6} \approx -360 \; \textrm{kph}$$
Galileo: $$w = 0$$
Lorentz: $$w = 0$$
Masterov: $$|w| = \frac{\sqrt{18 \times 10^{12} - 1}}{9 \times 10^{12}} \approx 509 \; \textrm{kph}$$ (inconsistent with experiment)
In addition, the Masterov transform doesn't even convert motionless worldlines to worldlines with motion.
I'm going to try to present MT-idea of again just.
When the observer moves with respect to hours, increases the path traveled by photons in clocks, despite the fact that there is a reduction of the longitudinal-scale. Therefore in SRT Einstein introduces time dilation.
$$\Delta x'=\Delta x\sqrt{1-v^2/c^2}$$
$$\Delta y'=\Delta y$$
$$\Delta z'=\Delta z$$
$$\Delta t'=\Delta t/\sqrt{1-v^2/c^2}$$
That is not a good summary of SRT. SRT also has a relativity of simultaneity effect which is necessary for invariance of the (one way) speed of light. The full relation between coordinates for a boost along the
x axis is given by a Lorentz transformation:
$$
\begin{eqnarray}
t' &=& \gamma (t \,-\, \frac{v}{c^{2}} x)
x' &=& \gamma (x \,-\, vt)
y' &=& y
z' &=& z \,,
\end{eqnarray}
$$
with $$\gamma \,=\, (1 \,-\, v^{2}/c^{2})^{-1/2}$$. SRT length contraction and time dilation can be derived as special cases of this transformation. Your summary is also misleading because if two events occur a distance $$\Delta x$$ from one another, the distance between them in a different frame is generally
not $$\Delta x \sqrt{1-v^2/c^2}$$.
The Lorentz transformation leaves the speed of light invariant, e.g. $$x \,=\, ct \,\Rightarrow\, x' \,=\, ct'$$..
Each assumption of a value of K gives one mathematical structure as internally self-consistent as the other, but in physics we let Nature decide what value of K we should use. To deny Nature the deciding vote is to abandon physics.
Masterov's "summary" of special relativity is badly flawed in three ways.
1) His "SRT transform" of a non-moving object doesn't make it move with velocity v -- this is also a fault of the MT transform
2) His "SRT transform" of an object moving with velocity u in the x direction doesn't make it come to a halt until |v| = c -- this is also a fault of the MT transform
3) His "SRT transform" of +v, when composed with -v doesn't equal a transform with velocity 0 -- this is also a fault of the MT transform
4) His "SRT transform" of any non-zero velocity u, when composed with any non-zero velocity v in a different direction doesn't equal any transform for any velocity w -- this is also a fault of the MT transform
So of course both Masterov's "summary" of special relativity and the MT transform lead to physically inconsistent predictions like two objects in the same state of motion need not have clocks ticking at the same rate. These flaws are not shared by any of the generalized Galilean transforms. And the Lorentz transform is exactly what we get when we assume the hypothesis that $$K=c^{\tiny -2}$$.
(slight edits for correctness and clarity)
I seems that I'm screaming into the void.
Please stop screaming until you understand the topic.
