Piggy reorganized the materials about the mass – space equation and put it here for reference.
The Concept of the Mass – Space Equation
Below is a thought experiment to demonstrate the insufficiency of the traditional Lorentz transformation.
When someone stays stationary relative to the sun, he will see that the sun is a round ball. When he moves to the sun in constant velocity (the sun moves to him relatively), he will see that the sun is an oval ball/thin due to the "length contraction effect" in the direction of movement.
The effect of gravity is even in all directions, so the sun is round; if the sun is thin, that means the effect of gravity is not even in all directions. Physics rule is not equivalent in different inertial frames? But one of the basic principles of SR is "physics rule is equivalent" in different inertial frames...
Actually, there is another very simple thought experiment to demonstrate the inherent flaw in Einstein’s SR: assume an object is moving in speed v in frame S, the same angles with all axis x,y,z for simplicity. Then, in frame S, the components of speed v along x,y,z axis are the same. While in frame S’, because the Lorentz transformation formulas in the cross direction is not the same as that of the along direction (the moving direction of frame S’), that’s mean the components of speed v’ along x’,y’,z’ axis are NOT the same. Then, physics rule is not the same in different inertial frames.
Next, introduce the mass – space equation.
The equation for the traditional Lorentz transformation of length contraction is: L’ = L /γ
The mass – speed equation is M = γM0
Then, ML’ = M0L so, L’ = M0L / M
Because M0 and L are constants, then: L’ ∝ 1 / M. This might be called the “mass – space equation”. (note: I am habitual to use upper case letters in this equation because the lower case of L looks like a “1”).
Mass M is a scalar, so the equation reflects the contraction of size in all directions due to the increase of mass.
It seems that the “mass – space equation” is a derived one. But its components “mass” and “space” are most basic physical elements. Actually, it should be a more basic equation than the equation for the traditional Lorentz transformation of length contraction and the mass – speed equation. It describes more basic natural rule.
During the course of exploration, people perhaps touch the leaves of a tree first, then the sticks, and so on the stock, at last the root. But for a tree, the root is the most basic.
From the angle of the physical substance of the object itself, perhaps the research might be more in depth and sufficient.
If we resort to the space contraction in all directions (Lorentz transformation is the same in all directions) which is disclosed by the mass – space equation, the above flaw can be amended easily.
Perhaps the natural logic should be “the movement in 3D space causes the increase of mass and the increase of mass causes the size contraction in all directions”.
Current in Different Inertial Frames
Blow is a third thought experiment to demonstrate the insufficiency of the traditional Lorentz transformation.
Assume a part of stable DC circuit with the shape of “L” rests in inertial frame S: section 1 horizontal; section 2 vertical; wire cutting face is a square for convenience. Another inertial frame S’ moves rightward at velocity u.
The purpose of this thought experiment is to verify whether the “length contraction effect” is in all direction as the “mass – space equation” shows or just in the moving direction as traditional Lorentz transformation shows.
First, analysis resorts to traditional Lorentz transformation.
In frame S:
For section 1, I1 = n1qv1; for section 2, I2 = n2qv2
(Here take the moving direction of electron as the direction of current for convenience, n is the density of free electron in the wire, q is the charge carried by electron, v is the moving velocity of free electron.)
I1 = I2, n1 = n2 = n, v1 = v2 = v
In frame S’:
For section 1, △x’ = △x / γ , △y’ = △y , △z’ = △z
V’ = △x’△y’△z’ = △x△y△z / γ = V / γ (V’ is volume in frame S’, V is volume in frame S)
So, n1’ = γn1 = γn
Lorentz transformation of velocity:
v1’ = (v1 - u) / (1 - u v1/c² )
I1’ = n1’qv1’ = γnq (v1 - u) / (1 - u v1/c²)
For section 2, also V’ = V / γ
So, n2’ = γn2 = γn
Lorentz transformation of velocity:
v2’ = v2 / γ(1 - u v1/c²)
I2’ = n2’qv2’ = γnq v2 / γ(1 - u v1/c²) = nq v2 / (1 - u v1/c²)
I1’ ≠ I2’
Physics rule is not equally applicable in inertial frame S’.
Next, resort to the space contraction in all directions which is disclosed by the “mass – space equation”.
In frame S’:
For section 1, n1’ = γ³n1 = γ³n
v1’ = dx’ / dt’ = (v1 - u) / (1 - u v1/c² )
I1’ = n1’qv1’ = γ³nq (v1 - u) / (1 - u v1/c²)
For section 2, n2’ = γ³n2 = γ³n
v2’ = dz’ / dt’ = dx’ / dt’ = (v1 - u) / (1 - u v1/c² )
I2’ = n2’qv2’ = γ³nq (v1 - u) / (1 - u v1/c²)
I1’ = I2’
Physics rule is equally applicable in inertial frame S’.
Of course, the “L” shape DC circuit scenario can be verified. Just fix two electric meters in the sections and watch if their values are the same. It’s not a difficult experiment to do.
The mass – space equation L’∝ 1 / M discloses Lorentz transformation is the same in all directions. So, there is no what “longitudinal mass” or “transversal mass”. The appropriate conception should be the “dynamic mass” (is the same in all directions).
The mass – space equation can be transformed to be M ∝ 1 / L’. It means the contraction of space leading to the increase of mass. So, the employment of “dynamic mass” / “relativistic mass” is reasonable.
The mass – space equation L’ ∝ 1/ M contains just two most basic physics quantity: space and mass. It’s the most basic equation in cosmos and reflects the most basic natural rule. Its existence does not depending on SR. So, shake off the effect of reference frame, it will be L ∝ 1/ M.
The “mass – space equation” can transform into another form: L ∝ 1/ρ, where ρ is mass density. The derivation course is as below:
Assume V is a certain value of any finite volume, then: L ∝(1 / V)﹝1 / (M / V)﹞,
1 / V is a constant; M / V = ρ
Cosmos can be fashion, passion and inflation, but physics must be step by step.
The mass – space equation reflects the basic physics property of 3D physical space, the most basic thing in nature.