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- TL;DR Summary
- Links between the Lorentz equations and the Theories of SR and GR

I have a question linked to the equations of Lorentz:

The Theory of the Special Relativity (SR) of Albert Einstein comes from the equation of Lorentz and we have the following equation on the time

The space time (x’, y’, z’, t’) is moving at a speed

If we write

with

And so we find:

And so

And the equation

And this result is due to the fact that we have for Lorentz

And according to the SR we have also:

and also

Or we can see also that it will work if we replace

And so it seems to have some errors somewhere to explain the equations of the SR starting from the equation of Lorentz.

Could you explain me what happen in this reasoning ? am I right or not ?

The Theory of the Special Relativity (SR) of Albert Einstein comes from the equation of Lorentz and we have the following equation on the time

**t’**in the moving frame:The space time (x’, y’, z’, t’) is moving at a speed

**v**measured from the space time (x, y, z, t)**t**’ =**. (***g***t**– (**v**.**x**)/**c^2**)If we write

**x**=**v.t**we have the following equation:**t**’ =**. (***g***t**– (**v^2t**) /**c^2**) =**.***g***t**(**1**– (**v^2**)/**c^2**)with

**=***g***1 / (√(1 – v^2/c^2) )**And so we find:

**t’**=**(√(1 – v^2/c^2) ) . t**And so

**t**= (**1 / (√(1 – v^2/c^2) ) ). t’ =***g*. t’And the equation

**t**=**is the equation of the Theory of the Special Relativity and proves that the SR comes from the equations of Lorentz.***g*. t’And this result is due to the fact that we have for Lorentz

**x**=**v.t**(see above), or**v.x = v^2.t**And according to the SR we have also:

**v**=**x’/t**=**x/t’**and also

**x = x’/**and*g***t**=**in the equation of Lorentz, we should replace**

*g*. t’*But,***x**by**v**.**t’**and not by**v**.**t**in order to be OK with the SR (see the above equations). And if we replace**x**by**v**.**t’**we will have**v.x**=**v. v**.**t’**=**v^2.t’**and it is not**v^2.t**Or we can see also that it will work if we replace

**v.x**by**v.x’**in the equation of Lorentz in the sense that:**v.x’**=**v. (v.t)**=**v^2.t**because**v**=**x’/t**according to the SRAnd so it seems to have some errors somewhere to explain the equations of the SR starting from the equation of Lorentz.

Could you explain me what happen in this reasoning ? am I right or not ?