**PRESENTATION**

Reading in A. Einstein's book entitled: “On the theory of special and general relativity” the topic of the Lorentz Transformation Formulas, some doubts have arisen. Having analyzed these doubts, we have seen that they come from two errors. These are the same errors that we already exposed in our previous essays, in which we denounced that through relative movements the author of the aforementioned book confused the verb SEE with the verb BE. And, thus, we ironically say that he preaches “the miracle of transmutation.”

We dedicate this essay to highlighting the aforementioned errors and to proposing a method of analysis to construct and interpret the aforementioned formulas. For better follow-up of this study, we have divided it into two parts. The second part is somewhat more theoretical than the first and some mathematical developments appear.

**FIRST PART**

**1.- AN EXPLANATION THAT APPEARS IN A BOOK BY A. EINSTEIN**

“Given the quantities (x,y,z,t) of an event with respect to (k), what are the values (x`,y`,z´,t´) of the same event with respect to (k´)?

The relations must be chosen in such a way that they satisfy the laws of light propagation in a vacuum for one and the same ray of light (and also for any ray of light) with respect to (K) and (K´).”

And he goes on to say:

“The problem is solved by the equations”

Space Formula

And, on this same page of the aforementioned book, the following coordinate system (k) and (K) is drawn.

Later we will demonstrate that the expression:

*(v×X)/***that appears in the time formula, translates as a time and that with the “space formula” there would be enough to make “theoretical” applications.**

*c*^{2}**2.- WHERE DO WE FIND ERRORS IN THE EXPLANATION GIVED BY A. EINSTEIN IN THE LORENTZ TRANSFORMATION FORMULA?**

**3.- WHAT DO WE UNDERSTAND BY THE DIMENSION OF AN EVENT?**

**4.- WE ASKED, IN A THEORETICAL APPROACH, WHAT WOULD TRANSFORMATION FORMULAS BE USED FOR?**

**5.- FORMULA FOR THE TRANSFORMATION OF THE VISION OF THE EXTENSION OF AN EVENT**

**6.- ACTIONS IMPLIED IN THE TRANSFORMATION OF THE VISION OF THE EXTENSION OF AN EVENT**

**7.- TWO PHYSICAL PHENOMENA TO CONSIDER**

**8.- A RIGHT TRIANGLE TO ANALYZE THE VISION OF THE EXTENSION OF AN EVENT FROM A MOBILE PLATFORM**

points we define a triangle

**9.- WHY SHOULD THE TRIANGLE BE RECTANGLE?**

On the horizontal axis we will give the meaning as the path of the movement and the speed (v), and on the vertical axis we will express the dimension of the Extension of the event. Without going into more specialized mathematical expressions, we only say that these two reference axes must have different directions since they imply different concepts. That is, they must be linearly independent. They must have the quality of independence.

**10.- REPRESENTATION OF THE RIGHT TRIANGLE WITH THE EXPRESSION OF ITS ROUTES BETWEEN ITS POINTS**

**11.- WHY DO WE PLACE THE EXTENSION ON THE VERTICAL CATHETUS?**

**12.- RELATIONSHIP BETWEEN THE TIME (tp) OF THE EXTENSION OF THE EVENT AND THE DISPLACEMENT TIME (td) OF THE OBSERVER**

Placing the EXTENSION of the event in the vertical leg of the triangle, valuing it as (tp) and valuing the travel time (td) that exists between the observation point (O) and the aforementioned vertical leg, we express the relationship between them as follows:

the expression:

is the so-called LORENTZ FACTOR, where (c) is the speed of light and (v) the speed of a Mobile body.

**13.- THE LORENTZ FACTOR AS A TRANSFORMATION FACTOR OF THE DISPLACEMENT TIME (Ttd) IN MEASUREMENT OF THE EXTENSION (tp) OF THE EVENT.**

**14.- EXPRESSION OF THE DISTANCES IN TIME USED IN RUNNING**

*(X – v.(td))*From what we have mentioned, we can also express this distance in time spent traveling it (T), at a speed (v).

*(X-v.t)≡(T)***15.- THE FORMULA FOR THE TRANSFORMATION OF SPACE GIVEN BY A. EINSTEIN IMPLICITLY CONTAINS THE EXPRESSION OF THE TWO PHYSICAL PHENOMENA THAT WE HAD INDICATED.**

implicitly contains the two physical phenomena to be considered.

**which takes into account the physical phenomenon of displacement. We can verify this in Fig. 3.**

*(X-v.t)*As we had explained, if

is equivalent to allowing the (td) to be valued in units (tp) and since

**is equivalent to (td), we can deduce that:**

*(X-v.t)***is valued :**

*(X-v.t)***16.- ANOTHER FORMULA TO ASSESS THE VISION OF THE EXTENSION OF AN EVENT FROM A MOBILE PLATFORM**

**17.- WHY DO WE CALL THE FORMULA FOR THE TRANSFORMATION OF SPACE THE FORMULA FOR THE TRANSFORMATION OF THE VISION OF THE EXTENSION OF AN EVENT?**

the extension of an event” has suggested to us when investigating the construction and possible use of this formula. So the reader can call it whatever he wants.

If we consider that there is no movement and that the observer is fixed at the point (O), this observer WOULD SEE the Extension of the event located on the axis (K) and with a dimension equal to (E – F). But, if we now consider that the observer is moving and his reference coordinates are (K'), the VISION of the aforementioned event on these coordinates will have a dimension: (e – f). So we can say that the VISION of the event has BEEN TRANSFORMED. And this dimension of Extension is what the observer must operate with.

**18.- IS THE RELATIONSHIP td/(tp) MAINTAINED WHEN THE MOBILE REFERENCE SYSTEM MOVES?**

**SECOND PART**

**1.- CONDITIONS OF VALIDITY FOR THE VIEW OF THE EXTENSION OF AN EVENT FROM A MOBILE OBSERVATION POINT. SYNCHRONIZATION CONDITIONS.**

*(tr) = (td)***2.- MATHEMATICAL DEDUCTION OF THE RELATIONSHIP BETWEEN THE**

OWN TIME OF THE EXTENSION OF THE EVENT AND THE TRAVEL TIME TO THE PLACE OF OBSERVATION

OWN TIME OF THE EXTENSION OF THE EVENT AND THE TRAVEL TIME TO THE PLACE OF OBSERVATION

Requiring compliance with the Synchronization Condition:

*(tr) = (td)*Grouping terms we have:

**3.- DEMONSTRATION THAT BY MOVING THE VISION OF THE EXTENSION ON THE MOBILE REFERENCE SYSTEM, THE RELATIONSHIP BETWEEN THE (td) AND THE (tp) IS MAINTAINED.**

**4.- DEMONSTRATION THAT THE SECOND FACTOR OF THE NUMERATOR OF THE TIME FORMULA CAN BE TRANSLATED AS A TIME**

*(v×X)/***is nothing more than the expression of a “time”.**

*c*^{2}**(uvl) meaning that a certain length (x) is found, or would require k (uvl) to reach it.**

*x = k*

*l = x.( v /c)*I mean:

*(td) = (l) / (c)*

*l = x.( v /c)*

*(td) = (l) / (c) = ( x).(v / c) / (c) = ((x).(v))/c*^{2}