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Theory of relativity. The format of Lorentz's transformactions delat the falacia of the time dilatation


By means of the present Essay we try to demonstrate the fact that they are the very expressions of the Formulas of the Transformations of Lorentz which discard the idea of "time dilation". We will see that they themselves are the ones who "talk" to us and inform us of what is the action that the so-called Lorentnz Factor performs within them.

With the present study we will see how the AMPLIFIER action of the VISION of the IMAGE of an Event (E) is produced that takes place in a certain SITUATION of the outer space. Thus we will discard that it is not the physical phenomenon itself or Event that is AMPLIFIED, but of the VISION of its IMAGE.

The procedure of analysis that we will use to get to interpret what these formulas tell us is the following:

We will use figurative language and situate ourselves as an Observer of the physical phenomenon to be quantified, "within the formulas". This Observer, represented by the proper use of figures, will be who will make us understand the mechanism of the same. We emphasize that this procedure of investigation that we describe. Which acts from within the formulas, is precisely the inverse of the approaches that we have seen to use in dealing with these formulas. These methods pursue, through mathematical approaches. We obtain a mathematical expression that coincides with the already known formulas. These approaches, which are truly great, have the defect of not revealing the true mission of the Lorentz Factor. In the present essay we have departed from this path that could lead us to accept the fallacy of the "dilation of time"

We consider the present study as an extension or annex to the Essay that we publish through Monografias.Com, with the title of "Theory of the special interactivity.- Their misinterpretations" (

Definition of concepts and previous considerations

In this essay we will use some concepts and expressions that we had used in previous trials published through "Monografías.Com" However to facilitate monitoring of this study we transcribe the meaning of some of these concepts:

SITUATION .- The concept of SITUATION includes the idea of POSITION in sidereal space and of the instant, TIME, in which it occurs..

In our study we will see that we will use the idea of: A set of Situations contained in an environment of outer space.

We assume the reader knows what an Inertial Reference System (IRS) means, consisting of a Fixed Reference System (FRS) and a Mobile Reference System (MRS). These concepts and those discussed above are defined and expanded in the book: "Theory of Relativity. A False Theory "

EXTENSION.- We will call EXTENSION the values of the variables Space (e) and Time (t) that must be considered in the formulas that govern in the natural phenomena that are intended to observe.

We have chosen to give this name considering that in observing an Event (E) first we will detect its appearance and then the duration of it.

We consider this Essay as a complement to the last published by "" named "Special relativity. His misinterpretation

FIGURED LANGUAGE.- In order to find where the action of the Lorentz Factor resides within the so-called Transformation Formulas, in his exposition we will use the figurative language that, together with the support of drawings, we have developed our research work


DIVISION OF STUDY.- An analysis of how they inform us

The formulas leads us to the conclusion that we must realize that they fulfill the following two purposes:

1.- SITUATE in the outer space the place of the observation of the physical phenomenon

2.- VISION from the (MRS) Extensions produced in the (FRS)

For the second phase we have used the word VISION to emphasize that we will use the ELECTROMAGNETIC WAVES.  For this reason we have avoided using the verb to Observe that perhaps it would make us cover up this characteristic


An interpretation of the formulas of the transformations of Lorentz

In Einstein's book "On Special and General Relativity", on page 32 (Editing "Editorial Alliance"), he describes the form and usefulness of the formulas called Lorentz Transformations, as follows:

"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`)?

Relationships must be chosen in such a way that they satisfy the laws of propagation of light in the void for one and the same ray of light (and also for any ray of light) with respect to (K) and (K '). "

He goes on to say:


"The problem is solved by the equations"

Space Formula

Time Formula


Monografias.comAnd, in this same page of the mentioned book, the following coordinate system (k) and (K')

The variable (v) means the speed of the system (K ') with respect to the system (K)

We use the methodology to graphically represent, as much as we can, the necessary developments to better make us understand.


We repeat what we have already stated in the presentation of this Essay. Rather than trying to get the expressions of these formulas, we will follow the reverse process. We will try to interpret what they tell us and that A. Einstein incorporated in his theory. We will rely on graphic descriptions and "a little" mathematical support, available at a non-high level of this subject.

Situate in the sideral space the place of the observation of physical phenomenon

We will use the figurative language of which we have already spoken, and will rely on the following figure to analyze how the formulas "speak to us"


Figure 1

This figure represents that in a certain Situation of the sidereal space an Event (E) has occurred.This (E) can be, for example, a certain physical phenomenon to which we want to evaluate its Extension, in space (e) and in time (t), from other Situations of sidereal space.

This (E) is considered or annexed to a Fixed Reference System (FRS)

The variable (tp) represents the value of the amplitude of the extensions, either in space (e) or in time (t), to be observed in Event (E) being analyzed

The variable (tp)´is the measure obtained from observation Extension (tp) Event (E) being assessed. The value of (tp)´is greater than (tp) for the reasons discussed later.

The Positions that from (E) correspond to the vertical movement are points that we consider that belong to the same Situation. This situation corresponds to the scope of the (SRF).

Point (S) 1 defines the situation in outer space, at the time of the appearance of the physical phenomenon to study. On these axes of reference we locate the Observer of the phenomenon.

We assume that this reference axis system, which serves as a platform to the observer, travels at a constant (v). Constant velocity with respect to the (SRF). (Note that we are dealing with an Inertial Reference System (IRS))

The distance to be found (S) 1 (SRF) is detected when the (E) is represented by: (vt)

The system of reference axes, placed initially on the situation (S) 1 while being observed phenomenon Extension advancing speed (v) until complete observation and is in the situation (S)2

The measure of the VISUALIZATION of this observation between (S)2 - (S)1 should be (tp), equal to that represented in the (SRF), but in reality it is somewhat larger for the

reason that we will expose following paragraphs. They are represented by the variable (tp) '.

The above data allow us to POSITION the observation of the Event Extension (E), placing the observer attached to some reference axes.

Looking at the figure we can deduce the expression:

We realize that this expression is equal to the Formula of Space:

In that expression the action exerted by the denominator in the Space Formula is concealed and which makes (tp) ' > (tp) but as we will justify in the following paragraphs, the stroke (tp)' which we have drawn in the Figure , is considering the performance of that denominator. So we can write::

(tP)´= (x')

The first consequence we can draw from the sketch we have drawn from the Formula of Space Transformation is that it is pointing out how to identify the scope of observation of the Extensions of a physical phenomenon.

For the Formula of Time we will use the following figure and we can say the same


Figure 2

In this case (tp)´represents the extension of the variable" time "

From this figure the following expression

Which reminds us of the Formula of Time

We must repeat what has been explained in the case of the Space Formula and conclude that: (tP)´= t'


Doubt may arise when questioning whether the second member of the numerator: ((v / c 2). x) it is really a time (t) so that you can subtract the first member, which is regarded as a "time"

In the following paragraph we demonstrate that it is a time.

Correction factors of the second member of the numberer of the time formula

In the perception of the image of an event between two Inertial Reference Systems with a velocity (v) between them, we must keep in mind that we are using two types of velocities completely different in nature and orders of magnitude. These are two different Physical Magnitudes. We can say that the relative velocity (v) between the two Reference Systems is between two bodies, or "containers" of possible physical phenomena, whereas the speed of transmission of the information corresponds to an electromagnetic wave with a very high speed (c) Above or at least very different from the velocity (v).

It is obvious that although these are two expressions that are related to "The speed", are different. They do not have the same physical nature. They should be treated as different. The speed of light (c) is always the same, remember that in previous Essays we said that it is inherent to itself, it is a constant and with an order of magnitude infinitely greater than that supposed to occur on the axis ( X), ie (v). We can not compare or establish a relationship between two lengths or two times that are measured using different patterns of velocity measurement. They must be standardized so that both use the same type of pattern

We use the velocity of light (c) as a pattern. That is, the 300,000 kms / sec. As speed unit

To make such conversions we must take into account the following criteria:

All lengths will be quantized using: "light speed units" (uvl).

This means that: (uvl) are the ones that would be consumed to move between two determined points of reference. For example, we can write: x = k (uvl) by referring to a given length (x), or would require k (uvl) to get to it.

The "light unit" is a speed measure that is worth: 300,000 kms / sec. That is, one (uvl), in the void, is always approximately equal to 300,000 km / sec.

A relation such as: (v / c) assigns a fraction of (uvl) to a given velocity (v), since (c) is a fixed quantity that is taken as unity, while (v) is the relative velocity between (SRI), different value in each case in particular.

To quantify a length (l) we apply the expression:

L = e (v / c)

This expression answers the question: A length (e) that has been traversed at velocity (v) at what length (l) is equivalent if the velocity were that of light (c) ?.

For the travel time (t d) a Reference System Mobile (SRM) on the axis (X), operating (UVL), we divide the space (l) by the speed of light (c).

That is:

Expression of a "Time" that we have seen written in the numerator of the formula of the Transformation of Time.

Vision from the (srm) extensions produced in the (srf) .- condition necessary to observe the totality of the vision of the extension of a physical phenomenon

With the present paragraph we enter in the second part of our analysis ..

That is, transported and placed the observer on the observation platform (S)1 that serves to make the observations, now we will examine the requirements required for a correct collection of data.

We will state a CONDITION NECESSARY so that an observer, placed in Situation (S)2, at the end of the observation, can record the amplitude of the variables (e) and (t) of the observed phenomenon

The following figure will serve to illustrate this condition.


Figure 3

Monografias.comWe call (tr) the time of the VISION tour of the Event Appearance, from the (SRF) to the Final Observation Situation (S)2 (Use Figures 1 or 2 to view this Situation (S)2


Being (c) the speed of light, the expression ( means the VISION TRIP OF THE IMAGE of the occurrence of Event (E)

We call time by the origin (tp) while occupying the Event Extension (E) measured in the Fixed Reference System (SRF) in which Event (E) occurs. The expression ( means the VISION TRAIL of the EXTENSION within the Reference System (SRF) in which Event (E) occurs.

We call Displacement Time (td) at the time it would take the observer initially located in the (SRF) to move to the observation situation (S)2.

Assuming that (v) is the velocity of movement with which said observer has moved, the expression: (v.t) is the measure of the space between the Situation in which Event (E) and Observation Situation occurs. We can say that it is the OBSERVER'S TRIP to be placed in the Observer Situation (S)2

(Note: Looking at Figure 1 or Figure 2, we see that the observation space or time is placed between Situation 1 and Situation 2. Now we are placed in Situation 2 when the whole Extension of the phenomenon has already been developed)

These tours must converge into a meeting point. This is the point of observation (S)2 and, to produce this meeting point, using these paths with different velocities: (v) and (c), where (td) the travel time must occur:

which is a Necessary Condition to be able to observe the totality of the Extension of the physical phenomenon studied,


We will rely on Figure 3 of the previous paragraph. Imposing the aforementioned condition we will get to obtain the so-called FACTOR OF LORENTZ

We will make a mathematical approach using the Pythagorean Theorem.

Observing Figure 3, applying this Theorem, we have:

Interpretation of the function of Lorentz's factor

In the previous paragraph we have obtained the expression


This expression tells us that (L) is evaluating this time of displacement (td) in units (tp) of the Extension of (E). That is, we are TRANSFORMING the displacement units to the Observation Situation (S)2 in units of the Extension. Therefore, when applying the value of (L) to the NUMERATORS of the formulas of Space or Time, they allow us to TRANSFORM to the place of observation, Situation (S)2 , the values of the Extensions that were obtained in the (SRF) .

Considering that the values of the variables (tp) 'appearing in Figures 1 and 2, are equivalent to, or are part of this Displacement Time (td). We can deduce that: as we have found that (td) > (tp). By dividing (td) / (tp) and assigning the units that come out as the Expansion of the physical phenomenon, this valuation criterion makes it appear that the Expansion has increased. What has been translated in Figures 1 and 2 interpreting that (tp) ` > (tp).

Why is the vision of the expansion of a phenomenical phenomenon observed extended?

By means of a mathematical approach we have found and emphasized in Figures 1

and 2 that: (tp) ` > (tp). We can reason this inequality in the following way.


The observation space that should be equal to (tp) is delayed, elongated, due to the lengthening of the observation end (S)2.

Note that it is not just a matter of moving the Observer to a new observing zone other than that which has occurred (E) and from there time the lengths of the Extensions. If it were only this, we would be measuring the time between two fixed limits, which we could identify as Initial Situation (S)I and Final Situation (S)F. But this does not happen. Occurs that the observer sitting on the platform (S)1 moves with this platform while the "meter" of the Extensions is running. You will close the meter of these Extensions in Situation (S)2, when you do not receive any further information. This displacement is what adds an additional amount to the Extension valued as (tp).


(Notes: To the expert reader in these subjects we emphasize the difference existing in the action of the "transfer of coordinated axes" In which we have now studied a transfer of the axes of the recipients of the variables. Variables to other new receptor axes in cases of applying the "Velocity Addition Theorem" and hence associating it with the so-called "Galileo Transformation" the reference axes of the variables remain immobile to the Initial Situation (S)I .

In our previous essay published by Monographs.Com: "Theory of special relativity. Their misinterpretations ( in the third paragraph of their last paragraph we stated the following: " They agreed that this variation was experienced by observers outside the experiment.) The Fixed Reference System (SRF) "

Perhaps this test would have been able to dispel this doubt.)

Mental experiment of the train wagon in the enlargement of the vision of the images of the extensions of the event

We have observed in some treatises on the theory of relativity, which purport to affirm the idea of ??"time dilation" by misusing the typical mental experiment of the "train car", or also called the mirror.

We will comment on where your error

We assume that the reader already knows the argument that is presented in presenting this experiment and, consequently, we only transcribe the image that we have already used in previous Essays. In our Essay entitled: "Theory of relativity. Their misunderstandings "may expand what we will now comment. The link is:

These treatises, based on this experiment, reach the equality we obtained in the previous paragraph:


                               (td) = (tp). (L)


And as (L) is greater than one, they argue that (td) is greater than (tp) and ... here it seems that the fallacy of time dilation and the "mysterious" contribution of the Lorentz factor are beginning to be generated. We transcribe the image that we gave there.

Where is the confusion? ... The confusion is that we should not consider EQUALITY of times but an EQUIVALENCE. That is, we must write:

Which indicates that the vision of the physical phenomenon valued in (td) is EQUIVALENT to the vision of the phenomenon valued since (tp). But this does not indicate that there should be a quantitative comparison between both types of measurement. This is a qualitative comparison. In the aforementioned test cited above, what we are discussing is reflected.


We will take a closer look at this issue in order to justify that the application of (L) contributes to the EXTENSION OF THE VISION OF THE IMAGE OF THE EVENT and NOT to the idea of the DILATATION OF TIME.

The error of the explanations supported by the mental experiment of the train car, or also called of the mirrors, is to consider the observation as if it were a single phenomenon, when in fact it is a question of TWO phenomena. The consideration of a single phenomenon deforms the compression of the experiment. We want to equate the evaluation of an event, the reflection of a ray of light, with the evaluation of two events: the reflection of a ray of light and the movement of the reflection mirror.

(NOTE: To further expand the explanation of the possible error committed in the referred treaties, see Chapter III of the book "Theory of Relativity, A False Theory".


In it appears the drawing "of the courtyard of the mental experiments" in which is located the real observer of these "games". We call this observer "the third eye.")


Group of events

We must make a small analysis of the differences that exist in the approach and interpretation of the mental experiments that are used to expose the Theory of Special Relativity. This will avoid doubts and false interpretations

To perform this analysis we will use the mental experiment of the train car and the phenomenon of relativity of simultaneity, commented on our repeated Essay: "Theory of special relativity. His misinterpretations (

We can state the case in which it is the Image of a single phenomenon physical. This case will be represented by the following figure:

                            A single physical phenomenon


With the car immobile, we only appreciate the reflection time of the ray (tp) (round trip). It is actually the only phenomenon that occurs and the observation of its duration offers no doubts. When evaluating the variables (e) and (t) of an Event produced within the same (SRF) its Extension is the own value of (tp)

The observation time of the VISION OF THE EVENT IMAGE, DOES NOT lengthen with respect to the (SRF), is the observer on top of the car or on the ground.

The following figure pretends to represent this circumstance.

Another case to consider is when the action of a particular phenomenon is added to the action of another phenomenon.

In order for both physical phenomena to be compatible, we must

Impose that both begin and end at the same instant. This requires:

Which is the condition we had already discussed (L)

The following figure pretends to be an approximation of what we are talking about

                                                Figure 1

A physical phenomenon supported by the action of another phenomenon


If we want to apply everything explained so far to the mental experiment of the train car, we soon realize that it is necessary to add something more so that everything fits. In this experiment we are not only dealing with a single action of a physical phenomenon, such as the oscillation of a pendulum, but the consideration of two actions of a Ray of Light. We must consider the shot Event beam path toward the mirror, which identify it as (E1) and the reflection of this ray and its route to the final, which will identify it as (E2).

If, for example, consider the action (E2), Figure 3 transcribe then, is what might stage behavior

In the paragraph in which we gave this figure explained the explanations of its variables.

If we consider the action (E1) should give a twist to the previous figure.

In summary, the analysis of this mental experiment requires seeing it from two different points of focus.



Enrique Martinez Viladesau