A MISINTERPRETATION BETWEEN THE VERBS TO SEE AND TO BE AND THE SPEED OF ATOMIC PARTICLES

INTRODUCTION

In our previous essay, "The Deception of the Muon Evidence and the Speed ​​of Atomic Particles," we demonstrated the possibility of atomic particles reaching speeds greater than that of light. Now, in this essay, we aim to demonstrate the basis for denying such a possibility.

We will rely on a concept already repeated several times in our previous essays. In them, we addressed the confusion introduced by Albert Einstein when, in his thought experiments, he conflates the verbs "to see" and "to be." We believe that in the relative motion of observed phenomena with respect to a point of reference, they appear transformed, but they are not different.

In this essay, we will demonstrate that this confusion is an aggravating factor in asserting that atomic particles can travel at speeds greater than that of light.

We will use the well-known train car thought experiment to develop our thesis.



A BRIEF SUMMARY OF THE TRAIN CAR THOUGHT EXPERIMENT

For our study, we begin with the train car thought experiment described by A. Einstein in his book, "On the Special and General Theory of Relativity."

Just as a reminder, we will say the following: The train car, traveling at a constant, straight speed (V), has a mirror attached to its ceiling. Inside the car, a person shines a beam of light toward the mirror to observe its reflection. The goal is to find a formula that relates the amplitude (∆x) of the physical phenomenon of the light beam reflected in the mirror to the displacement (td) of the car.

This thought experiment serves to justify, INCORRECTLY, that time dilation occurs. They say that for the observer (o) who is fixed on the ground, the time it takes for the light beam to travel (td) is longer than the time perceived by the person inside the car who shone the beam. The aforementioned approach confuses the verb "to see" with the verb "to be."

Books that address this topic present figures such as the one in the following drawing:

Figure 1

This drawing is taken from one of the chapters of the first book in the two interesting volumes titled "Physics" by Raymond A. Seway and John W. Jewert, Jr.)

On the left side of the drawing, the stationary train car and the round trip of the light beam reflected by the mirror are depicted. In the center of the drawing, three positions of the train car's forward motion are shown, intended to demonstrate time dilation (∆t) justified by the extension (v.∆t) encompassed by the physical phenomenon of light reflection.



A MISCONCEPTION THAT WOULD VALIDATE THE IMPOSSIBILITY OF CONSIDERING SPEEDS GREATER THAN THE SPEED OF LIGHT

Books dealing with the theory of relativity relate the proper time (tp) of the physical phenomenon of light reflection to the travel time (td) of the train car in which the experiment is performed. The equation they give is the following:

(NOTE: This displacement time (td) is what has been represented in the previous figure as: (∆t) . In this formula, (v) is the speed of the wagon and (c) is the speed of light. We can observe that this formula loses its validity for speed values ​​(v) equal to or greater than the speed of light (c). By accepting this idea of ​​invalidity, we reject the possibility that there can be bodies, like the aforementioned wagon, that can travel at speeds (v) equal to or greater than the speed of light (c). And here, the aforementioned incorrect idea generates the denial that there can be atomic particles that travel faster than light.)


(NOTE: Keep in mind that this entire argument is based on the absurdity of accepting the verb "to see" as the verb "to be.")



INTERPRETATION OF THE FORMULA

The aforementioned formula is interpreted as evidence of time dilation. We will see later that this is a fallacy. Let's examine what the formula tells us.

As a first step, we say the following:

We could assume that, in principle, (td) is equal to (tp).

(td) = (tp)

Also, keep in mind that the value of the radicand appearing on the right side of the equation will be less than one.

Another point to consider is that:

(tp) divided by a value less than one increases its value.

For example: 

Consequently, we can say that if we previously proposed that (td) was equal to (tp), we must now admit that the equality has become an inequality.

(td) > (tp)

If we consider that (td) is the length of time the phenomenon lasts as seen by an observer fixed on the ground, and (tp) is the proper time (tp) of the physical phenomenon of the reflection of the light ray, they arrive at the fallacy that time has dilated.



INVALIDITY OF THE FORMULA 

THAT ARE PRESENTED BY BOOKS THAT DEAL WITH THE SUBJECT OF THE THEORY OF SPECIAL RELATIVITY

In the previous paragraph, we saw that:

When the amplitude (td), the time of observation of the physical phenomenon, is greater than the amplitude of the proper time (tp) of said phenomenon, we arrive at the erroneous conclusion that time has dilated. We say that it appears that time has dilated.

But, apart from the invalidity of the interpretation of said phenomenon, we must study an inconsistency that invalidates the aforementioned formula.

The formula 

Given the involvement of the speed of light, it is practically difficult to verify its validity; we will see that theoretically it cannot be correct.

We present below the mathematical development on which it is based.

We draw the three positions of the wagon's movement.

Figure 2

We select the central carriage. On the right triangle drawn on the right side of the figure, we will relate the Proper Time (tP) of the ray's path to the mirror with the Displacement Time (td) of the carriage from when the ray impacts the mirror until it impacts the carriage

Note that the hypotenuse of the triangle is the Return Time (tr) of the ray; the vertical leg is the Proper Time (TP) of the light ray's travel to the mirror, and the horizontal leg indicates the Displacement Time (td) of the carriage.

(NOTE: The reader should note that this triangle is drawn on the right side of Figure 1)

To relate (td) to (tp) in the aforementioned triangle, we will apply the Pythagorean Theorem. Before formulating the mathematical approach, we impose the following condition, which we mistakenly believe was introduced by one of the authors of the aforementioned formula:

The portion of the wagon's displacement that occupies a time

(td), represented in the diagram as (Δx), is equal to the return time (tr) of the light beam. That is: (td) = (tr)

According to the Pythagorean Theorem.

Demanding compliance with the condition:

(td) = (tr)

This allows us to substitute (tr) for (td), which gives us

Grouping terms gives

We can transform the denominator as follows

And from this we obtain:

Regarding the invalidity of this formula, we say the following:

In the formulation and derivation of this formula, two mathematically incompatible events occur.

Even accepting the error that it were real for physical phenomena to transform simply by moving relative to a fixed observer, we can denounce the other error.

Starting from the right triangle that serves as our mathematical model, we say the following:

If, as we agreed in the previous mathematical development, we impose: (tr) = (td) (a condition)

And

We assume that there exists a speed (v) that is greater than the speed of

That is, (v) > (c) (another condition)

these assumptions produce an inconsistent event in mathematics

since then it implies that: (td). (v) > (tr). (c)

and in a right triangle, it is inconsistent for a leg to be longer

than its hypotenuse.



FACTOR VALIDITY

IN LORENTZ TRANSFORMATION

We may have the following doubt: The expression : 

It appears in the topic of Lorentz Transformations and is called the Lorentz Factor. Because this expression is included within the formula: 

Having ruled its invalidity, we might think that our reasoning lacks coherence.

To validate our reasoning, we state the following: We are dealing with two different aspects related to the relativity of motion. The topic we are addressing in this essay is whether the formula that attempts to relate the duration of a physical phenomenon to the relative time of its displacement from a fixed point is valid. In this matter, we reject this formula and the fallacy of time dilation.

A different topic is the following: It concerns how the variables of a physical phenomenon appear transformed when observed by a moving observer as they move away from the event. We emphasize that here it is the observer who moves, not the physical phenomenon itself, as was the case with the physical phenomenon of light reflection. As a consequence of this approach, the factor: 1/√(V^2/C^2 ) is a way of reducing the units of velocity (v) of displacement to units of light (c). That is, to units of vision according to the distance of the observer.

For more information, the reader can read our essay entitled:

“Theory of Relativity - Mathematical Interpretation of the Lorentz Factor.” In this essay, the formulas indicate that it is a lengthening of the perceived extent of an event depending on the observer's distance. It is not a dilation of time. The events are not different, but they appear different.



A REAL VERSION OF THE PHYSICAL PHENOMENON OF THE REFLECTION OF A LIGHT RAY IN THE MIRROR OF A MOVING TRAIN CAR

We reiterate what we have already discussed in previous essays regarding the confusion introduced by A. Einstein when he considers in his thought experiments that phenomena ARE, that is, that they ARE transformed, instead of saying that they ARE SEEN differently.

Now, regarding the phenomenon in the train car thought experiment,

we say the same thing. The extension of the physical phenomenon of the reflection of the light ray APPEARS longer. It IS NOT that the duration of the phenomenon is longer.

In reality, the lengthening of the physical phenomenon is fictitious; it is due to the combination of the physical movement of the train car, which "drags" the phenomenon, along with the firing of the beam MOUNTED ON THE CARRIAGE.

If we want to SEE the representation of the reality of the movement of the physical phenomenon of the reflection of the light ray, we can draw the following figure, which aims to move from the ideal to the real.

Figure 3

With this drawing, we intend to demonstrate that the speed at which the light ray propagates and the speed of the train car are completely independent.

In this fantasy world of thought experiments, we have drawn what an observer (O) fixed on the ground would SEE inside the train car. The train car moves relative to the observer, and the physical phenomenon of the reflection of a light ray in a mirror occurs.

Four positions of the train car's forward motion are presented. The first two positions represent the light ray traveling towards the mirror. The next two positions of the train car represent the reflection of the ray in the mirror and its movement towards the floor of the train car.

We can be represented as an observer outside the train car, and thus we can say that we ACTUALLY SEE the physical phenomenon. And this physical phenomenon does not depend on the movement of the train car.

This independence of motion allows us to state that the speed (v) of the train car can be any speed, even greater than the speed of light, while the speed of the light beam is equal to the speed (c) of light.

(NOTE: The path of the light beam if the train car were stationary is shown on the right (a). This is not a good example since it suggests that the phenomenon IS different when it has relative motion, and this disrupts the idea that it LOOKS different.)

WE BELIEVE THAT WITH THE ABOVE ARGUMENTS WE CAN SAY THAT IT IS POSSIBLE FOR ATOMIC PARTICLES TO TRAVEL AT SPEEDS GREATER THAN THE SPEED OF LIGHT

THE DECEPTION OF THE MUON TEST AND THE SPEED OF ATOM PARTICLES

INTRODUCTION

We have recently read an author who still attempts to justify the validity of the fallacy of A. Einstein's "Theory of Relativity" by presenting "the muon test."

In this essay, we will demonstrate that such a test is nothing more than a fallacy intended to lend credence to his beliefs.

Next, we provide some definitions to refresh the content of concepts we had already defined in previous essays.

WHAT IS A MUON?

A muon is a subatomic elementary particle that decays shortly after being produced.

HOW ARE MUONS PRODUCED?

Muons are produced naturally when cosmic rays, which contain them, collide with the Earth's atmosphere. Muons can also be produced in nuclear physics experiments in laboratories.

MUON BREAKDOWN TIME (tr). HEIGHT FROM WHICH THEY ARE PRODUCED AND TRAVEL TIME (td).

To perform our calculations, we compiled the following data.

It has been observed that a muon at rest, in the laboratory, in artificial mode, decays in an average time, which we will define as the Breakup Time (tr) = 2.2 microseconds.

The height from where they are produced to the ground surface is estimated to be approximately 50 km/s.

If we assume that a muon travels at the speed of light, or 300,000 km/s, which we will see later cannot be true, the travel time (td) until reaching the ground is calculated to be:

td = 50/(300,000) km/(km/s) = 0.0001666 sec. = 166 microseconds.

In the laboratory, a breakup time (tr) has been estimated to be equal to 2.2 microseconds before a muon decays.

Therefore:

With a td = 166 microseconds of travel to reach the Earth's surface, it would be impossible for them not to have disintegrated. They shouldn't exist, and yet they are.

The following figure is intended to represent the two forms of muon production.

With this reasoning, they admit that time dilates, that is, by adding more time, as if time were a material entity... and thus leaving more time for the muon to decay.

WE AFFIRM THAT MUONS TRAVEL AT A GREATER SPEED THAN THE SPEED OF LIGHT. TIME DOES NOT DILATE.

In the approach put forward by the followers of the Theory of Special Relativity, they use the speed of light as the muon's travel speed. Based on this erroneous concept, they have no choice but to resort to the fallacy that time dilates. Of course, this statement conceals another fallacy of A. Einstein's. In his book "On the Theory of Special and General Relativity," he gives a mathematical approach that leads to the error of trying to justify that the speed of light cannot be exceeded.

Some time ago, we published an essay on our blog entitled: "Theory of Relativity: It is possible for an atomic particle to travel faster than the speed of light." In this essay, we demonstrated this possibility mathematically. Now, we present this possibility empirically in a real-life scenario.

WE PROVE THAT THE MUON TRAVELS AT A SPEED GREATER THAN THE SPEED OF LIGHT

We argue that on the journey from the collision with the atmosphere to the Earth's surface, it's not that time dilates, but that muons, as atomic particles, travel faster than the speed of light.

If we propose a proposal in which we demonstrate that a muon can travel faster than the speed of light, we can rule out the fallacy that time dilates.

In this demonstration, we will carry out the following two steps:

1. Express the speed of light in microseconds

2. Determine the speed of a muon in microseconds

By evaluating these concepts in the same unit of measurement, comparisons can be made between them.

1.- EXPRESSION OF THE SPEED OF LIGHT IN MICROSECONDS: µs

Remember that we represent a microsecond as µs, and that it is equivalent to: (1 / 1,000,000) seconds.

We will take the following unit of measurement: µs

The speed of light is represented by (c)

To measure seconds in microseconds, we take the dimension µs as the unit of measurement.

c=300,000 km/sec×(1 sec)/µs=(300,000)/(1,000,000) km/µs=0.3 km/µs

2.- DETERMINE THE SPEED OF A MUON IN MICROSECONDS

We ask ourselves, what speed must muons have to arrive from an altitude of 50 km above the ground without disintegrating?

To answer this question, we proceed as follows:

Identifying the speed of the muon as (Vm); the distance traveled as (e); and the time taken as (t), we apply

the formula: Vm = e/t

We observe that the value of (Vm) is determined by two variables. The value of the Space variable (e) is known: 50 km. To determine the value of time (t), we will rely on the data provided in the laboratory.

In the laboratory, for the entire muon to arrive, the maximum travel time is: (td) = 2.20 µs. We will take this duration of NOT decaying as the time the muon is traveling.

Thus, we have:

Observe the difference in speed obtained with respect to the speed of light. We believe this is the reason why muons reach the ground without decaying.

FALLACIES IN THE THEORY OF RELATIVITY

To conclude this essay, we would like to highlight some of the fallacies that appear in the Theory of Relativity.

We have just analyzed one of these fallacies. We can call it the "muon decay time" fallacy. In truth, this is not a fallacy presented to us directly by the aforementioned physicist. Rather, it is indirectly constructed by "believers" and followers of that theory in order to justify it. However, in the aforementioned theory, we can mention fallacies created and supported by the aforementioned physicist. You can find them summarized in our "little book," published by Amazon, entitled: "The Errors of A. Einstein. A Brief Summary." We briefly comment on these fallacies: When discussing "The Simultaneity of Relativity," he comes to an erroneous conclusion by saying that:

"The time required for a process relative to the wagon cannot be equated with the duration of the same process judged from the reference body of the embankment".

"We ask ourselves: Do you really believe that matter and biological processes are transformed...?"

To this statement, we ironically reply that he is preaching "the miracle of transmutation." This is one of the fallacies.

Another fallacy, also discussed in the aforementioned "little book," is that of the "deformation of space." Through false arguments, the aforementioned physicist attempts to justify the attraction between two masses, not because of a force we call "gravity," but because space is deformed. We jokingly wonder why the supporters of the theory of relativity, when performing the muon test, instead of saying that time dilated, did not argue the nonsense. that space is deformed...

We see that followers of this theory claim that:

Time dilates; space is distorted; processes are modified… What else can be changed?

In this type of "science," one fallacy supports another.

We believe that to justify the presence of such nonsense, we must recall what we have already stated in one of our essays: "the verb SEE was confused with the verb BE."

(NOTE: We draw our readers' attention to an explanation found on Google that may cause confusion. This platform states the following:

“A muon travels at speeds very close to the speed of light, generally around 0.998c. This high speed is key to their detection at the Earth's surface, despite having a very short half-life at rest (approximately 2.2 microseconds).”

The reader will observe that this statement is incorrect or, at the very least, contradicts those who use the muon test as a thesis to justify “time dilation.” Recall that these same people claim that: “due to the time it takes them to travel 50 km, they shouldn't reach the Earth's surface”.

We, contrary to the previous assertion, have shown that the speed of a muon exceeds the speed of light, and this premise allows us to admit that muons do reach the Earth's surface.

A. EINSTEIN'S CONTRADICTIONS – THE FALSE USE OF THE VERBS "SEE" AND "BE"

1. REASON FOR PUBLISHING THIS ESSAY

In our "little book" entitled "A. Einstein's Errors – A Brief Summary," we stated that this physicist's error was confusing the use of the verb "SEE" with the verb "BE" in the thought experiments he proposed to justify his theory.

It is possible that the validity of our statement, perhaps somewhat gratuitous, was doubted. In an attempt to be somewhat pedagogical on this subject and to convince our readers of this assertion, this is the reason why we present this essay.

 

2.- THE PRINCIPLE OF RELATIVITY

In A. Einstein's book entitled "On the Theory of Special and General Relativity," on page 18 (Ediciones Altaya S.A.), he cites the following as the Principle of Relativity:

"If (k´) is a coordinate system that moves uniformly and without rotation with respect to (K), then natural phenomena occur with respect to (K´) according to the same general laws as with respect to (K)."

To be consistent in our study, this is the principle we will use as a guideline for our critique.

 

3.- OBSERVER POSITIONING IN THE THOUGHT EXPERIMENTS PRESENTED BY A. EINSTEIN

Thought experiments should allow us, as observers, to deduce the validity of the result to be obtained. If not, what would be the purpose of the thought experiment?

Following this criterion, in the drawings with which we intend to capture A. Einstein's thought experiments, we will position ourselves as the observer, with this figure appearing in the corresponding drawing.

Through the following drawings, we will see that:

IF A. EINSTEIN DOESN'T SAY THAT THEY LOOK DIFFERENT, AND SAYS THAT THEY ARE DIFFERENT, IT CONTRADICTS THE FIRST PRINCIPLE OF RELATIVITY, WHICH REQUIRES THEY BE EQUAL.

Below, we reproduce the thought experiments mentioned in the aforementioned book by A. Einstein in which the observer shown in the drawing (Fixed Reference System (K)) is ourselves.

 

1.- REFLECTION OF A RAY OF LIGHT IN THE MIRROR OF A MOBILE CAR

Time LOOKS different

2.- DISTANCE MEASURING BAR

The length LOOKS different

3.- THE RELATIVITY OF SIMULTANEITY

We, as observers, SEE that the flashes of the two rays do not reach the person riding in the carriage simultaneously. But they are simultaneous for us.

 

4.- TRANSFORMING THE VISION OF THE EXTENSION OF AN EVENT

We must note that in this case, it is the observer who moves (SRM), while the event occurred in a fixed location. Furthermore, we see the extent of the event transformed, not because the translational motion or velocity (v) has transformed it, but because the field of view has been deformed due to distance.

 

4.- OUR DISTINCTION IN THE USE OF THE VERBS "SEE" AND "BE"

If, as we indicated in the previous section, we are the ones who stand at the observation point (SRF) in the drawings, to be consistent with the Principle of Relativity, we must say that we SEE phenomena differently, but that they ARE NOT different. This is the error Einstein makes, contradicting himself, going so far as to state in his book that we take the following as a reference:

"The time required for a process relative to the wagon cannot be equated with the duration of the same process judged from the reference body of the embankment."

If we accept this contradiction imposed by Einstein as correct, we must ironically say that the "miracle of transmutation" occurs.

In our essay on the Lorentz Transformation Formulas, Einstein's error in accepting the verb "TO BE" as valid instead of the verb "TO SEE" is most clearly evident. In our study, we demonstrate that it is: "The transformation of the vision of the extension of an event." These formulas measure the extension of an event not because it has been transformed due to movement, but because the field of vision has been modified due to distance.

5.- GENERAL THEORY OF RELATIVITY. THE SAME ERROR AS IN THE SPECIAL THEORY.

In the so-called general theory of relativity, we can highlight the same confusion between the application of the verbs "SEE" and "BE."

Recall that to demonstrate the validity of this theory, Einstein used the thought experiment of the elevator. We will draw this thought experiment, posing as observers. We will be the Fixed Reference System (FRS).

Reasoning in the same way we did previously when considering the theory of special relativity, we say the following:

We translate SEEING as noticing the "trick" of the rope pulling the elevator at an accelerated speed (∆v).

The IS NOT refers to the elevator pulling the traveler's body and IS NOT a gravitational field that produces compression on their feet.

As the reader can see, this is another way of arguing the invalidity of the aforementioned thought experiment, in addition to what we explained in our aforementioned "booklet."

A COMMENT ADDED TO THE ESSAYS OF THIS BLOG

PURPOSE OF THIS COMMENT

The inclusion of this writing within the different essays that we have presented in our Blog, obeys the purpose of making known to our regular readers, the appearance of a “little book” that we have titled:

“The errors of A. Einstein. A brief summary”.

This “little book”, published on AMAZON, with about 50 A5 pages, aims, in a few words, and trying to be as pedagogical as possible, to make known how A. Einstein proposed his theory of relativity, and the errors he made in his approach and his conclusions obtained.

In this “little book” we believe that, briefly and with the help of schematic drawings, we can present our criticism of the book by the aforementioned physicist, entitled: “On the theory of special and general relativity”. In the “little book” the reader will be able to appreciate the nonsense committed both in the approach and in the answers obtained in “the special theory and in the general theory of relativity”.

Although in the essays that appear in the cited Blog these essays are presented with a certain independence from each other, in the mentioned “little book” we will see that all the errors that A. Einstein commits both in his approach and, as a consequence, in his results, obey the same common cause. This allows us to express in a few words the interconnection of errors in his theory.

A. Einstein, connecting between each other the different nonsense that he proposes and that he intends to authenticate by relying on the mental experiments that he proposes to carry out.

We hope that this new approach is to the liking of our readers.

THE DECEITS OF A. EINSTEIN. AN UNREAL WORLD OF FANTASY

PRESENTATION

In this essay we present a group of critical ideas on the mental experiments that A. Einstein uses in his book entitled: “On the theory of special and general relativity”. With these mental experiments he intends to validate his theories. This grouping of ideas allows us to see that a fallacy that we criticize in a mental experiment generates another fallacy that we criticize in another mental experiment. These errors are so obvious that we have been suggested to use the word “deception” to give the present study its title.

In this study we will deal only with “Special Relativity”, leaving the criticism of “General Relativity” for a second study.

The transcriptions that we make of the cited book by A. Einstein will be written in quotation marks and in italics.

In a short time we will publish a book that will group the essays published in the Blog of the author of the present essay that will be isolated criticisms and that we title as: “Errors and fallacies of A. Einstein in his theories of relativity”.



1.- A GENERAL ERROR IN ALL THE MENTAL EXPERIMENTS PROPOSED BY A. EINSTEIN

In all our essays we have exposed the same error committed in the mental experiments proposed by A. Einstein:

The error is to consider that the natural phenomenon IS different instead of considering that it LOOKS different when it is subjected to a relative speed with respect to a reference point.

We will see that this error is so serious that it not only attempts to change the appearance of a physical phenomenon but the cited Physicist says that it transforms a “process”.



2.- AN ERROR BY A. EINSTEIN IN THE INTERPRETATION OF THE LORENTZ TRANSFORMATION FORMULAS.

In the reference book, the cited Physicist gives a false interpretation of the Lorentz Transformation Formulas. We give a brief summary of this error that the reader can find expanded on this subject in our mentioned book.

A. Einstein, in his mistake of confusing the verb SEE with the verb BE, interprets the Lorentz Transformation Formulas as a way of knowing how the variables of an event have changed in value due to the relative MOVEMENT of the observer of the event with respect to this event. In this way, he can include it in his theory and it seems that the events change, that is, they ARE due to the relative movement.

In reality, these formulas serve to see how the VISION of an event observed from a mobile platform is transformed with respect to this event. The variables of the event are not transformed by the movement between the two reference systems but are SEEN transformed by the decrease in the visual field due to the distance (event-observer).

We can affirm our thesis by saying that A. Einstein applies the referred formulas precisely when he exposes the mental experiment of the measuring bar set in motion on a train car.



3.-THE DECEPTION OF THE LENGTH-MEASURING BAR

We now begin the subject of the “trickery” mental experiments proposed by A. Einstein in his book: “On the theory of special and general relativity”. It is about the subject of the “shortening of the length-measuring bar”. We will see that it is a fallacy that generates another fallacy. In the cited book that we take as a reference, speaking of a rigid ruler for measuring lengths placed on top of a moving train car, it says the following:

“The rigid ruler in motion is shorter than the same ruler when it is at rest. And it is shorter the faster it moves”

We say that the bar IS not shorter but that WE SEE it shorter. The faster the train passes in front of the observer, the shorter it will be. We believe that this is correct reasoning.

The following figure represents three forward positions of a train wagon that has a bar inside it for measuring lengths whose length is equal to that of the wagon.

The ends of the bar have been indicated as: Start (I) and End (F)

An observer fixed on the ground, Fixed Reference System (FRS), sees the aforementioned wagon containing the bar for measuring lengths pass in front of him.

In this passage of the wagon in front of the observer, we can see in the drawing that: In the first situation of the wagon, the observer will SEE the end (F) of the bar. In the second situation of the wagon, the observer will SEE the middle part of the bar and in the third situation, the observer will SEE the end (F) of the bar.

Figure 2

If the wagon containing the measuring rod passes very quickly in front of the observer, he will estimate the VISION triangle of the rod to be very short. But the reader can already judge that here no shrinkage of the rod occurs.



4.- THE DEFORMATION OF SPACE.- A FALLACY THAT HAS BEEN GENERATED BY ANOTHER FALLACY

Starting from the error of considering the shortening of the rod for measuring lengths due to a speed relative to a reference system, from this fallacy, in an ideal world, we can propose another fallacy. We believe that an ideal reasoning that A. Einstein could use could be the following:

In a fantasy world we can argue that, as the unit of measurement (L) of the rod for measuring lengths, with speed has decreased its dimension, this is equivalent to the fact that space has been deformed. It has expanded to maintain the relationship between space and units of occupation of the same. And thus we will justify the fallacy of the deformation of space. We will discuss this fallacy later.



5.- A MISCONDUCTED HYPOTHESIS DERIVED FROM THE FALLACY OF THE DEFORMATION OF SPACE

We will now discuss the error of assigning the mutual approach between two masses to a deformation of space, instead of attributing it to the force of gravity's traction.

Linking with the fallacy of the measuring rod of lengths, we see the

fallacy of the deformation of space as the author of the interaction between two masses.

The reader will find this topic in our Blog or in our book that we gave as a reference. We transcribe from these writings a piece of this subject:

THE THESIS OF A. EINSTEIN

On the “deformation of space” we have read the following:

“A. Einstein said, denying Newton, that gravity was not a force that attracted things, but that things do not move when they are attracted by something, but when they are pushed, and with this he wanted to say that if something falls on another thing it is not because it attracts it but because that thing curves space like a whirlpool in a bathtub.”

The writing continues saying the following:

“In Einstein's universe,” the researcher continues, “space and time are deformed by gravity. The Earth distorts the space that surrounds it very slightly because of its gravity.”

The following figure is the one we find in some treatises on this subject:

Please note that the historian whose writing we have transcribed begins by saying: “A. Einstein said, denying Newton…”

With our criticisms we try to validate Isaac Newton.



6.- TWO MENTAL EXPERIMENTS AGAINST THE FALLACY OF THE DEFORMATION OF SPACE

In previous issues we have investigated the origin of the fallacy of the deformation of space. In this issue we have devised two mental experiments to demonstrate the impossibility of such a fallacy being fulfilled.

In the first mental experiment we place a mass just above the Earth. Touching the Earth. Since there is no space to deform between the mass and the Earth we reason the absurdity that there is no attraction between them. We can lift the mass without effort.

This incorrect conclusion is what invalidates the idea of ​​the deformation of space. The following figure tries to represent this circumstance.

In the second thought experiment we place two masses of very different size and at the same distance from the Earth (d1 ) = (d2), and we reason the absurdity that since the two masses have the same space from them to the Earth, the force of attraction that the Earth exerts on them is the same.

In the same experiment we mathematically demonstrate this absurdity.

(NOTE: We also clarify for the reader a doubt that may arise. Let us remember that the acceleration acquired by the two masses in their free fall is the same. Precisely because the “mass” of each of them and the “force” to which the bodies are subjected intervene in this acceleration).



7.- THE FALLACY OF THE RELATIVITY OF SIMULTANEITY

We will comment on another fallacy that is the origin of another fallacy. It is the subject that A. Einstein exposes in his book and which he titles: “The relativity of simultaneity.

On page 27 of the cited book, he asks the following question:

"...Two events (e.g. the two rays A and B) that are simultaneous with respect to the embankment, are they also simultaneous with respect to the train?... We will soon demonstrate that the answer has to be negative..."

And he continues dividing:

“…When we say that the rays (A) and (B) are simultaneous with respect to the tracks, we mean that the rays of light that come out of the places (A) and (B) meet at the midpoint (M) of the section of track (A)-(B). Now, the events (A) and (B) also correspond at places (A) and (B) on the train.”

The following figure attempts to interpret this statement

Figure 3

We interpret and place inside the train a person to whom the light of the two beams reaches from two different sides. Since the light of the right beam reaches him on the right side before the one that reaches him on the left side, because the train is moving in this direction. And since the person who is fixed on the ground, Fixed Reference System (SRF), receives the light simultaneously, A. Einstein dictates that the event of simultaneity IS different in a Mobile Reference System (SRM) than in a Fixed Reference System (SRF). We will comment later that this conclusion is a fallacy. 

8.- A. EINSTEIN'S ERROR IN THE MENTAL EXPERIMENT OF THE RELATIVITY OF SIMULTANEITY

To detect the error that A. Einstein makes in his mental experiment called "the relativity of simultaneity", we will start by explaining his First Principle of Relativity, which appears in his book:

"If a (RMS) moves relative to a (RFS) then natural phenomena occur relative to the (RMS) according to the same general laws as with respect to the (RFS)"

The error that A. Einstein makes in his mental experiment of the relativity of simultaneity is to consider simultaneous events that occur outside a Mobile Reference System.

If a simultaneous event occurs outside a Mobile Reference System (RMS), as is the case of the two rays, it is absurd to want to apply the theory of relative movements to it. This is what happens in the mental experiment proposed by A. Einstein. This “relativity of simultaneity” goes against the First Principle of Relativity that we have set forth.



9.- CONSEQUENCES OF THE ERROR IN THE MENTAL EXPERIMENT OF THE REELATIVITY OF SIMULTANEITY.- THE NONSENSE OF A. EINSTEIN

The author of the aforementioned mental experiment intends to establish a correspondence between what an observer sees, who considers it as a Fixed Reference System (SRF), and what an observer sees located inside the wagon. But, be careful, the error is that natural phenomena, lightning, do not occur inside the wagon. We cannot consider that an Inertial Reference System has been established. Natural phenomena do not travel within the Mobile Reference System (SRM).

Not realizing this error, he preaches the following:

“The time that a process needs with respect to the wagon cannot be equated to the duration of the same process judged from the reference body of the embankment”

This is where we say that his statement is equivalent to the “miracle of transmutation”.

Now he seems to forget the First Principle of Relativity that he cited and that we have written in paragraph 8. Now he speaks of “a process” and not of the laws that govern natural phenomena. The confusion he makes on the subject of the “relativity of simultaneity” makes him interpret differently the vision from the (SRF) of the events that occurred in the (SRM).

CONTRADICTIONS AND ERRORS OF A. EINSTEIN IN HIS THEORY OF RELATIVITY

PRESENTATION

In this essay we criticize the Theory of Special Relativity and the Theory of General Relativity of A. Einstein

The study is divided into the following three parts:

A.- Bases established by A. Einstein to argue his theory of special relativity

B.- Contradictions of A. Einstein in his theory of special relativity, with respect to the bases that he had established in another book

C.- Contradictions of A. Einstein in his theory of general relativity.- His error in the principle of equivalence

The texts transcribed from A. Einstein's books will be written between quotation marks and in italics.


A.- BASIS ESTABLISHED BY A. EINSTEIN TO ARGUMENT HIS THEORY OF SPECIAL RELATIVITY

We discuss the basic principles that A. Einstein uses to argue his Theory of Special Relativity and that later, we will see that he contradicts them.


1.-INERTIAL REFERENCE SYSTEMS

We remind the reader of a basic concept that appears in the theory of relative motions.

Let us imagine in sidereal space a body that is moving relative to another with a certain uniform and rectilinear speed. By definition, we will say that an Inertial Reference System (SRI) has been established between these bodies.

We will designate the body that we assume moves with respect to the other with the name Mobile Reference System (MRS). The other body, which we will take as a reference or as the origin of the movement, will be designated as the Fixed Reference System (SRF).

A further step will be to consider that these “bodies” are containers of physical phenomena, with their corresponding laws that govern them.


2.- THE FIRST PRINCIPLE OF RELATIVITY.- GALILEO'S PRINCIPLE.

In order to observe the contradictions that the Theory of General Relativity presents, by attempting to include accelerated movements, we must begin our essay by stating the Principle of Relativity.

Taken from A. Einstein's book titled: “On the theory of special and general relativity” (Page 18) the first Principle of relativity says:

“If a (SRM) moves with respect to a (SRF) then natural phenomena occur with respect to the (SRM) according to the same general laws as with respect to the (SRF).

Just as a comment we cite as an example that: Galileo Galilei already announced this principle in 1632, using the mental experiment of the hold of a ship in uniform and rectilinear motion)

3. WHAT DID A. EINSTEIN INTEND TO JUSTIFY WITH HIS THEORY OF RELATIVITY?

Knowing the concepts of relative movements and what is understood by inertial reference systems, we will be in a position to understand the answer to the question: what do we think A. Einstein intended to justify in his theory of relativity?

We find the answer in his book: “The meaning of relativity” by A. Einstein (Page 38). There the author notes the validity of Inertial Reference Systems (IRS) to be able to examine and measure the laws of nature in the same way and with the same results in each of them. Using mathematical and non-physical terms, we could say that the (SRI) are reference coordinate systems with respect to others.

On the aforementioned page of that book the following explanation appears:

“…there are Cartesian coordinate systems, the so-called inertial, with respect to which the laws of Mechanics (more generally, the laws of Physics) have the simplest form. We can infer the validity of the following theorem: if K is an inertial system, any other system k', endowed with uniform motion and without rotation with respect to K, is also an inertial system and the laws of nature are consistent with each other when use any inertial system to express them. We will call this statement the “principle of special relativity.”

In short: in an Inertial Reference System, the same natural phenomena develop and are conditioned by the same laws.


B.- CONTRADICTIONS OF A. EINSTEIN IN HIS THEORY OF SPECIAL RELATIVITY WITH RESPECT TO THE FOUNDATIONS HE HAD ESTABLISHED IN ANOTHER BOOK

Everything that we have exposed in “part A” of this essay and preached by A. Einstein himself, we will now see what he denies. It enters the dark tunnel of confusing the use of the verb SEE with the verb BE, an error that we have already commented on in our previous essays.

This confusion consists of the fact that, just because there is a relative movement between a Mobile Reference System (SRM) with respect to a Fixed Reference System (SRF), natural phenomena and their laws are modified. And this is the confusion that we have exposed.

The aforementioned Physicist says that physical phenomena and their laws ARE different when in reality, to be consistent with his previous statements, he should understand that they LOOK different. The statement that they ARE different contradicts their previous arguments that we have presented.

Next, we will comment on some of our previous essays in which we already warned of the error of confusing the use of the verb SEE with the verb BE.

(NOTE: The reader can consult in our Blog the topics that we are going to briefly summarize. All the topics that we criticize appear in A. Einstein's book titled “On the theory of special and general relativity)

1.- THE LONGATION OF THE REFLECTION TIME OF A RAY OF LIGHT IN THE MIRROR OF A TRAIN CAR CIRCULATING AT A CONSTANT AND STRAIGHT SPEED.

We show that the (SRF) VE extends the duration of the longest light ray. But it is not that time has dilated as some physics books argue. You SEE the extension of time at the speed of light, added by the speed of the train itself. “Added” but not dilated.


2.- THE SHORTENING OF THE MEASURING BAR

In one of the paragraphs of the aforementioned book, it presents a length measuring bar on top of a mobile train car. And it says that the bar is shortened with respect to (SRF), simply because of its relative movement. By considering the verb BE you come to admit the nonsense that the measuring bar has become shorter. The bar has not been shortened, it LOOKS shorter because the end of the bar travels on the car against the vision of the (SRF)


3.- THE RELATIVITY OF SIMULTANEOUSNESS

In another paragraph of the book he raises the “relativity of simultaneity.” Due to the same confusion already mentioned, he manages to admit the nonsense, which we ironically call “the miracle of transmutation.” The matter has changed state.

(Note: In one of our previous essays we explained where the trap lies to justify such an error of trying to destroy the simultaneity of two events and consider them different)


4.- THE PARADOX OF THE TWIN BROTHERS

The same books that deal with the subject of the theory of special relativity already classify as a “paradox” that the astronaut twin brother, when he returns to Earth, finds his twin brother older.

Confusing the verb SEE with the verb BE turns the story into a science fiction story


5.- THE PHASE LAG IN CLOCKS WITH RELATIVE MOVEMENTS

Another issue with the same justification that we have been exposing is found in the fictitious phase difference between clocks with relative movements. We could combine this nonsense with that of the paradox of the twin brothers. To justify the nonsense, dubious publications appear that try to validate it, mentioning experiments of dubious authorship and accuracy.


6.- LORENTZ'S TRANSFORMATIONS

These transformations of the variables of a formula do not occur as described by A. Einstein in his aforementioned book. The variables involved are not transformed. We demonstrate in one of our essays what they consist of, how to obtain them and what they LOOK like.


C.- CONTRADICTIONS OF A. EINTEIN IN HIS THEORY OF GENERAL RELATIVITY.- HIS ERROR IN THE PRINCIPLE OF EQUIVALENCE

This third part of this essay will serve to criticize the error of wanting to include accelerated movements in the fulfillment of physical phenomena and their corresponding laws.

In this third part we will distinguish two themes. One topic is focused on demonstrating non-compliance with the laws of natural phenomena if we intend to use accelerated speeds in relative movements. We dedicated the other topic to speculating about the possible erroneous arguments that the aforementioned Physicist used to reach such confusion of ideas.


1.- SUMMARY OF THE ELEVATOR MENTAL EXPERIMENT

With the thought experiment of the elevator, A. Einstein intends to justify the extension of his theory of relativity to reference systems that move with accelerated movements. We will see that this is a chimera

(NOTE: In our essay titled: “Theory of general relativity. - A science fiction story” the reader can read the entire elevator thought experiment” that we have transcribed from A. Einstein's book: “On the theory of relativity special and general)

A summary of the approach to this thought experiment, as described by A. Einstein, is as follows:

A box, which we will identify as an elevator and place in sidereal space, is pulled upwards, with a uniformly accelerated speed: ∆(v), by a rope attached to the roof of the box. Inside this elevator there is a person who is a passenger. This person notices the pressure exerted by the elevator floor because the traction force exerted by the aforementioned rope is transmitted throughout the elevator casing to the elevator floor.

The following figure is intended to signify the elevator thought experiment.

2.- CONCLUSIONS DRAWN BY A.EINSTEIN FROM HIS MENTAL ELEVATOR EXPERIMENT 

If we read the aforementioned mental experiment in its entirety we can make the following summary: Since the accelerated movement that the rope gives to the elevator causes in the person who is inside it a SENSATION equivalent to that caused by a gravitational field, this allows him to extend his theory to accelerated relative movements. We transcribe some final pieces of his conclusions: “But how does the man in the box judge the process?”… … ”Based on his knowledge of the gravitational field, as we discussed in the last section, the man will conclude that he is, along with the box, within a fairly constant gravitational field.” ..."So we have good reasons to extend the principle of relativity to reference bodies that accelerate with respect to each other, and thus a powerful argument has been won in favor of a postulate of generalized relativity." With these statements it seems that everything would fit to accept the expansion of the aforementioned theory. However, a deeper analysis will show us that this approach has very little consistency. It is a fallacy and the laws subject to natural phenomena could not be fulfilled as we discussed in our previous chapters.

3.- AN INCORRECT INTERPRETATION OF THE CONCEPT EQUIVALENCE

Reading the latest statements that A. Einstein makes in the elevator thought experiment, we wonder if we can call EQUIVALENTS the traction force generated by the elevator rope through the casing to the floor of the elevator and a hypothetical gravitational field. We believe that in the sense that A. Einstein uses the similarity of the aforementioned effects, the word EQUIVALENT is not correct. The aforementioned Physicist uses this similarity to indicate that the two CAUSES produce the same EFFECT. They produce a sensation of pressure on the feet of the traveler who is inside the elevator. We say that the word EQUIVALENCE is not correct because its extension limits it to a single type of EFFECT. The equivalent word must be more demanding. It must require that ONE CAUSE can be replaced by another giving the same EFFECT or result. And this is what does not happen in the EQUIVALENCE that A. Einstein presents in the story of his elevator thought experiment. Admitting the meaning of EQUIVALENTS as he presents it, is as absurd as justifying that a pot with boiling water inside and an electric stove plugged into the outlet are EQUIVALENT, because the two utensils give off heat.


4.- THE CONFUSION OF A. EINTEIN.- THE WRONG EQUIVALENCE OF ONE FORCE FOR ANOTHER OF A DIFFERENT SIGN

Now we will try to find out what A. Einstein's confusion was that led him to preach an error.

He says that the traction force of the rope and the fictitious gravitational field are equivalent, because they make the same SENSATION perceived in the feet of the passenger in the elevator. However, he forgets that the important thing is to determine how the forces he says are involved ACT. And, if we take this into account, we must consider that two different types of force actually ACT and, therefore, we cannot speak of EQUIVALENCE.

We must consider that in the aforementioned experiment a Contact force and an Attraction force intervene. The Contact Force can be Traction or Push.

The following figure aims to expose the ACTIONS of these two types of forces:

We can transfer the performance of the two types of force: Traction Force and Attraction Force, to the elevator floor of the thought experiment.

The following drawing aims to simulate the elevator pulled by a rope that imposes a uniformly accelerated speed.

∆(v), and the forces that are said to act on the feet of the traveler inside it.

In the image we can see that the traction force exerted by the rope on the floor of the elevator through its casing and a hypothetical force of attraction due to a hypothetical gravitational field are not at all EQUIVALENT. Using terms from Physics, these forces are vectors of different signs and we cannot quantify them with the same value. Their EQUIVALENCE is not useful for us to exchange them in the formulas of the laws that govern natural phenomena.


5.- INCAPACITY OF REFERENCE SYSTEMS WITH ACCELERATED RELATIVE MOVEMENTS

Reference Systems with accelerated relative movements, unlike Inertial Reference Systems, cause displacements of the mass and, consequently, the laws of classical mechanics are not applicable.

As an example we can take that of a train car in a phase of its movement in which it is accelerating. Its uniform increase in speed: ∆(v) causes the mass (m) inside to move from the front wall of the car to its rear wall. At this point, the dough will be “stuck” to the front wall without being able to move.

This image can also serve to highlight that there is no EQUIVALENCE between the gravitational field that operates throughout the carriage and its contents, and the traction force caused by the engine of the train carriage, in a direction perpendicular to that caused by the previous force . The acting forces cause two different CAUSES. These are attachment to the ground and accelerated movement. Physically speaking, they are vectors that have different directions. They are linearly independent. Not EQUIUVALENT.

Continuing with accelerated movements we can also use as an example a pendulum anchored inside the car. If we assume that when the movement of the wagon begins, the ball of the pendulum is near the front wall of the wagon, as the speed accelerates, in the end the said ball will be near the rear wall of the wagon and from there it will no longer be able to move. . The law of the pendulum will not be fulfilled.

The following figure aims to expose this circumstance.

This tells us that accelerated movements do not allow include them within natural phenomena and the laws that govern them. A pendulum clock inside this accelerated car (SRM) could not indicate the passing time as a pendulum clock located in its response (SRF) would do.


6.- SPECULATION ABOUT A. EINSTEIN'S ERROR IN HIS PRINCIPLE OF EQUIVALENCE

With the understanding that we are going to express our own opinion, we are going to speculate regarding A. Einstein's error in trying to establish an EQUIVALENCE between a Traction Force and an Attraction Force corresponding to a fictitious gravitational field, and we propose the following:

In his book titled “On the Theory of Special and General Relativity,” the chapter in which he describes the elevator thought experiment begins with the following title:

“The equality between inertial mass and gravitational mass as an argument in favor of the postulate of general relativity”

This distinction between two types of dough that behave in the same way is the beginning that causes confusion.

In the aforementioned book he starts from the concept that a body has two types of mass. The inertial mass and the gravitational mass. After using a twisted tour of concepts and arguments, on page 60 of the book, he comes up with a formula, of dubious validity and without any type of demonstration, to try to justify that the quotient between the Inertial Mass and the Gravitational Mass is worth “1” , and from here he draws the conclusion:

“The Gravitational Mass and Inertial Mass of a body are equal”

Regarding this statement we make the following reasoning:

As he started from making the distinction between inertial mass and gravitational mass, by applying the “mysterious formula and saying that “they are equal” he is referring to the fact that they are numerically equal, but we must understand that he maintains the idea that there are two different types of mass.

In this statement we perceive that it rather refers to a numerical equality and NOT to “which is the same.” In other words, it does not refer to congenital equality or material identity, and this is his big mistake. He considers the existence of two types of dough.

We believe that: for all bodies there is only one type of mass. This mass behaves, or reacts, differently depending on the type of force to which it is subjected. The forces are the CAUSES and the behavior of the mass is the EFFECT. These forces are of two types and their BEHAVIOR on the mass is totally different. Let us remember that we classify them as: Force of Attraction and Force of Traction or contact.

In summary, we believe the following:

By considering that it is not forces but masses that act, it distorts the meaning of the experiment. By omitting the forces as operating factors in the experiment, it makes them equivalent to each other. That is, a Traction Force equivalent to a Force of Attraction and here is the error.

A. EINSTEIN'S ERRORS ANALYZED WITH LORENTZ'S TRANSFORMATION FORMULAS

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

In this first part we will propose and explain the steps to follow for the construction of the Lorentz Transformation Formulas. We will call these formulas: “Formulas of the VISION of the Extension of an event observed from a mobile platform”, in order to correct the distorted acceptance between the verbs: SEE and BE.

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

In the book “On the theory of special and general relativity” by Einstein, on page 32 (Edition “Alianza Editorial”), 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´)?

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

Formula of Time

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

Figure 1

Later we will demonstrate that the expression: (v×X)/c² that appears in the time formula, translates as a time and that with the “space formula” there would be enough to make “theoretical” applications.

2.- WHERE DO WE FIND ERRORS IN THE EXPLANATION GIVED BY A. EINSTEIN IN THE LORENTZ TRANSFORMATION FORMULA?

The first error we found in the explanations given by the Physicist about the Formulas and Lorentz Transformations is the following:

When asking:

What are the values (x`,y`,z´,t´) of the same event with respect to (k´)?

We believe that you are thinking about “transformation” or “converting” rather than SEEING the event from a mobile platform regarding the event. We believe this is one of the errors. He falls back into the error that we have already commented on in previous of our essays. Through relative movements he confuses the verb SEE with the verb BE. In this way he prepares what we have called “the miracle of transmutation”. We say that he is thinking about the “transformation” since in the mental experiment of the bar for measuring lengths, subjected to a relative movement, he applies the formula for the transformation of space and preaches the nonsense of the shortening of the aforementioned bar. This error consists of believing in the “transformation” of matter.

The second mistake consists of wanting to apply the conclusions drawn in a mental experiment to a real-life physical experiment.

We wonder if the results obtained from a thought experiment can be applicable in real life.

We believe that the answer has to be negative. Precisely, the problem is reasoned by applying a mental experiment because it is not possible to apply a physical experiment. And, so far, it seems that it is a chimera to try to build a physical experiment that transcribes the results of a mental experiment. All this is aggravated if in the mental experiment the action of SEE has been confused with the verb BE.

In this essay we will see that the expression will appear.

In which (v) is the speed of a moving body and (c) is the speed of light. Even considering (v) one of the greatest speeds in our real world, for example the speed of a space rocket, its speed is so small with respect to that of light (c) that the quotient that appears within the radical of the expression that we have written would be an infinite value. That is why we say that, as we will see, it would be a chimera to transfer it to a physical experiment.

(NOTE: Do not confuse, as A. Einstein states, that the limit speed that can be reached is the speed of light. The reader can read the essay contained in our Blog, titled: “Theory of relativity. - It is possible that a particle can travel at a speed faster than light." Note that there we are talking about a particle and not a body endowed with movement.)

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

We will understand the dimension of an event as its duration from its appearance until its extinction. We can value this duration in length or time. We will call this dimension EXTENSION of the event.

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

According to our approach we will say that its purpose would be: Assess the dimension of an event, which occurs in a certain position in space, by an observer who is moving at a constant and rectilinear speed (v) with respect to this event.

(NOTE: The reader should note that we are talking about a “theoretical” approach. At the end we will explain that this approach, using mathematical resources, could hardly be applied in our real life)

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

In order not to confuse with the erroneous purpose that Einstein intends to give to the Lorentz transformation formulas, in our analysis we will call them: Transformation formulas of the VISION of the Extension of an event. The reader should note that we highlight the verb SEE.

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

To build the “formula for the transformation of the VISION of the Extension of an event”, in our study we will consider three actions implicit in it. These actions are the following:

APPEAR the event; REMAIN your visibility; SEE your Extension.

7.- TWO PHYSICAL PHENOMENA TO CONSIDER

When constructing the transformation formula we must take into account that two physical phenomena overlap. One is the movement and displacement of the observer of the event at a speed (v). The other physical phenomenon is the VISION of the event, from the place where the observer has moved, and in which the speed of light is involved (c).

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

To analyze the VISION of the Extension of an event from a mobile platform we will use a right-angled triangle.

We must define the situation of three points representative of: Appearance of the event (E); Completion of the Extension of the event (F) and Observation of the event (O). With these three
points we define a triangle

9.- WHY SHOULD THE TRIANGLE BE RECTANGLE?

To position the event and its observation position in space, we will consider the two legs of the triangle as coordinate axes. The legs of the triangle must be perpendicular to each other. This is so since:
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

The following figure presents the aforementioned three points and their routes between them. This triangle will be used to calculate the relationships that exist between the paths of the light and that of a mobile observer of the event.

Figure 2

Point (E) is where the event has appeared.

We interpret the vertical leg as the equivalent of the route of the EXTENSION of the event. We indicate it as (c.tp), being (c) the speed of light and calling (tp) Proper Time of the Extension.

We represent the end of the Extension with the point (F)

The horizontal leg serves to indicate the path and direction of a mobile body that moves at a uniform and rectilinear speed (v) from point (F) to point (O). We could consider it to be the body of the “observer.”

The hypotenuse of this triangle represents the path of the light ray that the observer has to perceive to SEE the appearance and development of the event. We write its travel time as (tr).

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

We already said that the two legs had to be linearly independent. Now we can ask ourselves why we put the Extension of the event as a length on the vertical leg and call it (tp). The answer is that this value represents the time in which an observer located at the end point (F) would be contemplating the entire development of the Extension. And so, in this way we capture an evaluation criterion of the Extension in a sketch.

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

We have developed a mathematical procedure that allows us to value the time (tp) of the EXTENSION as a function of the Travel Time (td) required by the observer of the event to travel the itinerary described by the points (F-O).
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.

(NOTE: The mathematical development to obtain this equation is in the Second Part of this essay)

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

To justify that the Lorentz Factor allows us to transform the value of the Travel Time (td) on the horizontal leg of the triangle to the observation point (O), into units of the Own Time (tp) of the event, that is, its EXTENSION, we will observe the formula given above from which we can deduce the following:

With which we can affirm that the Lorentz Factor is equivalent to valuing (td) in units (tp). It is a transforming factor that allows us to evaluate movements made at speeds (v) and transform them into speeds (c).

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

Expressing the distances in times spent traveling them will allow us to consider only one of the transformation formulas set forth in the aforementioned book by A. Einstein.

We can express the distance between two points as the TIME taken to travel between these two points at a certain speed. This speed can be that of a moving body (v) or that of light (c).

Since we can consider the speed of light (c) constant, we can take it as a measure to evaluate distances and measure these distances in units of the speed of light (uvl).

In the following figure we can see that the distance between the observation point (O) and its mobile reference axes (K'), which has the observer as a reference, can be quantified by:

(X – v.(td))

Figure 3

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

So we establish the equivalence: (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.

The fact that A. Einstein's space transformation formula does not fulfill the purpose that he assigns to it, this does not mean that its expression
implicitly contains the two physical phenomena to be considered.

Let us note that the numerator of the formula is: (X-v.t) which takes into account the physical phenomenon of displacement. We can verify this in Fig. 3.

Regarding the denominator of the aforementioned formula, we propose the following:

As we had explained, if

is equivalent to allowing the (td) to be valued in units (tp) and since (X-v.t) is equivalent to (td), we can deduce that: (X-v.t) is valued :

in units (tp). That is, in the Extension of the event.

Let it be clear that it allows us to SEE the Extension of the event. DO NOT transform the event.

16.- ANOTHER FORMULA TO ASSESS THE VISION OF THE EXTENSION OF AN EVENT FROM A MOBILE PLATFORM

In the previous issue we have seen that the formula for the transformation of space that A. Einstein gives us, although it does not fit the purpose that he proposes, we could use it with a theoretical approach to measure the extension (tp) of a event.

For theoretical purposes we can also give another expression that allows us to obtain (tp) as a function of the travel time (td) necessary to cover the distance between points (F) and (O).

Please note that this expression is obtained by solving for variables in the equation expressed in Point 12.

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 name “vision transformation formula”
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.

We have called it this way because of the following:

We can make a composition of figures 1 and 2 by superimposing them one on top of the other so that it globally represents the graphic expression of the aforementioned formula which, as we had commented, is the expression of the two physical phenomena.

In the following figure we can see that both the variables that imply the transfer of the coordinate axes appear, as well as the variables related to the vision of the event from a mobile observation point. That is, the variables corresponding to the right triangle.

Figure 4

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?

The doubt might arise if with this displacement of coordinates.

The relationship remains constant: td/tp, which allows us to measure the value of the Extension of the event. Using Geometry we can say yes, applying Thales' Theorem.

(NOTE: See the geometric explanation of Thales' Theorem in the second part of this study)

SECOND PART

This second part serves to expose the mathematical approaches and ideas that support the criteria that have been used in the first part, for the construction of the aforementioned formulas.

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

Let's look at Figure 2. At a given instant it happens that: at point (E) in space an event appears and at this same instant the possible observer of this event is at point (F) in space.

From this initial instant begins the path of the light ray that carries the image of the event and the path of the observer who has to detect said event. Calling (tr) the time spent in the ray path and (td) the observer's path time, as the two paths must coincide at the observation point (O), we will impose as a synchronization condition:

(tr) = (td)

This is the condition that we will impose in the calculations that we will carry out below.

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

To relate the Proper Time (tp) of the Extension of the event, with the Displacement Time (td) we will apply the Pythagorean Theorem to the right triangle that we gave as a reference.

Requiring compliance with the Synchronization Condition:

(tr) = (td)

It allows us to replace (tr) with (td) with what we obtain:

Grouping terms we have:

We can transform the denominator in the following way:

Eliminating (c), gives as result

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.

To demonstrate this fulfillment we must remember Thales' Theorem. We can say that in a right triangle the proportionality relationship between the path of the horizontal leg and the vertical leg is fulfilled.

Let us remember that in the vertical leg we will represent the Extension (tp) of the Event and in the horizontal leg the travel time of the observer.

The following figure aims to demonstrate the validity of this theorem, by observing that the aforementioned proportions are maintained

Figure 5

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

When exposing the formula for the transformation of time we said that the expression: (v×X)/c² is nothing more than the expression of a “time”. 

Let's prove this statement.

In the VISION of an event, which we use a mobile Reference System (SRM) with respect to a Fixed Reference System (SRF), it must be taken into account that we use two types of speeds of a completely different nature. Let us remember that it is about: (v) and (c). 

We must homologate these two concepts if we want to incorporate them in the execution of the same physical phenomenon. We use the speed of light (c) as measurement pattern. That is, the 300,000 km/sec. as a unit of speed.

To make the aforementioned conversions we must take into account the following criteria to follow:

All lengths will be quantified using: “light speed units” (uvl).

This means that: the (uvl) are those that would be consumed to move between two certain reference points. For example, we can write: x = k (uvl) meaning that a certain length (x) is found, or would require k (uvl) to reach it.

A relationship such as: (v/c) assigns a fraction of (uvl) to a given velocity (v), since (c) is a fixed quantity taken as a unit, while (v) is the relative velocity between Inertial Reference Systems, different value in each specific case.

To quantify a length (l) we will apply the expression: l = x.( v /c)

This expression answers the question: A length (x) that has been traveled at speed (v) is equivalent to what length (l) if the speed were that of light (c)?

To obtain the travel time (td) of a Mobile Reference System (MRS) on the axis (X), operating with (uvl), we must divide the space (l) by the speed of light (c).
I mean:

(td) = (l) / (c) 

and since 

l = x.( v /c)

we obtain: 

(td) = (l) / (c) = ( x).(v / c) / (c) = ((x).(v))/c²