In view of the dilemma seems unavoidable abandon either the principle of relativity or the simple law of the propagation of light in a vacuum. The reader who has followed closely the above considerations certainly expect to be the principle of relativity, which by its nature and simplicity is imposed on the mind as almost inevitable, which remains standing, instead replacing the law of propagation light in a vacuum by a more complicated law and compatible with the principle of relativity. However, the development of theoretical physics showed that this path was impassable. Innovative theoretical investigations of HA Lorentz on electrodynamic and optical processes in moving bodies showed that experiences in these fields lead to urge a theory of electromagnetic processes that result irrefutable law of constancy of light in vacuum. For this, art theorists rather bowed to dispense the principle of relativity, while unable to find a single fact contradicted experimental.
This is where came the theory of relativity. Through an analysis of the concepts of space and time was actually there was no inconsistency between the principle of relativity and the law of propagation of light, but, one systematically paying attention to these laws led to a theory logically impeccable. This theory, to differentiate it from its expansion (discussed below) is called "theory of relativity", is what will be presented here in its fundamental ideas. "
We make the following comments on the above underlined phrases
Now … this result goes against the principle of relativity
It is a contradiction to say that goes against the principle of relativity, if we admit that the speed of light is always the same and behaves precisely the aforementioned principle maintains the idea that all physical phenomena behave similarly in all Inertial Reference Systems.
We have also emphasized:
Innovative theoretical investigations … HA Lorenz on electrodynamic and optical processes in moving bodies
Wanting to reconcile the two ideas to which we referred was found "salvation" in the Lorentz transformation formulas. These were intervened by the speed of light and considered as constant. It is possible that with this more will be build more than just a "rehash" that was called, and called, "special relativity theory" or also "theory of restricted relativity".
We have used the concept of "rehash" and tried twin concepts: addition of speeds, speed of light always fixed and validity of the principle of relativity appearing by formulas called Lorentz transformations. And, in these formulas appeared in a mathematical expression "mysterious", we call Lorentz factor, which is our view, that were attributed magical properties: the "time dilation". (See Chapter 9)
Considering that Hendri Antoon Lorenz had exposed some empirically derived formulas to resolve right inconsistencies between electromagnetism and classical mechanics. (Consequently not known the "anatomy" of formulas, to know the role played by each of the variables that composed). Lorenz had discovered in 1900 that Maxwell's equations were invariant under this set of transformations now called Lorentz transformations.
(NOTE: In the chapter on how to obtain the Lorentz transformations we shall see the true meaning of the Lorentz factor (L))
Analysis of the validity of the mathematical expression obtained in the mental experiment of the train wagon
So far we have discussed what is it that is mistaken for admitting the fallacy of "time dilation" and what false argument it uses to justify the validity of the theory of
Theory of Restricted Relativity. (We recall that the argument set out in the treaties of Physics to support the above fallacy, is the emergence of inequality: T2> T1 after departing from a false premise and obtained the appearance the "mysterious" Lorenz factor). Now we should analyze the validity of the mathematical expression obtained in the experiment of "Wagon Train" to try to find out what we can confuse, in interpreting its meaning.
We have divided these analyses into the following topics:
1. – Field trip validity of the mathematical expression obtained in the mental experiment
2. – Possible origin of the misinterpretation of the result of the mental experiment.
Then we develop these themes.
8.1. – FIELD OF VALIDITY OF THE MATHEMATICAL EXPRESSION IN THE MENTAL EXPERIMENT OF THE WAGON TRAIN
We know that a specific mathematical formula is valid within certain values ??of its independent variables on which it remains defined. If we trespass those values, it"s possible that it can obtain absurd answers. We say that those values ??define the field limits of validity.
Considering that mathematical expression which was obtained by exposing the example of "train wagon"
Where:
Note that we are using the term "mathematical expression" instead of calling it "formula". By this we want to make a distinction between the term "formula" that we shall be using for making a determined calculation and which leads to a correct answer or "adequate" to the environment, and the name "mathematical expression" that well indicated that certain mathematical operations are performed, we don"t know very well to what it leads to or what is it that is intended with it.
Dealing with mathematical expressions that we are not sure to where they lead, let"s think that it would be necessary to distinguish between two types of validity of them.
We shall distinguish them between: operational validity and mathematical validity.
We shall understand that for operational validity that we shall obtain using values ??of the independent variables, which are "normal" in real life. That is, the "world in which we move." We shall understand by mathematical validity those that will allow to obtain using infinite values ??(positive or negative) of both the independent variables and the responses obtained. We can also include in this category that can operate with zero values ??although this represents an absurdity in real life.
We use the concept of "operational validity" (It"s possible that if we think en using the other type of validity, we would be taking the first step in another utopian dream).
In the aforementioned "mathematical expression" what happens if we consider the speed (v) infinitesimally less than the speed (c)? … Actually this is what happens in real life, in which we move. The truth is we have not found any treaty in a direct response to this question. And, it makes us guess that here we are enclosing a mistake. (In the next chapter we will explain why we use the word "direct"). We support ourselves in all that we have discussed, that is, interpreting the said expression as the "Calculation of Time Information", or as "Calculation of travel time of the image", we can give the following answer to this question:
It is obtained: (L) = 1 and hence: T2 = T1 (or very approximately).
This response would not have a logical interpretation if we wanted to follow the path of " Restricted Relativity". On the contrary, it does makes sense if we rely on the formula "Calculating Time Information". We shall see why, when applying this formula variables are considered: (T1) as "Own Time" event, and (T2) as "Time Information".
We justify the previous comment. In real life, the PERCEPTION of the events are "almost" instantaneous. We recall what we discussed in Chapter # 5, speaking of the "Own Time" event, in all its breadth, and amplitude "Time of Display or of Information". We put as an example the explosion of a given artifact. The ending of its "Own Time" (T1) is practically instantaneous with their PERCEPTION. That is we could write: T1 + T2 = e, where (e) is an infinitesimal.
If we speak of the PERCEPTION of (TIC-TAC) of pendulum we can say the same. The (TIC) or (TAC) perceive each one of them "almost" instantly ( the other thing will be the amplitude of time that exists between them, this would be their "Own Time").
Summarizing, we can speak of a "formula" if the result obtained in applying the aforementioned expression give the meaning of: obtaining the " Time Visualisation", or the "Time of path of the image" in terms of the speeds: (v ) and (c) used.
8.2. – POSSIBLE ORIGIN OF THE MISINTERPRETATION OF THE RESULT OF THE MENTAL EXPERIMENT OF TRAIN WAGON.
We have written in the previous chapter we had not seen a DIRECT answer to the question we asked and made ??us guess that a mistake was enclosed. By this we meant that, it seems that it pretends to argue the validity of the mathematical expression used in the example of "Train Wagon", passing through the equations called "Lorentz Transformations". What constitutes an indirect form to justify the aforementioned validity. We shall argue why:
Factor (L) appearing in the mathematical expression obtained by considering the thought experiment of "Train Wagon", we have seen been called "Lorentz factor". This is by the same factor appearing in the formulas of the Lorentz Transformation ":
These formulas have the following expression:
In these transformations although the (L) factor appears, this does not justify to establish similarities between the previous formulas and these, and here it seems that the adaptation of a pipe dream starts.
. We shall see at the end and that indicates us these formulas in arguing the same way as we did before:
These results indicate us that for the speeds that we move in the real world, thus we can apply the theory of movement of Galileo. That is, it is the formula which relates the displacement of the origin on the X axis considering the same instant of time.
Let"s recall that we said that the Lorentz Transformations allowed to include all laws of physics within the relative movements of different reference systems that may exist or be defined in space. We do not relate them to the mental experiment of "Train Wagon", although it may be temptation which appears called "Lorentz Factor".
A little history. Lorenz factor appearance
In our attempt to determine when, how and where the above fallacy generates, we will rely on some historical comments that appear in some treaties of "Physics" and you can also find them by looking in Web pages.
The story we believe begins with the experiment of Michelson and Morley. The same that the waves and sound require means to transport (such as water or air) it was assumed that the light would need half called "ether". This apparatus was designed to verify the existence of the "ether" (called interferometer). It is not our purpose to enter into technical explanations that we find in the above pages. We can only say, as we shall discuss later, this experiment failed. It could not prove the existence of "ether" (not for default of test or apparatus used but simply because the "ether" was an invention, and didn"t exist)
We have transcribed the following comments taken from different sources:
"In the 1890s and Hendrik A.Lorenz GFFitzgerald tried to explain each one seperately, because of the null results obtained in the Michelson-Morley experiment apart from the following ad hoc assumption. They proposed that the longitude of an object moving at the speed (v) would shrink along the direction of movement by a factor of:
Wherein (c) is the speed of light.
The net result of this shrinkage would be a change in the longitude of one arm of the interferometer so that there would be a difference in trajectory when the apparatus revolve. This physical contraction tried to explain completely the Michelson-Morley experiment. Yes … but it would be inconsistent with the same experiment as the two arms of the interferometer would have different longitude ".
Without going into the development of the aforementioned experiment and only for the purpose of being able to continue our exposition we make the following brief comments:
The aforementioned experiment was done to confirm the existence of "ether" (as a support of the electromagnetic waves). Curiously, when this experiment did not produce the desired result (the confirmation of the existence of the ether) was sought artifices to force to obtain a pre-established result (Note: It is our opinion.) To justify the two light beams simultaneously always arrived at their destination (arriving in phase), and therefore it was against the existence of the "ether" ( that according to the direction of the ray, "ether" would have to indicate more or less on the light beam) was used sophistry to claim that the arms of the interferometer had changed their longitude …
In this historical data it seems to say that we can support ourselves by saying that it plants the seed of the concepts "time dilation" and "longitude contraction", based on the elongation assumption, no contrast, in the arms of a "device" that then hesitated of its validity.
(We repeat again that there are many websites that allow you to extend this issue we are dealing here only informative summary plan).
Another historical comment that we found referring to historical find Lorenz factor is as follows:
"In the special theory of relativity the Lorentz factor is a term that appears frequently in the equations of the theory, so it is usually given a name (L). allowing more briefly to write the equations and formulas of the theory. Appearing in the calculations of time dilation, contraction of the longitude, or in the relativistic energy expression kinetics and linear movement.
It owes its name to the presence of the first factor in the work of Lorenz on classical electrodynamics "
It is evident that the above description is "contaminated". As we will see in Chapter 13, to explain the "Deduction of formulas of Lorentz transformation", the Lorentz factor is simply an operator that allows us to streamline the system speed and time units used. We can express in units of speed of light (c) the speed (v) in which it moves an (SRM) with towards an (SRF).
Relations synchronized between inertial reference systems (CRS) and events (E)
Before beginning the study of formulas of Lorentz transformations it is important to briefly comment on what we will understand by synchronized relations between Inertial Reference Systems (IRS).
We can give the POSITION of a body in space by using three coordinates are taken as reference. But this will not be enough for us when dealing with an event (E). In these cases we will discuss the SITUATION of a (E), or also an (IRS), wanting to indicate that we are defining for them a position in space (e) and time (t) that is happening.
If we are thinking and admitting a space in which, by the same, there are no references to position of the bodies, but it is the existence of same bodies which means that there are references between them, it will be useful to use the word POSITION for the study of the relationships between events (E) and between (IRS).
We will use the idea of POSITION whether we refer to the existence of a particular (IRS) or a particular event occurence (E).
We always consider in the observations that we do will establish synchronized relationships between (IRS) and (E), in other words, that there exists in a given moment, and that otherwise would have no meaning. We repeat: the relationship between (E) and / or between the (IRS) understand that they are of the type: SYNCHRONIZED. That is, that they occur at the same moment.
This is the idea that we should stay with and which we shall use in the following chapters.
The Lorentz Transformations
The study of the Lorentz transformations constitutes the main part of this essay, as we rely on them to justify as a fallacy to consider the concept of "time dilation".
We commented that the factor called Lorenz (L) could be a cause of confusion when trying to associate a possible "time dilation" and the own time, to have it related with the results and conclusions drawn from the mental experiment of "train wagon ". Let"s recall that this factor (L) is incorporated in the formulas that we"ve already exposed, and that these formulas will leave our research.
But, first of all it is obvious that we wonder, "for what good do these formulas serve?" …We shall find different ways to answer this question. Our answer is constructed as follows:
We know that for Inertial Reference Systems (IRS) it complies the "First Principle of Relativity".
For the responses obtained in applying the formulas of value of the variable "t" and "e" to be equivalent in (SRI), we must require that between them, they produce synchronized relationships.
Consequently, values ??of the variables (t) and (e) obtained and referred to a specific (SRI), or to an (E), which occupy a determined SITUATION in space, must be TRANSFORMED by wanting to apply them to another (IRS) that moves with a relative movement towards the first speed (v) and which may continue occupying different SITUATIONS.
To make these "transformations" we shall use formulas called Lorentz transformations. In the following chapters we shall deal with this topic.
Now, in this chapter, took the opportunity to highlight two different concepts that cannot be left confused. At the end of chapter 2.3. speaking of the "First Principle of Relativity" we made ??the following observation:
"Here there seems that two concepts are intermixed that should be considered separate, each by itself autonomous and can confuse us…"
This observation we had put with an object to highlight and separate the contents of two concepts in the ones that are not left sufficiently detailed of their performance.
A concept is:
If we imagine the Inertial Reference System (IRS) as a drawer inside which can contain formulas, mathematical variables and parameters, we can say that among the (SRI) is the same behaviour when the result obtained by applying the aforementioned formulas under determined conditions, to a determined physical phenomenon,
This would be the mathematical approach that could give the "first principle of relativity" that we have exposed and discussed by experimental form.
A second concept, different from the above is:
Under what conditions INFORMATION IS TRANSMITTED proceeding from the occurrence of a certain event, from one (SRF) to another (SRM). This is the issue that we discuss now. These are the formulas of the Lorentz transformations.
Graphic vision according to our form of discussing the utility of Lorentz transformations
We will use a graphical form to discuss on the purpose and application of Lorentz transformations. Just as we do in the next chapter to explain the "Deduction of Lorentz transformations". We believe that the method of demonstration is the most intuitive graphic.
The figure that we shall use will inform us that an event (E) "occurred". Later we shall use the graphics to assess the time "t" of length to an (E).
We consider two Inertial Reference Systems (IRS). We assume that the environment of the system that we shall consider fixed reference (FRS) produces an event (E) and that exists an (MRS) that has a relative velocity (v) with respect to (FRS).
In saying that the event (E) occurs in the "environment" (FRS) we mean that it occurs within it. Which has no relative movement within it. Which is closely linked to (FRS) and that it produces a determined distance with respect to an observation point located in this (FRS).
The two (IRS) we have bonded by a line would imagine that we will assume that it is the axis (X). Since the (E) we shall also assume that there is an imaginary line which is perpendicular to the axis (X). This line we have designated as "time of the foot of the event"
(t p) It"s time that it takes to reach the vision of the event to the point (O), the coordinate origin.
It has represented as (t r) the travel time of the image from the site of the "birth" of (E) to the end point (F), observing site located at (MRS). This information is transmitted to the speed of light (c).
Let"s recall that we have agreed to comply with the First Principle of Relativity for Inertial Reference Systems (IRS). But, we need to impose another condition. So that between the two (IRS) they process the same information and can give the same answers from a particular event (E), should receive an EQUIVALENT INFORMATION. What is required in this condition?. This condition requires taking into account the possible SPATIAL LAG and SPACE at one certain point may exist between the two (IRS) to receive the information from the (E), due to the speed (v) and their different positions occupied in the space at the given time (MRS) with respect to (FRS). That is that in every moment the Synchronized Relations exist. The
(td) It represents the time to be employed (MRS) to move from the origin (O) to the point (F) in which they are currently found.
It is important to note the following:
It is understood that these formulas transform the value of the variables (t), (e) that are assigned to different (IRS) or (E) and involved in a certain formula that quantifies a physical phenomenon. The formula is not transformed as they would then cease to be true, the "First Principle of Relativity".
Obviously, with this transfer (E) to (FRS) we do not try to reproduce the phenomenon (or reproduce nor modify the physical phenomenon). What we try is to quantify the variables "t" and "e", by the information received from the image (E), which will operate with the formula that quantifies the phenomenon.
Deduction of formulas of the transformation of Lorenz
The issue that we shall now deal with is the main part of this essay.
We have seen in various different forms of Web pages to obtain the transformed formulas of Lorenz, each more obscure and complicated. It is not a criticism to these forms of obtaining and that one of them is quite original. What happens is that sometimes confuses the "abstract" with "opaque" This is dangerous because if we get lost in the dense forest, we would very easily be ready to admit the fallacy of "time dilation".
We have decided to investigate the form of capacity by using more visual mathematics, as is the use of the elements of geometry. This allows us to break down, and to have a better view on the phenomenon we want to study. (To try to clarify this issue … what better tribute to the light that will be our main guest!)
In the following chapters we shall dedicate to expose the obtaining of formulas of transformation of processing time and space, deduced using a visual procedure. Furthermore, to better interpret the analysis that we shall realise will break them down, and obtaining in two following parts:
1. – Conversion Factors of physical units to use in formulas
1. – Speed ??correction factor. – Measuring the displacement time (t d)
2. – Time correction factor used in the displacement of a Mobile Reference System
(MRS). – Lorenz Factor
2. – Deduction of transformation formulas.
1. – Time transformation Formula
2. – Space transformation Formula
3. – Observations with respect to the two transformation formulas obtained
This decomposition of concepts allow us to observe the "anatomy" of the integral parts of the aforementioned formulas.
13.1. – CONVERSION FACTORS OF THE PHYSICAL UNITS USED IN THE FORMULAS
We know that in the various fields of physics for answers in a certain system of units, we have to apply some conversion criteria. This allows us to move from one type of expression of the other units, quantifying the amounts to be assigned in these exchanges. In this essay, we must do the same. These operators can also call them: Factor Corrector. There will be mathematical type relationships that allow us to calculate the equivalent of a physical magnitude in other type of the order of magnitude to be able to operate with homogeneous factors.
13.1.1 – CORRECTIVE FACTORS OF SPEEDS. – MEASUREMENT OF DISPLACEMENT TIME (td)
In the perception of the image of an event between two Inertial Reference Systems with velocity (v) between them, we must remember that we are using two completely different types of speed as to nature and orders of magnitude. We can say that the relative velocity (v) between the two (IRS) is assumed between two bodies, or "containers" of possible physical phenomena, while the speed of transmission of the information corresponds to an electromagnetic wave with velocity (c) well above the velocity (v) ..
Obviously, although there are two expressions that are related to the "speed" are different. They have the same physical nature. It should be treated as different. The speed of light (c) is always the same, is a constant and an order of magnitude infinitively larger than it assumes that it gives on the axis (X), in other words (v). We cannot compare or establish a relationship between two longitudes or two lengths of time that are measured using different patterns to measure the velocities. They must be standardized in such a way that both use the same type of pattern. We use the speed of light (c) as pattern. In other words, the 300,000 km / sec. as speed unit
To make the aforementioned conversions we must take into account the following criteria to be followed:
All the longitudes will quantify using "light speed units" (lsu).
This means that: (lsu) are those that would be displaced between two certain points of reference. For example, we can write: x = k (lsu) referring us to a certain longitude (x) is, or would require k(lsu) to get to it.
The "light unit" is a measure of speed is worth: 300,000 km / sec. That is, a (lsu) is equal to 300,000 km / sec.
A relationship such as: (v / c) assigns a fraction (lsu) at a certain speed (v), as is (c) a fixed quantity which is taken as a unit, while (v) is the relative velocity between the (IRS), having a different value in each individual case.
To quantify a longitude (l) the following term applies:
l = x. (v / c)
This expression answers the question: a longitude (x) which has been travelled at the speed (v) to what longitude (l) equivalent if the speed was that of the light (c).
To obtain displacement time (td) to an (MRS) on the axis (X), operating with (lsu), we must divide the space (L) by the speed of light (c).
That is:
(td) = (l) / (c) = (x). (v / c) / (c) = (x). (v) / (c 2)
Expression that we shall use later to discuss the formula of Transformation of Time.
13.1.2. – CORRECTIVE FACTOR OF TIME USED IN THE DISPLACEMENT OF A MOVING REFERENCE SYSTEM (MRS). – FACTOR LORENZ,
A necessary condition for determining the value of displacement time (td) we have seen that it was by operating with a homogeneous system of units, this required the transformation of speed taking as the unit of measurement (lsu). But this condition is not sufficient.
Once the (td)is obtained which must be assigned to (MRS) due to the appropriate corrections of the speed (v), this (td) will still have to suffer another transformation due to another conditions that we must impose to it. It deals with the fulfillment of Synchronized relations. We shall discuss this issue.
When the event occurred (E) values ??of mathematical variables (e) and (t), that is, the SITUATION of (E) we can appreciate from the (FRS). But … can we say the same from a hypothetical SITUATION that has moved on (MRS) during this time? .. We cannot say that at the very moment the (MRS) is seeing the same image of the event that the (FRS) is watching, that is to say that they are synchronized, if they don"t comply with the condition.
For the two (IRS) to be synchronized, it will be necessary that the displacement time (td) of (MRS) from (FRS), or point of origin (O) to the
Observation point (F) is equal to the travel time (tr) of the image from the start point (E) of the event until that point (F).
Only in this way may coincide at the same point (F) of sight, the axis (X), both arrivals. (Arrival of the image and arrival of the image viewer). In other ways it would be impossible to detect and record the image. It requires synchronized visions.
The following figure is intended to represent schematically in (FRS) and the corresponding (MRS) and highlight the aforementioned condition:
The space covered by the image of the event (E) to the point (F) of observation is equal to (c . tr). The space covered in the displacement path (MRS) on the axis (X) from the origin (O) to the point (F) is: (v / c). (td) The space existing between the event (E) and the origin of coordinates (O) is: (c . tp).
In continuation, we shall impose the condition of compliance with the Synchronized Relationships. We shall see the end of it that this condition requires quantify (td) in units corresponding to (tp).
Approaching of the condition of "Synchronized relationship"
In mathematical deduction that we do, we will impose the condition: tr = td, and the end result will lead us to it.
Noting the previous figure and, although it is quite evident, as follow-up help, we will inform you that the first thing to do supports on the Pythagorean Theorem.
As tr = td we can used either will do. We´ll choose (td).
We can obtain => (L) = (td) / (tp) .
We see that in this deduction appeared Lorenz Factor
We also note that by imposing (td) = (tr)) these two times are related by (L). This factor quantifies the (td) using units (tp).
Note that the (tp) is a fixed value, a parameter of the event (E) under investigation and that it is taken as reference or means pattern. The same doesn"t happen for the values ??of (td) that will take different values ??as we place the different points of observation (SRM). We can also say that the Lorenz factor complies with Synchronized Relations
13.2.1.-TRANSFORMATION FORMULA OF TIME
Before starting this study we emphasize that we are talking about the "transformation of time", NOT the "time dilation". We want to avoid any confusion or idea associated with the so often mentioned fallacy. We shall understand the transformation of time as we have stated at the beginning of the subject of the Lorentz transformations, that is it obtains by relating the equivalence between two reference frames or coordinate axes.
To better the following process that we use in obtaining this formula by writing the times we indicated whether they refer to the Moving Reference System (MRS) or
to the Fixed Reference System (FRS)
We shall analyze the meaning of this formula, using the following two steps:
A. – Geometric approach to see the meaning of the formula.
B – Application of the corrections necessary to make the aforementioned approach to operate with homogeneous physical units. Transformation of units.
We shall do that in two steps.
STEP "A"
We present a geometric approach relying on the following figure ..
In this drawing we should distinguish the following elements:
The existence of two Inertial Reference Systems. A moving reference system (MRS) which we consider is moving with respect to another reference system that we consider as fixed (FRS), with a velocity (v).
A point (O) of origin of coordinates, which serves as a reference to be able to define a relative position between the two (IRS). For formula approach, we consider that the (MRS) was located at the starting point (P) and let"s consider that it has shifted to the right, to the end point (F).
For the point (O) intersect the axis (X) and the line (t p ) Its interpretation as "time to the foot of the event." The longitude of this line indicates the time it takes to be seen or detected the event image (E) at the point (O).
The remaining indications that appear in the figure by considering the following three concepts:
1 °. – The longitude of the vertical line (tp) extending from the event (E) to intersect the axis (X) which joins the (FRS) and (MRS) places us (E) to a certain distance of this axis. Quantifies the time it takes an observer located at (FRS) to see the image of Event has "born" in point (E).
2º. – The distances are valued at times. That is, the equivalent in time to travel to a certain distance. The expression t(FRS)f represents the distance from the coordinated origin (O), which means from the situation considered fixed where lies the (FRS), until you reach the end point (F) we have planted that has displaced (MRS). This is the time it would take the fixed reference frame (FRS), if in fact it moved, from the coordinated origin (O), and would reach the point (F).
(NOTE: By saying "if in fact it moved" we are referring to the relative motion (MRS) with respect to (FRS). Done with this warning, we recall that the system (FRS) – (MRS) can move together to a certain speed.)
3 °. – But if instead of moving the (FRS) we used a (MRS) and already parted to an advanced position towards an (O), for example if the (MRS) is located at the point of parting (P ) drawn in the figure, we shall be reducing the value t(FRS)f that we spoke about. That is, we are TRANSFORMING that value to its EQUIVALENT when using a (MRS) that parts to another situation that is not the (O). Agreeing with the figure, we see that the time
t(FRS)f we should subtract the corresponding time: x / c.
The calculation to perform will be:
t(MRS)f = t(FRS)f – (x / c)
STEP "B":
In the above formula we have to apply the Correction Factors corresponding to each physical unit, so that it can operate with homogeneous values.
The first corrective factor must be applied to the entire time it is assumed that runs through the axis (X) that we have drawn in the figure. We Note that all the expressions contained in the second member of the equality of the above formula, is a time to be normalized. Let"s recall that time we must normalize it by applying the Lorentz factor (L). Which we will obtain as a result:
t(MRS)f = (L) . ( t(FRS)f – (x / c) )
The second Factor Corrector will correspond to the relationship between the speeds:
FCV = v / c, which is obtained by:
t(MRS)f = (L) . ( t(FRS)f – (x / c). (v / c) )
Being expressed as:
t(MRS)f = (L) . ( t(FRS)f – (x. v) / c 2 )
which is the formula we wanted to obtain.
FORMULA 13.2.2.-SPACE TRANSFORMATION.
The steps we shall follow to obtain this formula are the same as those described in the previous paragraph, changing the variable "time" for the variable "space"
We shall analyze the meaning of the formula:
To better the continuing process that we use in obtaining this formula by writing spaces (longitudes X) we have indicated whether they refer to the Moving Reference System (MRS) or to the Fixed Reference System (FRS)
STEP "A"
We present a geometric approach relying on the following figure ..
The concept (O) has already been defined in the previous chapter.
As the same in the previous case we must observe three concepts:
1 °. – The longitude of the vertical line (T p) extending from the event (E) to intersect the axis (X) which joins the (FRS) and the (MRS) places us (E)
For the point (O) it crosses the axis (X) and the line (tp) Its interpretation is "time to the foot of the event." The longitude of this line indicates the time it takes to see or
detect the event image (E) in the point(O).
2º. – The distances come valued in space (Not in times like they did in the previous chapter). The expression x(FRS)f represents the distance from the coordinated origins (O), that is to say from the situation considered fixed where lies the (FRS) to the covered final point (F). It is the distance that the Fixed Reference System (FRS) should cover, if in fact it moved, from the coordinated origins (O), until reaching the end point (F). (Note: See the comment made ??in the previous chapter).
3 °. – But if instead of moving the (FRS) we used an (MRS) and already parted from an advanced position with respect to (O), for example if the (MRS) is located at the point (P) drawn in the figure, we will be reducing the value: x(FRS)f we have spoke about. That is, we are transforming that value to its EQUIVALENT when it uses an (MRS) that parts from another situation that is not the (O).
We will see that the distance if we would not have had to do any correction would be:
x(MRS)f = x(FRS)f – v . t(FRS)p
"B"
As we must normalize these displacements on the axis (X), we shall apply the Lorentz factor to both components of the second member of the previous equality
x(MRS)f = (L) . ( x(FRS)f – (L) . (v . t(FRS)p )
Being expressed as:
x(MRS)f = (L) . ( (x(FRS)f – (v. t(FRS)p ) )
which is the formula we wanted to obtain.
13.2.3. – OBSERVATIONS WITH RESPECT TO THE TWO TRANSFORMATION FORMULAS OBTAINED
The formulas of the Lorentz transformations we have seen generally written in the form in which we have given in chapter 8.2. That is:
Without giving explicit references, it is difficult to interpret that represent each of the variables involved and may cause a doubt to appear. For example, we can ask if the same variable represents the letter (t) that appears in the second member of both formulas. For this reason we decided not only
indicate whether the variables (t) or (x) were associated with (FRS) or (MRS), but also if at the same time were related with the point (P) or with point Final (F).
It is understood that we are dealing with two independent formulas. Not with a system of equations, then yes, it would be indispensable to consider that the variable (t) was the same in both equations.
Another doubt that, indeed, was also raised to us is why does in the second member of the formula appear the value of the variable (v) without being affected by the conversion to (uvl). We shall interpret this value (v) must come already transformed and valued in (uvl).
13.2.4. – REDUCED FORMULAS OF LORENTZ TRANSFORMATIONS
The research we have conducted over the interpretation of mathematical formulas of Lorentz transformations, has led us to consider a point (P) of the parting point of (MRS). We believe that this is a general case of a smaller one. This is the case in which the point (P) is located in the same origin (O) of coordinates. That is, at the initial moment, the (FRS) and the (MRS) coincide at the same point. So we can say: (P) = (O).
Observing the figures given in the formulas for the transformation of time and space, we must consider that now the longitude does not exist that which had been drawn between the points: (F) and (P). Its corresponding figures are:
Figure 1
Figure 2
In consequence the reduced formulas will be as follows:
t(MRS)f = (L) . ( (vx / c 2) )
x(MRS)f = (L) . ( v. t (FRS)f )
The Lorentz transformations and transmission of the type of information
The figures that we have discussed so far correspond to cases in which there was a single event (E). These figures are associated to the cases in which we inform that (E) has been produced. But, by themselves, would give a contribution somewhat limited. Take an example. If we assume that the test to be performed includes examining the oscillation of a pendulum, and we consider as an event (E) which has produced a "Tic" (this happens on reaching its path of oscillation at the top left), it"s possible that with this sufficient information we would have some issues raised. However, is it obvious it will have much more application if we inform ourselves about (Tic) and also (Tac) (when the pendulum reaches the other stop on the right side of the course). We can already guess that this is the second case that will serve us to determine the duration of a given experiment, in which we observe two events (E) of the same phenomenon, the (Tic) and (Tac). With this information we know the extent of the duration.
In short, if we quantify the duration of a determined phenomenon, we should obtain two reports for two "Synchronized Phenomenon Relationships". And, as you can assume, we will need to apply in each case the Lorentz transformations.
The following figure is intended to give information on the case of two events produced in the environment (FRS). Due to the relative speed (v) between the two (IRS) on the (MRS) receives the information in two different positions. In each position there will be a "Synchronized Relationship" between the events (E) and (IRS).
The information written in the figure correspond to the same geometric approach that we discussed for the case of a single event, more than without having extended this information to the case of two events.
The Lorentz transformations and relative movements between inertial reference systems (IRS)
In Chapter 2.1, we spoke about the relative movements between Inertial Reference Systems, but we did not discuss anything about the transmission of information of one (IRS) to another. That is, with respect to the existence and application of the formulas of the Lorentz transformations. We must now address this issue.
We know that in considering the "relative motions" we can switch roles between a Moving Reference System (MRS) with its counterpart Fixed Reference System (FRS). But, if we think of making this change, we have also to taken into account in the formulas of Lorentz transformations. It deals in transporting the variables corresponding to an equal member to another member of the same.
Which means, if they had t(MRS) => t(FRS), change it to: t(FRS) => t(MRS)
We can assume the existence of the reverse case commented in the previous chapter. This time we shall assume that the events (Tic) and (Tac) occur in the Moving Reference System (MRS), while the observation or recording of these events take place in the (FRS).
The figure that represents this case will be:
The fallacy of the example of the "Twin brothers"
The present theme aims to banish the misconception that appears in the books, that: "the rate of passage of time depends on the movement of the clock." That is, a second measured by a stationary clock, fixed in an (FRS), corresponds to less than a second as measured by another clock in relative moment with respect to the first. And, in this way, it has an utopian dream that the astronaut brother who has travelled with the rocket, he has spent less time than the other twin who remained on Earth.
Instead of saying that the time "passing" differently between two clocks with relative movements between them, we must say that the time reference system as "we see it registered" with a difference of figures with respect to a clock located on another reference system that moves.
We shall use the figure of the previous chapter, which contemplates the case of "two events produced in the (MRS) to interpret what we are saying now. The comment that we will now do could appear in part a repetition of what we discussed when talking about "the Lorentz transformations and the transmission of the types of information." But we preferred to "refresh" to be able to add new comments.
In the (MRS) suppose there is a pendulum that will serve us as a clock. In one occurs a (Tic) (for example, on the left side of the pendulum) and its signal via electromagnetic waves (not the very phenomenon that produces) it transmits in the vaccum at the speed of light (c) until point of perception (PTIC) of an observer located at (FRS).
The (Tac) of the pendulum (made now on the right side of the pendulum) produced inside (MRS), travelling at a velocity (v) and when this (MRS) has been displaced to a certain distance. Like the (tick) the signal is transmitted at the speed of light (c) to the point of perception (ptac) of an observer located at (FRS).
We recall the First Postulate that says that (IRS) are completely equivalent in regard to the measurement of the laws of physics. And, on the other hand by intervening of electromagnetic waves, we shall use the Lorentz transformations (and not those of Galileo) to transfer or transform (FRS) values ??of the variable (e) and (t) being recorded in the (MRS). In this case the events are the arrival of the pendulum to each of the covered limits (Tic-Tac). The physical phenomenon deals with the displacement of the pendulum according to a certain oscillation law, and its arrival or percussion at each of its limits or boundaries of oscillation.
In accordance with the explanation, the amplitude of oscillation (tic-tac) detected in the (FRS) differs from the amplitude that it produces in the (MRS). But this does not occur as a result of a "degeneration" of the phenomenon itself, but as consequence of the "transmission" of information, an information transmitted in two stages of displacement of (MRS).
(Note: We believe it is important to take into consideration this idea. For the "First principle of relativity" the law of the pendulum is governed by the same variables and determining in the two (IRS). Therefore, that which obtain different recordings of the variables (e) and (t) between (MRS) and (FRS), is only due to the different SITUATION of the two (IRS).
If we assume that within the (MRS), a recording accumulates the time it takes the amplitude covering of each oscillation and in the (FRS) are being recorded and the aforementioned times accumulated, it is clear that when one wants to make reading of the same, its figures do not match. The figures which have been left registered in the (FRS) will outweigh. But this DOES NOT MEAN THAT THE TIME HAS STRETCHED for the astronaut brother, as they seem to want us to believe¡ So discard the fallacy of "time dilation" and the story that the astronaut brother on reaching the earth will see his brother with a long beard…
The fallacy of the difference of time in the clocks with relative movements among them
We spoke about the fallacy of "time dilation", that is, as if time "stretches" now we shall refute another argument which exposes to give credibility to this fallacy: the timing differences that some clocks mark with relative movement among them. Speaking in metaphor we can say that in the previous chapter we considered the fallacy that "life is extended." Now we shall consider the fallacy that "clocks get delayed" with respect to each other.
We've seen written the phrase, "a moving clock IS DELAYED." We think that we should say "in a moving clock an observer WILL SEE that it delays." The delay is not an intrinsic property of the clock. (The same could be said of twin brother who stays on the ground. The one that SEES that the "TIC-TAC" of his brother astronaut detects with more amplitude of time, or that occurs more slowly, this does not indicate that what is happening to his brother).
At the DISPLAY TIME, we could also call it TIME INFORMATION, that which already deals of the duration of time in which the OBSERVER is informed of the duration of the event.
It"s logically to think that you must first create a certain phenomenon or event, before we can see it. We can also say that before it has to "occur in its entirety" so that we can "detect it". This "detection" can be performed by an observer located at the very foot of the experiment or hundreds of miles away.
By saying "occur in its entirety" we mean that the creation time will end from the starting to the end of the event. Only then can we separate the "time of the event itself" the time it takes to see it. Let"s take for example the explosion of a given artifact. We shall assume that the explosion takes place in a certain Reference System. The time ranges from "start" to "end" will possibly seem to us as instantaneous though, if we could refine more, maybe we could do a breakdown between the two phases. What we mean is that we are using the time of the event itself, or time "contained" at the event. This is what we shall call "creation time" or OWN TIME.
Another aspect will answer to the question: when will the event SEE an observer situated on the same or another Reference System? It"s evident that we must respond that it depends on the distance to where the event is. This INFORMATION transmits light speed and, again, the observer may be present at the experiment or thousands of miles away. With this example we intend to emphasize the difference between the length of time of the event, or OWN TIME, and duration of arrival of information to a possible observer located at a certain distance.
We can use an example similar to the "twin brothers" but with the variant we shall assume that the pendulum is located in (FRS) while observing of times perform from the (MRS) (see figure in Chapter 14).
As we have already said, we shall establish that there an agreement that it produces a "TIC" when the pendulum reaches, for example, in the upper left. In consequence, we shall say it produces a "TAC" when the pendulum reaches the top right.
The event of producing a "TIC" will have been caused by laws and causes that we will not get into any detail. What we stress is that "it has created the" TIC ". Let"s suppose that when it creates the "TIC" it produces a flash of light. An observer situated more or less far away from the point where the event occurs takes more or less time to SEE (perceive) the event.
In the same way we reasoned that in the upper right, the pendulum will have reached and will have "created a TAC". We repeat what we said. An observer situated more or less far away from the point where the event occurs takes more or less time to SEE (perceive) the event.
What we want to emphasize now is that the time covered between the "TIC-TAC" of a pendulum will be perceived and, consequently, with record with different amplitude by an observer situated "far" from the point where events occur.
If we consider the "TIC-TAC" of the pendulum as a single phenomenon, that is to consider its global time or amplitude of such type of time, we can use it to measure the duration of some event. It may be for example the length of stay of an astronaut in the rocket or, by analogy to the pendulum, the frequency of the beating of a heart. These times are inherent to the event. For a system using electromagnetic waves, we can reveal that, or VISUALIZE, by an observer who will record the event. And this amplitude of DISPLAY TIME recorded by the observer, it is clear that it will not be the same as it has or requires the event itself. That is, the OWN TIME of the event.
Wrong or erroneous arguments that try to validate the fallacy of "time dilation"
We believe that after having unravelled the "mysterious" role of Lorenz factor, of having made ??clear the existing confusion between the concepts of the event itself and the time covered of the same image, and of having interpreted the corresponding chapters to the fallacy of example of two twin brothers and the fallacy of the difference in time in the clocks with relative movements, there should not be left any doubt in classifying as a fallacy in the idea of "time dilation". We thought we have possibly set the right path to reach accurate conclusions.
As there are certain arguments that seek to validate to what, for us, is a fallacy, we think it appropriate to say something about these arguments. The two arguments are:
1 º. – The misconception to consider that in the system (GPS) of the artificial satellites, the application of special relativity intervenes, and in consequence, acquire to validate such theory.
2º. – Proof of muons
Then we discuss these arguments.
18.1. – THE MISCONCEPTION OF CONSIDERING THE APPLICATION OF SPECIAL RELATIVITY IN THE SYSTEM (GPS) OF ARTIFICIAL SATELLITES
Some reader after having read our first digital writing entitled "Monografias.com => Theory of Relativity => Philosophy => Theory of Relativity. Fallacies and utopies "intended to continue supporting the validity of the theory of SPECIAL RELATIVITY, or restricted, based on its application in the system (GPS) satellites, so we briefly dedicate to comment on this WRONG argument.
The name we used for the "length of time in the path of the image" that is "INFORMATION TIME" we shall use it to talk about the system (GPS) and clarify the doubt expressed by these readers. These readers presented to justify the validity of the theory of relativity, its necessary application in satellites of the system (GPS). In this system, they observe differences of time recorded by atomic clocks, between satellites and receiving stations, if such a Theory does not apply. This is only half true.
It"s possible that we may agree as to when the application of GENERAL RELATIVITY, which uses as one of its variables the concept of "gravity". It uses to correct the errors of assessment that would occur between the satellites and receiving stations if this theory is not applied. On what we have NOT agree on is to admit that it is also uses the theory of restricted relativity, since this title has been associated, by mistake, a misinterpretation of the mental experiment mentioned.
The information exchanged between satellites and receiving stations are transmitted via electromagnetic waves. Broadly speaking we can say that these waves by means of a previously established coding transmit the necessary information to make the necessary corrections of time, synchronize the clocks of the different satellites and receiving stations, and thus to determine localizations. Without going into technical details, what we want to emphasize is that it is transmitting INFORMATION between different moving systems with relative velocities between them using the support of electromagnetic waves. It is obvious that we are dealing with a case of information transfer that occurs in a gap of time and we will apply the Lorentz transformations.
In the synchronization of clocks we must apply what we have called: the formula of "TIME CALCULATION INFORMATION", which is what quantifies the "time spent in the path of an image" in terms of the relative velocity (v) between two Reference Systems. We recall that this concept is exempt from consideration in regards to the "time dilation" and "shortening of one body." For what we must NOT justify such utopies based in the utilization of satellite system (GPS). (Remember what we discussed in Chapter nº 17 "The fallacy of the difference in time in clocks with relative movements")
18.2. – THE FALSE TESTING OF THE MUONS
We recall that we mentioned that a muon is a subatomic particle that disintegrates into other subatomic particles shortly after being produced. The muons can be produced in nuclear physics experiments in the laboratory, and it was found that a muon at rest in the laboratory disintegrates in an average time of 2.2 x 10-1 s. after being produced. In addition to its production in the laboratory, the muons are generated in the top layer of the Earth's atmosphere. Energetic bombings from outer space, called cosmic rays, are constantly falling on the Earth and collide with the upper layers of Earth's atmosphere. These collisions produce muons that displace towards the Earth disintegrating a part of them during their journey.
We have read another written test is given as the "time dilation" we also believe that it is a fallacy. We transcribe some of its contents: "In 1976, at the laboratory of the European Organization for Nuclear Research (CERN) in Geneva, Switzerland, muons injected into a large storage ring reached speeds of about 0.9994 c. The electrons produced by muons in decay were detected by counting meters around the ring, enabling scientists to measure the decay rate and therefore the lifetime of the muon. The lifetime of moving muon was measured and obtained a value about 30 times larger than a stationary muon, in agreement with the prediction of relativity "
We transcribe the argument exposed in some book of Physics, used to justify the idea of "time dilation" on the basis of proof of muons: "As we know the time it takes a muon to break into in the laboratory and on the other part, due to the height at which it finds the top layer of the atmosphere (10 Kms), place where the collisions occur and muons born, should not reach any of the mouns to the level of the surface of the Earth. " However, and wanting to justify the concept of "time dilation", it adds that, as some muons are detected at ground level, this confirms the "time dilation", as if time had not been "expanded" it might have been extinguished before reaching land.
With respect to this conclusion, we shall be adding two opinions to rebute such evidence. It is understood to be our own opinions against those who still continue to be admitting the "time dilation"
1º. – In the referred evidence, it worked and verified infinitely small quantities and obtained results with infinitely small differences. But … an infinitely small difference does not mean running the risk of committing an infinitely large error. (Note: the lifetime of a muon, estimated in a laboratory are: 2.2 x 10 -6 sec.). We think that the desire to justify a predetermined criterion did see what was not possible or realizable.
2º – We believe that the sample obtained in the tests performed in the laboratory
(Figure 1), or from the top of the atmosphere (Figure 2), we cannot consider them as two compatible experiments.
In the laboratory setting and muon detection is performed within a Fixed Reference System (FRS). In Figure 1 the event (E), that is, the birth of the muon, and the perception of the event by an observer, occurs within the same Reference System. That is, on the same floor of the Earth. Consequently, there's no need to apply any correction. Do not apply the Lorentz transformations for a speed (v) to operate with units of the speed of light (c).
In this case, as there are no relative movements, the time covered since "the birth" of the muon until the observer located in the same Reference System, detected, equals to the speed of light (c) divided by the space existing within the laboratory, from where it produces the phenomenon to where the observer is located. (The tour kilometers of the path of the ring)
Figure 1
The same does not happen when you want to evaluate the time it takes the observer on Earth to record the time that has been covered ever since the muon is generated on the upper layer of the atmosphere. In this case we shall assume as Fixed Reference System (FRS) just in the environment where the muon has occurred.
We see that we are considering two Inertial Reference Systems (IRS).
The (FRS), around the place where the event occurred (E) and (MRS) which is the Earth that is moving with respect to the place where the event occurred at a
v = 30 km / sec.
The following figure shows the two (IRS). Does it occur to the reader if in this case, we should think of some correction by wanting to obtain the time that it took to be able to observe the appearance of the aforementioned event (E)? .. Given that the Earth is moving with a velocity (v) , we should be transforming this speed to express it in units of speed of light (c). It deals in using the formula of the Lorentz transformations. (The reduced form as the (MRS) parted from (O)).
Figure 2
Figure 2 depicts this case. Earth is moving at speed
RELATED: v = 30 km / sec. towards another point in space, or environment, in which "was born" the muon. (At a height h = 5.103 m.) This will represent a very small increase in the time of observation with respect to the mentioned test performed in the laboratory. We say "small" because, we remember, when applying the Lorentz factor, we must divide: v = 30 km / sec. for c = 300,000 km / sec. To this we referred at the first point in saying that very small differences were obtained. What amazes us is that in those books say: "Although the difference found is very small, this shows that the time has dilated"
The next chapter in speaking of the "dilation of the image" can also serve as support in the issue at hand.
We think the testing of muons CAN SERVE PRECISELY TO SHOW THAT TIME DILATION IS A FALLACY
The transformation of image path. Image dilation
So far we have been treating electromagnetic waves as a means of transmitting information and we used the speed (c) by which it transmitted an image.
In this paragraph we shall look at the image path. The figure below will help us interpret what we shall discuss. The drawing shows several points of observation of the image of the event depending on the path which has performed by the observer (MRS) from the foot of the event (E). In the drawing we suppose that the observer is located at the point(P4)
The space covered by the image will become larger in function of the distance (v. t d) It will deal to determine the COVERED TIME OF THE IMAGE (tr) from the point where the event occurs (E) to one of the points (P1), (P2) … located on the axis (X).
The application of the factor (L) can be used to measure as they lengthen the covered time (tr) of the IMAGE of an event (NOT the event) to displace itself and separate the spotlight event of the perpendicular line of the same, the axis (X)
To calculate the covered time of the event image (tr) and the implication that the factor has (L), we shall proceed in the same way we had done to deduct (td)
. Only now when considering that the values ??(td) and (t r) must be equal, instead of choosing the variable (td) to continue the calculations, we shall choose the variable (tr)
In this way we obtain:
With what we see that the factor (L) allows us to TRANSFORM the Image Time (tp) of the event (E) to (O) in the Covered Time of its image up to be perceived by the (MRS) .
OBSERVATION: It is important to take into consideration that here only the implicated geometric calculations intervened in the structure that must be assigned to the factor (L) and which we are talking about a TRANSFORMATION of (tp) in (tr) and NOT of an EQUALITY. What rules out the idea of "time dilation". Maybe for this reason we should call it "the third equation" transformation. We leave this domination to the reader"s judgement.
We can also see that here the "correction factors" don"t intervene, since we establish the relationship between these two times is developed using the same yardstick, that is the (c).
Relativity concurrency. Case about the appearance of two simultaneous events. Doubtful approach
First we shall give the example of "simultaneous events" as stated in that book A.Einstein, with what we shall give the idea and vision of what has been explained in the book. In continuation, we shall show where is the "error" that generates the admission of the error mentioned.
The book presents again an example of a "train wagon" in which is mounted an observer and states that:
Events that are simultaneous with respect to a stationary wagon are NOT about a moving wagon (read as: Moving Reference System (MRS)
Each body of reference (coordinate system) has its special time.
The following figures are intended to clarify what we are discussing. In the first figure shows a stationary wagon. At the same moment it produces two beam lights simultaneously from (A) and (B). .
(BEWARE, it was understood that the positions (A) and (B) are a way to place the parting positions of these beamlights. That is to mark the parting coordinates. Do not confuse with the idea that the rays part from within the wagon just attached to its walls. The position of parting of the beamlights is fixed rays from outside the wagon).
Because the wagon is stationed, the observer located at the midpoint of the wagon perceives at the same time, simultaneously, the two beamlights.
The aforementioned book continues: "the same does not happen when the wagon is in motion (Moving Reference System)".
The figure below shows the previous wagon but now in motion. It represents three forward positions at a speed (v), and so that they can be better visualized, drew each of them distinctly under one another.
The two beamlights that trigger at the same time, just when the wagon occupies the first place in the drawing, are not perceived simultaneously by the observer located at the center of the wagon. Due to the movement toward the right, velocity (v), the observer will not perceive the existence of the two beams simultaneously. The beam starting from (A)
takes longer to get to reach the point of the observer's focus, as it is moving along with the wagon in the sense of getting away from the starting point (A) of shooting. Regarding the beam that started from the situation (B) the opposite occurs to the one proceeding from (A). The observer will have moved closer to the situation (B) shortening the duration of the arrival of that beam. This is what is intended to expose the second and third place in the drawing above.
In seeking to establish a "relationship" between what happens between a Fixed Reference System (FRS) and a Moving Reference System (MRS) are committed errors of interpretation. Especially if it leads us to admit the "shortening of longitudes" and "time dilation". We shall not get into discussing the "artificial" form which it seeks to justify the above concepts, since our purpose is totally different.
In continuation, we present our theory that aims to expose the previous fallacy.
We must repeat this warning again: DO NOT CONFUSE THE IMAGE OR RESULT OF AN EVENT WITH THE EVENT ITSELF.
In dealing with the two rays of light, perhaps the reader might not identify the two concepts: "event" and "image" of the event itself. The "event" is the production or appearance of rays of light at point "A" and point "B". The rays of light may have been generated for different reasons. For example, a beam generated by certain atmospheric conditions, in activating a depositive light generator … Here its story ends. What follows is the image of the event. It is the information which is being transmitted through the advancement of electromagnetic waves and may or may not get to reach a given point of observation.
In short, a traveller located in a Moving Reference System (MRS) two events
which were born at the same moment be considered as such, as instantaneous. We think it is logical to consider as well. Another consideration is that he SEES or DETECTS with outdated times. That is, his VISION is not simultaneous. The Lorentz transformations allow us to calculate these offsets.
It must remain clear that: IT DOES NOT EXTEND THE TIME OF THE EVENT.
Relativity between observations performed from different frames of reference. Equivalent reference systems. Identity condition
In physics books is discussed the issue in two Inertial Reference Systems (IRS) in which one moves towards another, without which we can say which is the one moving towards the other, we shall obtain the same results with respect of the measuring of times of a given experiment. This affirmation is correct, although we have observed that its approach is somewhat convoluted and open to possible confusion. This is the reason why we present this issue.
We define Inertial Reference Frame (IRF) to the sets of two Inertial Reference Systems (IRS) in which, either one can be considered as Fixed Reference System (FRS) and the other as Moving Reference System (MRS).
We wonder what conditions must exist in the observation of an event (eg the tic-tac of a pendulum identical in both frames) considering from two different (IRF) to identify that it deals with the same event. We shall say that it deals with doing a test of event IDENTITY. Or also, that an (IRF) is a REPLICA of the other. We can also ask ourselves, in the example of the train wagon, will our affirmation continue to remain valid saying that the only thing better is the data obtained by the operator (O1) ? Let"s recall that the observer (O2), the only thing that tells us is the time it takes for the observation of the event taking into account the "Extention of the Path of Observation" In short we have to study the variables involved and how they intervene in order to testify we are observing the same event.
For the aforementioned study we will help with the example of the following drawing, in which appears a third observer, whom we can call the "Third Eye". The drawing shows two different (MRI) seen by the same observer: the "Third Eye" …
We shall consider that in the first (IRF) it is the wagon that moves towards the second (upper picture). In the second (IRF) is the wagon which is fixed ..
First (IRF) (top of the drawing)
Equivalent to test of the train wagon we talked about, the operator (O1), moving from being inside the wagon is the one which performs the test. It"s the one which will record the actual time which occurs "in the EXPERIMENT"
The Observer (O2) is fixed on the ground. The train moves with velocity (vt) towards the fixed observer (O2). It will be affected by the "Path of the Observation" if it intends to know how long it takes to learn.
Second (IRF) (bottom of picture)
Is a reverse vision of the above. It deals with second (IRF). The operator (O1) that performs the test is still. That is, in this case is fixed, is above the wagon and the wagon does not move. The person (O2) observing the test is moving at a velocity (vp), or is movable. It moves from right to left passing in front the wagon. (To make a graphical representation of this displacement, the person (O2) has been represented with wheels on the feet).
VARIABLES TO CONSIDER. – IDENTITY CONDITION
To determine whether the two Reference Systems are EQUIVALENT we must consider the variables that are attributable to the phenomenon itself (physical, chemical, biological) that are observed, and the variables that refer to both (IRF).
The variable that we shall be attributing on the very phenomenon will be the one which we shall present in the Systems through (d). That is, using the metaphor, it deals with the height of the wagon. This variable indicates the duration of the event. ( We recall the example of the ticking (pendulum). Two events that are the same type, having the same nature, are not equal, much less is the same, if they have different variable value (d). This requires that the Second System have the same value (d) than the First. Since this is the VALUE ITSELF of the event.
As for the variables inherent in the two Reference Systems involved, will be the speed in which they move. If we say that it is to be the same thing, that the First System to move relative to the second, conversely, the Second System moves towards the first, we will impose the condition of IDENTITY, and we shall express it as follows:
IDENTITY CONDITION
Call:
PS = First System. SS = Second System
VPS = Speed of the first system. VSS = Speed of the second ??System
We require that it complies:
VPS with regards to SS = VSS with regards to PS
In continuation, we shall discuss with an example which could lead to a confusion if observing the above drawing we would be approaching for the condition of Equivalence, the equality: vt = vp and not the equal condition we discussed.
We note that the Identity Condition does not require neither of the two Systems be still (perhaps the drawing above would lead one to commit such an error). It deals with inertial systems in which each maintains its own speed. The "Third Eye" as it shall see them.
In the previous mentioned example of the astronaut, it is mentioned in the books that, according to the calculations, for the astronaut, the time will have passed much slower than for the person on the ground. While for the person on the ground will be seen in reverse. The astronaut consumes more time. Having done with this affirmation, the example concludes with the disconcerted affirmation that both times will have been equal. It is clear, this had to have been like this, and without many twisted calculations!
Where is the weak point of such reasoning and its incoherent conclusion? We justify this contradiction with the following argument:
It deals just with what we have discussed in previous chapters, but we will not get tired of repeating. It confuses the speed of the process (in this case the tic tac of a physical clock and, associating it with him, a passing of the biological clock corresponding to the astronaut) with the speed of observation corresponding to the PATH OF OBSERVATION.
The length of time recorded by the aforementioned tic-tac, comes in function of the variable (d) shown in the drawing and has the same value in both systems (ITS OWN VALUE). Furthermore, we are dealing with two equivalent references since one is a replica of the other. Although the astronaut goes at a speed (vt) and the person on the ground travels at the speed (vp) displacement of land (approximately 106,000 km / h) the IDENTITY condition does not impose equality between these variables but that it agrees with the regulations we have set.
SIMULTANEITY OF TWO EVENTS
We have read in the physical treatises relativistic that the events that are simultaneous for an observer are not simultaneous for another observer who is found in relative motion with respect to the first. We believe this is not well explained. We should say: the events that are simultaneous in a certain frame of reference are also in another frame of reference but with a certain delay of vision due to the "Extending of the Path of Observation". (Note: Remember the definition of Inertial Reference Frame (IRF) given in the previous chapter). We shall observe in the following figures in applying our logical relative movements within an "absolute space":
We assume that it deals with the two EQUIVALENT reference systems.
First (IRF) (first figure)
We shall consider the observer (O2) fixed.
You could check that: l 1 + l 2 = l 3 + l 4. Seeing that the two events born together, end together.
(NOTE: For check this, we could use mathematics. But we do not think that it is necessary since a simple vision and with the scale drawing, we can see the symmetry between the aforementioned sums of values).
Second (IRF) (Figure II)
We consider the observer (O2) mobile.
You could also check that: l 1 + l 2 = l 3 + l 4. By seeing that the two events born together, end together.
(NOTE: The same as in the first system for its testing, we could use mathematics. But we do not think that it is necessary since a simple vision eye and with the scale drawing, we can see the symmetry between the said sums of values).
If we are situated in absolute space, at a point which we shall call the "Third Eye", we would only notice for any of the two (IRF), the delay of vision due to the "Expanding of the Image Path."
Autor:
Enrique Martinez Viladesau
Depósito Legal: B-3045-12
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