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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