PRESENTATION
To help
interpret and understand the metaphorical meaning given to the title of this
essay, we transcribe the following definition and explanation: "PARADOX:
Fact or saying contrary to logic." “TRANSMUTATION: It implies the
change of the atomic nuclei. Change one element into another. We believe that
in the course of this study we will be able to clarify the metaphorical meaning
of the aforementioned title. In order to criticize the aforementioned theory, we have highlighted a
paradox that we have called the paradox of transmutation.
1. ARGUMENT THAT FOLLOWS THIS ESSAY.
In order to justify that the postulates cited by A.
Einstein and that with them he builds his theory are a paradox, we will take as
a guideline for follow-up his book entitled: "On the theory of special and
general relativity" (Ediciones Altaya S.A. February 1999) The affirmations
and postulates that appear in the book are transcribed between quotation marks
and italics.
Interpreting the meaning and the order in which its
paragraphs are written, we have realized that it leads us to the aforementioned
paradox. This being so, this is the path that we will follow in the study of
this essay. We believe that our essay is an investigation about what he thought
and came up to Einstein when he made his Theory. We will expose these ideas in
the same order in which the paragraphs of it are written. And, on these, we
will make the pertinent comments that, as we will see, lead us to the
acceptance of the title of this essay.
Next, we write the titles that appear in our essay and,
in abbreviated form, we summarize the ideas that we get from the paragraphs of
the aforementioned reference book:
PRINCIPLE OF
RELATIVITY. It establishes an identity of results between a Fixed Reference
System (SRF) and a Mobile Reference System (SRM). The idea is that the events
PASS in the same way
THEOREM OF THE ADDITION OF VELOCITIES. It proposes two
ways of assessing the same event viewed from two different Reference Systems.
THEY SEE WITH DIFFERENT VALUES
INCLUSION OF THE SPEED OF LIGHT. It includes the light in
the postulates of it. We identify it with the verb SEE. Expresses the intention
of being able to SEE from a Reference System what happens in another
LOOKING FOR A COMPROMISE SOLUTION. It fits the constant
speed of light with the Velocity Addition Theorem. You need time and space to
be "elastic." Use the “trick” of the space-time idea
THE RELATIVITY OF
SIMULTANEITY. The genesis of the paradox. An ill-conceived thought experiment.
A THESIS.- Explanation of the path of how we have arrived
at the concept: Paradox of a Transmutation
Next, we
develop the previous concepts.
2.- THE PRINCIPLE OF RELATIVITY
As we have said in the “Argument that follows our study”:
It establishes an identity of results between a Fixed
Reference System (FRS) and a Mobile Reference System (MRS). The idea is that
the events PASS in the same way
In the book by A. Einstein that we take as a study
reference, he gives as an example the mental experiment of the train car, which
we have already talked about in other of our essays. Starting the reading of
this book the first postulate that we find is the following:
“If a (MRS) moves with respect to a (FRS)
then the natural phenomena occur with respect to the (MRS) according to the
same general laws as with respect to the (FRS).”
(NOTE: A Fixed Reference System is abbreviated as (FRS)
and a Mobile Reference System is abbreviated as (MRS))
We accept that it is true that "natural phenomena
PASS according to identical laws", but, as we read the following
paragraphs, it seems to us that the Physicist's intention is not only to
indicate that "they pass" but that he has the intention of wanting say
that they can be SEEN and MEASURED. Corroborates our affirmation, the one that
in the following paragraphs dedicates them to the speed of light (c) and to how
the speed of a body launched from inside a moving mobile is SEEN and calculated
from the ground. We talk about this topic in our next paragraph.
2.- THEOREM OF THE
ADDITION OF VELOCITIES
As we have said in the “Argument that follows our study”:
It proposes two ways of assessing the same event viewed
from two different Reference Systems. THEY SEE WITH DIFFERENT VALUES
In paragraph 6 of the aforementioned book it appears as a
title; “The velocity addition theorem according to classical mechanics”. We
will consider this paragraph as the beginning of the RERELATION between the
(SRF) and (SRM), in order to expose the fallacies of the special theory of
relativity.
HE Give as
an example:
A train runs
at a speed (vt). Inside it a person walks at a speed
(vp). The total speed (vT) with which an observer outside the train will
appreciate that the person inside the car moves will be:
(vT) =
(vt) + (vp)
That is, the two speeds are added. This (VT) is the speed
that the man moves with respect to the track.
We think that by saying that "I WILL
APPRECIATE", this verb includes the intention to SEE and then CALCULATE.
(NOTE: We highlight the verb SEE since at the end of this
essay we will use this verb to demonstrate a contradiction between the
postulates preached by A. Einstein)
The same statement of the Velocity Addition Theorem can
also be explained as follows:
inside the wagon a
person throws a stone, and it is a question of calculating at what speed the VE
circulates an observer who is outside the train wagon.
This version, which we give now, may help us more in the
following explanations that we will present.
We insist that the inclusion of this Theorem in his book
is the first step in wanting to relate the (SRM) with the / SRF)
3.- INCLUSION OF THE SPEED (c) OF LIGHT
As we have said in the “Argument that follows our study”:
It includes the light in the postulates of it. We
identify it with the verb SEE. Expresses the idea or intention of being able to
SEE from a Reference System what happens in another
If the first step was wanting to RELATE the (SRM) with
the (SRF), we detected a second step by trying to include light in its
postulates. It is intended to include the speed of light (c).
In the aforementioned book, he comments on the
impossibility of including the speed of light (c) within the variables that
make up the Velocity Addition Theorem. At that time, it had already been
verified that this speed is constant. Unlike the stone that is thrown from
inside the wagon, the speed of light does not depend on where the
electromagnetic wave is “mounted”.
But he makes a comment that he intends to relate: the
VIEW of an (FRS) of what happens in an (MRS), as he has described in the
Velocity Addition Theorem:
“… Later we will
see that this reasoning, which expresses the theorem of the addition of
velocities according to classical mechanics, is untenable and that the law that
we have just written is not valid in reality. But in the meantime we will build
on its validity.”
This is where we say that an intention to SEE manifests.
We repeat what we have already said: "it seems to us that the intention of
the Physicist is not only to indicate that they "elapse" but that it
has the intention of wanting to say that they can be SEEN and MEASURED".
SEE, when wanting to make light intervene and MEASURE
when starting from the Speed Addition Theorem.
(Note: Perhaps in the present times it seems obvious to
us that we cannot make variables that represent a mass and those that represent
an electromagnetic wave intervene in the same equation. Another thing that we
can do is use the mathematical operator that can relate us the speed (v) of a
mobile with the speed (c) of light in the same equation. This operator is
known: Lorentz factor)
4.- LOOKING FOR A COMPROMISE SOLUTION
As we have said in the “Argument that follows our study”:
It fits the constant speed of light with the Velocity
Addition Theorem. You need time and space to be “elastic”
If as announced in the First Law of Relativity:
“…natural
phenomena occur with respect to the (MRS) according to the same general laws as
with respect to the (FRS).”
and, according to what we have commented in the previous
number, when SEEING THEM and MEASURE THEM, according to this postulate we must
obtain the same results, the Physicist has a problem. To relate to each other
and be able to SEE from an (FRS) exactly the same events that occur in an (MRS),
if the speed of light is constant (it is not a function of the speed of the (MRS)),
to adjust this vision gap requires that time and space are not fixed but
"elastic" so that both the passenger and the observer SEE and VALUE
the natural phenomenon in the same way. And, it seems, that then the following
idea arises: The time of VISION, becomes relative like space and makes
"the invention" of space-time. This is how you adjust what doesn't
fit. Observe the reader that we have pointed out the verb “TO SEE”. We are in
the first step in which, by making the speed of light (c) intervene, everything
revolves around using the verb VISUALIZE.
(NOTE: In order not to mix concepts, we warn the reader
of the following. Another different aspect is that, as we are dealing with
relative movements and we are talking about the occurrence of Events, to
position them we must give their SITUATION (in space) and their moment(time) it happe. in which it is
happening), that is, the instant in which this SITUATION occurs.)
5.- THE RELATIVITY OF SIMULTANEITY
The title of this issue corresponds to paragraph 9 of the
aforementioned book. This is where the nonsense begins that we have called
"the paradox of transmutation
On page 27 of the aforementioned book, he asks the
following question:
“…Two events
(for example, the two lightning strikes A and B) that are simultaneous with
respect to the embankment, are they also simultaneous with respect to the
train?... We will soon show that the answer must be negative...
We transcribe the drawing that appears in the aforementioned book to answer this question.
Figure 1
The explanation that Einstein writes in his book is transcribed at the end of this paragraph. We, sticking to exactly what the book says, to make it more intelligible to the reader, we explain it graphically using the following drawing.
This figure represents the railcar in motion (SRM). An
observer sits in the center of the car. Three forward positions are
successively represented, at a speed (v). Two rays are fired at the same time
from (A) and (B), just touching the opposite walls of the wagon and when it
occupies the first position in the drawing. These rays, which are represented
by short arrows, are not perceived simultaneously by the observer located in
the center of the wagon. Why, due to the movement of the car to the right, at
speed (v), the observer will not perceive the existence of the two rays at the
same time. The beam coming from (A) will take longer to reach the observer's
crosshairs, since the observer is moving along with the wagon in the direction
of moving away from the starting point (A). Regarding the ray that has started
from situation (B), the opposite occurs than the one that comes from (A). The observer
will have been approaching the situation (B) shortening the duration of the
arrival of the aforementioned ray. Observing the aforementioned arrows, this is
what the second and third position of the previous drawing intend to expose.
In the lower part of the drawing an observer has been
represented who is on the ground and who remains immobile in the same starting
situation as the observer who, on top of the wagon, occupied the central part
of it. Rays (A) and (B) reach this stationary observer (FRS) simultaneously.
From here A. Einstein deduces that the SIMULTANEITY of
two events must be valued differently from a (MRS) to a (FRS).
And his response appears on page 28 saying:
“…Events that
are simultaneous with respect to the embankment are not so with respect to the
train, and vice versa (relativity of simultaneity). Each reference body
(coordinate system) has its special time. A temporary location only makes sense
when the body of reference to which it refers is indicated…”
and then in the same paragraph he writes:
“The time that a
process needs with respect to the wagon cannot be equal to the duration of the
same process judged from the reference body of the embankment”
It is in this statement that we state the Paradox of
Transmutation.
We believe that Einstein's reasoning is not correct.
We are looking at events that have a Proper Time (tp)
inherent to them. Let us remember that we already said this in the thought
experiment in which the event was “the reflection of a ray of light in a
mirror”. Now the event is "a simultaneous occurrence" We think that
this "simultaneous occurrence" is the event and we must design it in
a different way from how the aforementioned Physicist poses it. The following
drawing is intended to illustrate our reasoning.
Figure 3
In the figure we want to express that now the roles have
been changed regarding the evaluation of Proper Time (tp) that we made in the
phenomenon of the reflection of the light ray. Now the observer who quantifies
the Proper Time (tp) of the simultaneous perception is the one outside the car.
He fixed on the ground. That is, the (FRS). The event: "a simultaneous
occurrence" has its (tp) that reaches the (FRS) from both sides.
It is evident that its value would be the same on both
sides and would depend on its distance (FRS) from the train car'.
A COMPARISON WITH THE THOUGHT EXPERIMENT OF THE
REFLECTION OF THE RAY OF LIGHT IN THE MIRROR
We can establish
a comparison of the current case with that of the mental experiment of the
event "reflection of the light ray in the mirror" that we commented
on in some of our previous essays. Figure 4 4 serves to illustrate this case.
Figure 4
The person that A. Einstein places inside the wagon, in
the light ray reflection experiment, was the operator who carried out the
experiment and measured his Proper Time (tp). The person who was on the
embankment (FRS) is the one who perceives the effects of the movement of the
wagon.
On the contrary, in the example in which the object of
observation is "a simultaneous event" the person who observes the
(tp) becomes the person outside the car (FRS). while it is the person inside
the wagon (MRS) who observes the changes that occur due to the displacement of
the wagon. Nothing to invent different perceptions of a simultaneous
occurrence! There is a Proper Time (tp) of the simultaneous event, and only
one, no matter how much the author of the book wants to fit the events so that
they adapt to his Theory. This is what leads to nonsense.
Let us remember that he had already used the space-time
trick to avoid "compromise situations".
As we announced at the beginning of this paragraph, we
transcribe the explanation that A. Einstein makes regarding the relativity of
simultaneity:
“When we say that
the rays A and B are simultaneous to the tracks, we mean: the rays of light
that leave places A and B meet at the midpoint M of the section of track A-B.
Now events A and B also correspond to places A and B on the train. Let M´ be
the midpoint of the segment A-B of the moving train. It is true that this point
M' coincides with point M at the instant of the lightning strike, but, as
indicated in the figure, it moves to the right with the speed (v) of the train.
An observer sitting on the train at M', but not having this speed, would remain
constantly at M, and the light rays from sparks A and B would reach him
simultaneously, that is, these two light rays they would gather precisely in it.
The reality is, however, that (judging the situation from the embankment) this
observer goes to meet the ray of light that comes from B, instead fleeing the
one that advances from A, therefore, he will see the light that comes from B
first. than the one that comes out of A. In short, the observers who use the
train as a reference body have to reach the conclusion that the electric spark
B has fallen before the A. We thus arrive at an important result: Events that
are simultaneous with respect to the embankment are not simultaneous with
respect to the train, and vice versa (relativity of simultaneity).”
6.- A THESIS
Analyzing the content and the order in which the
paragraphs of the book that we have taken as a study guideline are written, we
believe that we have been able to find out the idea, the intention and the
mistake made by A. Einstein when considering the theory of special relativity.
Our thesis based on everything we have discussed in the
previous issue is as follows:
It seems that A. Einstein, with the idea of
investigating the Relativity of Simultaneity, wants to be able to affirm
that, when an event that occurs within a (MRS), this same event can be SEEN
SIMULTANEOUSLY from its corresponding (FRS). So there is no doubt that the
event is IDENTIFIED.
To make such an identification, he tests using a thought
experiment whose approach is wrong.
And, with this erroneous approach, he makes his thesis.
He says that an event that occurs within an (MRS) can NOT be seen
simultaneously from its corresponding (FRS)
And, with this erroneous thesis, he is forced to not be
able to IDENTIFY from an (FRS) an event produced in an (MRS).
And, here is born the nonsense or the Paradox of
Transmutation. We repeat his statement:
“The time that a
process needs with respect to the wagon cannot be equal to the duration of the
same process judged from the reference body of the embankment”
Regarding the content that we have commented on the
previous paragraphs of the aforementioned book, we can appreciate that now he seems
to forget the Principle of Relativity that he cited and that we have written in
the second paragraph. Now he speaks of "a process" and not of the
laws that govern natural phenomena. Perhaps the confusion that he commits on
the subject of "relativity of simultaneity" makes him interpret in a
different way the vision from the (FRS) of the events that occurred in the (MRS).
Note the reader
that the nonsense comes from having considered the "Relativity of
Simultaneity" as two events, and not just one with its corresponding
Proper Time.
Here the author of such a statement, using his error as a
postulate, no longer tries to SEE in a different way from the (FRS) what
happens in the (MRS), but affirms that they OCCUR in a different way when they
are located in the ( FRS). This is where the nonsense is generated. The meaning
of the given statement makes us think of the verb BEING in a different way, and
not of SEEing in a different way. We could only accept it if a TRANSMUTATION takes place...
which is a PARADOX. Nonsense!
