PRESENTATION
In this essay we criticize the mental experiment exposed
by A. Einstein in which he tries to relate an event that has the quality of
SIMULTANEOUS, with RELATIVE movements.
The interest of this study is that the author of this
experiment draws a crazy conclusion, which we ironically baptize as: "the
miracle of transmutation"
We will take as a review guideline the book by A.
Einstein entitled: "On the theory of special and general relativity"
The transcriptions that we will make of this book will be written in quotation
marks and in italics.
GRAPHIC INTERPRETATION OF THE MENTAL EXPERIMENT PROPOSED
BY THE AUTHOR OF THE AFOREMENTIONED BOOK TO EXPLAIN THE RELATIVITY OF
SIMULTANEITY
We transcribe the text of the mental experiment that
appears in the book by A. Einstein.
For your best interpretation, we break down the
transcription of the aforementioned experiment into pieces and, then, we will
make its corresponding comment. Interested that the reader
Stay with the last two conclusions that we have
transcribed from the aforementioned experiment.
The author of the book, using the well-known train car,
begins by asking the following question:
"Two
events, for example, two lightning strikes (A) and (B), which are simultaneous
with respect to the embankment, are they also simultaneous with respect to the
train?"
The following drawing shows three phases of advancement
of the wagon. In it we make appear the two
LIGHTNINGS (A) and (B) and the RAYS OF LIGHT (A') and
(B') that emerge from it.
In the drawing we have made the rays reach the ground and
we have drawn a person at the midpoint (M´) of the distance between the rays
..." Now,
the events (A) and (B) also correspond in places (A) and (B) on the
train."
In the first stage of the drawing, the beam (A) passes
just touching the rear of the wagon and the beam (B) just touching the front of
the wagon.
…” Let (M´) be
the midpoint of the segment (A)-(B) of the moving train. This point (M´) is
true that at the instant of the lightning strike it coincides with the point
(M), but, as indicated in the figure, it moves to the right with speed (v) of
the train.”
At this midpoint (M´) we have painted a person fixed on
the floor of the wagon and, as such, moves with him. This causes it to move
toward the path of the light ray (B') and away from the light ray (A').
…” An observer
who was sitting on the train at (M´), but who did not have this speed would
remain constantly at (M) and the rays of light coming from the sparks (A´) and
(B´) would reach him simultaneously , that is, these two rays of light would
meet precisely in it.”
BEWARE! To make this paragraph more intelligible, instead
of placing this observer inside the wagon but without speed, in the drawing we
have painted him outside the wagon. He fixed on the ground. He would constantly
remain at point (M), but we place him outside the wagon. The ray of light (A´)
and of (B´) arrive SIMULTANEOUSLY to him
…”The reality is, however, that (judging the situation
from the embankment this observer goes to meet the ray of light that comes from
(B), fleeing instead from the one that advances from (A).
He refers to the observer who is inside the wagon, in
(M´), and fixed in the center of it.
…” Consequently,
you will see the light coming from (B) before the light coming from (A). In
short, the observers who use the train as a reference body have to conclude
that the electric spark (B) has fallen before the (A).”
The observer that
we have placed outside the wagon, as we have indicated in the previous section,
says that this observer sees that the person who is inside the wagon reaches
the ray of light from (A) before the one from ( B).
…” In short,
observers who use the train as a reference body have to conclude that the
electric spark (B) has fallen before (A).
We thus arrive
at an important result.
Events that are
simultaneous with respect to the embankment, are not with respect to the train,
and vice versa (relativity of simultaneity).”
Here the narration of the aforementioned experiment ends.
We will criticize this conclusion, which goes against the
First Principle of Relativity.
FIRST PRINCIPLE OF RELATIVITY
In the book that we take as a reference, he considers a
Fixed Reference System (SRF) and a Moving Reference System (SRM) and announces
as the First Principle of Relativity:
"If a (SRM) moves with respect to a
(SRF) then natural phenomena occur with respect to the (SRM) according to the
same general laws as with respect to the (SRF)"
This
Principle was already announced by Galileo. Summing up, his explanation, he
mentions a ship that advances at a constant and rectilinear speed. He says that
in his winery natural phenomena, for example, the flight of a fly, the fall of
water from an upside-down bottle... occur in the same way that they occur on
the coast.
SIMULTANEOUS EVENTS OCCURRING OUTSIDE A MOBILE REFERENCE SYSTEM.- CRITICAL
If a
simultaneous event occurs outside of a Mobile Reference System (SRM), it is
absurd to want to apply the theory of relative motions to it. This is
what happens in the mental experiment proposed by A. Einstein. This
"relativity of simultaneity" goes against precisely the First
Principle of Relativity that we have commented on in the previous paragraph.
In the conclusion
of the aforementioned experiment we have transcribed that it says:
“We thus reached
an important result.
Events that are simultaneous
with respect to the embankment, are not with respect to the train, and vice
versa (relativity of simultaneity).”
This can be
interpreted as what happens in the Fixed Reference System (RRF) does not happen
in the Mobile Reference System (SRM), which is the first step to doubt the
validity of such a mental experiment.
A second step that corroborates that the mentioned mental
experiment is a fallacy, is the following:
We know that a fallacy occurs when a logical syllogism is
to be taken for true and one of its premises is false.
In the aforementioned thought experiment we put forward
the following syllogism:
1st PREMISE The First Principle of Relativity considers
the
performance of natural phenomena
2nd PREMISE Simultaneity is a natural phenomenon
CONCLUSION SIMULTANEITY considers the performance of
natural phenomena
The second premise is false. Simultaneity is not a natural
phenomenon. It is a quality that the event of an event has.
Grammatically it is a qualifying adjective. It is not a verb. Consequently, the
above syllogism is a fallacy.
THOUGHT EXPERIMENTS WHERE SIMULTANEITY OCCURS WITHIN THE
MOBILE REFERENCE SYSTEM (SRM)
If the simultaneity of an event occurs within a Mobile
Reference System (SRM), it is logical that we can apply the theory of relative
movements. The event occurs "inside Galileo's ship" of which we had
spoken.
We have devised a mental experiment, with relative
movements between the train car and a fixed observer outside the car, and where
the SIMULTANEITY event occurs inside the car. In this case, we could talk about
the relativity of movements.
The following drawing represents three phases of advance
of a wagon that goes at a rectilinear and constant speed.
In the center of the wagon there is a person who holds a
mass in each of his hands. The masses have equal weight.
Outside the wagon there is a fixed observer on the ground
Due to the displacement of the wagon, at the moment that
the person who is inside passes in front of the observer who is on the ground,
that person who is inside releases the two masses at the same time. We consider
this as a SIMULTANEOUS event.
We observe that in the intermediate step of the drawing
it is seen that the masses have not yet touched the floor of the wagon.
In the last stage that represents the drawing, the masses
have already arrived on the ground.
The observer who is fixed on the ground (SRF), will see
the different phases in which the masses fall, in the different phases of the
wagon's advance.
We can observe that the physical phenomenon of the masses
falling to the floor of the wagon is exactly the same as what would happen to
the person outside the wagon (SRF). Therefore, the First Principle of
Relativity is fulfilled.
THE NONNESS OF A. EINSTEIN
The author of the aforementioned mental experiment
intends to establish a correspondence between what an observer sees, who
considers it as a Fixed Reference System (SRF), and what an observer located
inside the wagon sees. But, be careful, the gazapo is that natural phenomena do
not occur inside the wagon. We cannot consider that an Inertial Reference
System has been established.
Not realizing this error, he preaches the following:
"The time
that a process needs with respect to the wagon cannot be equaled to the
duration of the same process judged from the reference body of the
embankment"
This is where we say that his statement amounts to the "miracle of transmutation"
Now he seems to forget the First Principle of Relativity
that he cited and that we have written in the second paragraph. He now speaks
of "a process" and not of the laws that govern natural phenomena. The
confusion he commits on the subject of "relativity of simultaneity"
makes him interpret the vision from the (SRF) of the events that occurred in
the (SRM) in a different way.
