Re: THE GENERAL RELATIVITY.

Stamenin wrote:
Paul B. Andersen wrote:
Stamenin skrev:
THE EQUALITY OF INERTIAL AND GRAVITATIONAL MASS AS
AN ARGUMENT FOR THE GENERAL POSTULATE OF RELATIVITY.

At the page 68 of his book Relativity Einstein writes about the General
postulate of relativity. He imagines a large portion of empty space, so
far removed from the stars, that we have before us approximately the
conditions required by the fundamental law of Galilei. It is then
possible to choose a Galileian reference body for this part of space
relative to which points at rest remain at rest and points at motion
continue permanently in uniform rectilinear motion.
From this supposition is visible that Einstein uses the name
Galileian system only to not make use of the Newton's absolute
coordinate system, because between them in this portion of space they
are both of them valid and both are impossible to be determined.
And by there definitions they represent the same thing, a coordinate
system that is staying in a large portion of the cosmos where do not
exist gravitational forces.
In continuation he says: In this large space he puts a chest and a man
in it. To the lid of the chest is fixed a hook with a rope and by an
imaginary being is pulled "upwards". But how does the man in the
chest regard the process, asks Einstein.
The acceleration at the chest will be transmitted to him by the
reaction of the floor of the chest. This situation is complete similar
with the situation in a room at the earth and that there is a
gravitational field.
To the end of the page 69 Einstein says: "Ought we to smile at the
man and say that he errs in his conclusion? I do not believe we ought
to if we wish to remain consistent, we must rather admit that his mode
of grasping the situation violates neither reason nor known mechanical
laws. Even though it is being accelerated with respect to the
"Galileian space" first considered, we can nevertheless regard the
chest as being at rest. We have thus good grounds for extending the
principle of the relativity to include bodies of reference which are
accelerated with respect to each other, and as a result we have gained
a powerful argument for a generalized postulate of relativity".
So we can see that Einstein by using the behavior of the inertial and
the gravitational forces to acct upon every atom of the material body
reached the conclusion that an accelerated coordinate system is an
absolute inertial system.
Evidently this conclusion is in contradiction:
1) With the starting supposition that the chest is in an accelerated
motion.
2) With the principle of the relativity that says that is not valid for
the accelerated systems of coordinates because it is valid only for
systems of coordinates that are in right line motion and with a
constant speed.
3) By this he makes confusion between the gravitational and inertial
forces considering them as being of the same nature. But we know that
that they are different, the gravitational force is an external force
of the body and inertial force is an internal force in the body. The
only thing that is common to these forces is the behavior to act upon
every atom of the material body.
4) And by this he concludes that has gained a powerful argument for the
generalization of this principle of the relativity!!!!
This kind of logic could be named, the negation of the affirmation.
And after that Einstein continues: " We must note carefully that the
possibility of this mode of interpretation rests on the fundamental
property of the gravitational field of giving all bodies the same
acceleration, or, what comes to the same thing, on the law of the
equality of inertial and gravitational mass"!!!
This final argumentation shows how difficult was for Einstein trying
in such a way to trick the reader by using such an illogical
argumentation.
What I can conclude after all that is said, is the fact that the
General theory of the relativity has a tricky base and not powerful
arguments and fundamental laws of the nature.
2/10/2006.
Einstein's book "Relativity" is a popular book, not a scientific
paper.
It can at the very best give you a vague idea of what GR is about.
Believing that you after having read a popular book are competent
to critisize the theory described in that book is a rather naive idea.

And you failed to grasp the basic idea which Einstein tried to mediate.
You say: " the gravitational force is an external force of the body"
Is it?
If it is an external force, why can't you feel it?
The only external force you now can feel is the force
from your chair, pushing you upwards.
If you jump out the window, you feel nothing.
That is because no external forces are acting on you while
you are in free fall.

From the Einstein book I took this topic. Your problem is in the fact
that you do not take in account that only these two forces the
gravitational and the inertial force act upon every atom of the
marerial body in motion or at a state of staying. this is the cause wy
you don't feel the gravitational force. For this I recomend to read the
point (3) of this mine topic. For more information about this fenomenon
I send and the followig article:
THE INERTIAL AND GRAVITATIONAL MASS
Is possible to exist two masses, the inertial and the gravitational
mass? Einstein
considers that they exist and are the basic argument for his general
theory of the relativity. Is that true?

You have got it backwards.
In relativity, there is but one type of mass.
In Newtonian mechanics, there are two - inertial and gravitational.

Einstein in his book RELATIVITY in page 65 and 66 makes a parallel
analysis between the gravitational field, the electric field and the
magnetic field. Everything that is said there represents known facts
about the fields. But at the end of the 66th page he has written:
"According to Newton's law of motion, we have:
(Force)=(inertial mass) x (acceleration), or [F=(mi). a.]
Where the "inertial mass" is a characteristic constant of the
accelerated body. If now gravitation is the cause of the acceleration,
we than have:
(Force)=(gravitational mass) x (intensity of the gravitational field),
or [F=(mg). g] where the "gravitational mass" is likewise a
characteristic constant for the body.
From these two relations follows:
a=(mg/mi).g
Where g is the intensity of the gravitational field.
If now, we find from experience, the acceleration is to be independent
of the nature and the conditions of the body and always the same for a
given gravitational field, then the ratio of the gravitational to the
inertial mass must likewise be the same for all bodies. By a suitable
choice of units we can thus make this ratio equal to unity. We then
have the following law: The gravitational mass of a body is equal to
its inertial mass. It is true that this important law had hitherto been
recorded in mechanics, but it had not been interpreted. A satisfactory
interpretation can be obtained only if we recognize the following fact:
The same quality of a body manifests itself according to circumstances
as "inertia" or as "weight". In the following section we shall
show to what extent this is actually the case, and how this question is
connected with the general postulate of relativity".

Exactly.
Note that the two types of mass isn't Einstein's invention.
He points out that there has always been two types of mass in
Newtonian mechanics, but it has been taken for granted that
they always are equal.
(You could call equality of the masses an empirical law,
but it doesn't follow from the basic laws of Newtonian mechanics.)
Einstein states:
"The same quality of a body manifests itself according to circumstances
as "inertia" or as "weight"."
That is, the inertial mass and gravitatonal mass is one and the same
quality of the body. There is but one mass.
This is the equivalence principle on which GR rests.

This is what Einstein says about the two masses. Everything seems to
be right, but it isn't. Let us analyze the mathematical relations
shown above by Einstein.
The second law of the mechanics is:
F=m.a...........(1). And the law of the universal attraction
is:
G=kMm/r^2.....(2)

Note that these are two different laws.
There is nothing in Newtonian mechanics that say the constant
of proportionality m in the former law and ditto in the latter law
have to be the same constant.
Experiments indicate they are the same, but in Newtonian mechanics,
this is accidental, there is no law which say they have to be the same.

We can say that G is the gravitational force of attraction between
the two material bodies with mass M and m. But we can't say that F of
the second law of the mechanics is an inertial force or an external
force without describing and the phenomenon of the motion of the
material body, because the accelerated motion doesn't appear without
the action of an external force. According to the third law of the
mechanics the two forces are opposed and equal between them. So if we
write the second law as being:
Fi=m.a ........(1a) ,then it should be considered as a relation for
the calculation of the inertial force when we know the value of the
acceleration. And is very important to be mentioned that this force is
an internal force which appears in the material body. But the
acceleration doesn't appear if there do not exist the external force
Fe that determines the material body to move in an accelerated motion.
In the case of the gravitational forces, if we let a material body
with mass m to fall down free it will be attracted by the earth's
gravitational force G, which is an external force for the material
body. From the relation (1) will have:
G=m.a........(3) and, results that the acceleration is:
a=G/m=(k.M.m/r^2)/m=k.M/r^2=g.
Results that g is, simply an acceleration and not the intensity of
the gravitational field.
This is absolute correct because we know the gravitational force by the
Newton's law of the universal attraction. So the mass of this example
evidently is an inertial mass and the work done by other scientists to
demonstrate that the inertial mass and gravitation mass are equal
between them was done in vain. As a result we can write:
G=m.g. ......(4).
By this we can conclude that the term (m.g) represents in fact the
inertial force that appears in the material body that is falling down
and opposes to the gravitational force expressed with the Newton's
relation (2).
The relations (1) and (2) are in fact of such a huge importance that
we can conclude that with the aid of these relations we can calculate
the inertial and the gravitational forces that act upon all the stars
and planets. At the same time these two notions the inertial and
gravitational forces because they act upon every atom of the material
body enable the existence of the cosmos in the shape in which they are
known now. If one of them disappears everything will be destructed.
Out of that we can name the second law of the mechanics as being the
general law of the inertia, because by making the (a=0) we obtain the
first law of the mechanics as a particular case.
The relation, G=m.g is an application of the second law of the
mechanics.

If I understand you right, your point is that according to Newtonian
mechanics, gravitational mass and inertial mass must be the same,
there is but one kind of mass, and the equivalence principle is true.

I don't think you have proved that, your proof is basically:
"if we assume the two m's in the two laws are the same m,
then there is but one m."

And your conclusion is weird indeed:
> And the most important conclusion is that do not exist gravitational
> mass and inertial mass but exists only one mass of the material
> bodies. The supposition that Einstein uses as a fundamental law of the
> nature for his general relativity is a false supposition and because of
> that we can conclude that his general theory of the relativity is false
> theory.
> 28/09/2006.

You assure that the equivalence principle is true,
and conclude that general relativity, which rest on
the validity of the equivalence principle, is a false.

An extraordinary achievement! :-)

Paul
.

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