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 齐绩 （qiji8111@yahoo.com.cn） 2007.04
( School of Electronic Engineering ,Daqing Petroleum Institute,Daqing 163318,China.E-mail:qiji8111@yahoo.com.cn)
[Abstract]
Through analyzing a variety of physical
phenomena ,the author proposes that there exists a special kind of substance
—No-Shape-Substance .
In the last two papers, the properties of
No-Shape-Substance are introduced, as well as an elementary calculation to the
density and volume modulus of it. In addition, we have given out a commendably
explanation on many a optical experiments and phenomena, such as Fizeau’s
experiment, sagnac effect, Michelson-Morley experiment, Millar experiment, the
aberration phenomenon, Ariy’s experiment and the like.
In this paper, by
analyzing the interaction between the body and the No-Shape-Substance, we will
have a newer and better understanding of physical laws or concepts as inertial
mass, Newton’s Second Law, kinetic energy equation, mass-energy equation and
momentum. And now we are going to uncover the essence of the physical laws.
Keywords:
Inertial Mass, Newton’s Second Law, Kinetic
Energy, Mass-Energy Equation, Momentum
All laws of motion of bodies
depend on the total No-Shape-Substance Space where it is instead of the
absolute Mathematical Space.
Again we need the previous example about
the fish swimming in water flowing with reference to the bank.
Here the bodies are analogous to the fish
while the No-Shape-Substance is analogous to the water. Therefore the laws of
motion of bodies depend on the No-Shape-Substance Space, but not directly on
the Mathematical Space.
Before learning the physical laws, we must
have a clear idea about the most basic physical concepts. Physics would not be
firm unless these physical concepts were clarified.
1. Gravitational Mass and Inertial Mass
People usually don’t distinguish the gravitational
mass from the inertial mass, and instead they often call the two ‘uniformly
mass’. However, in fact the two kinds of mass are essentially different.
[Gravitational Mass]
The gravitational mass, which is still
denoted by , reflects the quantity of substances
contained in a body and is a constant.
[Inertial Mass]
While the inertial mass reflects the
characteristics of motion of a body and its ability to accelerate when there is
an external force acting on the body. It is a variable.
The inertial mass of a body associates not
only with its gravitational mass but also with the density of the
No-Shape-Substance of the space where the body is. Moreover, the inertial mass
of a body also connects with its moving speed relative to the
No-Shape-Substance Space where it exists.
If we denote the inertial mass of a body by
Q, we will get
 (1.1)
 is the function of the inertial mass of a body
and the density of the No-Shape-Substance of the space where the body exists.
 is the function of the
inertial mass of a body and its moving speed in the No-Shape-Substance Space.
In the space nearthe earth’s
surface, the density of the No-Shape-Substance, which is denoted by , is
uniform. If , then .
From the experiment conducted by Kaufmanns
and some other people seeking the relation between mass and speed we can learn
(1.2)
approximately equals 1 when
speed is a low value, therefore with the case of low velocity on the earth’s
surface,  .
Obviously, on the earth’s surface, when a
body moves at a low speed, its inertial mass is numerically equivalent to its
gravitational mass. But this is just the equivalence on the numerical value;
they are completely different in nature.
Please note that the light speed in
equation (1.2) is that of the No-Shape-Substance Space where the body exists.
[Eötvös Experiment]
……
In 1906, Eötvös, a Hungarian physicist,
conducted a famous experiment to verify that the gravitational mass is equal to
the inertial mass. As shown in figure 2.1.The suspended mass point will
eventually reach a position of equilibrium. There are three forces acting on
it:
1)
The gravitation  of the
earth, which directs the center of the earth;
2)
The centrifugal force  of inertia
, generated by the rotation of the earth;
3)
The tension , acted by
the hanging thread.
What is important is that is
proportional to the gravitational mass, whileis proportional to the
inertial mass. Eötvös found no difference in the position of equilibrium with a
variety of substance, such as wood, platinum, copper, asbestos, water and
copper sulfide. So people believe that the ‘zero’ result signifies that the
gravitational mass is equal to the inertial mass.
……
How should we explain the experiment?
First, we need to note that the experiment was conducted at the same spot on
the earth’s surface and the velocity of the object was zero.
From the above analyses we have derived
that the inertial mass and the gravitational mass satisfy the following
relation .
Well, on the earth’s surface, and , when , thus we
get .
From this we can see that in this
experiment the equivalence between the inertial mass of every single body and its
gravitational mass is inevitable.
Either the density of the
No-Shape-Substance of the space in which the body is, or the speed the body
travels, is different, the gravitational mass will not equal to the inertial
mass.
2. Newton’s Second Law
When a body is acted by a resultant force
of zero, its acceleration relative to the total No-Shape-Substance Space where
it exists is zero.
When a body is acted on by a certain
external force that is not zero, the product of its acceleration relative to
the total No-Shape-Substance Space where it exists and its inertial mass is
equal to the resultant force the body is acted on.
(1.3)
The above is the more exact presentation of
Newton’s second law.
3. Kinetic Energy Equation
The kinetic energy of a body is the energy it possesses
when it moves with reference to the total No-Shape-Substance Space where it
exists.
We then deduce the kinetic energy  of a
body. We assume that at first the particle is immobile relative to the total
No-Shape-Substance Space , which indicates that its original kinetic energy is
zero. And then we exert an external force on the body to make it move along a
straight-line path. When the speed of the particle increases to , its
kinetic energy equals the work done by the external force acting on it. That
can be expressed as
If substituting  forin the
above equation, we get
Again replacing  for  and then  for in
above equation, it follows that
 (1.4)
(1)
In the
No-Shape-Substance Space near the earth’s surface, when the body moves at a low
speed, Q is a const with its value equaling with m. Then at this time
the kinetic energy of the body is
(1.5)
(2)
In general case
As a result,  (1.6)
(3)
On the earth’s
surface, when the speed of a moving body approaches the light speed
(1.7)
Unexpectedly,
this is the mass-energy equation we are familiar with.
4. Mass-Energy Equation
Mass is conservative and energy is also
conservative. Mass and energy can not be converted to each other while they are
in essence two completely different kinds of things.
When a nuclear fusion happens, an
atomic nucleus will release a great number of particles with high energy and their
speed is approaching to the light speed. The mass taken away by these particles
is the mass the atomic nucleus loses. And the kinetic energy acquired by these
particles is converted from the potential energy of the atomic nucleus. Both
mass and energy are conservative.
From the above equation (1.7), we can get
the following equation between the mass and energy taken away by these
particles
(1.8)
Now it is natural for us to understand the
existence of the mass-energy equation.
Photons are
No-Shape-Substance in nature. So a photon’s mass is not zero. It is
[The Change of Phases of Matter]
We all know that the heat of fusion for solid and that of
evaporation for liquid. Taking ice for example .The fusing heat of ice is the
heat input required to fuse ice of unit mass to water at the same temperature
of 
, which is the
fusing point of ice. The transformation between No-Shape-Substance
and Shape-Substance is a more essential change in the state of matter. Then, is
it accompanied with a process of heat absorbing or releasing?
Can we
say that No-Shape-Substance is the basic component of the universe, while
Shape-Substance is the spray in the No-Shape-Substance?
No-Shape-Substance is corresponding to a state of energy .It’s a state with low
energy, which is a hiding state. While Shape-Substance is corresponding to
another state of energy. That is a state with high energy, which is an
uncovering state.
We
demonstrate the state with low energy by 0, which is corresponded with
No-Shape-Substance, while 1 demonstrating the state with high energy of
Shape-Substance.
When transforming No-Shape-Substance to Shape-Substance, the matter
is changed from a hiding state to an uncovering one. This is a process of heat
absorbing. The energy absorbed and the mass transformed satisfy mass-energy
equation .
Oppositely, energy is released when Shape-Substance is changed into
No-Shape-Substance. The matter is changed from an uncovering state to a hiding
one. Then the energy released and the mass transformed also satisfy mass-energy
equation as above.
Energy is conservational and mass is too. But the process of the
transformation of matter’s state is accompanied with energy absorbing or
releasing.
[The Annihilation of an Electron-Positron
Pair]
Experiments
show that an electron-positron pair can annihilate into photons. The energy of
photons and the mass of electrons are linked by mass-energy equation.
……
This is a transformation
from Shape-Substance to No-Shape-Substance. Energy is released in this process.
So the energy released and the mass satisfy mass-energy equation.
In contrary, the energy absorbed in the
transformation from no-Shape-Substance to Shape-Substance and the mass also
satisfy mass-energy equation.——Manyphenomena, such
as photons producing phenomenon of an electron-positron pair, are just the
reaction of such transformation.
We will inquire into the annihilation of an
electron-positron pair briefly from the viewpoint of basic physics as follows.
Does an electron have a radius?
Certainly it does since it is a particle. We assume its radius to be
and its electric charge to be distributed uniformly on its surface.
Thus we are in an ideal position to probe the annihilation and we consider
stationary electric force uniquely.
At the beginning, the electron and positron are far away from each
other, so the electrical potential energy is zero.
In general case, the electrical potential energy is expressed as
(1.9)
When the electron and
positron syncretize completely, the electrical potential energy is:
In this situation, the Shape-Substance is transformed into the
No-Shape-Substance. It’s perceived that the No-Shape-Substance is in a state
with lower energy.
The energy released is equal to the electrical potential energy
reduced:
From this we can calculate the radius of an
electron as bellow:
(2.11)
What to illuminate is that it is a very ideal calculation. We know
that the distribution of No-Shape-Substance has different levels. The density
of No-Shape-Substance near the electron is greater than that in a vacuum near
the earth’s surface. In this case, the ratio of electric capacity
is
greater than , so the
radius of the electron is much likely to be less than the calculation.
Therefore, the saying that the transformation of the state of the
matter is accompanied with energy absorbing or releasing in the annihilation of
an electron-positron pair, is equivalent with the description that electrical
potential energy is transformed into light energy.
5.
Momentum
Does the momentum of a body preciously satisfy the
relation as follows?
(1.11)
No, the above expression of the momentum of
a body is not exact. Such expression doesn’t uncover the essence of the
momentum. Exactly speaking, what the momentum theorem reflects is the essential
source of the momentum. That is, the impulse acting on a body equals the
increment in momentum of the body. That can be expressed as
 
As shown in figure 1.2, a system free of
any external force is conservational in momentum because the internal forces of
the system are actions and reactions which are equal in magnitude, opposite in
direction ; and the time duration of the pairs of forces is always
corresponding equal. Therefore the resultant impulse acting on this system is
zero, which means the momentum of this system is conservational.
The impulse acting on a body equals the
increment in momentum of the body.
The expression can be written as
If we make a body’s initial velocity zero
and let it move along a straight-line path, we will deduce the relation for
momentum as follows,
By substituting  for and then substituting for in
above equation, we get
When the velocity of a body is zero (), its
momentum is also zero , so the momentum of a body at any
time is:
 (1.12)
(1) On the earth’s surface, when a body moves at a low
speed, its value of , which equals , is a constant. So
(1.13)
(2) In general case
 (1.14)
(3) Now let us look at the particular case. On
the earth’s surface, when the velocity of a body v equals the light
speed c, what is the magnitude of its momentum?
(1.15)
6. The Pattern of Function f(S)
In this part we will primarily discuss the functional
form of .
The inertial mass is the result of interplay between
an object and its No-Shape-Substance Space. The inertial mass is desired by
logical reasoning to increase by times when the density of a No-Shape-Substance
multiplies. Then the function of is:
(1.16)
Wherein is the inertial coefficient. Since, .
In which is the density of the
No-Shape-Substance on the earth’s surface.
 Let’s examine the energy of a certain photon moving in
the No-Shape-Substance Space of different density. We want to know whether the
energy is the same when the speed of the photon varies.
As shown in figure 1.3, assuming the mass
of the photon is m0, now we calculate its energy when it
moves in the No-Shape-Substance Space of different density. From equation (1.6)
we can obtain the energy of a photon:
In the space in which the density of No-Shape-Substance
is S1, the energy of the photon is:
In the space in which the density of
No-Shape-Substance is S2, the energy of the photon is
Obviously, when a photon propagates in the
No-Shape-Substance of different densities, although its speed varies, its
energy is conservational.
 7. Law of Refection and Refraction
As shown in figure 1.4. As we
all know, there is no energy lost during a perfect elastic collision happened to a
ball on a smooth plane. The outside force acted on the ball is in the normal
direction, so the tangent component of the ball’s momentum is invariable.
 As shown in figure 1.5. Similarly, when a
photon is reflected or refracted at the interface, its energy is invariable,
and its tangent
component of momentum is invariable too.
In area 1:
The magnitude of the photon’s momentum is:
In area 2:
The magnitude of the photon’s momentum is:
[Law of Refection]
The tangent component of the
photon’s momentum before refection is:
The tangent component of the
photon’s momentum after refection is:
(1.17)
The angle of incidence is equal to that
of reflection,
——this is just the law of refection.
[Law of Refraction]
The tangent component of the
photon’s momentum before refraction is:
The tangent component of the
photon’s momentum after refraction is:
With  ，and
, we get
(1.18)
Since,
,
, we get the following
relation:
(1.19)
This happens to be the law of refraction
of light at the interface.
Reference:
[1]
Ji Qi. New
Physics[M[. Harbin
: Publishing House of NortheastForestry University
, 2006.
[2]
Guangjiong Ni,
Hongfang Li. Modern Physics[M]. Shanghai: Shanghai Science and Technology
Publishing Company, 1979.
[3]
Shujie Tan, Hua
Wang. Important Experiments on Physics[M]. Science and Technology Literature
Company, 1987.
[4]
Yiling Guo,
Huijun Shen. Famous Classical Physics Experiments[M]. Beijing: Beijing Science and Technology Publishing Company, 1991.
[5]
Wenwei Ma.
Physics[M]. Beijing: Higher Education Press, 1999.
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