Chapter 23Outline of Special Theory of Relativity


0. Let us consider the world in which the power exerts an infuence on nothing. That is, there is no acceleration in the world.
Nothing stands still absolutely. All things are traveling through space with linear uniform motion relatively. The velocity of an object is various depending on an observer.


1. Electromagnetic wave travels through space fastest in the world.
*Let us make a new system of units to make a speed of
electromagnetic wave be to make relativity symple.


2. Ms. B is traveling with linear uniform motion relative to Mr. A.
The speed of electromagnetic wave relative to Mr. A is .
The speed of electromagnetic wave relative to Ms. B is , too.


3. All objects keep traveling through four-dimensional space-time.
Established theory :The space-time is composed of three-dimensional
space axes and one-dimensional time axis.
My view :The space-time is composed of three-dimensional space
axes and one-dimensional relative-time axis.


4. Law of universal traveling through four-dimensional space-time

Established theory :Ms. B is traveling with linear uniform motion
relative to Mr.A.
The value of the expression showing universal
traveling through four-dimensional space-time
with respect to Mr. A is equal to the value of the
expression with respect to Ms. B.

We call this expression 'proper time.'


My view :Ms. B is traveling with linear uniform motion relative to
Mr. A. The value of the expression showing universal
traveling through four-dimensional space-time with
respect to Mr. A is equal to the value of the expression
with respect to Ms. B.

I call this expression 'absolute-time.'


5. The above-mentioned law is shown with the following coordinate
conversion :
Established theory :Lorentz transformation
My view :'Bioring's transformation'


6. Lorentz transformation leads us to some paradoxes.

a)Two events, which occur at different space point at the same
time with respect to Mr. A, don't occur at the same time with
respect to Ms. B. Two events, which occur at different space point
at the same time with respect to Ms. B, don't occur at the same
time with respect to Mr. A.

b)The relationship of Mr. A and Ms. B is as follows with respect to
Mr. A and Ms. B :
"You are aging more slowly than I."

c)The relationship of Mr.A and Ms.B is as follows with respect to
Mr. A and Ms. B :
"Your chest is narrower than my chest."
Proviso :When Mr. A and Ms. B stand still,
their chests are the same width.


7. Owing to Lorentz transformation, we find that composition of speeds is expressed as follows :
Proviso:The movement direction of the object C relative
to the object B is equal to the movement direction of
the object B relative to the object A.

:The speed of the object B from a standpoint of the object A
:The speed of the object C from a standpoint of the object B
:The speed of the object C from a standpoint of the object A


8. Owing to composition of speeds, law of conservation of momentum, and law of conservation of energy, we find that mass ( ) of an object changes as follows due to a speed ( ) of the object :
* Proviso :Let be rest mass of an object.


9.Definition of force No1 :We obtain force by differentiating
momentum by time intervals.
Definition of force No2 :We obtain force by differentiating
energy by space intervals.


Owing to the above-mentioned three items, we find that mass of an object shows amount of energy of the object as follows :





10. The unification of a composition of speeds of objects and traveling of wave

Wave traveling through medium, like sound, tranvels at a common and constant speed with respect to all observers standing still relative to medium of the wave regardless of a velocity of a source of the wave.
Electromagnetic wave traveling through not medium but space travels at a common and constant speed with respect to all observers regardless of a velocity of a source of electromagnetic wave.
Electromagnetic wave, if it might travels through medium, travels at a common and constant speed with respect to all observers, regardless of a velocity of medium and a source of electromagnetic wave.
Quantum travels at a common and constant speed with respect to all observers, regardless of a velocity of an object which emits the quantum.
An object traveling with linear uniform motion travels through space of an observer at each constant speed relative to the observer.

We can find following four kinds of speed relative to the 2nd observer traveling with linear uniform motion relative to above-mentioned observers from a standpoint of the 2nd observer with an identical equation :
Speed of a traveling object
Speed of quantum
Speed of electromagnetic wave
Speed of wave traveling through medium
It is the bridge connecting between Electromagnetics and Newtonian mechanics.

( Qestion )
Please imagine; you are standing along the bank of a river. Your friend on a raft is 100m away in the upper stream of the river; the raft is traveling on the flow of the river at a speed of relative to you. The wind blows above the river at a speed of relative to you. A boat is passing the raft at a speed of ‚‚ relative to the raft. At this moment, your friend exploded gunpowder. Under the condition of windless, let and be the speed of the flash due to explosion of gunpowder and the speed of the sound due to explosion of gunpowder, respectively. How much are the speed of the boat, the speed of the flash, and the speed of the sound from your standpoint?

( The answer in the early days of the controversy about the ether )
The speed of the boat :
The speed of the flash :
The speed of the sound :

Note :Let be a speed of the ether.


( The answer soon after Michelson-Morley Experiment )
The speed of the boat :
The speed of the flash :
The speed of the sound :

Note :The ether is not absolute; it stands still with respect to
all observers traveling with a different velocity!?


( The answer after Lorentz transformation was placed in coordinate conversion )
The speed of the boat :
The speed of the flash :
The speed of the sound :

Note :The common conception is 'Traveling on a traveling
vehicle.' An object and quantum are traveling on a
traveling vehicle. Wave is traveling on medium as a
traveling vehicle. Speeds of them are shown with an
identical expression.
If we consider light as quantum, is a speed of a light
source. If we consider light as wave, is a speed of the
ether. If the ether might exist and be traveling at a free
speed, the speed of light is regardless of a speed of
the ether. Therefore, we can say that the ether exists
and does not exist at the same time.


11. Non-realisic standpoint of a third party

Three things keep linear uniform motion on the same straight line in the same direction at different speed. All distance between three things are gradually becoming long. I show three things in order from the back as follows :

The 2nd observerThe 1st observerObject A

Let be the velocity of the object A relative to the 1st observer from a standpoint of the 1st observer.
Let be the velocity of the object A relative to the 2nd observer in the observation of the 2nd observer.
Let be the velocity of the 1st observer relative to the 2nd observer in the observation of the 2nd observer.

'The fictitious velocity of the object A relative to the 1st observer in the observation of the 2nd observer' is expressed as follows:

However, it is not the velocity of the object A relative to the 1st observer in the observation of the 1st observer. It is expressed as follows :




We obtein this equation owing to the following equation :


Let be the velocity of the 2nd observer relative to the 1st observer in the observation of the 1st observer.
Owing to , we obtain the following equation :

This equation is the same as the above-mentioned equation.

That's why, a speed from a standpoint of the person concerned is realistic, and a speed from a standpoint of a third party is not realistic. Therefore, composition of velocities in Newtonian mechanics is not necessary. A movement of an object depends on a kinetic relationship between an observer and the object. It is impossible that we observe a movement of an object and transmission of an electromagnetic wave from a standpoint of a third party in the theory of relativity.
It is the conclusion of theory of relativity. Nevertheless, we try to observe movements from a standpoint of a third party to fall in the maze of paradoxes such as 'disappearance of simultaneity' and 'paradox of a light clock.'


12. The knack to understand relativity

 We must know that 'relative' has three meanings.

a )Non-absolute traveling
It is the kinetic relationship between an observing person (the second party) and an observed object (the first party). There is no 'absolute standing still' and no 'absolute traveling.' We must say correctly 'traveling of the object B relative to the observer A' without saying 'traveling of the object B'.

b )Symmetrical traveling and symmetric relationship between an observer and an observed person
It is the symmetric kinetic relationship between an observing person (the second party) and an observed person (the first party) and relationship between observing person and observed person as 'if you are, so am I.'
Only one of persons observing each other never gets older slowly, because the first party is the second party and the second party is the first party with respect to the first party.

c )Non-standpoint of a third party
We can do realistic observations with respect to a velocity or collision of an object relative to a stationary object. We can not do realistic observations with respect to a velocity or collision of an object relative to a traveling object. That is, an observation from a standpoint of the person concerned is realistic, and an observation from a standpoint of a third party is not realistic.

An observer is an absolute observer in his/her coordinate system, like God. However, if we think that an observer can not observe an object correctly as long as he/she is by the object or as long as his/her sense organs get information of the object, we fall in a maze. We must understand correctly what an observation in physics is.

The clock does not determine time, but time determines the clock. A clock is one of object acting regularly in cycle. When you think about time in your coordinate system, you must not look at the traveling clock. If you insist, you must look at another stationary clock at the space point on which the traveling clock exists. But, it shows the same time as the clock in your hand. This lesson is very important to understand the established theory.

With respect to velocity, we don't mistake easily, if we use the following standard sentence :
We consider that Mr. A and the object C are traveling on linear uniform motion with the same velocity relative to Mr. B .

Example No.1 :
In the subjective observation of Mr. A from a standpoint of the person
concerned,
the velocity of Mr. B,
relative to looked-like-stationary Object C.
Example No.2 :
In the objective observation of Mr. A from a standpoint of the person
concerned,
the velocity of Object C,
relative to looked-like-stationary Mr. B.
Example No.3 :
In the subjective observation of Mr. A from a standpoint of a third
party,
the velocity of Object C,
relative to looked-like-traveling Mr. B.

Notes :
The observation from a standpoint of the person concerned
has 'relative to looked-like-stationary' in the fourth line.
The subjective observation is done with a stationary scale
and a stationary clock relative to the observer.
The objective observation is done with a scale and a clock
belonging to the object in the fourth line.

Two objects are traveling with linear uniform motion relatively. If they are very different in weight, we tend to think by mistake that the heavier one is stationary and the lighter one is traveling. We must not forget this lesson.
Two objects are traveling with linear uniform motion relatively. If one of them is a spacecraft and the other is a space station, we tend to think by mistake that the space station is stationary and the spacecraft is traveling. We must not forget this lesson.

Mr. A is approaching Ms. B with linear uniform motion relative to Ms. B. It is wrong that Ms. B thinks time intervals until Mr. A collides with Ms. B in the world of Mr.A are shorter than time intervals until Mr. A collides with Ms. B in the world of Ms. B.
And it is wrong that we think Ms. B has the illusion that time intervals until Mr. A collides with Ms. B in the world of Mr.A are shorter than time intervals until Mr. A collides with Ms. B in the world of Ms. B.

Many things are traveling with linear uniform motion with various velocities. The 1st observer Mr. A and the other 1st observer Ms. B are two of them.
In the space-time coordinate system of Mr. A, Mr. A observed by him is standing still in the middle of space, and traveling only in the direction of time axis.
In the space-time coordinate system of Ms. B, Ms. B observed by her is standing still in the middle of space, and traveling only in the direction of time axis.
True coordinate conversion, which can express the real world, is found by comparing two kinetic styles of identical object separated by piling up Mr. A observed by him and Ms. B observed by her.

We must know that contradiction of relativity comes from Lorentz transformation. And, we must know that special theory of relativity of today is based on Lorentz transformation.





Chapter 24Summary of Bioring's Inertial Systems Theory of Relativity


1.We use a new system of units which sets the speed of light to .


2.In the new system of units, a unit of distance is the same as that of time.


3.Four-dimensional space-time is composed of three-dimensional space and one-dimensional 'relative-time.' Four axes of this space-time coordinate intersect each other perpendicularly. 'Relative-time' is similar to 'proper time.' 'Relative-time' is a vector. In this sense, 'proper time interval' is a magnitude of 'relative-time interval.'
Four-dimensional space-time has a shape of sphere. It expands following 'absolute-time' from a space-time point on which an observasion starts.


4.All objects are constantly traveling through above-mentioned four-dimensional space-time at the speed of light. 'Time' is a paramater of travels of all objects through above-mentioned space-time. Moreover, quickness of an action or aging of any object does not become slow even if a speed of the object increases.
[ Axiom of four-dimensional space-time velocity ]


5.'Time' is absolute, 'Proper time' is relative.


6.Natural laws take the same form in all inertial frames of reference. That is, as long as an observer is traveling with linear uniform motion or keeps still, the same physical law holds good for all observers.
[ Principle of relativity ]


7.Mass is a number of vibrations of a graviton in an object per unit relative-time interval.
Rest mass is a number of vibrations of a graviton in an object per unit absolute-time interval. That is, a frequency of a graviton in an object shows rest mass of the object.
[ Definition of mass and rest mass ]


8.'Absolute-time intervals' are constant regardless of a coordinate conversion. What changes is the ratio of traveling intervals of four axes through which an object is traveling. What decides the ratio is a velocity of an observed object through space relative to the observer.
The conversion of the speed of an object through space, i.e. composition of speeds of object through space, is not simple addition or subtraction. It depends upon the relativistic composition of speeds.


9.A causality of mutural relationship is constant regardless of a coordinate conversion. All objects are constantly traveling through four-dimensional space-time while keeping a causality of mutual relationship due to collisions of objects, including elementary particle and electro magnetic wave.
[ Axiom of causality ]


10.The theory of relativity does not mention how information is given to an observer and how it is recognized by him/her. It is a physical theory; physic asks for objectivity; an event and existence of an object is realistic and cirtain regardless of a recognization of an observer. Therefore, 'observation' means that we decide the space-time point on which an object exists objectivity.


11.We make researches into coordinate conversions between inertial frames of reference of following three kinds of observer.

The 0th observer :An observer who observes only stationary objects.

The 1st observer :An observer who observes objects observed by many
0th observers while traveling with linear uniform
motion relative to all 0th observers.

The 2nd observer :An observer who observes objects observed by the
1st observer while traveling with linear uniform
motion relative to the 1st observer.


12.It is wrong that we regard proper time intervals as follows, insted of regarding them as the magnitude of relative-time intervals through which an object travels :
The 1st observer recognizes that the 0th observer observes a stationary object for some proper time intervals, which are shorter than absolute-time intervals of the 1st observer's observation.
When the 1st observer observes an object for absolute-time intervals of , the 0th observer actually observes the object for absolute-time intervals of .


13.A difference in length of time intervals between two coordinate systems as a result of 'Lorentz transformation', which is a relativistic coordinate conversion from the 1st observer to the 0th observer, is the diffrence in length of absolute-time before and after a coordinate conversion on the condition that proper time intervals are constant regardless of a coordinate conversion.
However, it is wrong that we regard this difference as the difference in length of realistic time intervals. Moreover, it is wrong that we consider that time in a traveling coordinate system passes more slowly than time in a stationary coordinate system.
It is the reason that Lorentz transformation comes from an over-interpretation as follows :
Proper time intervals of an object may constant regardless of a coordinate conversion, because proper time intervals of traveling light are in all inertial systems.
In contrast, 'Bioring's Inertial Systems Theory of Relativity' comes from a selfish imagination as follows :
Proper time intervals of the traveling light, which is the fastest all over the world, are , and proper time intervals of a stationary object are equal to absolute-time intervals. Traveling space intervals of a stationary object are , and taveling space intervals of the traveling light are equal to absolute-time intervals. Therefore,


14.Space intervals and relative-time intervals, through which an object travels per certain absolute-time intervals, change in length owing to a speed of an object relative to an observer. That is, they change in length as a result of a coordinate conversion.


15.A difference in length of space intervals between two coordinate systems comes from disappearance of simultaneity as a result of the 'Lorentz transformation.' Space intervals never extend or contract as a result of a coordinate conversion.


16.If you observe your world obediently without comparing the space- time point on which an object exists in your world and the space- time point on which the object exists in other's world, and without comparing the action of an object in your world and the action of the object in other's world, we can observe correctly objects.


17.We must not observe the world from the point of view of the third party to find how an object gets an information or recieves a force as a result of a collision with other object, including elementary particles and electro magnetic wave. We must observe the world from the point of view of the person concerned. Theory of Relativity denies 'The objective observation from a point of view of a third party, i.e. Newtonian mechanics.'


18.We can observe a kinetic relationship between two traveling objects only from a point of view of a third party. Nevertheless, our world is not useless or empty. If we think from the point of view of the person concerned, we can discuss about physical phenomenon with others without reservation.


19.'Frequency of graviton' in an object, i.e. 'rest mass', is constant in all inertial frames of reference. 'Frequency on electromagnetic wave of photon' in a light source is constant in all inertial frames of reference. 'Frequency on electromagnetic field of photon' in an object with electric charge, i.e. 'quantity of electricity', is constant in all inertial frames of reference.


20.A number of vibrations of graviton in an object per unit absolute-time interval, in other words, 'frequency of graviton' , i.e. 'rest mass' , is constant, even if any observer traveling with linear uniform motion observes it. Vibration of graviton is compressed only in the relative-time direction, and then it transmits through space. It produces gravity.


21.A number of vibrations of photon on electromagnetic wave in a light source per unit absolute-time interval, in other word, 'frequency of photon on electromagnetic wave', is constant, even if any observer traveling with linear uniform motion observes it. Vibrations of photon on electromagnetic wave are decomposed into relative-time axis component and the space axes components, and then only the relative-time axis component of vibrations travels through space at the speed of light. It bears a role as light which is a kind of electromagnetic wave.


22.A number of vibrations of photon on electromagnetic field in an object per unit absolute time interval, in other ward, 'frequency of photon on electromagnetic field of', i.e. amount of electric charge, is constant, even if any observer traveling with linear uniform motion observes it. Vibrations of photon on electromagnetic field travel through space at the speed of light. There are two ways that vibrations travel as follows :
a ) Vibrations travel keeping a form as it is. It produces the
'Coulomb's force.'
b ) Vibrations are decomposed into relative-time axis component
and space axes components. Then only the space axes components
of vibrations travel. It produces the 'Lorentz force.'


23.A traveling magnetic field produces an electric field. And, a traveling electric field produces a magnetic field. Because, they are the identical quantity of 'electromagnetic field', and those composition ratios only change by the view.


24.The physical facter which produces 'Coulomb force' is not a quantity of electricity but a vector obtained by multiplying the speed of light by a quantity of electricity of the object. That is, the physical facter which produces 'Coulomb force' is a vector obtained by multiplying a velocity of an object traveling through four-dimensional space-time by a quantity of electricity of the object.


25.When an electric zero point is separated into the different signed numbers of electric charge, a magnetic field is produced. It is prescribed by a vector; we obtain this vector by multiplying a relative velocity of the separated positive electric charge relative to the separated negative electric charge by the separated quantity of electricity.


26.When an object approaching or going away from the observer A begins moving in the perpendicular direction in addition, the perpendicular speed of the object relative to the observer A is smaller than the speed of the object relative to the observer B traveling with the same velocity as the object before the perpendicular movement.
An object is traveling with linear uniform motion relative to the observer B. The observer A is traveling with linear uniform motion relative to the observer B. The movement direction of the observer A is perpendicular to the movement direction of the object. The perpendicular speed of the object relative to the observer A is smaller than the speed of the object relative to the observer B.


27.Coordinate conversion in 'Inertial Systems Theory of Relativity' is not general coordinate conversion. General coordinate conversion keeps magnitudes of optional vectors constant regardless of coordinate conversion. Coordinate conversion in 'Inertial Systems Theory of Relativity' keeps magnitudes of only optional position vectors of space-time points, on which traveling substances on linear uniform motion exist after being on the space-time origin, constant regardless of coordinate conversion.


28.An object, the 1st observer, and the 2nd observer are on the identical straight line in the following position :
The 2nd observerThe 1st observerAn object
They are traveling on linear uniform motion to the right side. The distances of each other are extending gradually.
Let be the speed of the object relative to the 1st observer.
Let be the speed of the 1st observer relativewith to the 2nd observer.
At the absolute-time point of , the object, the 1st observer, and the 2nd observer are on the identical space point.
We show space-time coordinates as follows :

The object is on the space-time point with the following coordinates at the absolute-time point of in the 1st observer's coordinate system :

The object is on the space-time point with the following coordinates at the absolute-time point of in the 2nd observer's coordinate system :

This coordinate conversion from the 1st observer to the 2nd observer is just a root of Inertial Systems Theory of Relativity.


29.Traveling is a change of space point on which an object exists. Traveling through space is a change of relative position between an object and an observer. It is relative in inertial system. That is, we can not decide either an object is traveling or an observer is traveling. It is a natural law that all things are traveling through space-time at the identical speed.


30.Lorentz transformation is not a tool for relativistic coordinate conversion but a tool for interpreting an observation of Newtonian mechanics and an observation of relativity. 'Complex number Lorentz transformation' is a tool for relativistic coordinate conversion, but it is not a realistic coordinate conversion, because it requires the imaginary number time. What can be a tool for realistic coordinate conversion of relativity is the mapping by rotation in four-dimensional space-time with one dimension of 'relative time.'




Reference

1.Lewis Carroll Epstein, Relativity Visualized, Insight Press, 1983


Note :The other references are written in a japanese page.




Postscript

I apologize for having used many laws made of my own idea without premission to make selfish interpretation of the special theory of relativity consistent.

When I was seeing a car running in the distance in a rice field in one evening of the rainy day, following idea suddenly occurred to me:
After all, a person in the car doesn't act slowly. What is important is not how I am observed by others, but how I observe others. That is, just an observer is the hero/heroin. An observer is observing many objects, including him/herself, at the same time. And also, an observed object is observing many objects at the same time. So, all objects must grow older equally. For that purpose, first, we must cosider that the 'extension of life span of muon' depends not on the general reason but on unknown reason. Second, we must adopt the view that Everything is constantly traveling through space-time at the speed of light. suggested by Epstein in the book of 'Relativity Visualized.' Third, we must not regard 'proper time' as inherent time, but regard 'time' as absolute time. Last, we must consider that a period of 'proper time' changes owing to a speed of an object relative to an observer; only when an object keeps still, a period of 'proper time' is the same as a pariod of 'time'.

I hope my misunderstanding brings your understanding of the theory of relativity.







Guidance of Inertial Systems Theory of Relativity was published in 2004.

Bioring

PREVIOUSCONTENTS