*by Nobuo Miyaji e-mail nobuo.miyaji@hotmail.co.jp*

**What is rest mass ?****dated June 20th 2012**

**Preface**

Many people get confused about the concept of rest mass in the theory of Special Relativity.

Scientists have also deliberated over a rest mass (Gary Oas1, L.B.Okun2 , Max Jammer3).

A single rest mass has been thought to be equivalent to rest energy because relativistic mass is divided into rest mass

and kinetic energy according to Taylor expansion. However, there remains a question on what rest mass is. This article aims

to indicate the concept of rest mass. The common definition that rest mass is the observed mass with no kinetic energy is not

complete. A group of moving masses with arbitrary velocity also forms an equivalent rest mass.

Relativistic mass and its momentum are defined as a vector of Lorentz transformation. Developing this concept, there is

a possibility that a single rest mass is resolved into a group of small rest masses, furthermore, resolved small rest mass is

also repeatedly resolved into smaller moving masses. A single rest mass contains confined kinetic energy. In other words, inner kinetic energy is the composition of rest mass (rest energy). For example, a stationary object is also composed of numerous molecules which have active molecular motion by thermal energy. This energy of confined motion is a part of rest mass. The procedure of decomposition of the molecules means that rest mass of the molecules is resolved into moving atoms which contain kinetic energy and rest mass.

When we consider photon, we cannot see the light resting because light speed is maximum. All of the photon energy

is attributed to momentum not to rest energy. Rest mass of a certain object except for photon can be observed if we can pursue moving mass and see it resting. In this case, we can say its macro momentum is zero because its position is not

moving. However, we must remember inner part of rest mass has momentum in the micro world. If the total of momentum of

micro world is zero in our stationary coordinates, observer considers it to be resting. According to this concept, it is proved that rest mass has kinetic energy by mathematical analysis.

**(Please click on page2-6)**

## *Hexagonal resolution of rest mass*

*Hexagonal resolution of rest mass*

**Contents**

1. Preparation for modeling of a group of mass

2. Application of Lorentz transformation for a group of mass

3. Extension of the theory to x-y-z three dimensional space

4. Increase of energy in the system is equal to increase of mass in case of free particles (dE=dM=FdX)

5. Modification of F=dP/dt=d(MV)/dt in the theory of special relativity

6. Resolution of rest mass

7. Existence of stationary object in Minkowski space-time

8. E=M=P in case of light

9. Conclusion

10. Postscript

11. Appendix 1 ( Proper time )

12. Appendix 2 ( Lorentz contraction )

13. Appendix 3 ( Time dilation )

14. Appendix 4 ( Spherical light wave )

15. Appendix 5 ( Accelerated motion in special relativity )

16. Appendix 6 ( Variation of relativistic energy observed from different inertial frames )

17. Appendix 7 ( Introduction of relativistic mass 's formula )

18. Appendix 8 ( The difficulty of concept of rest energy in Newtonian mechanics )

19. Appendix 9 ( Exponential summation of zero rest mass )

20. Appendix 10 ( Transmission of momentum in one dimensional object )

21. Appendix 11 ( Four-vector expression by Lorentz transformation in t-x-y dimension )

22. Appendix 12 ( Lorentz contraction of distance between moving objects )

23. Appendix 13 ( Increase of inertia caused by the excitation of inner kinetic energy )