WAVE MECHANISM OF MOVING BODY

Kapil Chandra

Guru Ghasidas University , Bilaspur (C.G.) INDIA

E-mail – dr_kapil_1@hotmail. com

Abstract

A relation for the wave and particle properties is derived,

when a body is moving with high velocity than the total energy or

Relativistic energy is the sum of two energy. Rest mass energy and

energy due to moving of body to accordingly Dual nature this energy is

wave properties energy, this leads us to a equation for wave and particle

properties of matter, which gives successful theoretical base for Bohr's

complementary principle and solve many drawbacks of De Broglies

dual nature equation of matter.

Introduction

It is a general question what is light wave or particle from

Einstein "Photo electric effect" light seems as particle [1] where as

interference of light show it as wave De Broglie did in 1924 when he

proposed that moving object have wave as well as particle charestenic.

A moving body behave in certain ways as though it has a wave nature

[2] according to this hypothesis when the velocity of particle increase its

wave properties increase and the total energy of moving body also

increase as here we assume what when particle propagating with

Relativistic velocity than total energy at moving body can express

accordingly Einstein Relativistic Energy [3].

From Einstein's "Special Theory of Relativity" the

relativistic Energy is given by the equation

E2 = m

20c

4+m

2v2c2

_____________________(1)

But we know that for a electron

h ______________________(2)

Kπx C3

Where K = 9.433 M-1LAT

X = 1.03 TA1 L

-2

Eliminating mo from education (1) with inserting value from

equation (2) we get

hc m2v2c2_______________________(3)

Kπx

Above equation RHS show the first term Rest mass energy and

second term show Energy due to moving of body, rest mass energy

must be always constant but second energy term is variable respect to

the velocity. Here we assume that if accordingly De Broglie Dual

nature relation moving body propagate as wave so we take the energy

due to moving is wave properties energy at propagating body, Here we

assume that the below relation must be satisfied the equation 3.

λ

Kπx

λ ________________(4)

Kπx

This equation show wave properties energy of moving

body. Here a point is notable that is wave properties are the

E =

Mc2 = = E

E2 =

M20 =

+

wavelength of massive body. This is not similar to the wavelength of

radiation it is complete different wave properties it is directly

proportional to the energy.

Now we will discuss about the dual nature equation. First

at all we will derive relation between mass & wave properties of matter

above relation can be derived by

λ

Kπx

λ

m

above relation called WAVICLE equation .

From above relation it is clear that when the velocity of particle

increase its wave properties increase, and when velocity decrease its

mass properties increase, above relation is proved itself we don't need

verification.

Advantage of Wavicle Equation

There are many advantage of wavicle equation with

respect to De Broglies dual nature relation according to De Broglie's

equation

h _____________________(6)

mv

From above equation it is clear that when any body at

mass m moving with the velocity at than what would be the wavelength

λ =

= v CKPlx _____________________(5)

mc2 =

C ≡V

at matter wave which can be computed from equation (6). De Broglie

relation inform us about mass & wavelength of moving particle just, but

the wavicle relation give us information about the wave & mass

properties at moving body.

THEORETCAL MATHEMATICAL BASE FOR BOHR'S

COMPLEMENTY PRINCIPLE

The wavicle equation provides us the base for

complementary principle according to this principle wave & particle

properties are complement to each other or we cannot measure both

wave & mass properties at matter with same experiment in same time.

From equation –(5)

λ

m

From above it is clear that it we measure wavelength than

propagating matter will be wave so it associate mass properties, it is

not mass just like as a mass of wave and we can not measure direct to

it same procedure in another next case if we measure mass than

moving matter will be particle it associate wave properties due to

motion which can not be observed. But accordingly dual nature of De

Broglie, matter associate both wave to mass so we can measure both

in same experiment which contradict to complementary principle.

= V

KπxC

Explanation of Relativity of time

De Broglies dual nature relation can not count for Einstein

relativity of time which as follow

According to De Broglie hypothesis

MoC2 = hν _____________________(7)

So here

mo

√ 1-v2 /c2

and same as

νo

√ 1-v2 /c2

but from Einstein's relativity at time

ν = νo √ 1-v2 /c2 ___________________(10)

It is clear from above discussion that equation (9) to (10)

are contra to each other this contradiction can be end by applying the

wavicle equation 5

λ

m

from above equation

= VC Kπx

ν =

m = ___________________(8)

__________________ (9)

mo

√ 1-v2 /c2

ν = νo √ 1-v2 /c2___________________(11)

Hence it is proved that equation (10) & (11) are same so

it prove the equation (5) is true.

Conclusion

From the above discussion we conclude that when a body

is moving with high velocity it associate wave properties, which is

complete different form introduced by De Broglie dual nature this wave

properties is directly proportional to the energy, main difference

between De Broglie's Dual nature & wavicle theory is that former

provide equation for calculating matter wavelength and latter relates

wave properties & mass properties. Wavicle equation we can't prove

directly because we can not measure or detect to the wave or mass

properties by experiment they are just can be feel very important

aspect of wavicle relation is that it give mathematical base for

complementary principle & relativity at time in the word of wave

mechanism very important conclusion we find the relativity also follow

the wave mechanism of matter. Above hypothesis connect to Relativity

& Wave mechanism.

m =

Reference

[1] A. Einstein, Ann.d.phy(4)77,132 (1905)

[2] L.Debroglie , Thesis , Paris, 1924

L. Debroglie , Ann. D physics (10) 3,22 (1925)

[3] H.M. Schwariz "Introduction to Special Relativity" Chp. 3,4,8

(Mc Graw – 414 , New York 1968 )

P.G. Bergmann "Introduction to Special Relativity" , Pt. I

(Prantice – Hall Engle wood eliffs , N.S. ,1946)

C.M. Llar , "The theory of Relativity" Chap I-II (Oxford, Londan,

1952)

[4] L.I. Schiff "Quastum Mechanics " 3 ed. McGraw 414 Singapor

1968

[5] A. Beiser , "Concept of Modern Physics"

TATA Mc Craw –414, 5, Ed. New Delhi , 2003

[6] Tipler "Physics" Vol.2 , Worth Pub. New York, 1976

[7] Bondi Hermann: Relativity Common Sense, A new Approach to

Einstein , Doubleday , Gardeneity Ny , 1964

[8] G. Stanely ,"understanding Relativity" Birkha euser,Bostan ,

1984"

[9] F. Gerald , "Light" Scientific American Septemember 1968 , P-

50

[10] IA. Wheeler "Neils Bohr, THE man" Physics today Vo. 38 No.

10,1988

[11] M. Planck , Ann. D . Physics (4), 4,553 (7901)

[12] www.wbabin.net/physics/chandra. htm