Natural Science Forum / Physics / Relativity / September 2006

When light energy is emitted, Mass increases,: Einstein’s Sep.1905
derivation.
  It is not consistent prediction from Einstein’s Sep 1905
derivation.
                          (written in response to comments)
 How   eq.(13)  at page 201 in my paper I incorrect ? Then what is
correct equation?
In fact Eq.(13) in paper at page 201 is correct absolutely.

””””Eq.(13)  is based of Einstein’s Sep 1905 derivation ,
that THEORETICALLY  when body emits Light Energy , the mass of body
INCREASE  in some cases.”””””””
It is explained below in THREE SECTIONS.
                                  Section A.
(i) Einstein has considered A body of mass 10gm (say), it emits two
waves under special conditions (two waves of equal energy L/2 each ,
emitted in  opposite directions  w.r.t measuring system) . Obviously
mass decreases, which is converted to light energy and Einstein‘s
equation is
          L =dmc2
Energy emitted = decrease in mass .c2         (1)
(ii) If we  consider the same body  , it emits light energy at angle 90
w.r.t  to the moving system , then again Einstein’s derivation gives
L =mc2
Energy emitted = decrease in mass .c2          (2)
Both the cases are correct . Eq.(2) is not derived by Einstein.

Einstein’s 27 Sep 1905 paper available at
http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

(iii)  If we  consider the same body , it emits light energy at angle
90 o w.r.t  to the moving system , then again Einstein’s derivation
gives

Ho = H1 +  β L( 1 – v/c cos89 o)
Ho = H1 +  β L (1– 0.017452406 v/c)
 Now proceeding as in Eq.(5) to Eq.(10) we get
     Δ m =  –  0.03490L/cv + L/c2                        (13) at
page 201 of paper
Thus Einstein’s derivation implies that when body emits light energy
at angle 89 o then its MASS must INCREASE. If this angle is 0 then
Einstein’s derivation implies that  when Light Energy is emitted ,
mass decreases.

Sharma June 2004 paper is available
http://www.burningbrain.org/pdf/ajaysharma_einstein.pdf
For further elaborated discussion link is

https://www.novapublishers.com/catalog/product_info.php?cPath=23_48_324&products
_id=4554

Thus Einstein’s derivation is not true in general, it holds good
under special conditions only.
I have given 2nd and 3rd example purposely that up to which extent
Einstein’s derivation depends upon angle.  Angle up to 90 o is OK in
Einstein’s derivation of Sep 1905. If it slightly decreases (even
89.9 o ) then, then RESULTS ARE CONTRADICTORY  to results.

                                 Section B
It is crystal clear that  as Einstein’s  derivation as applicable to
first  example  ( two waves of equal energy  L/2 each , emitted in
opposite directions  w.r.t measuring system) and  second example ( a
single wave of energy L  emitted at  89 o or 89.5 o w.r.t  measuring
system ).Thus  Einstein’s derivation  is also applicable to  third
example (a single wave of energy L  emitted at  89 o or 89.5 o w.r.t
measuring system).

As results are inconsistent then it is due to LIMITATIONS of
Einstein’s derivation only, as it is equally applicable in all the
three cases.
                                            It is explained below that
law of ‘conservation of momentum’ holds good and ‘conditions of
applicability’ of Einstein’s derivation are applicable to ALL THREE
CASES.

                                            Part I
(a)    Law of conservation of momentum is obeyed completely.
Conservation of momentum is meant for isolated system and
mathematically implies that
       Initial Momentum = Final Momentum           (3)
              mu=mv
As mass remains same in classical mechanics.
So   u=v
which is Newton’s First law of motion
It is used to calculate the velocity of recoil of body after emission
of energy in any way.

--It is applicable if body moves or remains at rest after emitting
energy.
Einstein has done the case when body remain at rest ONLY, I have
extended to it even if MOVES.
Take example of
-----Shot fired from gun, gun moves backward.
------ Light bullet fired from TOY Gun, system remains at rest.
Momentum is conserved in ALL THREE CASES and velocity of recoil is more
or less can be calculated using Law of conservation of momentum. This
is the use of law of conservation of linear momentum in this case.
As Einstein did all CALCULATION UNDER CLASSICAL CONDITIONS, hence net
REALTIVE velocity of body after recoil must be in classical region.
Again as Einstein did calculation under CLASSICAL CONDITIONS then
momentum variation has no effect on MASS.

                                          Part II
Einstein’s derivation is applicable when body remains at REST or
MOVES.
The basis for this TRUTH lies in Einstein’s derivation. Purposely and
Especially eq.(1) shown below which is applicable  for one or  n waves.
(i)  The central equation in Einstein‘s equation is

 l* = l{1 – v/c cos φ } /√[1 – v2 /c2]       (1)      at page
196 of the paper.

This equation is from Einstein’s June 1905 paper AND Einstein used it
in derivation of   L =mc2.
With this equation magnitude of light energy is measured when one there
is relative velocity between light emitting body and measuring system.
                 Einstein considered two frames i.e.  (x,y,z)  at rest
(body placed in it)  and second frame (X,Y,Z) moving with velocity v (
measuring system) .
Let body moves with velocity v’, then relative velocity will be
v+v’  and eq.(1) becomes

l* = l{1 – (v+v’) /c cos φ } /√[1 – (v+v’)2 /c2]    (4)

So  after emission of light energy, body  remains at REST or MOVES,
eq.(1) [ at page 196 of paper ]  is  applicable.
When ever under any condition, body emits light energy, EINSTEIN’S
Sep. 1905 must give that MASS MUST DECREASE.

Thus out of three cases first one (two waves) , second one (for one
wave) interpretation for  Einstein derivation is correct. How it
becomes incorrect for third case (one wave, with angle difference of 1
or less) becomes incorrect.
It is limitation of Einstein’s derivation.
Thus Einstein’s Sep 1905 derivation is correct UNDER SPECIAL
CONDITIONS not in GENERAL.

          Explanation for eq.(16) in paper at page  202.
                              Consider two waves  of energy 0.5001L
and 0.4999L , then apply law of conservation of momentum the velocity
of  RECOIL can be calculated as
          Vr = 1/10000000000000000000000000000000  = 10-^32 m/s.
Now  v+v’ =  v +10-^32
So eq.(1) is valid whether  body is  at REST  or  MOVES  after emission
of light energy.
Einstein’s derivation of L =mc2, the body may remain at REST or
MOVE, is applicable there is no rule of science which stops it.

                          Section 3
                                Part I
Thus it is concluded that Einstein’s derivation has four variables
(i)  Number of light waves
(ii)  Magnitude of energy of light waves
(iii) Angle at which light energy is emitted
(iv)  Relative velocity v  ( must be in classical region).

All these variables in Einstein’s Sep 1905 derivation have numerous
values. Energy may be emitted in any way, the mass of BODY DECREASES
experimentally ALWAYS.

        But THEORETICALLY according to Einstein’s 29 Sep. 1905
derivation, in every time, result is not  eq.(1) .
L =mc2
Energy emitted = decrease in mass .c2         (1)
Einstein’s Sep. 1905 derivation also predicts MATHEMATICALLY that
when body emits Light Energy its mass must also INCREASE.  It is not
true.
Hence Einstein’s derivation is true under special conditions only.

                               Part II

                  In addition after deriving
L= dmc2     (1)
Einstein simply replaced L and SPECULATED ( not derived)
E=dmc2
where E  is EVERY FORM OF ENERGY ( light energy, heat energy, sound
energy,  chemical energy in form invisible radiation  etc.).  However
basis for derivation of eq.(1) is only for light energy eq.(1) at page
196 of my paper.

Thus we need to derive mass energy equation by other method and
generalized equation is
dE =Ac2 dm
where A is coefficient of proportionality, like others in the existing
physics and its value depend upon experimental conditions.
For details
https://www.novapublishers.com/catalog/product_info.php?cPath=23_48_324&products
_id=4554

References of Einstein’s work
.
A.Einstein,   Annalen der Physik     18      (1905) 639-641.
.  DOES THE INERTIA OF A BODY DEPEND
UPON ITS ENERGY-CONTENT?
Weblink is
Einstein’s 27 Sep 1905 paper available at
http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

                                PartII
   References of Ajay Sharma’s work

My work is available at
A. Sharma,  Physics Essays, 17   (2004) 195-222.
”The Origin of Generalized Mass-Energy Equation E = Ac2 M; and
its applications   in General physics and Cosmology”.
http://www.burningbrain.org/pdf/ajaysharma_einstein.pdf
For details
https://www.novapublishers.com/catalog/product_info.php?cPath=23_48_324&products
_id=4554

                                 International Conferences
It has been accepted for presentation over 55 conferences all over the
world
--------------------------------------few of them
1.  Sharma, A. presented in 19th International Conference on the
Applications  of  Accelerators  in Research and Industry ,  20-25
August , 2006 Fort Worth Texas,  USA

 2.  A. Sharma,   Abstract Book  38th European Group of Atomic Systems
(
Euro physics   Conference)   Isachia (Naples)   Italy   (2006) 53.

3. A. Sharma  , Abstract Book , A Century After Einstein Physics 2005 ,

10-14 April 2005 (  Organizer  Institute of Physics , Bristol )
University of Warwick , ENGLAND

4. A. Sharma  presented in 5th British gravity Conference , OXFORD
ENGLAND

5.  A. Sharma,. Proc.  Int. Conf. on Computational Methods in
        Sciences  and Engineering 2003 World Scientific Co. USA ,
(2003) 585.

6.  A. Sharma,  Proc. Int. Conf. on Number, Time, Relativity United
        Physical Society of Russian Federation, Moscow ,  (2004) 81
 plus more
--------------------------------------
                                Journals
This paper
”The Origin of Generalized Mass-Energy Equation E = Ac2 M; and
its applications   in General physics and Cosmology”.
is published in journal
  Physics Essays , CANADA
www.physicsessays.com
The paper
The past ,present and future of E=mc2
will be published in 2007 Galilean Electrodynamics, Massachusetts,
USA.
In parts it is published in various others journals.
----------------------
                              Book    100 Years of E=mc2
For details
https://www.novapublishers.com/catalog/product_info.php?cPath=23_48_324&products
_id=4554