**ON
THE FORMULA E = mc**^{2}
GS
Trần
Cao
Tần
Tiến Sĩ Toán học
Giáo sư Toán Đại học Loras
tại Iowa, Hoa Kỳ
** **
**
ABSTRACT**
In 1906
Einstein published a proof of the formula e = mc^{2}
in a thought experiment of an isolated tube with two masses
at the two ends, one of which emits radiation inside the
tube toward the other end. A.P. French pointed out three
problems in that proof:
1/ the
length L of the box suffers a contraction according to the
Theory of Special Relativity,
2/ the
velocity of radiation in the box is less than c,
3/ after
the emission of radiation, the mass of the box is M-m.
Then
instead of a box in the thought experiment of Einstein,
French considers two separate masses, one of which emits
radiation toward the other to fix the three above problems.
But I
still find three more problems in the proofs of the Einstein
and French:
4/ the
conditions set up in the two thought experiments do not
guarantee that the center of mass of the system is always at
rest,
5/ the
proofs do not study the motion of the radiation between the
two masses,
6/ the
proofs do not consider the effects of gravitation.
In this
paper I introduce a thought experiment with two masses which
both emit radiations in opposite directions so that
initially the center of mass does not move. Then I envisage
that one mass is placed initially farther and farther so
that it becomes smaller and smaller, and finally tends to
zero. At the limiting case I get the formula e = mc^{2}.
Note that the proofs of Einstein and
French use concepts of relativity while mine uses only
classical mechanics of and the principle of gravitation. I
conclude that the formula e = mc^{2} is true in the
absolute sense.
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On The Formula: E=mc^{2}
GS
Trần
Cao
Tần
Tiến Sĩ Toán học
Giáo sư Toán Đại học Loras
tại Iowa, Hoa Kỳ
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