In the journal "Nature" (12/14/73), Dr. Edward Tryon presented the theory that the sum of all energy in the universe is zero. Below is the mathematics behind that theory, quoted from the paper "Genesis of The Universe and Zero Point Energy" [*] (I would be very interested to hear any critiques of it):
"In 1973 the great contemporary scientific
thinker Edward P. Tryon demonstrated how the
universe could have formed [ from nothing ]
without violating the principle of the
conservation of energy. He said that the
total energy of the universe is zero. [1]
He said that the positive energy of the things
we observe is balanced by a negative gravitational
energy. Therefore the creation was formed without
violating the principle of the conservation of
energy. Let's explore his idea. When something
falls it loses gravitational potential energy.
The relationship between potential energy and
position, in a force field, is given by equation #1.
[ fixed-pitch font required ]
/
| -> ->
/\ PE = W = - | F . dr Eq #1
g | g
/
According to Tryon's theory if an object were to
fall into the universe from an infinite distance
away, the gravitational potential energy the object
lost would equal the total mass energy of the object.
[2] This is stated mathematically in equation #2:
/ rad of univ
| -> ->
mc^2 = - | F . dr Eq #2
| g
/infinity
Assuming that the universe is spherical with an
isotopic mass distribution, the amount of gravita-
tional potential an object will lose upon falling to
the edge of such a universe is given by equation #3.
/ rad of univ
|
mc^2 = -(G)(M)(m) | (1/r^2) dr Eq #3
|
/infinity
Given a radius of the universe is 15 billion light
years (1.42x10^26 meters) and the known gravitational
constant G, the mass of the universe may be determined.
M = 1.91 x 10^53 KG
If this is the mass of the universe then the total
energy of the universe is zero. To check this result
the mass of the universe was calculated from its den-
sity and volume. The universe was considered to be a
sphere. This sphere has a radius of 15 billion light
years and is filled with matter of the same density as
the density of space in our galactic neighborhood.
This "local" density is equivalent to one proton of
ordinary matter and nine protons of "dark" matter
per cubic meter. [3]
Given that the volume of a sphere with a radius of 15
billion light years = 1.2 x 10^79 M^3
Please note that at one proton mass per cubic meter
this is also the number of protons in the universe.
The mass of the universe was derived from its volume
and density in equation #4.
Eq#4
M = ((1 proton/m^3) +(9 proton masses dark matter/m^3))(vol)
The mass of the universe according to this second
argument is:
M = 2.00 x 10^53 KG
Amazingly the resultant masses agree even though they
were determined by two entirely different methods.
This agreement indicates that the universe has a total
energy of zero and that it formed without violating
the principle of the conservation of energy. There
is something very profound in what Edward Tryon said.
CONCLUSION
New scientific arguments have shown how something can
be created out of nothing. These arguments have tre-
mendous philosophical implications. ...
NOTES
[1] Edward P. Tryon, NATURE VOL 246, December 14, 1973.
[2] Technically, nothing can exist outside of the
universe. The universe is a closed structure in which,
according to the cosmological principle, all positions
are equivalent. The model presented in this paper, in
which an object falls from an infinite distance away to
the edge of the universe, does not represent reality.
The model does, however, allow for the calculation of
the negative gravitational potential shared by all
objects within the universe.
[3] Fritz Zwicky proposed that 90% of the matter in the
universe is "dark" in 1933. He came to this conclusion
from the study of clusters of galaxies.
Vera Rubin confirmed that 90% of the universe's matter
is composed of the so called "dark matter" from her study
of the rotational speeds of galaxies in 1977."
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[*] Source: http://www.eskimo.com/~billb/freenrg/zpepaper.txt
2
NOTE: I changed the awkward use of exponents as mc
to the more standard ascii-style exponent notation: mc^2.
I also took the liberty to insert footnote 2 where it seems
to be properly indicated, since it never appears in the text.
I also placed the footnote-numbers in brackets, for clarity.
"He who pursues learning will increase every day;
he who pursues Tao will decrease every day."
Lao Tzu (Tao Te Ching)