From: Ian Goddard (Ian@Goddard.net)
Date: Wed Nov 18 1998 - 01:32:02 MST
In his book "The Inflationary Universe" (Helix Books, 1997,
page 13) MIT physics professor Alan H. Guth discuses as fact
that the sum total of all energy in the universe equals zero:
"In 1973 [Dr. Edward] Tryon published an article in the
journal Nature, with the title "Is the Universe a Vacuum
Fluctuation?" He had understood the crucial point: the
vast cosmos that we see around us could have originated
as a vacuum fluctuation -- essentially from nothing at
all -- because the large positive energy of the masses
in the universe can be counterbalanced by a corresponding
amount of negative energy in the form of the gravitational
field." [IAN: thus the sum of all energy is exactly zero]
We might say that you can get something from nothing, if, and
only if, that something is equal to nothing, i.e., to zero.
Later in his book (pages 272-273), professor Guth states:
"[I]n any closed universe the negative gravitational
energy cancels the energy of matter exactly. The total
energy, or equivalently the total mass, is precisely
equal to zero.* With zero mass, the lifetime of a
quantum fluctuation can be infinite. . . .
* ...the fact that the total energy of a closed universe
is exactly zero had been explained some years earlier in
the widely known textbook, "The Classical Theory of Fields,"
Revised Second Edition, by L. D. Landau and E. M. Lifshitz
(Addison-Wesley Press Cambridge, Massachusetts, 1962),
pp. 378-379. "
You'll notice the stipulation that total energy equals zero in
any "closed universe." A closed universe will collapse in on
itself, but an open universe will continue to expand forever.
QUESTION: Would all energy in an Open universe equal zero?? <<---
Recent evidence -- the measured acceleration of universal
expansion -- tends to suggest that our universe is open.
So, does the zero-sum of energy hold in an open universe?
The case Guth makes for why gravitational energy is properly
denoted with in the negative (-) seems to apply to any universe.
GRAVITATIONAL ENERGY IS NEGATIVE
In Appendix A of The Inflationary Universe, Guth explains why
the proper sign for graviational energy is negative (-), which
Guth notes "is crucial to the notion of a zero-energy universe."
In his 5-page non-technical explanation of why gravitational
energy is negative, Guth observes the curiosity that in the
interior of a hollow, spherical shell of mass, there would
be no gravitational field exerted by the mass of the shell
itself; you'd be floating around inside it like an astronaut
in space (assuming that the shell itself is not in a g-field).
Yet the shell does create a gravitational field in its external
area, such that a particle outside the shell will fall toward
the shell, and toward the center of the shell, just as if the
hollow shell was a solid sphere with mass at the center.
But rather than falling to the empty center, a particle inside
the shell would experience zero gravity, since if it was inside
the shell closer to one side of the shell, the gravity of that
side is equally strong as the gravity of the larger amount of
mass on the other side that is further away, and so the grav-
itational forces from each side cancel out at any and all
points inside the mass shell. As such, the inside of the
hollow shell is an ideal example of a zero-gravity field.
Guth then observes that the shell still exerts a gravitational
force on its own mass, and the force lines of that force point
toward the center of the shell. Therefore, the shell will fall
into its center, or collapse, while keeping its same shape.
As Guth observes (in thought-experiment mode here):
"Outside the shell the gravitational field points
inward, and inside the gravitational field is zero.
Now imagine what would happen if the shell were
allowed to uniformly contract, keeping its spherical
shape. One can imagine, for example, extracting energy
by tying ropes to each piece of the shell... These
ropes can be used to drive electric generators as
each piece is lowered to its new position."
As the shell contracts to a smaller size, a region of space
that had been zero gravity and inside the shrinking shell is
now outside it, and that region is no longer a zero-gravity
field. As Guth notes, after the collapse "a gravitational
field now exists where no field had existed before." And
the inward "falling" shell has also released energy
that the hypothetical generators have extracted.
Guth concludes with this argument as to why the newly created
gravitational field is properly denoted as negative energy:
"The net effect of this operation is to extract
energy and to create a new region of gravitational
field. Thus, energy is released when a gravitational
field is created. The energy contained in the shaded
region must therefore decrease, just as the water
level in a tank decreases if water is released.
Since the region began with no gravitational field
and hence no energy, the final energy must be negative.
In most physical processes the exchange of gravitational
energy is much smaller than the rest energy (mc^2) of the
particles involved, but cosmologically the total gravita-
tional energy can be very significant." (page 292)
And presumably, the sum total of all gravitational energy is
exactly equal but opposite to the sum total of the positive
energy in all masses in the universe that create the cosmic
gravitational field, and thus the sum of all energy (and
equivalently of all mass) in the universe equals zero.
If you have or are aware of counter arguments to this zero-
universal-energy analysis, or if you know the answer to
the question cited above, please let me know. Thanks.
ZEROING In On Identity: http://Ian.Goddard.net/identity.htm
**************************************************************
Visit Ian Williams Goddard --------> http://Ian.Goddard.net
______________________________________________________________
The Utility and Value of Zero
" [T]he Indian sunya [zero] was destined to become
the turning point in a development without which
the progress of modern science, or commerce is
inconceivable. ... In the history of culture,
the invention of zero will always stand out
as one of the greatest single achi-
evements of the human race."
Tobias Dantzig
"Number, The Language of Science"
Macmillan Press, 1967
Zero: Gateway To Enlightenment
"He who contemplates on sunya...is absorbed
into space. . . think on the Great Void un-
ceasingly. The Great Void, whose beginning
is void, whose middle is void, [and] whose
end is void...By contemplating continually
on this, one obtains success [nirvana]."
The Siva Samhita (5:47,160,161)
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