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Violation of conservation of energy?
The enclosed paper outlines a discovery which I made in
1984. I have spent the last 10 years trying to understand how
this discovery fits into the overall scheme of things.
Since I lack formal credentials in physics there is no
chance of getting this paper published in any scientific journal
regardless of its merits. Science is a very closed circle -
laymen with troubling discoveries are about as welcome as a skunk
is at a picnic.
I am placing this work out on the computer networks in the
hope that someone will be able to show me what I am doing wrong -
or at least comment on what I have done.
I will worn you before you get started that demonstrating an
error in my work is not going to be easy: I'm a fairly bright guy
and I have spent a long time investigating the case I describe.
I once showed this work to a very well respected nuclear
physicist. He quickly wrote down the equations describing the
case. We talked about it for an hour and a half. He never said
anything about it that I didn't already know. He was so disturbed
by my discovery - even though he agreed his equations predicted
exactly the result I had discovered - that he finally wound up
saying: "I don't want to talk about this any more. This can't
possibly be true."
Abstract: A thought experiment which appears to show a
violation of conservation of energy is outlined.
Working with computers soon leads one to realize that estab-
lishing a set of rules governing the behavior of the machine
(i.e. writing a program) will very often lead to situations where
the machine will produce unexpected results. These "bugs", as
they are known, occur as a result of establishing rules for the
behavior of the machine, and are not the result of programmer
errors. Almost any program that can be written for a computer has
boundary conditions under which it will fail. In pure mathematics
dividing a quantity by zero will produce unexpected results. In
essence division by zero is a boundary condition which causes the
algorithm of division to fail. It is apparent that establishing
mechanical rules for the behavior of objects in the real world
has inherent possibilities for creation of situations in which
unexpected results may occur.
In physics, the conservation of energy hypothesis can be
viewed as a statement that there exist no boundary conditions
under which the algorithms for the calculation of energy produce
unexpected results. A simple experiment can be constructed which
demonstrates that at least one boundary condition which causes
unexpected results does exist, and that the conservation of
energy hypothesis is incorrect.
If measurements are made of the sound field surrounding a
speaker radiating a single frequency sound at a constant power
level into an obstruction free space, the following first order
approximations will be found to hold: 1. Power from the speaker
flowing through a fixed unit of area of the surface of a sphere
of radius 'r' centered on the speaker will be proportional to
1/(r^2). (The inverse square law) . 2. The amplitude of the sound
pressure from the speaker at a distance 'r' from the speaker is
proportional to 1/r. From these measurements it can be deduced
that the power flowing through a unit area of the surface of a
sphere surrounding a speaker in obstruction free space is pro-
portional to A^2, where 'A' is the amplitude of the sound pres-
sure caused by the speaker. Doubling the amount of power sent to
the speaker causes the power in the sound field produced by the
speaker to double; hence the sound pressure in the field has been
increased by a factor of the square root of two over the previous
If one now considers the case of two speakers located a
distance 'd' from each other, which are both producing the same
single frequency signal, the resultant sound field at the surface
of a sphere 's' of radius 'r' centered on the line connecting the
two speakers - will show interference effects from the two radia-
tors. Each speaker can be regarded as producing the same sound
field that it would produce were the other speaker not present.
The composite signal produced by the two speakers is the vector
addition of the pressure fields produced by the two speakers. In
areas where the sound waves are in phase the power level ap-
proaches a value of four times the amount which would be produced
by a single speaker alone. In areas where the sound waves inter-
fere destructively the limit which is approached is that no sound
may be found. Thus the energy which is missing from the case of
destructive interference, may be found in the regions of con-
structive interference. Integration of the total power flux in
sphere 's' surrounding the speakers would show the flux total to
be twice as great as the flux which would be produced by a single
speaker - thus supporting the conservation of energy hypothesis:
since it would be expected that the power level produced by two
speakers would be twice that produced by a single speaker. If the
phase of the signal to one of the speakers is reversed then it
will be noted that the regions of interference switch; what were
regions of constructive interference become regions of destruc-
tive interference, and vice versa.
If the distance between the speakers is held constant, and
the frequency of the of the sound produced by the two speakers is
decreased; fewer and larger interference patterns occur on the
surface of sphere 's' . If the wavelength of the sound being
produced is increased so that the distance 'd' between the speak-
ers is less than 1/4 of the wavelength of the sound then an
interesting phenomenon occurs. If the speakers are in phase with
each other then the sound field at the surface of sphere 's' is
everywhere the result of constructive interference. Conversely if
the speakers are wired out of phase the sound field at the sur-
face of sphere 's' is every where the result of destructive
interference. In the first case the power in the sound field
approaches 4 times the power produced by a single speaker. In the
second case the power in the field approaches 0. It can thus be
seen that the power missing in the case of total destructive
interference can be found in the case of constructive interfer-
ence. Thus the algorithm for the calculation of the energy in the
field is maintained. Since for a given pair of speakers either
the speakers are wired in phase, or out of phase, the unexpected
result is that the speakers are either producing more power than
the total of the power fed to them, or the power being fed to
them is disappearing. This is a direct violation of the conserva-
tion of energy hypothesis, and serves to be sufficient to cause
the rejection of the hypothesis.
If you attempt to actually construct the thought experiment
outlined - you will discover that the results of free field
measurements are in line with the thought experiment. I original-
ly made the discovery from an accidental physical experiment.
The only thing that I have not done is to construct a calo-
rimeter to measure the total energy involved. This would be a
fairly difficult and expensive thing to do: requiring an anechoic
absorption material matching the impedance of the air to prevent
multiple interference patterns, a vacuum thermal seal to prevent
energy leakage, and delicate temperature measurements. I am
prevented only by utter poverty from conducting such an experi-
ment. I would ask that you contact me before starting off on a
verifying experiment - I can save you some time chasing false
By the way, I think that I now understand how this discovery
fits into the overall scheme of things in physics: it makes
sense to me. I believe that I understand why nature would choose
to violate conservation of mass-energy in such a mundane place as
acoustics, and not in some esoteric case near the speed of light,
or in the heart of a nucleus. I'll be happy to talk about what I
think is going on to anyone who is interested.
This text was originally up loaded to CompuServe's Mensa
forum on November 4, 1994. I hope it is placed on the Internet
where it may be seen by those in Academia who may be interested.
Please direct comments to my CompuServe mail account. My
name is Robert E. Canup II, and my CompuServe number is
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