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 
        sound pressure. 
             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 
        experimental paths. 
             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 
        73513,216 .
        
                                           Sincerely, 
                                           Bob Canup
                                           73513,216