Violation Protocol

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Gravitational Energy Creation by a Free and Ordered Redistribution of a Coherent Interfering System


© Thomas Alexander Meyer


The Protocol


  In this protocol we wish to create energy by virtue of a redistribution of a physical system by setting it up to be a coherent quantum mechanical system which displays interference.  We will show that the ordered redistribution of the system which happens when a massive system is prepared for interference is also in fact a creation of gravitational energy of the system.  We begin with a simple interference effect as is illustrated in Figure 1 where a source of heavy molecules are prepared in a beam with a specific state description.  For convenience, we consider the system of this idealized interference effect and its preparation to be the only existing entities in the universe, so we assume no other systems to be present.

The source in Figure 1 is a heavy molecule which may still display interference.  The beam of molecules is directed at an aperture with a double slit and beyond this double slit is a distant screen where the molecule's positions are measured.  The distance of the screen to the aperture is assumed to be large enough that the "far field" approximation applies and interference fringes will appear in the measurement of molecules on the screen.  In this simple interference effect we will have a measurement of molecules on the screen which resembles the illustration in Figure 2(a) below.  If we prepare the system in such a manner that we measure the slit which the molecules pass through then we will have the non-interference measurement of molecules at the screen as is illustrated in Figure 2(b).

The results of measurement in the two preparations is greatly different.  In (a) we have a preparation for interference and the result is the presence of fringes in the detection of molecules at the screen (where the light areas indicated increased rates of detection and the dark areas indicate decreased rates of detection).  This may be calculated in the detection probability which may be shown to have a dependence upon the position across the screen and the frequency of the molecule.  The results depicted in (b) represent the preparation for non-interference where there is no such dependence of the detection probability on the position across the screen.  In this preparation we simply have an even distribution of molecules across the screen.  This preparation is setup with the additional apparatus required to measure the presence of the molecule passing through one of the slits.  This would make it in principle possible to determine the path which the molecule took prior to its arrival at the measurement screen.  This "in principle knowledge" of the path of the molecule is what "wipes out" or destroys the interference effect.  There are many ways to prepare the apparatus for knowledge of path and the destruction of interference, but the method of choice is of little interest here.

  We should note that the illustrations of Figure 2 only show a small portion of the total screen, so we assume that there is a much greater area of the screen that is covered by the molecules but we do not show this in FIgure 2.  It is also the case that as the position on the screen gets further away from the center of the screen (where the slit aperture is centered) the detection probability of the molecule's position will fall off exponentially.  The actual detection probability is a gausian which is centered on the screen but we do not illustrate this phenomenon in Figure 2.


Gravitational Considerations


  So, we must wonder whether there is in fact an increased gravitational energy that results from the distribution of molecules in the two possible preparations (remembering of course that we have considered this idealized thought experiment to only include the necessary apparatus as the whole of the universe).  We also point out that the measurement screen will force the molecules to terminate their propagation forward to a point beyond the screen, which would allow molecules to accumulate in the distribution predicted for the preparation in the event that we would run such an experiment.  Assuming we run such an experiment, in preparation (b) we have a uniform distribution of molecules which has a gravitational potential which results from the attractive forces of gravitation that are exerted form one molecule to another.  This distribution results from preparing the system for non-interference and it is identical to the distribution of the system that we would expect to be measurable at the time of emission.  In (a) we have the preparation for interference, which results in a non-uniform distribution of molecules which will also have an associated gravitational potential between the accumulated molecules.  So we would ask, what is the total energy associated with the gravitational potential for an experiment including N molecules for the two possible preparations?  Is the total gravitational energy associated with the two preparations different?  Basically the answer is yes, there is a difference between the two, and it is always the case that the "less-uniform" distribution will have the greater total energy associated with its state.  To put it bluntly, to locally "bunch up" or order the system requires energy put into the system, if we assume that the system is distributed over the same volume or area in the two cases.  In the two cases of (a) and (b) the total system is distributed over the uncertainty in position and this uncertainty is the same for both cases, and it is only the distribution within this unceratainty that changes.  With the screen area staying constant, the ordered distribution of state (a) is a state of much higher total energy than the energy of state (b).  The total energy created in the experiment is equal to the difference between the total gravitational energy of the two states/preparations.




  We might choose to remark at this point that the increase in energy is directly proportional to a decrease in entropy of the system, as the entropy or disorder of the system decreases the energy increases (or at least this would be the expectation).  This may be relatable to the laws of thermodynamics which predict that the total entropy change associated with a change in preparation will always be positive.  But this is thermodynamics, which is classical and strictly not quantum mechanical.  There is the Von Neumann entropy and the quantum mechanical entropy evaluated on principles of information and the number of degrees of freedom of the system, but these concepts of entopy cannot be reconciled with the classical laws.    So we consider what is happening in our thought experiment where there seems to be an increased order of the system.  I say there is an increase in order because the positional distribution has fringes which are ordered.  We should note first that the preparation for interference only requires a lack of path knowledge.  The lack of path knowledge leads to a different state description where we may calculate a different detection probability that has the fringes.  In interference effects we begin with a source and then we "split up" the source into multiple paths (we use the double slit aperture for this) which leads to a single pure state with a new multiple path basis.  So I would ask, do we consider this is a state of increased disorder or entropy?  Does splitting the system increase the entropy because it adds a degree of freedom with an expanded basis?  Anyway, after splitting the system is then prepared so that the paths are recombined at some point where there is a measurement.  The recombination will actually negate the "increased disorder or entropy" because we now know that the system is on one path only.  So in a sense we have returned to the original state of order or entropy accept with one difference, we do not know the path taken in the interim period.  Can we legitimately refer to this as a state of increased disorder and entropy?  Remember, when we perform our calculation of the detection probability which will predict the outcome of our measurements we must still evaluate the detection probability with the state that was achieved after splitting, so the actual state used in this calculation is the state of "increased disorder".  However, because it is a pure state we would say that it is a state of zero entropy.  Either way, the final calculation of detection probability and the associated measurements of the detection will both show what I am considering to be a definite decrease in disorder/entropy, because it has fringes in the position distribution.  The new posittion distribution is ordered in a way that the emission was not ordered.  Therefore we should consider this as an increase in order, and a decrease in disorder or entropy, even though, as we all know, pure states should have zero entropy.  Apparently, our understanding of entropy and thermodynamical law is not fit for the physics of quantum mechanics.  The new formalism of entropy in quantum mechanics is insufficient in understanding this thought experiment.  Our only relevant consideration of entropy is that the interference statistics are a state of increased order and decreased entropy which is a violation of the second law of thermodynamics.


Creation Only!


  It is worth noting that the energy difference is always an energy "creation" which occurrs as a direct result of the preparation for interference.  To begin with, the system is prepared as a source for which there is no such possible measurement of interference.  The initial state of the system is always that of non-interference, or as it is more commonly known, spontaneous emission.  In this state the system would only be measurable in a spatial distribution which is calculable from the state description as a gaussian uncertainty in position.  This "blob" of measurements is the normalized state of measurement and it is always the state of "zero energy created".  In this state the energy of the system is able to be calculated from the state description in position/momentum distribution.

  However, the final state of the energy of the system is able to be calculated from both the state description and from the change in position distribution which may result from its preparation.  If the preparation is one which will display interference, then we naturally must also consider the energy which results from the new position distribution, which is always a state of identical total volume (determined by the uncertainty in position) but increased local "bunchin up" in the position distribution (fringes) which is a state of increased total energy.  If the preparation is one which will not display interference then the total energy stays the same.  Therefore we must conclude that it is only an increase in the state of total energy which may result from the presence of interference, not a decrease.  There is no such possibility that the system begins somehow from the source in a state which has interference measured and then miraculously reverts to a state of non-interference.  Interference simply does not work this way.  Some might consider the example of the quantum eraser and its unique ability to destroy and re-create interference effects, but even in these examples the system is initially prepared in a state of non-interference.  It is intrinsic to quantum mechanics that all systems are naturally emitted in a spontaneous and non-interfering state.  Therefore this thought experiment does not prescribe a protocol for energy destruction, only energy creation.


Charged Particle Protocols


  Obviously, if this protocol exists for the case of gravitational energy in the fields between massive particles of an interfering system, then it must also be the case that we can get energy creation from a protocol for the increase in electromagnetic potential energy in the fields of charged particles of an interfering system.  We would imagine a protocol of the double slit experiment similar to that of Figure 1 accept with a source of a charged particle beam.  This type of system (charged particles) can also easily be used in creating a two slit interference effect.  The re-distribution or re-ordering of the system which occurs in the case of an interference effect with charged particles will result in a similar state of "increased energy" or "decreased entropy" as was the case in the molecular interference effect, with the only difference being that the energy difference is electromagnetic potential energy rather than gravitational potential energy.

  It is interesting that with the case of charged particles that the accumulation of measurements would give a similar fringing effect in an interference experiment, and that the resulting chage in the total energy would have an increase in the electrostatic potential, but that the resulting force which would ensue on the particles in such a situation would be one which is a repulsive force rather than an attractive force as would be the case with the gravitational potential of molecules.

  Anyway, the calculation of electric potential energy can easily be performed with use of two relations, the potential of a distribution at a point, V=INT{kdq/r}, and the electric potential energy surface integral, E=INT{sigmaVdA}, where sigma is the surface charge distribution.  One calculates the first integral for the potential at a point in the distribution and then uses this potential in the energy integral which is also evaluated over the distribution.  By doing this calculation for the two cases, interference and non-interference (where the difference is in sigma, the charge distribution), one simply takes the difference in the two energies calculated and this is the required energy to create the change in the charge distribution.  This is calculated for the case of electron double slit interference with sigma_n=constant for the non-interference case and sigma_i=1/2(1+sinx)*constant for the case of interference.  The calculation result is stated with differentials for both integrals (dx_p,dy_p for the energy integral and dx_dq, dy_dq for the potential integral, with r_p as a polynimial in x_p, y_p, x_dq, y_dq).  The final integral for the difference in energy (the free energy of electric potential) is given as:

Generalization of the Protocol


  The most general statement of this protocol would be put in terms of a coherent quantum mechanical effect which has a set of position measurements which can be calculated by means of an expectation value of an observable.  If there exists an effect which may have its measurements described as a position distribution that is calcuable with an expectation value of an observable, then as long as this effect has a position distribution which has an increased order from the position distribution of the system's emission, then the effect demonstrates an increase in the order of a position distribution and along with this is a decrease in entropy and an increase of energy of the system.  I'm quite sure that the only effect which fulfills these criteria is interference in quantum mechanics.  And it might be noted that in the case of electromagnetic fields (light) the interference might not cause an increase in energy because the EM field does not emit its own field like a charged particle or massive particle does.


Temporal Interference?


  We should also take note of the possibility of an energy creation taking place in temporal interference effects.  But we make note of the point in the last section, that photon interference effects might not have a similar interpretation of energy being created because photons do not emitt their own field.  Because temporal interference is strictly a photonic effect, we should not expect that temporal interference effects will exhibit any such energy creation.


Charged Particles


  In the section above entitled "Charged Particle Protocols" I have illustrated a protocol similar to the redistribution protocol of this page, except with charged particles instead of uncharged molecules.  I have since written a document on this subject which is published at the following link:

This writing outlines the calculation of electric potential energy for the case of interference with a Mach-Zehnder style electron interference effect and a normal spatial interference effect.  The conclusion considers that "interference" is a separate mathematical argument from "electric potential energy" in such a manner that the "interference argument" determines the output configuration of the system in the experiment and the "energy of electric potential argument" determines the additional energy of the system due to its output configuration.  Essentially, it is postulated that interfering electrons have the same unshifted energy as non-interfering electrons, but that the output configuration is different in the two cases that the energy of electric potential (on the order of 10^-9eVm/x where x is the electron spacing in the beam) is a free energy so to speak.  If this is correct, then the obvious protocol for energy creation is to repeatedly subject an electronic system to interference over and over again.  With enough iterations of interference, the electron's potential energy will be increased each time in a manner that adds up significantly.


This page was started on July 30, 2013.  It was updated on July 31 and August 1-2, 2013.  The section on Charged Particle Protocols was modified on August 29, 2013 to include the equation shown which was again changed on September 9, 2013.  The section on Charged Particles was added on December 16, 2013.