Violation Protocol

Conservation violation in the change of a statistical distribution by modulation of a coherent state description

 

© Thomas Alexander Meyer 2013

 

  In the literature surrounding the effects of interference and quantum erasing there is an argument concerning the fundamental mechanism behind the update of the state description which is occurring when one destroys interference or creates it.  In the popular quantum eraser protocols of the literature we usually begin with an established interference effect and an action is taken which destroys the interference and then an additional action is taken to re-create interference.  It is argued that the underlying mechanism behind the two actions which create and destroy interference is the ability for one to gain distinguishing information (or as I like to call it inferential information) of the path of origin of the system.  The other side of the argument is that the interference destruction and creation is due to a physical disturbance of the system.

  It is argued that the empirical evidence was decisively in favour of the former argument, that the presence or non-presence of distinguishing information is that which destroys or creates interference respectively.  If indeed this argument is correct, then one might ask how such a non-physical change in the system could lead to the physical change of the measurable statistics of the system.  What is the physical action on the system that leads to the physical change in the statistics, as would be expected by the laws of conservation of energy and momentum?  Or is there at all such an underlying physical action which would conserve energy and momentum?  Is information the root cause?  This would leave the local statistical change of the system without a “driving mechanism” so to speak, this would violate conservation.  A thought experiment is given below which will test this exact querry.  It is suggested that you familiarize yourself with the specific choice of quantum eraser used here, the ZWM, although we give a brief description of it first.

 

The ZWM

 

  The ZWM (Ref. 1,2), as illustrated in Figure 1, has an attenuation of the first idler, i1, by use of a neutral density filter (NDF which is actually a beam splitter with an empty input port) prior to the transmission of i1 through the second downconversion crystal where it comes in alignment with i2.  This attenuation has the affect of attenuating the visibility of interference at the signal detector.  This is the only historical demonstration of a single photon interference effect between the possible sources of photons where there is also the possibility of measuring an entangled partner photon in coincidence.  The interference is allowed on the grounds that the idlers are perfectly aligned and unattenuated.  But how are we to understand this loss of interference due to attenuation or misalignment, specifically how are we to understand it in a manner where we may better elucidate the theoretical mechanism behind this loss.

  The attenuation at the neutral density filter implies distinguishing information about the signal paths, and this distinguishability eliminates the interference.  The distinguishability here is provided by a detector, the idler detector Di, which is at a spatially separated distance to the detector which displays the interference, the signal detector Ds.  The presence or absence of a coincidental detection at this separated detector provides the distinguishing information, and most importantly it doesn’t need to actually be set up and detecting because it is the fact that it could in principle be set up to do so which negates the interference.

  It is the in principle knowability of signal path information by virtue of the presence of a coincidence detection at the idler detector which destroys the interference.  So how would we understand this as a violation of conservation?  When the system is prepared to produce no interference (100% attenuation at the NDF) the statistics will show the number of photons at the signal detector that corresponds to spontaneous emission of s1 and s2.  When the preparation is that of no attenuation and it is set up to produce interference at a central maxima of the pattern then there is a greater number of photons detected.  The standard explanation for this difference is the presence of “constructive interference”.  In both preparations the field strength of the emission of the signals is the same, but with constructive interference we have a greater detection rate.  The mere existence of this phenomenon, interference, is not a violation of conservation because we know that there are also preparations of destructive interference which occur at other path lengths.  The violation of conservation is in the ability to change the statistics by merely changing the preparation for a difference in the distinguishing information, whilst this change in preparation exists in the absence of a driving physical mechanism.  The negation of an interference effect might not require a physical disturbance to the system however it definitely is itself a physical change of statistics of the system.  Is it possible for us to explain this dramatic change in the statistics of the signal by virtue of an input of energy somewhere in the idler where the action was taken with the attenuator?  No.  The field of the idler i1 that is attenuated never interacts with the fields of the signals.  There simply is no explanation in terms of a physical disturbance to the idlers or signals somewhere.  The statistics of the idler are macroscopically adjusted by the inferential information at the idler beams.  It is information which is the “driving force” so to speak.

 

The Violation ZWM

 

  In this analysis of the ZWM we consider a modification to the protocol that is specifically intended to test our conclusion that there is a local violation of conservation.  We will call our setup The Violation ZWM and we illustrate it in Figure 2.

  In this setup the principle is identical to the ZWM.  The first modification to the setup is the addition of a time dependent attenuator of the idler i1 before it is incident on DC2.  In the illustration this is labelled TDA (time dependent attenuation) and it is driven by a modulator which varies the attenuation between 0 and 100%.  We set the path lengths of the apparatus so that the signals are producing an intensity which is indicative of the central maxima of the interference pattern (the interference that would result if we varied one of the signal path lengths).  So if the idler path is 100% attenuated then the intensity of the signals drops to the corresponding value of no interference.  Instead of a detector for the signals we use a screen-motor (SM) which performs the function of enacting a motor which efficiently heats up its surrounding environment when the photon detection count is modulated between the two extreme values.  And we do not use a detector for the idlers but rather a beam stop.  We imagine that the whole setup is immersed in a thermodynamically sealed bath with adiabatic walls and only three input holes for the modulator input, the pump input and an output for thermodynamic data collection.  We also have a temperature thermometer and pressure barometer inside of the bath to give us data on the change of temperature (assuming the pressure stays constant) as the system is heated by the inputs.  In addition, this setup assumes that all the components of the apparatus (beam stop, motor, TDA, etc.) are not thermodynamically reclusive so to speak, they must freely give up their energy to the bath.

  The idea of modulating the attenuation with a time dependent source is actually considered by the authors in a theoretical paper (Ref. 3).  This paper outlines a setup which is identical to the ZWM accept with a time dependent shutter instead of the neutral density filter.  The time dependent attenuation was found to affect the visibility of the interference in the same manner that it would in the original ZWM.  The authors make a clear statement on this matter in their discussion;

“The detected photon (s2) can originate in DC1...Because emissions from DC1 and DC2 almost never accompany each other, there is actually nothing for i1 to act on if it does reach DC2.  Alternatively, if the detected photon (s2) originates in DC2, then there is no accompanying emission (s1 or i1) from DC1.  Consequently there is no i1 photon to be stopped by the shutter when it closes at the critical time.

  Arguments like this suggest that it is not possible to identify a causal mechanism that destroys the interference between s1 and s2 when the shutter is closed.  Instead it is the possibility, in principle, of identifying the source of the detected photon when the shutter closes that is responsible for eliminating interference.”

  If it is the inferential knowledge due to the availability of the idler which leads to the modulation of the interference, then we must conclude that there is no local causal mechanism which leads to the change in the statistics of the signals when the attenuation is modulated.  So how does this work in our setup of Figure 2?  We look at two possible scenarios.  Scenario 1) Without modulation of the attenuation.  This is performed by allowing the modulator input to go into the bath and having it connected to the attenuator but having the attenuator removed from the path of the idlers so that the idler attenuation is nil.  If the temperature of the bath begins from a designated starting temperature, we would expect that because of the inputs the temperature will rise following a specific curve with respect to time.  Scenario 2) With modulation of the attenuation.  In this scenario the bath is at the designated starting temperature and the attenuator is in the path of the idler so that the idler is attenuated in a varying manner between 0 and 100%, as determined by the modulator.  This will similarly modulate the statistics at the signal detector screen in a manner that the intensity of the combined beam at the screen-motor is modulated between the value of the interference central maxima and the value of no interference, which correspond to 0% and 100% attenuation respectively.  This varying change in the intensity of photons at the screen drives the motor which adds an additional increase of the local input of heat energy which must be absorbed by the surrounding bath.

  We should mention that the photons which arrive at the screen in a greater number for the case of 0% attenuation are photons which are in the beam regardless of the value of the attenuation.  But this doesn’t matter to us, we are concerned with the fact that the photons are in a different configuration, which would normally require a local physical disturbance to change this configuration.  And this change in statistical configuration is driving a motor that adds heat to the surrounding bath.  So how does this affect our data concerning the temperature increase for the second scenario?  This would result in an increase in the rate at which the temperature increases.  In scenario 1 we will have collected data which confirms a specific curve of the temperature increase with respect to time.  In scenario 2 we would find a different curve of the temperature with respect to time, as the temperature would increase at a quicker rate.

 

Violation Protocols

 

  The general protocol for a demonstration of the violation of conservation laws, a violation protocol, can be described with reference to three stages; first the establishment of an existing means to quantum erasion, second the setup of the preparation "choice" by modulation between interference and non-interference, and third to setup the preparation to exploit the change in interference statistics.  (Here, when we use the term quantum erasion or eraser, we intend to mean any quantum mechanical protocol where by an established interference effect may have its interference created or destroyed by means of an action which is no more than a preparation which erases or introduces distinguishing or inferential information of the system’s path of origin.  The action may be a unitary operation on the system, or a unitary operation or measurement of another system which is entangled to the interfering system, but it may not be an action which destroys interference by means of a measurement collapse of the interfering system.  This is different from the popularly accepted definition of quantum eraser which assumes a protocol by which we introduce and then erase the distinguishing information to destroy and then allow for interference.)

 

Stage 1

  The first stage requires that the protocol begin with a quantum eraser of a specific type, one which has a preparation for the choice of single particle interference.  There are many types of quantum eraser for which the original proposal was given by Scully and Druhl (Ref. 4).  Most realizable quantum eraser protocols have a fourth order (two particle) interference effect which can be manipulated by the choice for inferential information.  These quantum erasers will not work as easily for our protocol because the fourth order interference is collected between two detection systems.  Each detection system when treated alone is only detecting at a rate that is consistent with the statistics of a spontaneous emission.  When the choice for interference or non-interference is made the result causes no change in the local statistics of each detector rate.  If we use such a quantum eraser we would have to drive the motor by comparison between coincidence counting rates for the two choices which would add a difficulty in the setup.

  The quantum eraser setup may be described by two central criteria;

1) It prepares the system for the possibility of interference, spatial or temporal.

2) The possibility of interference is determined by a "choice" of preparation, to include or not include inferential information of the path of origin of the particle.  The choice for non-interference must specifically be a preparation which only includes an action on the system which implies knowledge of the path of origin, not a physical disturbance to the system, this way the change in the statistics is solely due to inferential or distinguishing information (in principle knowability).

With the fulfillment of these two criteria in the choice of quantum eraser we complete the first stage in the development of a violation protocol.  Noting that the second criterion involves a choice of preparation we should mention that some quantum erasers have different total setups.  Some have a setup involving three stages; an established interference effect, a change to the preparation that infers information and destroys interference, and a second change to the preparation which erases the inferential information to regain interference.  Other quantum erasers have a simpler setup, as in the ZWM based eraser (Ref. 5) (this would be the form of quantum eraser that we use in The Violation ZWM of Figure 2), where there is only the established interference effect and a change to the preparation that infers path information and destroys the interference.  In either type of quantum eraser we have at least one opportunity to make a choice and the preparation can be set up to modulate between choices.  The only other type of eraser that is applicable would be one which begins with an established non-interference effect and has a choice of an action which allows for interference.  I do not know if this type of protocol even exists but it would also work if it is possible.

 

Stage 2

  The second stage in the development of our violation protocol is to simply prepare the eraser for the modulation between the two possible choices of interference and non-interference.  Because the choice for non-interference always involves a simple preparation which would imply inferential information it is a simple matter to prepare the setup so that there is maximally efficient modulation between the two extremes.  Each eraser is different so each has a different method of modulation which is nothing more than engineering specifications.

 

Stage 3

  The third stage is to set up the exploitation of the end change in interference so as to utilize the change in a maximally efficient manner.  By this we intend to mean that there must be a mechanism which is maximally efficient in its delivery of the change in statistics of the intensity of the system between interference and non-interference (which occurs due to modulation of the second stage) to an energy/momentum storage or end use.  This is similarly an engineering specifications problem which is different for each choice of quantum eraser.

 

References

 

1)  X. Y. Zou, L. J. Wang, and L. Mandel, Induced Coherence and Indistinguishability in Optical Interference, Phys. Rev. Lett., 67, 318 (1991).

2)  L. J. Wang, X. Y. Zou, and L. Mandel, Induced coherence without induced emission, Phys. Rev. A, 44, 4614 (1991).

3)  L. J. Wang, X. Y. Zou, and L. Mandel, Time-varying induced coherence, J. Opt. Soc. Am. B, 9, 605 (1992).

4)  Marlan O. Scully and Kai Druhl, Quantum Eraser : A proposed photon correlation experiment concerning observation and "delayed choice" in quantum mechanics, Phys. Rev. A, 25, 2208 (1982).

5)  A. G. Zajonc, L. J. Wang, X. Y. Zou & L. Mandel, Quantum Eraser, Nature, 353, 507 (1991).

A review paper concerning the ZWM study is published at this link: http://www.vixra.org/pdf/1306.0186v3.pdf

Secondary Protocol

 

  This protocol is the exact same as the first with one exception, that it uses a collapse instead of a unitary operation in Stage 1 of the protocol.  This would mean that we are not using a quantum eraser, but rather a quantum mechanical measurement.  Of course we would begin with an established interference effect of quantum mechanics and then the method of destroying the interference effect is by means of making a measurement of the interfering system prior to combination of the interfering sources.  Because the measurement must be performed on the system while it traverses at least one of its paths of origin, the measurement will have a probability of non-success.  It is always possible that the system traverses one of the other paths of origin.  This leaves the possibility that the system will reach the point of overlap where interference would have occured, and this will happen for an appropriate percentage of the statistics.  This allowance of one or many paths of origin to not be measured is up to the manager of the protocol, as it is equally valid in this protocol to measure many paths of origin, as long as at least one path of origin of the system is not prepared for measurement.  One must have at least one path of origin not prepared for measurement so that the percentage of statistics reaches the recombination where non-interference will occur.  We must remember that it is the difference between the two configurations of statistics (interference and non-interference) in the region of recombination/overlap which is the vital "action" of non-conservation.

  The point in this protocol is to exploit the interference creation and destruction in the same manner as the violation protocol, by modulation between interference and non-interference, with the exception that the non-interference choice does not require that all the statistics of the system arrive at the point of combination.  This still requires that in the preparation for non-interference a portion of the statistics arrive at the point of combination in a configuration which is different from the configuration that the same portion of statistics would arrive at the point of combination in had there been the preparation for interference, and the difference is still not causally explained.  This non-conservation may similarly be exploited in the manner that is outlined in Stage 3 of the violation protocol shown above.

   

Third Protocol

 

  This protocol is the exact same as the violation and secondary protocols with one exception, that it uses a mis-alignment or displacement of the system rather than a collapse or a unitary operation in Stage 1 of the protocol.  This would mean that we are not using a quantum eraser or a quantum mechanical measurement, but rather a simple preparation for reflection/refraction or another means of displacement of a quantum mechanical system.  Of course we would begin with an established interference effect of quantum mechanics and then the method of destroying the interference effect is by means of displacing, delaying or re-aligning at least one source of the interfering system prior to combination of the interfering sources.  Because the displacement/delay/re-alignment of the interfering source must be performed on the system while it traverses at least one of its paths of origin, the displacement/delay/re-alignment will have a probability of non-success.  It is always possible that the system traverses one of the other paths of origin.  This leaves the possibility that the system will reach the point of overlap where interference would have occured, and this will happen for an appropriate percentage of the statistics.  This allowance of one or many paths of origin to not be displaced/delayed/re-aligned is up to the manager of the protocol, as it is equally valid in this protocol to displace/delay/re-align many paths of origin, as long as at least one path of origin of the system is not prepared for displacment/delay/re-alignment.  One must have at least one path of origin not prepared for displacement/delay/re-alignment so that the percentage of statistics reaches the recombination where non-interference will occur.  We must remember that it is the difference between the two configurations of statistics (interference and non-interference) in the region of recombination/overlap which is the vital regime of non-conservation.  The best choice between the three of displacement, delay or re-alignment is probably delay, as it allows for all of the statistics to arrive at the recombination point so it is most efficient, but it is noted that the delay will cause a loss of time which leads to inefficiency.

  The point in this protocol is to exploit the interference creation and destruction in the same manner as the violation protocol, by modulation between interference and non-interference, with the exception that the non-interference choice does not require that all the statistics of the system arrive at the point of combination.  This still requires that in the preparation for non-interference a portion of the statistics arrive at the point of combination in a configuration which is different from the configuration that the same portion of statistics would arrive at the point of combination in had there been the preparation for interference, and the difference is still not causally explained (not conserverd).  This non-conservation may similarly be exploited in the manner that is outlined in Stage 3 of the violation protocol shown above.

  

The Combination Violation Protocol

 

  The theoretical assumption of this protocol is that not only may the effect of interference be used to violate conservation of energy and momentum, but also the effect of recombination may be used to violate conservation.  In the case of recombination we have multiple sources which must be coherently combined to produce a system with a pure state description which is a superposition of the partial states of the sources.  The end change in statistics due to coherence in the combination is a measureable change just as is the case of a coherent interference combination effect.  Because the statistics in the combination are different for the case of coherence and the case of non-coherent combination, and because the underlying mechanism of the destruction of coherence in a recombination effect is distinguishing information, we anticipate that the modulation between the extreme cases of the recombination effect might similarly be exploited for a violation of conservation of energy and momentum.

  This generalized protocol discussed below, the combination violation protocol, concerns a quantum mechanical setup which uses a recombination effect along with a modulation of distinguishing information.  The protocol may be described with a three stage process in its development; first the establishment of an existing recombination effect, second the setup of the "choice" in the preparation and modulation between choices, and third to setup the preparation to exploit the change in statistics that results from the change in choice.  Here, when we use the term recombination effect we intend to mean any quantum mechanical protocol where by the coherent combination of multiple distinguishable sources of a system leads to a single particle state with a description which is the superposition of the state descriptions of the distinguishable sources.  As an example we consider the case where a 45degree polarized source of photons is split with a polarizing beam splitter into its horizontal and vertical components and is then recombined with another polarizing beam splitter which has as its output the original 45degree polarized wave.  This would be a recombination of sources that are distinguishable by means of polarization.

 

Stage 1

  The first stage involves the selection of a specific recombination effect of quantum mechanics which could be a photon recombination effect, atomic spin recombination effect, or any other recombination effect where multiple sources of the system are combined coherently to result in a single particle state description.  Because we need to describe the resulting coherent combination with a single particle state vector we refer to this state as F(x) or |F(x)>.  This state has state operator

ρ = |F(x)><F(x)|

The variable x is the representation which is the distinguishable variable of the sources.  At times after combination when there is coherent overlap (no distinguishability of path and no relevant action taken on the system) we have the total single particle pure state description |F(x)> which is a sum of all the partial states |Fi(x)> with each weighted by its appropriate complex probability amplitude, ci,

|F(x)> = Σci|Fi(x)>

We also consider times after combination when there is incoherent overlap (with distinguishability of path due to an action taken on the system) we have a modified single particle pure state description |F’(x)>.  This state is the transformation of state |F(x)> that results from the action taken on the system.  We have assumed that this state will not show coherence upon recombination, so the statistical measurements for this state will be different from those of |F(x)> where there is coherent recombination. 

Stage 2

  The second stage involves the setup of a specific addition to the preparation which allows the protocol manager to choose to eliminate coherence in the combination of the sources by introduction of path information.  In the case of polarization recombination one can setup a choice to introduce distinguishing information of path by means of a measurement of one path, a delay of one path, a unitary transformation of the system on one path or a re-alignment or displacement of one path.  All of these actions are actions that would be equally valid in the destruction of coherence for a recombination effect.  It is possible also for the preparation to involve a dual action, where the first action is a unitary action intended to introduce distinguishing information of path and the second action is a unitary action intended to time reverse the first in order to erase the distinguishing information.  So we generalize our description of the action which is the manager's choice and refer to it simply as the action.  By action we intend to mean any action which may be taken upon the system prior to combination which would destroy (or re-create in the dual case) coherence so that the system is in the non-pure state (or pure state) after the time of combination.  If the action is taken, then the result of the combination changes as a result of the action.  The combination would change between the non-pure state and the pure state description of IF(x)> or vica versa.

  The next task in the development of our protocol is to simply prepare the setup for the modulation between the two possible choices of coherence and non-coherence.  We prepare the setup to modulate the action.  Our choice is always an action, and it is the protocol manager’s task to prepare the setup so that there is maximally efficient modulation between the two extremes of action and non-action.  Each recombination effect is different so each has a different method of modulation which is nothing more than engineering specifications.

 

Stage 3

  The third stage is to set up the exploitation of the end change in coherence so as to utilize the change in a maximally efficient manner.  By this we intend to mean that there must be a mechanism which is maximally efficient in its delivery of the change in statistics of the intensity of the system between coherence and non-coherence (which occurs due to modulation of the second stage) to an energy/momentum storage or end use.  This is similarly an engineering specifications problem which is different for each choice of combination effect.

  

Theory

 

  When we consider the effects of single particle interference and recombination, we must consider the mathematical treatment which models these effects in a manner that is consistent with the theory of quantum mechanics.  In these effects there is always a combination of at least two possible sources of the system which implies that there is two or more terms in the state vector which is used to describe the system, the description is a pure state superposition.  However, we must also explain how this state description evolves to that of a state which does not show coherence in the event that the preparation of the system is such that there is distinguishing information of the path of origin of the system.

  The first point to note here is that there is always a pure state vector that is appropriate to the system, regardless of what unitary action is taken on the system (coupling to another system, rotation of polarization, etc.), as long as there is no measurement collapse associated with the unitary action.  Up to and until measurement of the system there is a pure state description of the system, and all unitary actions taken may be time reversed so there is the possibility of regaining the original state.  This is important in the quantum eraser because it requires two actions, one which prepares the system to have distinguishing information of path and one which erases this information.

  When a measurement takes place (presumably a position measurement), there is a collapse to the system.  Collapse is irreducibly random and therefore it is non-reversible.  Because collapse is irreversible, if at the time of collapse/measurement the state of the system is that which yields no information of its path, then the path information is permanently “erased”.  There is no way to get information concerning path after such a collapse.  For this reason there is a primary set of rules concerning whether interference/recombination takes place coherently or not at the time of measurement.  The rules concerning interference and recombination for a single particle system can be states as follows:

 

When two possible origins of a system from two distinct spatial paths results in an overlap and there is a measurement at the point of overlap, the measurements will be indicative of a description of the system which is that of the coherent pure state superposition only if there is in principle no way to determine the path of origin of the system (up to the time of measurement or afterward).

 

When two possible origins of a system from two distinct spatial paths results in an overlap and there is a measurement at the point of overlap, the measurements will be indicative of a description of the system which is that of an incoherent pure state if there is in principle some way to determine the path of origin of the system (up to the time of measurement or afterward).  This does not necessitate that indeed the distinguishing information of path be measured and acknowledged, but that it be in principle possible to do so.

 

In an interference or recombination effect it is always possible to show that this state will not display the desired effect.  In optical interference effects we would show that the correlation function evaluated at the detector with state |F’(x)> does not have an interference term.  In a spin recombination effect we would be able to show that the state |F’(x)> is not the desired superposition of recombination.  All in all, the final state after the unitary action, |F’(x)>, can always be analysed further to show that it does not display the desired interference or recombination.  But is this the final explanation of the quantum eraser or can we explain the quantum eraser in terms of the above stated rules concerning indistinguishability?  I would argue that the principles concerning indistinguishability of path are fundamental to interference, and only they are.  The mathematical analysis given up to here which shows the change between coherence and non-coherence in terms of the state description is "complementary" to the analysis which would simply state that "distinguishing information" is fundamental to interference and recombination experiments.  It could be said that one cannot have knowledge of path (or no such knowledge) and still get the desired calculation of coherence (or non-coherence).  It could be added here that the interpretation of quantum mechanics which would state that a quantum mechanical system is its description (the information interpretation) is appropriate.  If a quantum mechanical system is its description, then a change to the knowability of path necessitates a change to the state description which explains the loss of coherence.

  So what about the preparation of the quantum eraser where a unitary operation is inserted into one path which infers distinguishing information and destroys the coherence and along with it the interference or recombination statistics, how does this violate conservation?  We explain this as follows; When the coherent setup is maintained, there is an allowance of the interference/recombination statistics due to the coherent state |F(x)> at the time of recombination.  When the incoherent setup is maintained, the statistical measurements are different due to the evolved incoherent state |F’(x)> at the time of recombination.  So when we change from one to the other we have a change in the measurable statistics, but do we have an associated explanation for the driving force behind this change?  No.  It’s that simple.  The only explanation of the change in statistics is that there is a change to the state description, and the change in the state description leads to a calculable change in the statistics, but where does the change in statistics become physically manifest?  It is in the collapse of the system at the time of measurement.  When the system is measured there is a collapse from a description which includes a position distribution (which is over three dimensions, usually two make up the cross section of a beam and the third is the uncertainty in the direction of propagation) to a single position eigenvalue.  My personal thoughts (although many disagree with this) are that the collapse is irreducibly random.  Because the collapse is random there is no explanation as to how the single measurement ends up as it does.  There is a non-zero probability that the measurement winds up at any point in the distribution, and this holds for both states |F(x)> and |F’(x)>.  There simply is no way to explain away the difference in the statistics between the two.  They just work out at the end of the day when a statistically relevant set is measured.  And we must remember, if we wanted to we could set up the experiments to collect individual trials one particle at a time and it would still show the proper state description at the end of the day.  The statistical difference when we toggle between the two cases of |F(x)> and |F’(x)> is in violation of conservation, it is free so to speak.  This is because there is no causal mechanism which is the driving force in the change of statistics.

  

Interference vs Recombination

 

  In the theory section above we postulated two rules governing when coherence is gained in interference and recombination effects.  The rule was based upon the distinguishability of the path of the source of the system, rather than the distinguishability of the description of the source of the system.  It could be argued that in the case of interference (but not recombination), coherence is not only contingent upon indistinguishability of path but also indistinguishability of the description of the sources also.  It is commonly argued that the interfering sources must be identical in description.  When analyzing that which is fundamental to interference effects, we consider this argument to be incorrect.

  In interference effects, there is only an additional contingency upon the identical nature of the sources because the detection systems being used are capable of discriminating between the distinct states of the interfering system.  It is always the case in interference experiments that the measurement system (for example an absorbing electron) is one which could in principle be measured itself to indicate the state of the system, which would in turn also infer the path of origin of the system.  Due to the unitary nature of the measurement transition, it is always possible in principle to measure the final state of the absorbing system to infer the state of the system absorbed which would infer the absorbed system’s path of origin.

  If one wishes to get interference between distinguishable states, then one must use a detection system which measures (absorbs) the exact state which is the superposition of distinguishable states which are the possible sources of the system.  For instance, in the case of a 45degree polarized wave, if we split this with a polarizing beam splitter (PBS) and then recombined it with another PBS at identical path lengths then we would have the original 45degree polarized wave (which could be tested with a 45degree polarizer and detector).  But if we modulated one path length of the recombination we would only find a sweep out of the intensity (the intensity of 45degree polarization) as a function of the coherence length, we would not find interference in the intensity with a modulation of path length.  However, if we don’t use a 45degree polarizer with a normal detector and we rather use a detector which absorbs only 45degree polarized light (which could be constructed with a medium which only absorbs 45degree polarized photons), then this detector would not be capable of discriminating between the paths of origin of the system by virtue of measuring the final state of the absorbing system.  This type of non-discriminatory detection would allow for the display of interference in the detected intensity with optical path difference of the two sources, regardless of the fact that the two sources are distinguishable by polarization.  Of course, this type of experiment has yet to be realized due to the fact that it has never been attempted.  (Actually it has, see the quantum eraser of Kwait-Englert, http://research.physics.illinois.edu/QI/photonics/sciam-supplemental.html

 where they use a +/-45degree polarizer to re-create interference with a Mach-Zehnder interferometer.  In this experiment the polarizer is acting as a detector that displays interference between H and V polarized photons.)

  It is argued that in interference effects, much like in recombination effects, there is no contingency upon indistinguishability of the description of the sources of the system, the inteference is only contingent upon the indistinguishability of the path of origin of the system.  Only indistinguishability of path of origin is fundamental to interference effects.  This leads to another method for violation protocol, if the detection system in an interference efffect was modified itself it could in principle destroy the interference.  Yet another way to skin a cat so to speak.  This method of interference destruction and recreation could be modulated in a violation protocol, although this would probably be an inefficient means to modulation.

 

Candid Remark

 

  In the case of conservation violation for all of the above matters, it has often been stated that the updating action of introducing or erasing distinguishing information has the consequence of violating the laws of conservation of energy and momentum.  This may be a mistake as it is noted that the violation of energy conservation might not imply an associated violation of momentum conservation.  For cases discussed above we always have a recombination or interference effect where the two choices of preparation result in different statistical configurations, which necessarily implies a violation of energy conservation.  However the difference in propagation of the system in the two preparations does not necessarily imply a change in momentum.  It could easily be the case that the two preparations have identical momentum of the system which would not violate momentum conservation at all.  Only definitive experimental and theoretical work can prove decisive in this affair.

  Considering all that has been said thus far, we might be of the impression that indeed momentum is conserved in the case of the violation protocols for interference and recombination effects.  This would be an important conclusion, as it would indicate an emphasis on the conservation of vector quantities of space time (momentum) but not scalar quantities of space time (energy and mass).

 

The Screen-Motor

 

  Little has been said up to this point concerning the construction of the screen-motor of Figure 2 which is also the central device in stage 3 of all the above mentioned protocols.  This device, which "is maximally efficient in its delivery of the change in statistics of the intensity of the system between interference and non-interference (which occurs due to modulation of the second stage) to an energy/momentum storage or end use" is the device which translates the change in interference statistics to an energy storage.  This device could easily be constructed in an optical interference effect by simply using a detection screen made of a sub-bandgap material.  If the bandgap of the screen media is less than the energy of the interfering light, then we would expect the light to liberate electrons to current carrying status.  These electrons leave behind holes in the crystal media which can be exploited.  If the screen is adjacent to a neutrally charged substrate media (behind it) which absorbs the electrons then the screen becomes net positively charged and the substrate becomes net negatively charged.  By simply setting up the screen and substrate in strips that match the constructive and destructive interference fringes of the interference pattern we have a model where the successive strips will become differently charged in the case of interference.  When there is interference, the screen (substrate) strips at constructive interference will become positively (negatively) charged and thier neighbouring strips at destructive interference will stay neutrally charged.  This builds up a potential difference between neighbouring strips of screen and the opposite potential difference between neighbouring strips of substrate for the case of interference.  When there is no interference, neighbouring strips become equally charged and there is no potential difference.

  To exploit this we set up our device in pairs of neighbouring strips of screen and substrate, each pair with one strip at constructive interference and one at destructive interference.  We set up each pair to drive a motor which runs on the modulation of the potential difference between the pairs.  The modulation of interference also modulates the potential difference between neighbouring strips of screen of the pair and it modulates the opposite potential difference between the neighbouring strips of substrate.  Both modulations of potential difference could be used to drive a motor which is used for the end storage/use of energy.

 

Generalized Choice

 

  We consider whether the "choice" of preparation in the violation protocols must indeed be a choice of the destruction or recreation of coherence and interference.  This relates to a simple question concerning whether the state of interference/coherence is the relevant state when modulating between the choices of interference state and non-interference state.  If the state of coherence and interference is (as we would expect) the "desired" state which is fundamental to this whole protocol, then we would expect that this state alone may be exploited to produce a violation without resorting to the state of non-interference and decoherence.  Upon further thought one realizes that indeed we needn't resort to the state of decoherence in our modulation and we may simply modulate between states of interference which display different statistics.  In the violation protocols we require a change of preparation which can be chosen, a change which results in a change in the measurable statistics of the system that does not require an input of energy into the system, and this criterion is met by a change in preparation which does nothing more than alter the phase of the interfering system along one path so that it changes the statistics of measurement between lets say a state of constructive interference and a state of destructive interference.  If our chioce of preparation in the violation protocols is to modulate the phase of one input in an interference effect, specifically so that the state of interference collection is modulated between constructive and destructive interference, then the measured statistics will modulate between these two extremes.  This would require no input of energy into the system (other than a small amount of radiation pressure if you use mirrors to delay one source) that is not locally conserved in such a manner that it does not affect the measured statistics of the system, but the measured statistics of the system does change due to a change in the state description that is appropriate to the change in preparation, an alteration of phase.  Because the state description is fundamental to interference effects, as long as we affect the description with our "choice" of preparation then the resulting change in statistics is a violation of energy conservation that can be exploited.

  We note that this answers our earlier question, as to which state is fundamental to the protocol between interference and non-interference, and the answer is as we would assume; interference and coherence are fundamental to the violation protocols.  We also note that this is a significant alteration to all of the above stated protocols involving interference, because the modulated statistics between states of constructive and destructive interference may differ by an amount that is twice the amount in going between states of interference and non-interference.  This makes the protocols twice as efficient in their "energy creation".

 

Generalized Protocol

 

  This protocol could be said to encompass all possible protocols which could be exploited for the creation of energy by means of a violation.  To start, we always require an experimental technique that is capable of demonstrating quantum coherence.  In order for an experiment to demonstrate coherence, it must be a quantum mechanical preparation which has a state description which is consistent with the laws of quantum mechanics, and the preparation must have an associated set of measurements which can verify this description.  With this starting point we have a demonstration of a unique set of measurement statistics.  To continue the protocol we also have a requirement that there be atleast one alternate preparation which is different from the first, but may be achieved by a modification to the first preparation.  The alternate preparation must have a state description which predicts a different set of results to the measurements that are performed with the first preparation.  This means that the alternate preparation must allow the same measurements as the first preparation and that the results of measurement must be different.  This defines our "choice" of the protocol; the choice is always between the different preparations.  The purpose of the choice is to allow modulation between the different possible preparations, which results in a change to the measurable statistics of the system under the conditions of the different choices.  The modulation of the choice is always setup to be as fast as possible while allowing for a statistically relevant set of measurements to be made in each preparation.  With this we now only have to add the final stage, to prepare the protocol for the maximally efficient use of the end change in the measurable statistics by creating a motorized system of energy storage/use which is driven by the modulated statistics.

  

Generalized Theory

 

  The theory section above explains conservation violation in the context of there being a change to the state description of the system which is responsible for a change to the statistical position distribution of the system.  Because the change to the state description requires little input into the system and the end change to the statistics is a larger amount of energy, then there must be a violation of conservation of energy.  This explanation never mentions probabilities, and because this concept is central to quantum mechanics, we will state the theory here in this context.

  The change to the preparation that causes a change to the state description results in a change to the end calculation of the associated probabilities.  In the case of a coherent experimental preparation (a recombination or interference experiment) the end calculation of the statistical position distribution is always a bra-ket calculation of the average position or expectation value of the position.  The distribution calculated is always a probabilistic distribution with many possible positions (often the position is even a continuous function).  So when we have two possible preparations there will be two associated probability distributions of the position.  For the specific case of spatial interference effects, the bra-ket calculation (for optics this would be the common correlation function) will have cross-over terms (terms where the bra and ket represent differing paths to interference) that result in a position distribution which is defined with a varying function whose argument is dependent upon the frequency/phase difference of the sources.  So in the case of interference, we have a position probability distribution which is dependent upon frequency/phase difference.  But we must be quick to realize that this is still a probability distribution that describes the position, even though there is a dependence upon frequency does not mean we are suddenly dealing with waves here.  It's still particles and their observation is described proabilistically.  The position distribution which may be measured by succesive trials is always going to be a randomly influenced distribution.  Somehow at the end of the day, whatever the description of the system, the observations of the system which are partially randomly actualized will always fit the description.

  This is the jist of the violation protocol, the random actualization will always fulfill the description at the end of the day.  We don't need to worry about it.  The change to the state description is simple and costs little energy.  The end change to the statistics is great in magnitude and costs us little.  When we create energy we only do so in depending on this "random actualization" to work it out.

 

  The most generalized manner in which we may describe a violation protocol is to simply require a coherent quantum mechanical effect which fulfills two central criteria.  First, the effect must be one which has a set of measurements which are describable with a calculation of the classic bra-ket form of an observable of quantum mechanics.  The measurements must be describable by an expectation value which has a specific probability distribution.  Second, the effect must have at least two possible preparations which may be chosen and the two preparations must have different statistical observations of the measurement which may each be predicted by calculations of the expectation value.  And it cannot be the trivial case that the multiple different preparations differ by an input of energy to the preparation which would account for the change in the measurements, for this would not violate conservation.  The difference in preparation should be one which locally conserves energy and requires as little energy as possible.  With these two criteria met, we only need modulate the choice of preparation between the multiple possibilities and exploit the rewards of the change in measurable statistics as a creation of energy.

 

Chronology of this publication:

 

Everything up to the end of the References section was completed on April 12, 2013.  A small change of spelling errors was added to The ZWM section on April 17, 2013.  Some minor changes were also made to the opening statement and The ZWM section on May2, 2013.

The Secondary Protocol and Third Protocol were completed on April 15, 2013.

The Combination Violation Protocol was completed on April 16, 2013.  Some minor changes were made on April 17, 2013.  There were subsequent modifications made on May 1, 2013 and May 8, 2013 and June 10, 2013.

The Theory section was added on April 22, 2013.  It was subsequently modified on May 1, 2013.  It was again modified on May 7, 2013. It was again slightly modified (the second stated principle) on June 18, 2013.

The Candid Remark was added on April 24, 2013.  Thereafter an additional section, Radiation Pressure, was added.  The Radiation Pressure secition was then removed on April 26, 2013 when only the last two sentences were kept and added to the Candid Remark.

The Interference vs Recombination Section was added on May 4, 2013.  It was added to on May 28, 2013.

The Screen-Motor section was added on May 24, 2013.

Many of the ideas presented here were also published at vixra on May 28, 2013 with a concise theoretical account of the violation protocol.  Interested readers may access this paper at this link: http://www.vixra.org/pdf/1305.0168v1.pdf

Another paper which discusses the ideas presented in the section on Interference vs Recombination is published at this link:

http://www.vixra.org/pdf/1305.0185v1.pdf 

The Generalized Protocol section was added on May 31, 2013.  It was modified on June 10, 2013.

The Generalized Choice section was added on June 10, 2013.

The Generalized Theory section was added on June 18, 2013 and modified on June 24, 2013.

Yet another paper which discusses the protocol in the most generalized form is published at this link: http://www.vixra.org/pdf/1306.0189v2.pdf

This publication was completed on June 24, 2013 and is finalized.

 

I guess its just another one of those absurdities of quantum mechanics.