Thursday, January 15, 2015

Does Quantum Mechanics Provide an Analog for the Holy Trinity?


A stumbling block in my conversion process was dealing with the concept of the Holy Trinity--as a Jew, a cornerstone of my minimal religious faith was the Sh'ma Yisrael, that God was One:
"שְׁמַע יִשְׂרָאֵל יהוה אֱלֹהֵינוּ יהוה אֶחָד - 
Sh'ma Yisra'el YHWH Eloheinu YHWH Eḥad"  Hear O Israel, the LORD is our God, the LORD is one. Deut. 6:4-9
The priest who was guiding my catechesis used the illustration below to clear up  my confusion:
The Holy Trinity from
As he explained it, the points of the triangle are distinct--as in three separate persons--but the triangle is one thing, God.   That explanation satisfied me, and I used it myself when teaching RCIA and giving catechesis classes to inmates.   And to enlighten me more, he used the following analogy:  God the Father is God above us;  God the Son is God beside us;  God the Holy Spirit is God within us.

Arguments from analogy have been criticized as being inductive rather than deductive and lacking substance, but I believe they are a valuable tool for understanding.   I'd like to offer one more analog for the Trinity:   the quantum mechanical superposed state of God the Father, God the Son and God the Spirit.    I'll not give here a detailed explanation of the relevant quantum mechanics.    That has been discussed in more detail in another post of mine (Free Will and God's Providence, Part IV) and in references contained therein.   Rather, I'd like to explain  why I believe there is an analogy, and what the theological import of this might mean.


Let's consider very briefly the example given in the link above for quantum mechanical superposition, the famed (to some) double-slit diffraction experiment.     A particle going through both slits (call them slit 1 and slit 2) is taken as a superposition of states.    The notation is given as
| state > =  | slit 1 >  +  | slit 2 > , that is the particle goes through BOTH slit 1 and slit 2 at the same time, as if it were a wave.     If we make a measurement to see if the particle has gone through slit 1, then the state is no longer a superpostion  but | state > = | slit 1 > ;   likewise, if we make a measurement to see if the particle has gone through slit 2,  we get | state > = | slit 2 > .     Only if we make NO measurements to determine which slit the particle has gone through will we see the particle behave as a wave and give on a detection screen a diffraction pattern (with many particles striking the screen).


Taking the analogy of the Trinity as a superposition  we have

| God, the Trinity>  = | God, the Father > + | God, the Son >  +  | God, the Holy Spirit > .

This is saying there is one God-state, God the Trinity which is the superposition--all three component states simultaneously--of the component states God, the Father,  God the Son and God, the Holy Spirit.

Now in quantum mechanics, the superposition is removed on measurement (either by collapse or by transfer to an alternate world/alternate mind--see Free Will and God's Providence, Part IV..) to yield the particular component state which the measurement was designed to detect.      If we are to carry the analogy further, what would be the analog of a measurement to detect one of the component God-states?

What do we seek when we seek God, the Father?  What do we seek when we seek God, the Son?  What do we seek when seek God,  the Holy Spirit?    Theologians and philosophers will give subtle and complex answers, but I'll state my own simple-minded view.    We seek

  • God the Father as the author of the Universe, of the laws of nature and mathematics, as Creator of all things, to worship and adore;  we seek God in prayer (the "Our Father); we offer up to him the sacrifice of His Son in the Holy Mass
  • God the Son as our salvation, to help us spread His Word and Message, by speech and deed;  we seek the the Son in Intercessions in the Liturgy of the Hours;  we take him to ourselves in the Sacrament of Holy Communion; we seek his forgiveness, when in the Sacrament of Reconciliation we ask Him (in the person of a priest) to forgive our sins.
  • God the Holy Spirit to change us, to alter our mind and heart to be better and approach the ideal given in Scripture;  we seek the Holy Spirit in the Sacraments of Baptism and Confirmation;  we ask His help when faced with moral dilemmas or attempts to avoid sin.

When we seek God in any of these modes, we reach to God as that person of the Trinity, we "decompose", collapse the Trinity to the one sought for.


When I started to write this post (last April) I thought it was an original idea.    Doing a Google search on "the Trinity as a quantum superposition" I find there are many entries.    I haven't read these, in order that only my own fresh thoughts  would be in the post.

I'd be grateful for those with deeper theological knowledge to correct me in whatever I've said that may be contrary to doctrines or dogma of the Catholic Church.

Wednesday, January 14, 2015

Scientific Integrity: Lessons from Climategate.

“The Scientific Method is a wonderful tool as long as you don't care which way the outcome turns; however, this process fails the second one's perception interferes with the interpretation of data."  Christina Marrero
INTEGRITY:  "The quality of being honest and having strong moral principles; moral uprightness.."Oxford Dictionary
“…if you’re doing an experiment, you should report everything that you think might make it invalid—not only what you think is right about it: other causes that could possibly explain your results; and things you thought of that you’ve eliminated by some other experiment, and how they worked—to make sure the other fellow can tell they have been eliminated.” Richard Feynman 


 Our graduate research group director, E.B. Wilson, Jr., would occasionally give homilies at the group's afternoon tea about what character traits a good scientist should have.  The most important of these was scientific integrity--honesty and openness in doing the research and reporting the results, and the capacity to be the severest critic of one's own work.  I agree--the ability to stand aside, to evaluate one's own research objectively--not as a parent would his child, but as a stern judge--is critical to the progress of science.     And a concomitant trait is the capacity to accept valid criticism.  These qualities are necessary for one's research to stand the test of time.

When I first started this post I wanted to examine what might be textbook cases for a study of scientific  integrity, focusing on the the Climategate expose of 2009 and the McIntyre/McKittrick analysis of the so-called "Hockey Stick" results of Mann et al.    (It is not my purpose here to debate the merits of Anthropogenic Global Warming (AGW)--there is an addendum at the end of the post that summarizes my own views).   As I developed the thesis it occurred to me that a broader issue was involved: how do ethical considerations limit and define  scientific goals?  Should researchers--presumably in pursuit of a greater good--modify or bend precepts conventionally given for doing science?   Should ethical considerations define boundaries for scientific research?   These issues will be addressed in subsequent posts.


A critical condition for science to progress is that experiments be replicable;   the dross has to be discarded if the gold is to be retained.   By this replicability requirement the first reports of cold fusion and polywater were shown not to be valid.   And of course by "experiments" we include computer modeling that is to predict future events predicated on the assumptions of the model.    In order for experiments and computer models  to be replicable, there has to be free access to data and to the computer programs used.     If you're to find out whether a computer model is correct and consistent you have to be able to use the same input and programs that the original researcher used.

If we examine some of the emails from the Climategate file and comments from McIntyre and McKittrick, who tried to replicate the Mann "Hockey Stick", we might wonder whether this requirement was acknowledged by proponents of AGW.   Here are just two excerpts: 

  • Jones (Head of CRU) to Wahl (NOOA) and Ammann (Natl. Ctr. for Atm. Res.): "(T)ry and change the Received date! Don't give those skeptics something to amuse themselves with."
  • Jones to Schmidt (NASA Goddard Institute) cc Mann: "The FOI (Freedom of Information) line we're all using is this, IPCC is exempt from any countries FOI...The skeptics this Even though we...possibly relevant info the IPCC is not part of our remit (mission statement) therefore we don't have an obligation to pass it on."
  • More emails and fuller versions are given in a Wall Street Journal article.
Here are some comments from Stephen McIntyre (from his presentation at Ohio State University, 2008) about difficulties getting data and programs to replicate Michael Mann's Hockey Stick calculation.
" I thought that it would be interesting to look at the underlying data, rather as I might look at drill data from a mining promotion. Business was slow and I browsed the internet for a due diligence package. I could not locate such a due diligence package nor the underlying proxy data for MBH98. Out of the blue (I was then a Canadian businessman unknown to climate scientists), I emailed Michael Mann, the primary author, inquiring as to the location of the MBH98 proxy data. To my astonishment, Mann replied that he had “forgotten” the exact location, but that an associate would locate it for me. The associate said that the data did not exist in any one location, but that he would get it together for me. I was dumbfounded. Here was a study that had been on the front page of the IPCC study, used in brochures sent to every household in Canada and there was no due diligence package. "
When McIntyre and McKittrick's attempt to replicate the "Hockey Stick" failed (see below) Mann said the original data and programming weren't used but refused to supply those:
"Mann also objected that we did not exactly replicate his computational steps or sequence of proxy rosters. No one had ever replicated his results, and we now know others had tried but were also unsuccessful. To date we are the closest anyone has been able to come in print. We were not bothered by Mann’s response on this point, but it did seem pointless to differ over trivial issues. So we requested his computational code to eliminate these easily-resolved differences. To our surprise he refused to supply his computer code, a stance he maintains to today. As for the proxy sequence, in building his PCs it turns out he had spliced together a number of different series in order to handle segments with missing data in the earliest part of the analysis. This was not explained in his Nature paper so Steve had not implemented it in the emulation program. We requested identification of the splicing sequence, which Mann refused to provide..."Ross McKittrick, What is the Hockey Stick Debate About?
Is this making  an open, dated, signed lab book with your results and calculations available to all, as we were enjoined to do as graduate students?


 The Oxford Dictionary gives the following definition of "fudge": "Adjust or manipulate (facts or figures) so as to present a desired picture".  This would include
  • altering given data to make it fit a hypothesis or discarding data that doesn't fit;
  • inserting fictitious data  or data not relevant to the hypothesis, for a better fit; 
  • cherry-picking data , taking selected data from a set that will fit and ignoring data that doesn't;
In this context I'll discuss first McIntyre and McKittrick's attempt to replicate the famed "Hockey Stick", the cornerstone of the IPCC dire predictions of the effects of AGW, and then cite just a few of the many relevant emails and computer program comments revealed in the Climategate documents.   I'll not give a detailed account, but only a summary and show some figures that justify McKittrick's and McIntyre's report that the hockey stick is, to put it charitably, not a compelling statistical analysis.   If you read both papers you can judge whether the statistical treatment, Principle Component Analysis (PCA) was adjusted, data were selected and replaced, in other words, whether "fudging" (as in the above definition) occured:
"How do we know 1998 was the warmest year of the millenium?"  Stephen McIntyre.
"What is the 'Hockey Stick' debate about?"  Ross McKittrick.
Here are some figures to illustrate the above:
From Ross McKitrick Hockey Stick article
Illustrated in the figure to the left are plots of two tree ring sizes (used as proxies for temperatures) one from California (top), the other from Arizona.  The x-axis is time, from about 1400 to present.  In the original hockey stick paper the top data set is presumably given 390 times the weight of the bottom.   One can see how this will force a huge temperature rise.

From Ross McKitrick, Hockey Stick article
In the figure to the left the top plot is data using the presumed principal component analysis of the original hockey stick paper.  The second down from the top is the simple mean of data.The third down is obtained with a conventional principal component analysis (no segmentation).    The fourth down eliminates one set of data (high-altitude from Idaho) and uses a segmented principal component analysis, as in the original paper.

There is also a figure in McKittrick's article (not reproduced here) that shows how they obtained a temperature (tree-ring proxy) rise in the latest years from random noise data, using a selection pattern presumed to underly the original hockey stick results.

Examples can also be had from excerpts from the Climategate files, emails and comments on computer programs  (see  CRU's Source Code: Climategate Uncovered HarryReadMe files for full texts):
  • "I’ve just completed Mike’s Nature trick of adding in the real temps to each series for the last 20 years (ie from 1981 onwards) amd (sic) from 1961 for Keith’s to hide the decline."
  • In two other programs, and, the "correction" is bolder by far. The programmer (Keith Briffa?) entitled the "adjustment" routine “Apply a VERY ARTIFICAL(sic) correction for decline!!”
  • Plotting programs such as print this reminder to the user prior to rendering the chart:     "IMPORTANT NOTE: The data after 1960 should not be used. The tree-ring density records tend to show a decline after 1960 relative to the summer temperature in many high-latitude locations. In this data set this "decline" has been artificially removed in an ad-hoc way, and this means that data after 1960 no longer represent tree-ring density variations, but have been modified to look more like the observed temperatures."
  • "NOTE: recent decline in tree-ring density has been ARTIFICIALLY REMOVED to facilitate calibration. THEREFORE, post-1960 values will be much closer to observed temperatures then (sic) they should be which will incorrectly imply the reconstruction is more skilful (sic) than it actually is. See Osborn et al. (2004)."
See also Climategate: The Smoking Code and Climategate: hide the decline for a more detailed analysis by Anthony Watts (a programmer) of the deficiencies;  for problems with temperature data stations as well as artificial corrections and deletions as applied to such data--see the links above.


The peer review process* is an essential mechanism in contemporary science to throw out the dross and keep the gold.    In order to be effective, it has to be applied objectively, without prejudice due to preconceived political, economic or theologic standards.  When such considerations enter into judgment of scientific work, the scientific method is tossed out the window.   Examples are shown in excerpts from Climategate emails  (see "ClimateGateKeeping" in Climategate and the Corruption of Climate Science [by David Pratt])
"The skeptics appear to have staged a ‘coup’ at ‘Climate Research’ ... My guess is that Von Storch [one of the editors] is actually with them (frankly, he’s an odd individual, and I’m not sure he isn’t himself somewhat of a skeptic himself) ...  I think we have to stop considering ‘Climate Research’ as a legitimate peer-reviewed journal. Perhaps we should encourage our colleagues in the climate research community to no longer submit to, or cite papers in, this journal." Michael Mann, March 2003, commenting about an article by Soon and Baliunas.
 "I will be emailing the journal to tell them I’m having nothing more to do with it until they rid themselves of this troublesome editor"  Phil Jones, again referring to the editor von Storch of Climate Research 
These are just two of many examples in which an effort was made (sometimes successful) to remove members of editorial boards who were not on board with the AGW dogma  (again, see the link ClimategateKeeping in Climategate and the Corruption of Climate Science.)

In my view the most reprehensible of these partisan attacks was the effort to get a skeptic, Chris de Freitas, sacked from his job at the University of Auckland.   See Climategate 2 and the Corruption of the Peer Review Process.

I'll leave it to the reader to judge whether the principles of scientific integrity outlined at the beginning of this post were followed by these proponents of AGW.


In the late 1980's the notion of AGW was very attractive to me.   However I read  papers by Richard Lindzen (Alfred P. Sloan Professor of Meteorology at M.I.T.), Frederick Seitz (former president of the National Academy of Science), Fred Singer, Willie Soon and Sally Baliunas that convinced me as a physicist with some statistics background, that many more factors are involved in climate than CO2 re-radiation, and that the non-linear differential equations involving heat transfer, cloud cover and condensation aren't going to be approximated as a predictive tool by computer models.  

Moreover, my wife (a historian with Medieval Period her specialty) pointed out to me that there was a Medieval Warm Period (MWP--a period from about 800 AD to 1300 AD), historical evidence that temperatures higher than those predicted by the AGW computer models existed--Greenland was called that because, presumably, it was green.  (The hockey stick model was presumably designed to belie the existence of the MWP and the Little Ice Age that followed it.)  The MWP was followed by a Little Ice Age, a cool period from which we are now recovering.   It is ironic that a graph of historic temperatures in an early 1990's publication of the IPCC showed the MWP and the Little Ice Age:
From Ross McKitrick, Hockey Stick article
The basic form of the above graph correlates well with earth bore core measurements and indirect measurements of solar output.

One last point:  I don't regard current temperatures taken by government agencies to be that accurate given the haphazard distribution of weather stations (near urban environments, near pavements, air-conditioning outlets,...) as the picture below illustrates:
From "Is the US Surface Temperature Record Reliable?"Anthony Watts

REFERENCES (other than links given above).

Climate Change: The Facts.   A collection of articles by various authors including Delingpole, Lindzen, Watts.

* A personal note:  I've been involved over the past 60 years as both reviewer and reviewed for papers and grant proposals.    When allowed, I've given my name as a reviewer, and have been thanked  on a few occasions by authors for pointing out errors that, if not corrected, would have prevented publication.    I myself have had more than one paper rejected because of legitimate errors, and in fact, on one of these, I rewrote the paper according to the reviewer's comment, including a major factor I had neglected and invited the reviewer to be a co-author.   (This was indeed possibly one of the few good pieces of work done in my scientific career, and I've been fortunate--one of the equations in the work has been used often enough that it is a "name" equation cited without footnotes.)

Friday, January 2, 2015

Free Will and God's Providence:
Part IV--The Many Worlds/Many Minds of Quantum Mechanics

"Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' [referring to quantum mechanics]because you will get 'down the drain', into a blind alley from which nobody has escaped. Nobody knows how it can be like that.” Richard Feynmann 
"If we look at the way the universe behaves, quantum mechanics gives us fundamental, unavoidable indeterminacy, so that alternative histories of the universe can be assigned probability."  Murray Gell-Mann

The video to the right (from YouTube) is from the introduction to the TV show Quantum Leap , which had the hero jump from one possible world to another, saving people in dire situations and altering history.


In the third post of this series on Free Will  my final comment was
"It seem to me that if God knows what we will do--even if he does not determine that we do it--we are not totally free in our moral choices.    There need to be options, different possibilities for what we can do, in order that freedom of choice--free will--be exercised... In the fourth post of this series I'll explore what quantum theory might offer to give this freedom."
That part of quantum theory that intersects with Molinism (God's Middle Knowledge) is Everett's Relative State Theory, more commonly known at the quantum Many Worlds Interpretation (MWI) or Many Minds Interpretation (MMI).    I'll give a bare bones summary of the relevant quantum mechanics (and references) and then try to show how the MWI can be joined to Middle Knowledge to give a frame for both God's omniscience and man's Free Will.    Quantum mechanics references are also given in a previous post.    Dear Reader: if all this quantum mechanics jazz makes you queasy (as it does my wife), you can skip to the end of this post to get my take on the connection with Middle Knowledge and Free Will.


Superposition in quantum mechanics is best illustrated by  the double slit experiment.   In classical optics, if you pass a light ray through two narrow slits you'll see an interference pattern as illustrated in the figure below.
Young's Double Slit Experiment,

The light beam at the top is split and passes through the two slits in the middle.    Each of the light rays passing through a slit is a wave, which has positive and negative amplitudes.   When a positive part of the wavefront from the left-hand slit meets a positive part from the wavefront from the right-hand slit, they reinforce, to give a bigger wavefront.    When a positive part of the wavefront from the left-hand slit meets a negative part from the right-hand slit, they cancel to give a smaller or null wavefront.   This phenomenon is interference.  The result of the interference is shown on the screen (bottom green band) where the reinforced waves (adding) give intense bands (white) and the canceled waves (subtracting) give dark bands.

One of the puzzling features of quantum mechanics is that particles (electrons, protons, etc.) can behave like waves (as in the light ray above) and waves  can behave like particles (e.g. light behave as photons) according to the kind of experiment used to study
them. Thus, in the figure below, we see particles showing interference patterns, as if they were waves.    (If the screen is removed and collimating tubes added as at the bottom of the figure--even after the particles pass through the two slits, as in the delayed choice experiment )--then there is particle-like behavior;   red and green particles behave as if they passed through the slit without interference effects--no wave-like behavior.

This behavior is represented in quantum mechanics as a superposition of states.    We use the notation " | state>" to indicate a system is in a given state, or for our example of the double slit experiment:
state> = | left slit> + | right slit>
which is to say that a particle going through the slits is going through BOTH the left and the right slits--it is a superposition, as would be the light wave.       Now if we put a measuring device near the screen with two slits to detect which slit the particle might have gone through (or use the detecting screen removal and collimators), then we get in the common interpretation of QM,
| state> = | left slit> + | right slit> --(measurement)-->| state> = | left slit>  or
  | state> =  | right slit>,
That is to say, the measurement process has "collapsed" the state function from a superposition to either a particle having gone either through the left slit or through the right slit, but not both simultaneously.   (Note: what I have termed "state function" is often termed "wave function", although in many instances there is no wave-like behavior associated with it.)


Measurement interaction with the particle before it reached the screen (in a superposed state)  has effected the collapse, but the mechanism by which this collapse occurs is mysterious,   It is represented by so-called projection operators, but these are not implied by or contained in the fundamental equation of quantum mechanics, the Schrodinger equation.   So the collapse of a superposed state by the appropriate measurement poses a problem of interpretation.

In the early days of quantum mechanics two great theorists, John von Neumann and Ernst Wigner, gave the following interpretation:  since an observer is required for a measurement, and since the final stage of an observed measurement is the belief in the observer's mind of the result of the measurement, one might conclude that consciousness is the means by which the collapse is effected.    This interpretation has been taken up with enthusiasm by followers of Eastern mysticism who do not understand quantum mechanics (see What the Bleep for an egregious example) and by some physicists and philosphers, although it is rejected by many physicists for the reasons given below.

If consciousness is the mechanism for collapse of a superposed state,  how does one explain what happens if no conscious observer is present?    For example, who would the observer be for the universe as a whole?  (One answer might be God--see  Quantum Divine Action via God, the Berkeleyan Observer, but that would clearly not satisfy many physicists.)    What happened in the early universe when there were no conscious observers?   The famed American physicist John Wheeler would answer in his Participatory Universe that the past is created by our observation of it.  
A more important objection was raised by Hugh Everett:  if you consider nested observers, for example, conscious A observes state | S>;  conscious B observes (conscious A observing state | S>), you can deduce contradictions if you try to employ  consciousness inducing collapse.    Such contradictions led Everett to his revolutionary  Relative State Theory (see below).


In 1957 Hugh Everett, then a grad student at Princeton under John Wheeler, produced as his Ph.D. thesis a revolutionary interpretation of quantum mechanics he called "Relative State Theory"and in a later publication (1973) "A Theory of the Universal Wave Function".    As Jeffrey Barrett puts it
"[Everett] wants to drop collapse dynamics from the standard von Neumann-Dirac formulation of quantum mechanics, then deduce the empirical predictions of the standard theory as subjective appearances of observers who are themselves treated within pure wave mechanics as perfectly ordinary physical systems.  The problem, however, is that is unclear precisely how Everett intended to account for the determinate records and experiences of observers." J.A. Barrett, The Quantum Mechanics of Minds and Worlds 
Everett's idea was to partition the wave-function (state-function) for the Universe into parts for observers and a part (the relative state) for the rest.   A given measurement result would be recorded by a given observer, another result for the same physical quantity by another observer.   The explanatory gap as to how exactly this would be done (pointed out in the above quote) has led to many theories building on Everett's, theories of "Many Worlds/Many Minds".


In 1970 Bryce DeWitt gave the first of many interpretations of Relative State Theory, a "Many Worlds",  in his Physics Today article.    DeWitt proposed that at each measurement all possible results occurred, such that worlds split.   Thus with the double slit experiment described above, two worlds would result:  one in which the particle had gone through the left-hand slit and one in which the particle had gone through the right-hand one.   Although this became a standard staple for science-fiction, this interpretation has problems, to name just two:

  1.  How are quantum mechanical probabilistic interpretations of measurement applied?
  2.  What happens to the identity of the observer--is he in the world with left-hand slit or right-hand?

Other interpretations followed.   (I'm not going to do more than list the most important of these with a brief explanation and online references (where available);  for fuller descriptions, see Jeffrey Barrett's book,  The Quantum Mechanics of Minds and Worlds.)

  • Many Worlds:  measurement splits the world into alternatives, one for each component state in the superposition
  • Many Histories: the linked reference gives Barrett's evaluation of Gell-Mann/Hartle's "Many Histories" approach to Relative State Theory, in which decoherence, interaction of a system with its environment, removes the superposition of component states.
  • Many Minds: instead of measurement splitting the world, each observer has an infinity of minds, whose distribution is probabilistic and evolves with time, but which are not superposed--a measurement is registered in one of these minds.   This approach has been advocated by Albert and Loewer, Lockwood and others.

In addition to the interpretations above, Barrett describes the Bell's (of Bell's Theorem) Everett(?) (sic) Theory,  Relative Facts Theory and Many Threads Theory in his book.

A common objection to all the above theories is that they are "ontologically extravagant"--they propose too much of reality.   But since God is infinite, is that a valid objection?     All the interpretations are supposed to fill  the following two requirements, among others:

  • They satisfy the same empirical requirements as standard quantum theory (give the same predictions).
  • They show how only one of the possible measurements made on a superposed state has been recorded by an observer.
None of the theories, according to Barrett, are totally satisfactory from a philosophical point of view.
Nevertheless, I will suggest below how one or another of the above might mesh with a Molinist point of view to reconcile God's omniscience and man's Free Will.


Now, finally we come to the point of this post and I will be brief.   Let's suppose that a science-fiction perspective for personal worlds exists, a multitude of possible worlds  in which there is one where I/my ego/my soul exists.    When I make a moral or ethical decision there will  be, not a splitting into the two different worlds that would ensue from different decisions, but a possibility for me--my ego, my soul--to go into one or another of those worlds.     In this view, God knows of all these possible worlds (the Molinist worlds of God's Middle Knowledge) that might ensue from my moral decisions.    Thus God's omniscience and the availability of choices required for truly free, Free Will, are compatible.

REFERENCES (other than links given in the post)

Quantum Enigma: Physics Encounters Consciousness, Bruce Rosenblum and Fred Kuttner--a clear, non-mathematical introduction to quantum physics with an emphasis on the many mysteries.

The Quantum Mechanics of Minds and Worlds, Jeffrey Barrett--a comprehensive review of the various interpretations of Barrett's Relative State Theory, deep philosophically but not mathematically.

The Philosophy, Theology and Science of Molinism, Max Andrews--I have not read this book (it has not been published at the time of writing this post) but it seems that it would be relevant and interesting