Catholic Teaching Science and Religion

The Quantum Catholic

Section 1–Science: Quantum Mechanics, A Primer

INTRODUCTION

Since 1900 the world of science has been turned upside down and inside out by two revolutionary theories: relativity (special and general) and quantum mechanics. Quantum mechanics originated from Max Planck’s explanation of black-body radiation (radiation from hot objects) and since that time (1899) has become a powerful and unchallenged tool of physics, down to DNA, quarks and the “God Particle”, the Higgs boson.Its predictions are highly accurate, yet as the Nobel Prize winner Richard Feynman remarked “I think I can safely say that nobody understands quantum mechanics”. Despite this eminent scientist’s remark (he received the Nobel prize for his pioneering work in quantum electrodynamics), it is possible to understand how quantum mechanics developed and how it is used.

In order to give the reader such a qualitative understanding, first there will be a preliminary, very qualitative discussion of the physical stuff, then a short history of the development of quantum mechanics, and finally a discussion of two experiments crucial to understanding theological implications, the double slit and entanglement experiments. It’s interesting that Richard Feynman used the double slit experiment in his undergraduate lectures at Caltech as a starting point for learning about quantum mechanics.

WAVES, RADIATION, MOMENTUM, ENERGY

This section was not in the first draft of this book, but my wife (my beta-reader, who is a math-phobe) read what follows and said “Too many symbols and numbers, my stomach aches”, so I thought I should do some preliminary discussion of the physics and math stuff—QUALITATIVE; FEW NUMBERS; MINIMUM NUMBER OF SIMPLE EQUATIONS. If you’re ok with numbers and formulae and remember some of your high school physics, you might skip this section.

Waves
Let’s talk first about wave-motion. This is particularly important for understanding quantum mechanics: an alternative name for quantum mechanics is wave mechanics and the thing that tells you what’s going on is more often called a wave function than its proper name (in my opinion), a state function. So let’s look at a picture of a wave:

 

Water Waves from a Bee’s Wings
From Wikimedia Commons (Bogdan Giusca)

What are the wave features shown in the illustration that are relevant to quantum mechanics?

• Most significant: the wave is not localized to one point; it’s spread out over an area;
• There are ups and down, crests and valleys—the light is shining off the high points and there are dark shadows in the low points;
• The pattern of ups and downs is repetitive with a common distance between high points or between low points; this common distance is the wavelength (In what follows the wavelength value will be denoted as “L” or, in common physics talk, “λ”, the Greek letter “lambda”.)

A mathematical way (please excuse!) of representing wave motion is by a moving sine curve, a traveling wave, shown in the illustration below:

Traveling Wave (moving sine curve)
From Wikimedia Commons

As noted above, “L”, is the value of the wavelength, the distance between adjacent peaks; it’s also the distance between adjacent bottoms. The wave goes up as high as it goes down (distances from the horizontal line, where there would be no wave).

Examples of a traveling wave are disturbing a liquid (as in the bee’s wings vibrating water in the first picture) or snapping a rope by one end. Suppose you’re sitting on a rock and count the number of wave tops that pass the point in one second. That quantity is the “frequency” of the traveling wave, which will be denoted here by “f” . [1]

If we think of a distance L between each wave top, and f wave tops pass in one second, then the distance covered by the wave in one second is f x L., which then is the wave speed (velocity if we take direction into account).

Radiation
Light and other electromagnetic radiation (heat, radar) consists of alternating electric and magnetic fields, at right angles to each other, as shown in the illustration below.   The speed at which the wave travels is the speed of light, commonly denoted by “c”:,

c = f x L.

IMPORTANT:
as frequency increases, wavelength decreases, and conversely.

3-D Diagram polarized electromagnetic wave:
The alternating electric field (red) in the vertical (yz) plane;
The alternating magnetic field (blue) in the horizontal (xy) plane.
From Wikimedia Commons,(Lookang)

Polarization of Light
You all are familiar with polarized sun glasses–the polarized material allows only light in which the electric field vector moves up and down in a given direction.    Light polarized in a given direction can be thought of as the superposition of two circularly polarized beams, one with the electric vector rotating clockwise as the beam travels, the other with the beam rotating counter-clockwise, as the animation below illustrates.

Left-handed Circular Polarization (electric vector rotates in a clockwise direction as beam travels)
from Wikimedia Commons
Right-handed Circular Polarization (electric vector moves in a clockwise direction as beam travels)
from Wikimedia Commons

If  two circularly polarized beams start out together, both with the electric field pointing up, they will combine to form a linearly polarized light beam, as in the preceding illustration.   When they start out together, the electric field add; when the wave has travelled a quarter of a wave-length, the electric fields are in opposite directions and cancel (zero field); when they have travelled a half-wavelength, the two field point combine in the downward direction.

The Electromagnetic Spectrum
To see how electromagnetic radiation wavelength and frequency refer to more common things like light, X-rays, microwaves, Infra-red, look at the diagram below.

Electromagnetic Spectrum:
Wavelength goes from long to short (rough scale indicated below);
(For example, radio waves are the size, roughly, of buildings);
Frequency goes from low to high (note colors in visible range);
Bottom bar gives rough temperature, color for blackbody radiation.
From Wikimedia Commons,

Momentum
In classical physics, the amount motion of an object is characterized by its momentum, designated by the letter p. (In Medieval physics it was termed “impetus”.) The momentum is equal to the product of mass times velocity. To get a notion of what this signifies qualitatively, consider the following:
The momentum of a 4000 pound car (e.g. a 2017 Cadillac) traveling at 20 mph is equal to the momentum of a 1000 pound car (e.g a 1951 MG-TD) traveling at 80 mph. [2]

Equal Momenta of 2017 Cadillac at 20 mph and 1951 MG-TD at 80 mph

Note that momentum is a vector, which is to say if the Caddie and the MG were traveling in opposite directions, their momentum would be opposite in sign. Thus the total momentum of the two cars, with speeds above, would be zero.  Since momentum is conserved, if the two cars collided head on and if the collision was elastic (as with billiard balls) the two cars would rebound in opposite directions with speeds as before the collision–total momentum zero. (Note: conservation of momentum is one of the fundamental principles of physics:  it applies in the absence of external agents doing work or taking energy.)   If the collision were inelastic, the cars sticking together, the cars would be motionless after the collision–total momentum zero. What would happen to the energy of motion? See below.

Angular Momentum
Another type of momentum, angular momentum, deals with rotation about a central point and is very important in quantum mechanics.  The earth has angular momentum in its motion about the sun, and it also has an intrinisic angular momentum, “spin”, due to rotation about the earth’s axis, as shown in the animations below.

 

Rotation of the Earth about its Axis (Intrinsic Angular Momentum–Spin) and in its Orbit about the Sun (Orbital Angular Momentum)
from Wikimedia Commons
Earth Rotating about its Own Axis ( Spin Angular momentum)
from Wikimedia Commons

Energy
Very briefly and qualitatively, energy gives the capacity to do work—lift objects, let a light bulb shine, heat a house. The energy of motion is called kinetic energy. For example, the kinetic energy of four Cadillacs going 20 mph equals the kinetic energy of one MG-TD going 80 mph. (Kinetic energy varies as the square of the speed.) There’ll be more discussion about the energy of elementary particles and radiation in subsequent sections of this chapter. Energy is conserved (if you don’t put any in or take any out), so what happens to the total kinetic energy if the Cadillac and MG were to collide head on? It would be converted to heat energy and work done crumpling the steel of the cars.

QUANTUM MECHANICS—A BRIEF HISTORY

At St. John’s College (Annapolis/ Santa Fe) students learn about science by studying its history—reading original papers and trying to reproduce original experiments. I also believe that the best way to understand a scientific topic is to follow its historical development—how ideas and applications changed. Science is not a smooth progression; the development is more like a recovering stock market chart, ups and downs, with a steady overall progression upwards. My historical account will be very selective, focussing on the developments that bear on the theme of this book.

Planck’s Quantum of Energy
At the end of the 19th century one of the biggest unsolved problems in classical physics was the “ultra-violet catastrophe”. The theory of radiation based on classical physics (no quantum mechanics) predicted that as the wavelength of  radiation from a hot object

Energy Radiated versus Wavelength for a “Black Body”. The “Classical Physics” curve goes to infinity as the wavelength decreases. The other curves, from Planck’s quantum theory, fit the data.
From Wikimedia Commons

 decreased to zero, the amount of radiation would go to infinity. But what is observed is that below a certain wavelength (the value of which depends on the temperature), the amount of radiation decreases.

Max Planck resolved this problem in 1899-1900 by proposing that radiation energy could only be transferred only in a discrete package, a “quantum” of energy. The amount of energy contained in this quantum would be inversely proportional to the wavelength of the radiation. Since the wave frequency is inversely proportion to wavelength, we can also say (and this is the usual formulation):

the amount of energy in a quantum is equal to hf, where h is the universal constant, Planck’s Constant and f is the frequency of the radiation. [3]

(Remember the inverse relation between frequency and wavelength.)

As wavelength goes to zero, frequency becomes infinite and the quantum of energy becomes too large to be transferred, and the ultra-violet catastrophe is avoided. [4] Planck’s formula fits the observed dependence of radiation output at various temperatures: as the temperature decreases. the maximum radiation is found at a longer wavelength, shorter frequency. This is in accord with everyday experience: as a hot object (say an iron bar) cools, the color goes from yellow to orange to red, thus wavelength of the maximum radiation increases as the object cools.

Illustration of Black-Body (Thermal) radiation: Notice red objects–fireplace coals–only 800 Kelvin (about 980 °F), much cooler than white-hot object, molten steel being poured, 1600 Kelvin (about 2420 °F).

Bohr’s Atom—Energy Levels
At the beginning of the 20th century, perplexed physicists faced still another problem: according to classical theory, negatively charged electrons surrounding the small positively charged nucleus at the center of an atom should fall into that positive charge emitting continuous radiation as they did. But this didn’t happen, only discrete radiation (spectral lines) were observed and atoms were stable.

Nils Bohr’s solution to this problem (1913) was simple but revolutionary. (Simple enough that it’s taught in first year chemistry courses.) An electron orbiting a nucleus could have only certain discrete energies, corresponding to discrete orbits about the nucleus. When an electron in a higher energy orbit made a transition to a lower energy orbit, radiation was emitted. The frequency (wavelength) of the emitted radiation corresponded exactly to that given by Planck’s relation:

Bohr Atom Radiation: electron goes from higher to lower energy level (from Wikimedia Commons)

change of energy = hf.

The change in energy was the difference in energies of the two orbitals.

Bohr’s relations worked very well for simple atoms, those with only one electron orbiting a positive nucleus, for example the hydrogen atom, the He+ atom (Helium with one electron removed), etc. However, for more complicated atoms and for molecules, it did not fit as well. Bohr’s theory was the first step to a complete theory, which was to be developed in the 1920’s.

Einstein, Compton and DeBroglie: the Wave-Particle Duality
In 1905, Albert Einstein’s great year [5], he proposed an explanation of the photo-electric effect. Following Planck, he assumed that radiation energy was carried by particles of zero mass, “photons”. The energy of a photon is given by

E= hf.

If Einstein’s theory of special relativity is applied to photons, they have a momentum,

p = h/wavelength.[6]

From scattering of x-ray experiments the American physicist Arthur Compton also showed in 1923 that photons had a momentum (given as above): when the x-rays hit an electron, their wavelength and direction was changed in a way that could be accounted for by the principle of momentum conservation. In 1927 Compton received the Nobel Prize for this work.

Duc Louis deBroglie, studying for his doctoral degree in Paris in the early 1920’s, made a leap of imagination: if photons had momentum  h / L (L= wavelength), why might not the same relation hold for particles with non-zero rest mass? If the relation between momentum and wavelength, is rearranged, the corresponding wavelength for particles with non-zero rest mass would be given as

wavelength = h/p = h/(mv),

where m is the mass of the particle and v is its velocity. [7] DeBroglie’s hypothesis was confirmed in 1923 when Davisson and Germer showed that electrons behaved as waves, with the wavelength predicted by the DeBroglie relation. They won the Nobel Prize in 1927 for this work.

Schrodinger, Heisenberg, Dirac—Modern Quantum Theory Is Born

A paradox, a paradox
A most ingenious paradox!
We’ve quips and quibbles heard in flocks,
But none to beat this paradox!”
William S. Gilbert, Arthur Sullivan, “The Pirates of Penzance”

So what was the electron to be—a particle or a wave? As one scientific jokester remarked, on Mondays, Wednesdays and Fridays we can take the electron to be a particle, and on Tuesdays, Thursdays and Saturdays a wave, and on Sundays let it rest. This wave-particle duality paradox was to be resolved in several ways in the 1920’s.

In 1925-1926 the paradox was resolved by Werner Heisenberg’s matrix formulation of quantum mechanics and by Erwin Schrodinger’s wave equation. I’ll not go into a detailed discussion of either of these approaches, since they’re not relevant to the main thrust of this book, but for those interested in a more detailed mathematical exposition, please refer to the references at the end of this book.

The arguments about which approach was valid—matrix mechanics or the wave equation—became quite heated (the German word for “crap” was used). [8] In 1927, Schrodinger showed that the two approaches gave the same result, and shortly after this the British physicist, Paul Dirac produced a theory from which could be derived matrix mechanics and the Schrodinger equation. This is the theory we’ll examine in somewhat more detail, because it will be more useful in explaining the quantum applications discussed later. (Also, it doesn’t demand an understanding of higher math.)

The starting point for Dirac was the idea of a “state function”. He represented this as an abstract quantity denoted by brackets:

| inside stuff>.

The “inside stuff” was notation to represent the properties of the state. For example, for an electron in a hydrogen atom the quantum numbers describing the state would do; for a free electron, the wavelength and/or position would be used.

Let’s use a highly artificial example to illustrate these ideas. [9] Consider designating the political practice of a married couple: How might the state of the couple be designated with this notation? One possibility would be the husband votes Democratic and the wife Republican, for which one could write |couple, vote> = |w,D> |h,R>;   the state of the wife voting Democratic is |w,D>,  the husband voting Republican is |h,R>, and the state of the couple vote is the product of these two. A pictorial representation is given at the right.

|couple, vote> = |w,D> |h,R>

 

Now if you have any couple (and we neglect minor parties and not voting) then you could have other combinations, for example, both Democratic, both Republican, the husband Republican, the wife Democrat.     One possibility is that before the vote, it is equally likely that each of the above combinations could occur, so we could write a

|Couple,vote> = |w,D>|h,D> + |w,D>|h,R> + |w,R>|h,R> [10].

or, again pictorially:

The individual product states are called the “basis” for the state function. [11]

The act of voting will pick out one of the component product pairs (it’s assumed that both husband and wife vote); the state function thereby “collapses” from three product pairs to one; for example if the husband votes Republican and the wife Republican, the state function collapses to

|Couple,vote> = |h, R>|w, R>
Wife Republican (blue hat); husband Republican (blue cap)

This measurement induced collapse of a state function, such that one basis state is picked out from all the rest, is a fundamental and puzzling feature of quantum mechanics. More will be said about this in Section 2.

Feynman, Gell-Mann, Schwinger—Mature Quantum Mechanics

“Is the purpose of theoretical physics to be no more than a cataloging of all the things that can happen when particles interact with each other and separate? Or is it to be an understanding at a deeper level in which there are things that are not directly observable (as the underlying quantized fields are) but in terms of which we shall have a more fundamental understanding?”
Julian Schwinger, Quantum Mechanics: “Symbolism of Atomic Measurements”

In the 1940’s two young physicists, Richard Feynman and Julian Schwinger, were engaged in World War II scientific work: Feynman at Los Alamos and Schwinger at MIT’s radar establishment. [12] Two more different personalities, in their teaching style, in their approach to physics, and in their personalities can not be imagined. Feynman is portrayed in a number of books and articles; Schwinger, not so much. Read about Feynman and then imagine a polar opposite for Schwinger. They carried quantum mechanics to a level of sophisticated analysis that enabled it to predict with startling accuracy for measurements in the atomic realm.

Feynman originated “Feynman diagrams”, a graphic way of illustrating complicated integrals and mathematical equations for processes involving sub-atomic particles. They enable physicists to talk on a blackboard, without using reams of paper. Schwinger devised creation and annihilation operators (see the quotation above) to solve problems in the quantum theory of radiation. Both Feynman and Schwinger received the Nobel Prize for their pioneering work in quantum electrodynamics.

Feynman Diagram of electron-positron collision and annihilation. From Wikimedia Commons

In the diagram above two photons, gamma rays, are emitted to enable conservation of momentum; their combined momentum will equal that of the colliding electron and positron. The red horizontal arrow connecting the electron and positron is at one instant in time;  accordingly it represents an interaction–collision/annihilation.  ( Also, note that the downward arrow for the positron (e+) does not mean it’s traveling backwards in time. The down direction is a convention for anti-particles; for example, an electron traveling backwards in time is equivalent to a positron traveling forward.)

Murray Gell-Mann, like Feynman and Schwinger, did pioneering work at a very early age. His interests were in theory of fundamental particles. Perhaps with an insight that a physicist’s reputation depended partially on how his theories were packaged, he invented the name “quark” (taken from James Joyce’s “Finnegan’s Wake”—“three quarks for Muster Mark”) for the elementary entity that makes up protons, neutrons and other sub-atomic particles. Quarks come with a rich variety of attributes: charge, flavor, color, strangeness, that enable a periodic table of the “zoo” of elementary sub-atomic particles to be categorized nicely. (See the post God, Symmetry and Beauty I: The Standard Model and the Higgs Boson.)

So we see that quantum mechanics has delved into the very smallest of matter and found answers confirmed to the highest degree of accuracy. Where are the mysteries referred to in the title? Before that’s discussed in Section 2, a brief foundation has to be laid.   Two experimental features of quantum mechanics, the double slit experiment and entanglement, have to be explored.

QUANTUM MECHANICS—THE DOUBLE SLIT EXPERIMENT

In teaching about quantum mechanics, Richard Feynman used the double slit experiment as a basic example in order to show qualitatively how quantum physics is different from classical physics.

Before discussing the quantum mechanical experiment, I’ll refer the reader to the preliminary section on wave motion. Recall that a wave is a disturbance that goes up and down—equally up from the middle and equally down—and that moves in distance and time.

Interference Pattern of Two Water Waves from Wikimedia Commons

A good example is a water wave. The water in a wave moves up and down, with the crest of the wave advancing. The up part of the wave as can be designated as positive and the down part negative. What happens when an up part of one wave (positive) meets a down part of another wave (negative)? They cancel each other out. When waves of like sign meet, they reinforce: the up gets higher, the down lower. For sound waves (same wavelength) from two speakers, reinforcement (constructive interference) and canceling out (destructive interference) will give rise to beats.

Let’s go further and look at light, electromagnetic waves. Let’s suppose light passes through a narrow slit or a hole. You can picture the light wave approaching the slit as a series of equidistant parallel lines, which represent the maxima in the intensity of the light wave. What happens when the light goes through the slit? It bends around the corners! The series of straight parallel lines becomes a series of curved lines centered at the slit, as shown in the animation below:

Diffraction of a Light Wave from Wikimedia Commons

This change of the plane wave to a curved wave as it goes through a hole or slit is called “diffraction”. If you put a screen in front of the diffracted wave you’ll see a pattern of broad lines, as shown in this linked video. The center line, opposite the slit or hole, will be most intense and the equally spaced lines on either side of the center will be much less intense. The lines are where the maxima in the waves have hit the screen.

Now, consider a double slit experiment with light. There are two spherical wave fronts emerging from the two slits. How do they combine? Because they are waves, they have positive and negative amplitudes, tops and bottoms of the wave, as discussed above. When the top of a wave from one slit encounters the bottom of a wave from the other slit they cancel out—yielding flat, zero amplitude; when the top of a wave from one slit meets the top of a wave from the other slit they combine to give a higher wave; when the bottom of a wave from one slit meets the bottom of a wave from the other slit, they combine to give a deeper wave.

This canceling and adding up is called interference, and is a general property of wave motion. The process is illustrated in this linked video. If a screen is put in front of the double slit, the most intense streak on the screen is centered between the two slits, rather than two intense streaks directly opposite each of the slits, as would have happened if there had not been interference.

What happens in the double slit experiment when quantum mechanics is at work? Consider a beam of electrons going through the double slits. If the electrons acted as particles, like bullets, we’d expect two intense streaks on the screen, directly opposite the slits, as if we’d fired bullets through the slits. If the electrons showed wave properties, as DeBroglie suggested, then we’d expect a diffraction pattern, as with light waves. That’s what is observed after a large number of electrons have gone through the slits. The diagrams below illustrates the difference between classical and quantum physics:

Particle Double Slit Experiment, Classical Physics from Wikimedia Commons
Double Slit Experiment, Quantum Physics
Modified from Wikimedia Commons

What happens if only one electron goes through the double slit? If we don’t try to find which slit it goes through, it can land anywhere on the screen—there’s no way of telling from the hit on the screen which slit the electron has gone through. However, after a large number of electrons have passed through the slits, the intensity pattern on the screen is just like that for a light wave diffraction. The dynamic situation is illustrated in this linked video featuring “Dr. Quantum” of “What the Bleep” and in the animation below.

Animation of a Particle Passing through the Double Slite and Behaving as a Wave
from Wikimedia Commons

Now, here’s something very strange: if you try to observe which slit the electron has gone through by putting a detecting device behind the slit, no diffraction pattern is observed. It’s as if the electron knows it’s being observed and decides to behave as a particle, not a wave. What is even more strange, is that if you put a detecting device in front of the slit, to determine what has happened after the electron has gone through the slit, it still “knows” it has been observed and goes through as a particle. This situation is described in the “delayed choice experiment”, discussed below, and has some interesting theological and philosophical implications.

QUANTUM MECHANICS–THE DELAYED CHOICE EXPERIMENT

In 1976 the renowned American physicist, John Wheeler[13]  proposed  a “thought” (“gedanken”) experiment that might answer the question “what happens if you try to change the type of measurement after a  particle has gone through  the slit?”   He outlined an astronomical version of the experiment, using gravitational lensing to provide two different pathways/slits.   Light from a distant star or galaxy is bent (refracted) by the mass of a large galaxy between the star and us, so that the light appears to come from two separated sources, as shown in the illustration below:

Gravitational Lensing–Two Images from a Single Source as Light is Bent by a Large Mass
from Wikimedia Commons
Wheeler’s Delayed Choice Experiment Using Gravitational Lensing
from Wikimedia Commons

If images from two spatially separated telescopes were looked at separately, as in the left part of the diagram, no interference would result;  if the images from the two telescopes were combined and looked at together, as in the right part of the diagram, phase interference would occur with a pattern of interference fringes.  The images are combined by using half-silvered mirrors as beam splitters (see below).

The delayed choice experiment has been realized experimentally.  Rather than using two slits, a beam-splitter (half-silvered mirrors) provide the two paths–reflection and transmission, and a technique called quantum erasure provides the delayed choice of measurement.   There are three YouTube videos that provide clear and graphic explanations of the experiment, here, here and here.  Each has a different metaphysical bias;  I’ll give my own interpretation below in Section 3.

The results are as Wheeler predicted in his gedanken experiment.   The observer controls the choice of quantum entity behavior  by his choice of measurement technique, even if the decision point for the observer is after the decision point for the quantum entity. If you observe the particle after it has gone through the slit (hit the half-silvered mirror), it behaves classically—there are no interference effects.    There is another interesting feature of the experiments diagrammed in the videos:  two “entangled” photons are used in the experiment.  Wonderfully, what occurs for a  photon traveling a short path and hitting a detector after traveling a short path is determined by what happens to its twin AFTER that detection.  In other words, there appears to be some sort of backwards in time effect and instantaneous action at a distance for the entangled pair.

There are two interesting and significant corollaries to this experiment.    The light source–some distant galaxy–is millions or billions of years in the past–but you’re affecting it by the present day measurement.   From this deduction Wheeler derived his notion of the participatory universe, a universe created by observation, both in the present and the past. As he put it in an article about quantum physics and information theory, the universe is created by answering yes / no  to questions about observations– so a binary response and thus “It from Bit.”.  (And, one might ask, what happens if you go far enough back in the past that no observer was present–but more of that below.)

QUANTUM MECHANICS—ENTANGLEMENT

In the section above, an example of a married couple was used to illustrate the quantum vector state formalism. Recall, we denoted the state of a husband voting Democratic as |h,D> and voting Republican as |h,R>; similarly the wife voting Democratic as |w,D> and Republican as |w,R>.

This can be used to illustrate an intriguing feature that is fundamental to “quantum mysteries”, “entanglement”.  Suppose that the wife and husband are of one mind politically, so that whichever way the wife votes, so will vote the husband. (We could consider the contrary, that whichever way the wife voted, the husband would vote the opposite, but that doesn’t really depict a harmonious marriage.) The votes are thereby entangled: if the wife votes Democratic, then so does the husband; or if the wife votes Republican, so does the busband. The state function is then

|Couple,vote,entangled> = |h,D> |w,D> + |h,R> |w,R>

or, pictorially

 

The act of voting would then yield for the state function either |h,D> | w,D> or |h,R> |w,R> .

The husband’s and wife’s votes are entangled, not independent; if the wife votes Democratic, so would the husband; if the wife votes Republican, so would the husband. According to quantum entanglement, such would occur even if the husband and wife had been physically separated for some time before voting: the wife in New York,say, and the husband in California, and they had not communicated about how they would vote.

How is entanglement realized physically? The usual treatment is to start off with a system of coupled particles. If these particles are photons, the quantity measured is the polarization of the light rays carried by the photons [14].   The most significant demonstration of this photon entanglement is the “Aspect Experiment”[15], carried out to test “Bell’s Theorem”.

The notion of entanglement is a profound and mysterious aspect of quantum mechanics. We’ll talk more about its philosophical and theological implications in Section 2.

QUANTUM MECHANICS–THE UNCERTAINTY PRINCIPLE

Another unreal fact about the world revealed by quantum mechanics was the “Uncertainty Principle”.    “Uncertainty” in this context means that you can not measure accurately and simultaneously  both values of certain pairs of variables:  position and momentum, time and energy, components of angular momentum.  For example, if you know the momentum of a particle exactly you can’t simultaneously know its position.   Looking at this from the point of view of the wave-particle duality, this is reasonable.  If a quantum entity has a precise momentum, it also has a precise value for its wavelength, according to the DeBroglie relation mentioned above.   But a wave is not localized–it’s spread out, so its position is not well defined.    Also, one can show that a particle, with a well defined position can be regarded as a “wave packet”, made up from the superposition of lots of waves with different wave-lengths (and therefore different momenta) as shown in the animation below.

Wave packet (envelope shows possible measurement positions; red and blue lines are two of the waves superposed to make up the packet);  this packet is dispersed (flattened out) by interaction with environment
from Wikimedia Commons

Section 2–Science: Quantum Mysteries and Interpretations

“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 Feynman, “Probability and Uncertainty — the Quantum Mechanical View of Nature”, p. 129

According to Feynman, we should not inquire into the “reality” underlaying quantum mechanics, because we won’t find an answer. Even though predictions based on quantum theory are highly accurate, a qualitative description of what “actually” occurs during a experiment can be subject to many different interpretations. Indeed, a Wikipedia article on quantum mechanics, lists 15 different interpretations, and a search of the Stanford Encyclopedia of Philosophy on interpretations of quantum mechanics yields at least as many references.

All of these interpretations try to deal with those aspects of quantum mechanics that seem mysterious to us, that don’t reflect our everyday experience. Some of these have been touched on in the previous chapter.

• How does a quantum entity “know” when to behave as a particle, and when as a wave?
• How does a quantum entity “know” when it is being measured in the double slit experiment?
• How do two entangled quantities communicate that entanglement relation instantaneously even when separated by some distance?
• What happens to the non-measured component of the state function when it collapses on measurement?

Most working physicists probably don’t concern themselves with such questions. I didn’t, myself, 20 to 50 years ago when my research involved applications of quantum mechanics to magnetic resonance [16]. This point of view is labelled “instrumentalism”—if it works, don’t wonder why. Although many physicists adhere to this interpretation, it’s not a fruitful approach to learning how quantum mechanics and Catholic faith intersect, so I’ll not discuss it further.

Four interpretations that do relate to quantum theory and Catholic teaching will be discussed:

“Copenhagen Interpretation”: a real state function;
Consciousness: the agent of quantum measurements;
“Many Worlds/Many Minds” (Relative State);
“Quantum Logic”;

The Copenhagen interpretation, promoted by Bohr and Heisenberg in the early days of quantum mechanics, is that to which most physicists adhere currently.  It maintains that everything we need to know about the system is contained in the state function, and that  measurements determine how the system behaves–as a particle or a wave.  It does not recognize that “The Measurement Problem” is a problem, even though this issue is a major concern for many physicists and philosophers.  The Copenhagen interpretation in itself is not that relevant to Catholic teaching, but we mention it here because of its historical importance and because it gave rise to Bell’s Theorem (see below), which is relevant

The last three interpretations do deal with the measurement problem, but in different ways.  Let me add that each of these interpretations is in accord with measured results. There is no way of distinguishing which is correct by experiment. [17]   Before discussing those, let’s see what Bell’s Theorem has to say about the reality of quantum mechanics.

BELL’S THEOREM, EINSTEINS’S REALITY AND HIDDEN VARIABLES

Einstein’s EPR Paradox: the Hidden Variables of Quantum Reality
Even though Einstein was a quantum mechanics pioneer (the photo-electric effect), he strongly opposed later developments in quantum mechanics: the uncertainty principle and the probabilistic nature of measurements. In 1935 he published (with Podolsky and Rosen) a  paper which is now referred simply by the authors’ initials, the EPR paradox.

The EPR authors claimed that quantum mechanics, as then formulated, was “incomplete”–it did not describe reality completely.   They used the example of a pair of entangled particles, such that measurement on one  particle would instantaneously determine the value of the measurement of the entangled  property of the other particle, even though these were separated by some great distance.   Such instantaneous linkage was “spooky” according  to Einstein, violating the special relativity condition that no interaction could travel faster than the speed of light.   Further, Einstein did not cotton to the notion that an observer dependent measurement determined how a system behaved;  his comment was “The moon is still there, even if you don’t look at it.”   They proposed that hidden variables were at the heart of quantum mechanics, and that these variables were “real”, not just resulting from a measurement.

Bell’s Inequality–and the experiments disproving it.

“I am a Quantum Engineer, but on Sundays I Have Principles.”
John Stewart Bell (of The Bell’s Theorem) as quoted in Quantum [un]speakables: from Bell to quantum information.

In 1964 an Irish (Northern) physicist, John Bell, proposed an inequality that would be obeyed if classical physics were followed, but not if quantum mechanics operates.  I won’t give a proof for the inequality, which goes by the name “Bell’s Theorem”, but only say that it follows from certain implicit assumptions about reality, logic, and laws of probability.  There are nice, not too mathematical, versions here, here and here. [18]  Rather, I’ll focus on the profound implications from falsification of the inequality by experiments.

For those who don’t want to go to the links, I’ll summarize what the experiments are all about.   First, consider how polarization for a electromagnetic wave (light, for example) is translated to the quantum behavior of a light particle, a photon:  the left- and right-handed circular polarization for a light wave corresponds to two different states for a photon.  A photon that behaves as linearly polarized light (e.g. a photon passing through a polarizing screen) is a superposition of these two states.   The same quantum mechanics that yields the Uncertainty Principle tells us that we can’t determine which of these two states the photon was in before it passed through the polarizer.

Now let’s consider entanglement.   There are processes, laser set-ups, that will emit two entangled photons in opposite directions, photons with the same circular polarization state (either both left-handed or both right-handed).   Einstein’s position is that these are emitted as |L>|L>  or |R>|R>;  if we knew enough about the hidden variables that govern the emission process we could predict which pair would be emitted.  Quantum theory says that the two photons are emitted as a superposed pair,|L>|L>+|R>|R> (like the entangled husband and wife example above), .

Bell derived an inequality for the number (probability) of detecting both photons with the same polarization if Einstein’s picture held.   This derivation can proceed along a variety of routes–a hilly road requiring some sophisticated probability calculations,  a country lane using a pictorial Venn diagram, or an interstate highway tabular demonstration  with “easy math” related to the experiment.

Each of the linked articles and videos gives an  explanation of how the violation of the Bell Inequality changes our view of reality.  I’ll give my version here which is more concise, but for a very complete view of the philosophy involved, I recommend Michael Redhead’s article in the CTNS series, “Quantum Mechanics–Scientific Perspectives on Divine Action” [19] or his book, “Incompleteness, Nonlocality, and Reality:  A Prolegemon to the Philosophy of Quantum Mechanics”.    

To sum up, if as Einstein suggests, there is a reality hidden within in quantum mechanics, it is nonlocal.   That says that entangled entities interact instantaneously even across astronomical distances.   Alternatively, there is no such reality, or as the French physicist / philosopher, Bernard d’Espagnat would have it, it is a “veiled reality” that we don’t understand.     But more of this in Section 3, when the intersection of quantum mechanics with theology is discussed.

THE MEASUREMENT PROBLEM:  STATE FUNCTION COLLAPSE

“Young man, in mathematics you don’t understand things. You just get used to them” John von Neumann, responding to a young physicist’s question.

Almost since quantum theory was first proposed, a fundamental problem in relating the mathematical apparatus to the “real world” was the “measurement problem”. To make this more intelligible, let’s use the entanglement example given in the husband and wife who vote the same way.

Recall we denoted the “state function” for a couple voting the same way as

|Couple,vote,entangled> = |h,R> |w,R> + |h,D> |w,D>

|h,D> means the husband votes Democratic, |w.R> means the wife votes Republican, etc. After voting the state function becomes either |h,D> |w.D> or |h,R> |w,R> , to represent the husband and wife both voting the same way, either both Democratic or both Republican, so that we can think of the state function as having collapsed after voting, with voting representing the act of measurement.

Here’s the question: what mathematics represents this collapse and how is it incorporated into the formalism? The problem was posed early on by Erwin Schrodinger (he of the Schrodinger equation) with his “Schrodinger’s Cat” Paradox.

Schrodinger’s Cat–Alive or Dead?
from Wikimedia Commons

The sketch above represents Schrodinger’s “Gedanken Experiment”, a thought experiment which has inspired both philosophers and science-fiction authors.
Here in short is the experiment: a canister containing a radioactive material is located beneath a vial containing hydrocyanic acid (HCN); when the radioactive material emits a single particle, it hits a detector which will trigger a hammer to break the vial, whereupon the cat will die from cyanide poisoning. Now the box is closed, so you don’t know before you open it whether that cat will be alive or dead, that is, whether a radioactive disintegration has occurred or not. Accordingly you say that the state function for the contents of the box is a superposition of live cat and dead cat.

|Cat, box unopened>
                   =  |live cat, no radioactivity> +|dead cat, radioactivity>

This result seems odd in the extreme, particularly since nothing like it has been observed for macroscopic objects. In fact, recent work shows that such a superposition applies only to systems on an atomic scale (and maybe a little larger); for macroscopic objects, interactions with the environment—“decoherence”—removes the superposition.[19]  Nevertheless, the measurement problem remains for objects on an atomic scale.

A mathematical tool to represent measurement can be introduced into the formalism of quantum mechanics, a “projection operator” that picks out one component of the superposition. Although this tool “works”, it is an add-on; it is not specified in the Schrodinger equation or equivalent formalism.  It does not follow some  of the core principles that are foundational for fundamental theories [20].  For that reason some physicists are unhappy with the Copenhagen conventional interpretation and propose others, such as described below.

THE FINAL MEASUREMENT AGENT, THE OBSERVER

In the early days of quantum mechanics two great theorists, John von Neumann and Eugene 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.

Von Neumann’s approach was mathematical: there is a causal chain of measurement between the system being measured, the measuring apparatus and finally the observer’s awareness of the measurement result—his/her consciousness. Quantum mechanical theory does not have anything to say about where the measurement process stops, so it is natural to take it as the subjective awareness of the result, involving consciousness, as the final step.

Fritz London, another early pioneer in quantum theory, amplified Von Neumann’s ideas about consciousness playing an important role in the measurement process:

“According to London and Bauer the main feature of consciousness is introspection: in giving an account to myself of the state in which I am, I know that what I see now is white rather than black, and I know that I know.” Andrej Grib, ‘Quantum Cosmology: Observer Logic’ in Quantum Cosmology and the Laws of Nature–Perspectives on Divine Action [21]

Wigner’s approach was different. He proposed a modification of the Schrodinger’s cat gedanken experiment, with his (Wigner’s) friend opening the box while Wigner is not present. Wigner learns how the experiment turned out from his friend: |live cat, happy friend> or |dead cat, sad friend>.

Then we want to know “Is the friend included in the superposition of states?” Was there such a superposition before the friend entered the lab or did it suddenly occur when he came into the lab? These questions led Wigner to conclude that consciousness is a different sort of beast, that in some way it is able to cause collapse. He later abandoned this idea and the general notion that macroscopic objects were subject to quantum rules.

The interpretation that consciousness is a terminal stage of quantum measurement has been taken up with enthusiasm by followers of Eastern mysticism who do not appear to understand quantum mechanics 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).

QUANTUM MECHANICS: MANY WORLDS, MANY MINDS

“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

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 it “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, “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/she in the world with the dead cat or the live cat (in the Schrodinger’s Cat experiment)?

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.

A common objection to all these 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 in a later chapter 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.

QUANTUM LOGIC

Quantum logic “explains” several puzzling features of quantum mechanics:

the uncertainty principle: we can’t get exact simultaneous measurements on complementary variables (for example, energy and time);
the wave-particle duality; shown in the double-slit experiment;
The entanglement of particles: shown in experiments testing Bell’s Theorem.

Quantum Logic denies the Distributive Law that holds in conventional Boolean logic. Suppose we have events or logical propositions A,B,C. Then the Distributive Law for Boolean logic says

[A and (B or C)] = (A and B) or (A and C)

where and, or are logical conjunctions. This difference can be illustrated by the double slit experiment diagrams, shown above (Section 1) and below

Two Slit Experiment, Boolean Logic
from Wikimedia Commons

If a beam of particles passes through the two slits and behaves according to classical physics (Boolean Logic), you’d expect two spots on the detecting screen, more or less opposite each slit. This is what you see in the illustration to the left..

Now suppose you have quantum behavior (Quantum Logic) as shown in the illustration below. You have a beam

Double Slit Experiment, non-Boolean Logic
Modified from Wikimedia Commons

of particles (electrons, photons, whatever!)–passing through the two slits. If one takes A to mean a particle hits the screen, B that it has passed through the upper slit and C that it has passed through the lower slit, then the classical experiment would have particle passing either through the upper slit and hitting the screen more or less opposite that slit (A and B), or passing through the lower slit and hitting the screen more or less opposite that slit (A and C) as in the illustration above. But that is NOT what happens. Instead you get each individual particle behaving as if it were part of a wave and “knew” about both slits.

In other words, the logical terms B and C can’t be separated into B or C, it remains B and C in quantum logic. A particle goes through both upper and lower slits at the same time, as does a wave-front.

According to Andrej Grib [21], our minds operate in a Boolean logic mode. We cannot apprehend non-Boolean logic, whence the apparent mysteries of quantum mechanics. The perception of time itself is a consequence of this Boolean mind / non-Boolean universe dichotomy. We must experience events separately and in succession, as past, present and future, even though the physics of relativity suggests they are conjoined, that is to say are not really separated in that non-Boolean universe.

Section 3–Intersections: Quantum Mechanics | Theology

“The one thing worse than a theology that attempts to draw connections between physics and God is a theology that believes it has no need of such connections, a theology that believes it can concoct the divine out of metaphysical whole cloth.”  Philip Clayton, “Tracing the Lines” in Quantum Mechanics–Scientific Perspectives on Divine Action. [23]

DOES QUANTUM MECHANICS SPEAK TO CATHOLIC TEACHING?

Or, is there a legitimate purpose to this Chapter?   Well, let me ask you to look at my blog, Reflections of a Catholic Scientist.   At the right you’ll see a list of the most visited posts.   The most visited had to do with quantum mechanics and transubstantiation, the transformation by a priest of wafer into the body of Christ.    Two of the remaining five also deal with quantum mechanics and Catholic teaching.    So if interest is a criterion, the answer is yes.

Let’s see what theologians, philosophers and physicists had to say about the intersection of quantum mechanics and theology, according to Philip Clayton (“Tracing the Lines” in Quantum Mechanics–Scientific Perspectives on Divine Action. [22]):

  1. 1.”No reasons can be given, other than purely subjective ones, for any theological position (Cushing)

  2. 2.”Serious theological positions can be given in some cases, but quantum physics is too unclear…to give rise to helpful theological conjectures (Polkinghorne).

  3. 3.”Some constructive theology can be written…even if our conjectures remain highly speculative (Chiao, Clayton, Russell, Stoeger, Tracy).

  4. 4.”..Strong theological conclusions can be reached on the basis of modern physics (Dombs)… Intelligent Design theorists (Behe, Dembski) argue that evolution requires a prior intention and an in-built design on God’s part.

  5. 5.”The convergence between the conclusions [of quantum physics] and the teachings of [Eastern] religious traditions is so great that they should no longer be regarded as separate realms…but as one integrated whole” [Bohm, Capra].

The names added in parentheses are those of physicists/philosophers/theologians who, according to Clayton, have taken the position in question.   My own position is between 3 and 4.    I’ll consider below how three aspects of quantum theory–Superposition, Entanglement/Non-locality, the Measurement Problem–might bear on theological matters.

But before doing that, let me bring up one very general question about quantum physics that bears on theology.    Bernard d’Espagnat has suggested that quantum physics manifests a “veiled reality” .   If that is so, can this theory then tell us  what God is like, or would that also be “veiled”, hidden?   My own opinion is that God is so great, above infinity, that we cannot comprehend Him in His entirety.  Then if God is not totally comprehensible to us–only partially intelligible–does that mean God and quantum mechanics are parallel or convergent mysteries? Is quantum mechanics a “veiled mystery” because in the end we’ll not be able to understand fully how God operates?  Read the linked article and decide; but whichever way you decide, it is clear that quantum mechanics does inform theology in this matter.

INTERSECTION: SUPERPOSITION AND THE HOLY TRINITY

A stumbling block in my conversion process was 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 Trinity Analogue, as a Triangle–the Corners are God the Father, God the Son, and God the Holy Spirit
from Catholic Resources
He also 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.   I’ve used both in RCIA classes and classes for prison inmates.
 
As time went on, I wondered whether the quantum superposition of states could, like the triangle, be used as an analogue for the Holy Trinity.  I conjectured how the act of measurement–picking out either God, the  Father,  God, the Son, or God, the Holy Spirit as the measured component state–might be envisioned:    for example, seeking God the Father in the prayer “Our Father”;  seeking God the Son in the Holy Eucharist or in Adoration; seeking  God the Holy Spirit by an examination of  conscience, as in the Examen of the Night Prayer (Liturgy of the Hours).
 
In terms of the theological implications, this is but an analog, a way of trying to comprehend the deeper mystery of the Holy Trinity,  much as the oft-used example of a triangle with God the Father, God the Son, and God the Holy Spirit at the corners of the triangle.

 

INTERSECTION: DIVINE ACTION AND ENTANGLEMENT/ NON-LOCALITY

Perhaps the most non-intuitive aspect of quantum mechanics involves the entanglement of two things, such that they seem to interact (instantaneously) even when physically separated at far distances from one another (the non-locality aspect).    There are many experiments that verify this.   The picture below is one such:  two beryllium atoms are entangled (in the lower part of the picture) by irradiation with entangled UV photons.
Upper: Two Beryllium Atoms Irradiated by unentangled photons; Lower: Two Beryllium Atoms Irradiated by Entangled Photons
from Wikimedia Commons
There is an even more intriguing picture here of such entanglement:  a cat picture drawn by photons that have never seen the original.
 

The principle of special relativity, requiring that no information can be carried at a speed faster than light, is not violated by entanglement, because information is not transmitted instantaneously by the joint behavior of separated particles.

In the Divine Intervention Series on Quantum Mechanics  Michael Redhead gives an exhaustive treatment of the assumptions–determinism, non-locality, etc–required for entanglement to hold. [23]   In the linked article Redhead argues that entanglement and non-locality yield an “indeterministic”, a “holistic non-separability” interpretation of quantum mechanics, such that

[this interpretation] allows ‘room’ for divine action on particular occasions…Holism is an anti-reductionist thesis that shows how every element of the universe has for its ground of being the  totality of the whole, which pantheists would want to identify with God.”

What are the theological implications of entanglement?   Eastern mystics hold that such entanglement shows that we are non-separable parts of a universe that is one entity and that the desired state is to immerse ourselves into that entity.

As a Catholic, I don’t believe that claim, which corresponds to the heresy of pantheism.  In the Judaeo-Christian theology, God treats each of us as individuals, and when (or if) we attain heaven, we go as individuals.    Indeed, if one examines the entangled state function, each “something” remains as an individual, even though there is a necessary connection between its properties and the properties of the “something else” with which it is entangled.

The vision of entanglement is not a new one;  Dante foresaw it in the 14th century in The Divine Comedy:

“In its depths I saw in-gathered, and bound by Love into one volume, all things that are scattered through the universe, substance and accident and their relations, as if joined in such a manner that what I speak of is One simplicity of Light. I think I saw the universal form, of that bond, because, in saying it, I feel my heart leap, in greater intensity of joy.”  Dante, Il Paradiso, Canto XXXIII, “The Final Vision””

One can also argue that entanglement justifies the relation between Jesus and us, as in the Parable of the King and the Final Judgment in Matthew:

 “Then shall the righteous answer him, saying, Lord, when saw we thee an hungred, and fed thee? or thirsty, and gave thee drink?
When saw we thee a stranger, and took thee in? or naked, and clothed thee?
Or when saw we thee sick, or in prison, and came unto thee?
And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me. [emphasis added]  Matthew 25:37-40 KJV

THE MEASUREMENT PROBLEM–GOD, THE OBSERVER, CREATES REALITY

“There was a young man who said, ‘God
Must think it exceedingly odd
If he finds that this tree
Continues to be
When there’s no one about in the Quad.’
REPLY–
‘Dear Sir:
Your astonishment’s odd:
I am always about in the Quad.
And that’s why the tree
Will continue to be,
Since observed by
Yours faithfully,
GOD.’ “
Msgr. Ronald Knox, commenting on Berkeleyan idealism.

Many articles and books have been written about possible mechanisms for
God’s action in the world by means of a quantum mechanical agency.   I can’t possibly in this brief chapter even summarize all of them;  however, a good summary is given in the references cited before from the Conferences on Divine Intervention, called by Pope St. John Paul II.

Rather, I’ll focus on a particular experiment, the delayed choice experiment first proposed by the great American physicist, John Wheeler, discussed above.   Recall the fascinating quantum behavior, that a single particle will seem to go through both slits simultaneously, interfering with itself until it hits the screen, at which point the wave collapses and the particle is at a single point.   When many particles go through, the pattern shown on the screen is one of interference fringes, just as produced by waves.

Also recall that if you try to detect through which slit a particle goes, then you perturb the situation and the particle loses its wavelike character, so that the screen pattern becomes that for classical particles going through the two slits, without the interference fringes. When does the quantum entity decide to behave like a particle or like a wave?  Is it just as it goes through the slit?  Is it after it goes through the slit?  Or???

If , as in the delayed choice experiment, you try to measure which slit the particle has gone through AFTER it has gone through the slit, the particle will still “know” that it has been observed, and will exhibit particle-like behavior–no interference fringes.  The delayed choice experiment has been realized experimentally.  Rather than using two slits, a beam-splitter (half-silvered mirrors) provide the two paths–reflection and transmission, and a technique called quantum erasure provides the delayed choice of measurement type.

There’s an interesting and significant corollary to this experiment.   In Wheeler’s thought experiment the light source–some distant galaxy–is millions or billions of years in the past–but you’re affecting it by the present day measurement.   From this deduction Wheeler derived his notion of the participatory universe, a universe created by observation, both in the present and the past. As he put it in another article, “It from Bit”: the universe is created by answering yes / no questions of observation.  (And, one might ask, what happens if you go far enough back in the past that no observer was present–but more of that below.)

Implications of the delayed choice experiment
Now, there’s been a fair bit of physics (mostly hand-waving) up to now, but no theology or philosophy.   What are the philosophical/theological implications of the delayed choice experiment?   I believe this has been best expressed by the American physicist Raymond Chiao, in his article “Quantum Non-Localities: Experimental Evidence” in Quantum Mechanics–Scientific Perspectives on Divine Action, V.5   [24]

“I shall assume as a basic principle that the universe we live in bears witness to the Creator who created it  (emphasis added)…let us generalize Berkeley’s philosophical principle to a ‘neo-Berkeleyan point of view’ in which God is the Observer of the universe, in the quantum sense of ‘observer’. This generalization starts from small systems…in which an observer created reality is seen to occur upon every elementary act of observation, and ends up with large systems–in particular with the entire universe.   In this viewpoint, every elementary, individual quantum event…is a result of a creative act of the universal Observer, in which all properties of all particles come into existence on their observation, in continual acts of creatio ex nihilo, which constitutes a kind of creatio continua  occurring everywhere at once.   Thus the existence of the universe itself is contingent upon the continual observations of the Creator.   The idea of contingency of existence, in the sense of the utter dependency of the universe for its properties and existence at each moment upon its Creator, is thereby introduced via quantum physics into philosophy and theology …Furthermore, this viewpoint suggests a new meaning of the immanence  of the Creator with respect to creation, since God is acting everywhere at once in the universe.   Thus God is omnipresent, omniscient, and omnipotent…The neo-Berkeleyan viewpoint introduced here suggests not only a continual creatio ex nihilo qua creatio continua by an immanent Creator, but also a singular creatio ex nihilo by a transcendent Creator.   Moreover, the above Einstein-Podolsky-Rosen effects imply a quantum non-separability, which ties together the universe non-locally as a whole.  This reminds one of the words of the Apostle John, ‘All things come into being through him, and without him not one thing came into being that has being.’  (John I:3)and of the words of the Apostle Paul,‘All things have been created through him and for him…and to him all things hold together.’ (Colossians I:16,17)...We infer that ‘all things’ refers to the universe.  Not only are all distant parts the universe woven together throughout space, but also its future and its past are entangled throughout time, as if the universe were one seamless garment. [Emphasis added]Raymond Chiao, op. cit.

I’ll add some comments of my own:

• quantum effects are not generally observed macroscopically because of decoherence effects, that is to say Schrodinger’s Cat would exist only on an atomic scale;
• the notion of creatio continua is, I believe, consistent with Catholic doctrine, and was proposed by St. Thomas Aquinas;
• does Chiao’s last sentence, with an entangled future and past, imply the universe is deterministic, a block universe,  and that there is no such thing as Free Will? (but see below.)

The most important point to keep in mind from the delayed choice experiment is, I believe, the last sentence in Chiao’s quote: we are, indeed, entangled (space-wise and time-wise) with the rest of the universe.

THE MEASUREMENT PROBLEM: MOLINISM, MANY WORLDS, FREE WILL[25]

“Of course I believe in free will. I have no choice.”
Isaac Balshevis Singer,  The Salon Interview, 1987

“…dearly beloved…be not disturbed by the obscurity of this question; I counsel you first to thank God for such things as you do understand; but for all which is beyond the reach of your mind, pray for understanding from the Lord, observing at the same time peace and love among yourselves..”.
St. Augustine of Hippo, “On Free Will and Grace” 

God’s Foreknowledge and Free Will–the Problem.
An essential attribute of God is His omniscience, that He knows everything.   This means, since God is eternal–timeless–that He knows not only the past but the future, that is to say God has “foreknowledge” of what we will do and what will happen to us.

If this is so (and I believe it to be so), then I find it difficult to reconcile with Free Will.   If our future is preordained, then even though we think we make a choice, it is not really a choice because there aren’t alternative futures for us.   This paradox is nicely summed up in the quote from Singer, given above. Now, rather than saying, as the quote from St. Augustine would have it, that the problem of Free Will is beyond us, I believe there is a solution, a solution which combines the teaching of the Jesuit theologian and philosopher Luis de Molina (1535-1600) and the Many Worlds / Many Minds interpretation of quantum mechanics.

Molinism
Molina attempted to deal with the perplexing problem of God’s Providence and Free Will by positing a new realm for God’s foreknowledge: Middle Knowledge. By “Middle Knowledge”, Molina meant that God knew not only what would happen (his foreknowledge), but what could possibly happen—a knowledge of counterfactuals or of alternate history, as in that science fiction genre. His proposal, which came to be known as “Molinism”, was strongly opposed by the Dominicans, who argued that it limited God’s power and made him less than omnipotent.

Intersection: Molinism | Many Worlds / Minds
The interpretation 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 claim that Molinism and the MWI or MMI interpretation give a mechanism to satisfy this requiremen mentioned in my quote above: a means for one to make free choices between different options and thus truly exercise free will, and for God to know of the possible options you have and what you will choose.

A bare bones summary of the relevant quantum mechanics  was given above in Section 2.   Recall that measurement of a system represented by a state function with superposed components brings about 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.

Everett’s Relative State Theory, the Many Minds / Many Worlds interpretation of quantum mechanics,  could engage  in the following way with Molina’s Middle Knowledge hypothesis to yield a satisfactory  account of Free Will.   I should emphasize that this account is satisfactory to me; it might not be to others, to philosophers or theologians;  there certainly no way to prove that it is true.  At the very least, I trust and hope that it does not contradict Catholic teaching.   Were someone to show that to be so, I would have to reject it.

Let’s suppose that a science-fiction perspective for personal worlds exists, a multitude of possible worlds  in which there is one world 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 the different decisions, but a possibility for me–my ego, my soul–to go into one or another of those worlds.   This perspective is that of “The Many Minds” interpretation of Quantum Mechanics, proposed by Albert and others.

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 is compatible with the availability of alternatives required for truly free Free Will (not predetermined choices).

Here finally is my take:   There is an infinitude of possible universes and our ego, our consciousness, traverses these as it makes choices.   If there is a universe where we measure the particle going through one slit, there is another (with other conscious minds) where it goes through both.

Such a view resolves a conflict between free will and God’s omniscience and omnipotence–if God knows what our future actions will be, how can our will be free?  And the answer would be a type of Molinism, God is aware of all possible counterfactuals, but they are only counterfactuals for our mind, our ego, not for God.

INTERSECTION: QUANTUM LOGIC AND RESURRECTION OF THE DEAD

“Now if Christ be preached that he rose from the dead, how say some among you that there is no resurrection of the dead?
But if there be no resurrection of the dead, then is Christ not risen:
And if Christ be not risen, then is our preaching vain, and your faith is also vain.
Yea, and we are found false witnesses of God; because we have testified of God that he raised up Christ: whom he raised up, if so be that the dead rise not.
For if the dead rise not, then is not Christ raised:
And if Christ be not raised, your faith is vain; ye are yet in your sins 1 Cor:13-17 (KJV)

“So the same combinations of atoms, the same space volumes corresponding to human bodies, cars, buildings and so on, will come again. All events in spacetime will be reorganized or ‘resurrected’ but not in such a way that they will be in time…It is not that the dead will arise from their graves, as it were, but rather sets of events of any life can arise again, together with the consciousness of those who were alive.” Andrej Grib, ‘Quantum Cosmology: Observer Logic’ in Quantum Cosmology and the Laws of Nature–Perspectives on Divine Action, [21]

One topic which has not been discussed in this chapter (it is in Chapter 4, on Creation) is that of quantum mechanical models for early stages in the life of the universe. However, there is one piece of that pie that is germane to the thrust of this chapter, and that is the suggestion by the Russian mathematician, Andrej Grib, that quantum logic governs the universe, and thereby there will be a “Big Crunch”—the universe collapsing to a singularity, and in this Big Crunch there will be a resurrection of the dead.   This is what I’ll explore below.

Quantum mechanics requires an observer
Grib’s fundamental thesis (relying on early interpretations of quantum mechanics by Von Neumann and London) is that quantum mechanics requires a measurement process and thus an observer must be the final link in the measurement chain, in order that the measurement be meaningful.

“In the end the final observer is just the abstract ego of the observer–the one who is the subject of observation [i.e. the one who observes]…So it is this abstract ego which is responsible for the collapse of the wave function. This is a strong form of the subjective interpretation of quantum mechanics.” Andrej Grib, op. cit. , p 169

Accordingly, to speak of the state function of the universe without specifying a measurement or an observer to make that measurement is “very bad philology” (to quote Grib), that is to say, contradictory to implicit assumptions on which quantum mechanics is based.

Grib then links what appear to be puzzling features of quantum mechanics– the uncertainty principle that says we can’t get exact simultaneous measurements on complementary variables, the wave-particle duality, the entanglement of particle shown in Bell’s Theorem experiments–to the following. The human mind operates by Boolean logic, whereas the universe in fundamental reality is governed by a non-Boolean logic, a quantum logic.

Boolean Minds vs a Non-Boolean Universe
Our minds, Grib says, operate in a Boolean logic mode. We cannot apprehend non-Boolean logic, whence the apparent mysteries of quantum mechanics. The perception of time itself is a consequence of this Boolean mind / non-Boolean universe dichotomy. We must experience events separately and in succession, as past, present and future, even though the physics of relativity suggests they are conjoined, that is to say are not really separated in that non-Boolean universe. [See Chapter 4.]

Grib supports this position by invoking the block universe given in special relativity; this is a block universe in which our life stories are embedded as peppers in a meat loaf. [26] He also proposes that a “Big Crunch”, a singularity at the end of time, will occur as suggested by possible solutions of the General Relativity field equations. This last suggestion is possible, but would occur only if the mass/energy density of the universe was less than a particular critical value, “Omega”. However, current research suggests that the density is almost exactly equal to Omega, or perhaps very slightly greater. So a Big Crunch seems to be unlikely in light of present knowledge. But…?

The notion of a “Big Crunch” is associated with a theological proposition, the “Omega Point”, set forth by the Jesuit paleontologist, Teilhard de Chardin and the American physicist Frank Tipler. Their idea is that the universe is evolving to a final end, in which those now living will be resurrected. I won’t comment on this in detail  other than to say there have been scientific, philosophic and theologic objections to how this “Omega Point” will come about.

Grib suggests that in this case, Revelation may be a better guide to what “will” happen. (“will”–a future tense–seems out of place given his joining past, present and future together.)

“The idea of the collapse of the wave-function of the universe after the Big Crunch corresponds to these lives coming into a new existence where different weights will be given to different events [emphasis added]. Some of the events could be annihilated (i.e. have zero weight), which is very close to the idea of The Last Judgment). How can we know in this life what will, and what will not be important for the eternal life after the Big Crunch? The only sure answer is Revelation [emphasis and upper-case added].” Andrej Grib, op. cit., p. 181

I agree with Grib’s last sentence in the quote above: “The only sure answer is Revelation.” This attitude is not an appeal to fideism, that through faith only will we know what is truly important. Rather, it concedes that our knowledge of material things is limited, that there is a “veiled reality” concealing the fundamental nature of things.

Science changes. What we take as established today may be tossed in the dust-bin a hundred years from now. Revelation does indeed supersede scientific theory, because it is the Word of God.

A NON-INTERSECTION: QUANTUM MECHANICS AND THE REAL PRESENCE

“Tantum ergo Sacramentum                 Down in adoration falling
veneremur cernui;                                  Lo! The sacred Host we hail;
et antiquum documentum                     Lo! O’er ancient forms departing
novo cedat ritui;                                       newer rites of grace prevail;
praestet fides supplementum               faith for all defects supplying,
sensuum defectui                                      where the feeble senses fail.”

The Eucharist
from Wikimedia Commons

The post most visited on my blog is that dealing with Quantum Mechanics and the Real Presence.   This is surprising, since the connection between the two is not that strong or obvious.   Perhaps those who read the blog begin with the question “Here are two mysteries–quantum mechanics and Transubstantiation–the Real Presence of Christ in the Eucharist; are they connected?”

I’m not going to repeat the material here, but will summarize it to say that there is no obvious intersection or connection.    There are two mysteries;   perhaps when we penetrate that “veiled reality” that d”Espagnat says lies behind quantum mechanics, we may understand more of the mystery of the Real Presence.   Or perhaps not.    Here, as Aquinas said so well in “Tantum Ergo”,  “Praestet fides supplementum sensuum defectui.”  

 

Notes

[1] In physics and mathematics frequency is denoted by the Greek letter v (“nu” as in what’s nu … : > ) )
[2] radiation momentum—that of photons—will be discussed in subsequent sections.
[3] The value of h = 6.626×10-34; note the exponential notation: 10-N means decimal point followed by (N-1) 0’s before the 1; e.g 10-3 means .001
[4] The reason for this is that the number of quanta that can be occupied decreases strongly, according to thermodynamics, with increasing energy at a given temperature; the higher the temperature, the greater the number of high energy quanta.
[5] he also wrote groundbreaking papers on special relativity and Brownian motion
[6] See this web site for a derivation.
[7] Putting numbers into that relation gives a very small wavelength for ordinary size objects; for example, for a baseball moving at 90 miles per hour, you’d get a wavelength about 10-28 cm (centimeters), too small to be observable. However for atomic size particles, e.g. electrons and neutrons, the wave lengths are of atomic dimensions, of the order of 10-8 cm , a value that is observable.
[8] See Burton Feldman’s book, A History of the Nobel Prize.
[9] Note to quantum mechanics experts: this example is totally unrigorous and unreal; as stated, it’s meant to illustrate the idea of a state function and its decomposition into basis states.
[10] Note to quantum mechanics purists: I know—there’s a normalization factor of 1/√(3) missing in the above, but I’m trying to keep it simple
[11] There’s an analogy, and it’s intentional, to the idea of a vector being represented by components along the unit vectors lying along the perpendicular axes of a coordinate system.
[12] I was fortunate to have both as teachers, Feynman as an undergrad at Caltech and Schwinger as a graduate student at Harvard.
[13] John Wheeler was an imaginative and productive theoretical physicist at Princeton University.   He was Feynman’s graduate research director, coined the term “black hole” for the discontinuities of immense gravity predicted from general relativity, and also proposed the “Participatory Universe” and the “It from Bit” notion explaining quantum mechanics and cosmology.
[14] (Refer to this high-level, but very clear video explaining the relation between polarization and quantization)
[15] See also this linked video, an hour-long talk by Alain Aspect, on a layperson level, about the quantum mechanics behind his Nobel Prize winning experiment–well worth watching.
[16] (nmr, MRI—Google “Kurland-McGarvey Equation” for an example)
[17] There’s an important principle here: science is theory confirmed empirically by experiment or observation.
[18] On the linked web page, click on the pink icon for the book “Quantum Mechanics”, then on the right author headings for each article will appear.  Click on that for Redhead and a summary of his article will come up.
[19]  Decoherence is highly mathematical and difficult to explain in concrete terms.   Perhaps the best way of explaining it is to say that interactions between a system and its environment remove the wavelike nature, the phase coherence between component states.   For example, we can  no longer right |couple, vote> = |w,D>|h,D> + |w,R> |h,R>;  we have to write |couple,vote> =|w,D>|h,D> or |couple,vote> = |w,R> |h,R>.
[20] The objections to state function collapse are nicely and humorously stated in a post, “If Many Worlds Had Come First“:

“Look, if this theory of yours were actually true—if whole sections of the wavefunction just instantaneously vanished—it would be… let’s see.  The only law in all of quantum mechanics that is non-linear, non-unitary, non-differentiable and discontinuous.  It would prevent physics from evolving locally, with each piece only looking at its immediate neighbors.  Your ‘collapse’ would be the only fundamental phenomenon in all of physics with a preferred basis and a preferred space of simultaneity.  Collapse would be the only phenomenon in all of physics that violates CPT symmetry, Liouville’s Theorem, and Special Relativity.  In your original version, collapse would also have been the only phenomenon in all of physics that was inherently mental.” 

[21] On the linked web page, click on the green icon representing the book, then click on the chapter heading on the right for Andrej Grib.
[22] On the linked web page, click on the pink icon representing the book, then click on the chapter heading on the right for Philip Clayton.
[23] On the linked web page, click on the pink icon representing the book, the click on the chapter heading on the right for Michael Redhead.
[24] On the linked web page, click on the pink icon representing the book, the click on the chapter heading on the right for Raymond Chiao
[25] There is a theorem, the Conway-Kochen Free Will Theorem, that asserts if we (humans or observers) have free will, so do elementary particles.   “Free Will” in this context means that what the particle does in the present is not contingent, in some sense, on its past history.   See here for more details.

[26] This supposition about the nature of time and the unchanging nature of such a block universe is not held universally. For example, G.F.R. Ellis posits a changing block universe, dependent on past events.

© February 11, 2017. Robert J. Kurland, Ph.D.

7 thoughts on “The Quantum Catholic”

    1. Y cuenta las cosas de una manera muy divertida; poner a un matrimonio es como ejemplo de partículas entrelazadas es un hallazgo impresionante y hace completamente entendible el fenómeno.

  1. Mr. Kurland. Thank you one more time for the excelent text. I would like to suggest a more detailed explanation about Feynman diagrams. I really could not understand this point, but this seems to me an important topic in the theme. Humbly ask you this for I have little time to study nowadays and your didatical approach is so helpful. I used to study Feynman’s Lectures on Physics and found it fascinating. God bless you.

    1. I’m not sure I can give you a complete explanation, but please visit the linked article.
      I added one explanation about the arrows. The horizontal red arrow is at one point in time and moves in space, indicating a collision / interaction / annihilation between the electron and positron. The moving up in the vertical direction indicates a progression in time. Moving horizontally to the right indicates moving in space. The wavy lines indicate radiation; the solid lines particles. I hope this is helpful. Actually the diagram encapsulates some heavy math–S-matrix integrals for scattering and such, which are way above my pay-grade at this time (I’ve been into magnetic resonance.)

  2. Hello! I’m loving this so far.
    I know from reading the ‘Confessions’ blog and your comments at Briggs’ blog that you are familiar with classical arguments and obviously you’re well versed in the physics and the scientific community. So, my question touches on all these.
    Reductionism seems to be widely held in the physics community and hotly defended by some. In the first chapter you state, “an electron in a hydrogen atom the quantum numbers describing the state would do; for a free electron, the wavelength and/or position would be used.” It seems to me that based on this and other examples that physicists know well the Schrodinger equation is not truly reductive but somewhat holistic. The holistic aspect is done conceptually before the variables are plugged and chugged from the equation. Would you agree? If not, why not? If so, why don’t more physicists that advocate material reductionism not see it, do you think?
    I’d love to hear your thoughts!

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