## Will the real god God please stand up?

[Updated Dec. 28, 2017, with a revised and expanded discussion of arguments from Sean Carroll's book The Big Picture. - SC]

There are many reasons why I’m not retired, but one of the bigger ones is that I haven’t figured out yet how to get at least a quarter (if not a dollar bill) from every person who’s ever asked me how I can believe in “a god or gods” in an age of “science” and “reason”. The question is usually sincere rather than an attempt to troll, but either way, the wording alone is enough to reveal where things are headed, and the ensuing discussions have been nothing if not utterly predictable. In virtually every case the underlying narrative was based on the same handful of fashionable just-so stories, none of which appeared to have ever been questioned.

Back in days of yore, I was told, bucolic ancients looked out on a universe resplendent with mysteries they could neither understand nor predict, yet depended on for their survival. For all its dependable seasons and regularities, the universe visited floods, fires, and other tragedies on them as often as it yielded its bounty. In their attempt to understand why and find a just order to it all, they attributed these mysteries to the capricious activities of spirits called “gods” who were like us in every respect, except that they were disembodied and endowed with vast magical powers over various parts of the natural order. As the rise of science rolled back these mysteries with rational explanations, such gods were no longer needed to account for them. Eventually, the faiths based on them were rendered superfluous, and thus did Science triumph over religion (note the capital “S” and lower-case “r”).

There are so many things wrong with this it’s difficult to know where to begin. Perhaps the best way to unpack this mess is to start with the origins of the God of Classical Theism on which the Abrahamic religions are founded. These cover the professed religious beliefs of well over half of humanity and roughly 80% of North America and account for virtually every instance of the above narrative I’ve ever personally witnessed.1

Contrary to widespread belief, Classical Theism as a formal system of thought didn’t originate with Christianity or Judaism, nor was it an attempt to explain any mystery of the natural world (which makes it quite telling that the God that eventually emerged from that tradition bore a striking similarity to the uniquely monotheistic God of the Old Testament that the Israelites had been worshipping via revelation for nearly a millennium). The seminal theological question never was “is there a god?”—it is, and always has been, “why is there something rather than nothing?” In the Fifth Century BC, the Greek philosopher Parmenides formulated an axiom that was later Latinized as ex nihilo nihil fit (“out of nothing comes nothing”). Unless you believe in magic this is as straightforward as axioms get, and for nearly 2500 years no thinker of any repute has seriously challenged it. [At least not until the present day, when a handful of metaphysically illiterate Atheist physicists decided that philosophy is “dead” because it hasn’t kept up with their profession, and gave themselves permission to redefine the word “nothing” and make Magic a sub-discipline of physics. But that’s a topic for another day.] This, in turn, raised other issues. Parmenides went on to argue that change and differentiation must be illusory, for to change, he said, is for something to cease to exist in one state and begin to exist in another. Because that would require things to come from nothing, and disappear back into it, he considered it absurd. And yet, change is every bit as indisputable a fact of life as existence itself. What are we to make of these two realities, and how they relate to each other? For the next one or two centuries, philosophers of different schools argued these questions, some emphasizing the primacy of change, and others the primacy of the unchanging unity of things.

The first true leap forward came circa the mid-Fourth Century BC when Aristotle published his Metaphysics. Aristotle argued that the apparent tension between being and becoming can be accounted for if we differentiate between the actual state of existence of real-world things (or substances) and their innate potentialities for existing in different ones (later Scholastic thinkers denoted these respectively as acts and potencies). Change occurs when the active potencies of one substance causally instantiate outcomes from the passive potencies of another via four types of causality—Their material constituents (material causality), their essential form and identifying properties (formal causality), their direct physical interactions (efficient causality), and their directedness toward ends (final causality). For instance, we could say that the motion of massive objects reflects their mass and other properties (material and formal causes), and the forces they interact with (efficient causes). Aristotle would also say that they fall to the ground when dropped because the earth is their natural resting place (final causality). Similar ideas were developed by Plato, and by the Stoics and Neoplatonists after him, and eventually brought to fruition by medieval Scholastic philosophers and theologians of the Christian, Jewish, and Islamic traditions. Various schools of thought were represented in each, but most if not all, eventually converged on some combination of the following axioms;

1)   The universe is contingent. Its essential nature, or form (and that of everything in it) is separate from its existence. [e.g. - We can meaningfully conceptualize horses and unicorns without regard to whether there are any.]

2)   The universe is causally interconnected. The acts and potencies of its physical constituents are interrelated in rationally consistent ways.

3)   The universe evolves. Per 2), its actual state of existence changes from moment to moment in dependable ways. [e.g. - Seeds grow into trees, objects fall toward a gravitational source, etc.] As such, science is a meaningful endeavor that gives us real, grounded knowledge about the way the world is.

4)   Potencies may be active powers or passive capacities for change, and the events that unfold from their activity may be (formal terms again) essentially ordered, or accidentally ordered (dependent on, or independent of the continuing activity of their cause/s). [e.g. - A father has the active power to father children, and his kids will continue to exist whether he continues fathering behavior or not (accidentally ordered events). A guitar has the passive power to make music by actualizing the passive power of air to produce sound, but only if it is played by a musician, and the music will exist only while the guitar is being played (essentially ordered events).]

5)   Purely passive potentialities cannot self-realize—they must be instantiated (made actual) by something else that is actual. [e.g. - wood has the passive potentiality to burn, but only if it's exposed to an actual source of heat. An infinitely long chain of stationary railroad cars (or one connected in a loop) cannot move, even though each car is connected to one that can pull it. There must be a least one engine with the active potency for inducing motion.]

6)   The universe's actualities and potentialities are a mix of active powers and passive possibilities. [e.g. - A locomotive has the active power to pull a train of cars with passive potentials for motion, but also has other passive dependencies, such as the need for an engineer; you have the active power to walk or run, but not to continue living without food and water; etc.]

7)   As persons with active and passive potencies of our own, we are rational, freely choosing, intentional agents. As such, our observations and thoughts can, and do, give us reliable knowledge of the universe.

From these (particularly the concept of essentially-ordered causality), they concluded that there must exist something that is pure act—the ground of all being and empowered possibility, with no passive potentialities or dependencies (Davies, 2004; Feser, 2010; 2014). Furthermore, this pure act must be;

a)   Eternal - Not within, or in any way constrained by time or space.

b)   Unchanging – Not evolving per any passive potencies susceptible to influences external to itself.

c)   Simple - A substantial, or essential unity without parts or differing properties of the sort possessed by physical things.

d)   Omnipotent - Unlimited in active powers.

e)   Omniscient - Present in, and aware of, all that is.

f)   Possessing both intellect and will, and as such, is the ground of all personhood (as opposed to being "a" person).

g)   The intentional cause of everything else that is, and thus, the objective source of the meaning, value, and purpose of things.

Aristotle referred to this pure act as the Unmoved Mover. Christian, Jewish, and Islamic philosophers recognized Him as the God of Classical Theism who appears in the Bible and Quran. How these conclusions were reached, and how this timeless, changeless God is related to the Christian Trinity and His portrayal in the pages of both Scriptures, would fill numerous posts and is beyond our scope today. But before we proceed, a few comments are in order.

First, it’s widely believed that Aristotle’s metaphysics is dependent on his outdated physics, and therefore no longer relevant today. In his 2014 debate with William Lane Craig, Atheist physicist Sean Carroll spoke for many when he addressed transcendent causality and the universe (Carroll & Craig, 2014) stating that,

“[T]here’s a bigger problem with it, which is that it is not even false. The real problem is that these are not the right vocabulary words to be using when we discuss fundamental physics and cosmology. This kind of Aristotelian analysis of causation was cutting edge stuff 2,500 years ago. Today we know better. Our metaphysics must follow our physics. That’s what the word metaphysics means...

[T]he way physics is known to work these days is in terms of patterns, unbreakable rules, laws of nature... There is no need for any extra metaphysical baggage, like transcendent causes, on top of that. It’s precisely the wrong way to think about how the fundamental reality works.”

All of this is either false or grossly misleading. In modern analytic philosophy, Aristotelian/Scholastic concepts of ontology and causality are every bit as active a field of study as they’ve ever been (e.g. - Martin, 1997; Davies, 2004; Feser, 2014; 2015; Oderberg, 2008, etc. and sources cited therein). There are, of course, differing schools of thought on them, and their relationship to the sciences is actively debated. Some lean toward a deep interrelationship between physics and these metaphysical ideas. Others such as Edward Feser (2010; 2014; 2015) argue that the two are entirely separate realms. Aron and I fall somewhere in the middle. [For more, see Aron’s entire series of posts on Fundamental Reality.]

While it is true that modern physics treats causality differently than Aristotle and the Scholastics did (e.g. - the notions of material and formal causes are largely redundant in physics and not really needed), clearly the two realms of thought speak to the same underlying realities and even share some common language. The very “patterns, unbreakable rules, laws of nature” Carroll speaks of inherently imply an underlying unity which not only makes physics possible but fits the terms act and potency beautifully. Potentials, for instance, are a regularly recurring theme in physics, and the fact that equations of motion can be derived from them also bears a striking similarity to the Aristotelian notion of final causality. The dynamics of a falling mass can be differentially specified in terms of a static gravitational potential, but a Scholastic would say that the mass falls to earth because that’s its natural resting place. The ideas being expressed here aren’t as different as many suppose. Another common misconception is that final causality involves teleology. In fact, it’s about directedness as much as purpose or design, if not more, and applies to inanimate objects as well as living things. It’s not a huge leap to see directedness in the way static potentials lead to equations of motion.

These Aristotelian concepts are less rigorously developed of course, but conceptually at least, they substantially overlap their counterparts in physics, which implies at least some unity between the two. But at the same time, as we saw in my last post, the fact that there are numerous ontic interpretations of QM alone should give us pause before assuming that one of these realms is entirely supervenient on the other. In any event, wherever one falls on this spectrum, the one thing that isn’t true is that "our metaphysics must follow our physics". Nor is that “what the word metaphysics means" as Carroll claims. Aristotle’s Metaphysics was so named because he wrote that book after he wrote his Physics, not because the former is in any less foundational than the latter, or entirely supervenient on it (in Greek, the root meta is equivalent to the Latin post, meaning “after”).

Second, it’s worth noting that this argument, which is known as the cosmological argument, is widely misunderstood. In popular writings, particularly those of its critics, it’s almost always presented as an argument for a historical creation event based on accidentally-ordered temporal chains of causality when in fact, it’s based entirely on essentially-ordered, or simultaneous causality.2 The traditional example given by St. Thomas Aquinas and other Scholastics is that of someone pushing a ball with a stick. The passive potency of the ball for rolling motion is realized only while it is being pushed by the stick’s passive potency for doing so, which in turn is realized only while the one wielding it is exercising his/her active potency for wielding it to push objects. The entire causal chain is simultaneous in the present moment and has nothing whatsoever to do with any cause or causes that may have existed even a few seconds prior. In fact, Aquinas, who developed the argument better than anyone else in history, famously believed that it wasn’t possible to demonstrate that the universe had a temporally-ordered causal beginning. He believed it did because Scripture said so, but he felt that observation and philosophical arguments alone couldn’t demonstrate that. Today, of course, Carroll’s dismissal of transcendent causes notwithstanding, the evidence for a beginning is considerable and whether they admit it or not, a source of dismay for Atheists. Aquinas’ claims to the contrary are relevant here, only to the extent that they emphasize that time-ordered causality plays no role in traditional cosmological arguments.

Furthermore, in the writings of Aristotle and the Scholastics, the term move denotes change in general, not just rectilinear motion as we understand it. To them, changes in any property—including say, color, temperature, or even a beginning of existence—would be considered “movement”. Interestingly, Carroll misses the subtleties of this as well. In his book The Big Picture (2017) he tells us that,

"[T]he whole structure of Aristotle's argument for an unmoved mover rests on his idea that motions require causes. Once we know about conservation of momentum, this idea loses its steam... What matters is that the new physics of Galileo and his friends implied an entirely new ontology, a deep shift in how we thought about the nature of reality. 'Causes' didn't have the central role that they once did. The universe doesn't need a push; it can just keep going." (My emphasis)

Clearly, this argument doesn’t account for accelerated motion, which anyone who’s ever dropped a \$600 cell phone off a balcony will tell you, is quite real. For some reason, this doesn’t seem to concern him. The real puzzle, however, is that he acknowledges that Aristotelian motion is a much broader concept than mere spatial displacement, and even uses the word transformation to describe it. Why he imagines that an argument against an untransformed transformer could be based on rectilinear motion alone is anyone’s guess. The metaphysical importance of conservation of momentum, he tells us, is “hard to overemphasize” and he sees in it an underlying principle that in his view, can be extrapolated to all contingency and change. But how this is supposed to work in practice is never clarified. Throughout this chapter (aptly titled The World Moves by Itself) he speaks of “causes” and “motions“ in the most general metaphysical sense and uses those terms interchangeably. But the only working examples he offers involve frictionless displacement of objects like coffee cups, which he supplements with glib remarks about how terms like “cause” and “effect” aren’t found in physics textbooks (as though the language of physics and its methods are the only ones that are meaningful in the real world).

Near as I can tell, Carroll believes that conservation of momentum is built on a metaphysical foundation that generalizes to all conservation laws. Essentially, this amounts to the claim that Noether’s theorem (and possibly its extension to quantum field symmetries) constitutes a sort of “blood-brain barrier” isolating all contingent change in the universe from the interventions of any creator god. If so, the problems with this are obvious. For starters, he points out (correctly) that Aristotle’s unmoved mover was later fully developed by Aquinas. As we’ve already seen, essentially-ordered causality and God as the universe’s sustainer as well as its creator are foundational concepts in his thought. Anyone even remotely familiar with this will immediately recognize a universe that “keeps going” after an initial “push” as one based on an independent temporally-ordered causal chain that some divine machinist occasionally tinkers with—an argument that Aquinas went to great lengths to refute, and clearly not the cosmological argument he defended. Second, attributing virtually all contingency and change to conservation laws is, to say the least, a stretch. What sort of conservation law gave me blue rather than brown eyes, for instance, or required me to order a triple-shot cappuccino this morning rather than a hot chocolate? Even if we ignore all this, there’s one rather large elephant in the room that isn’t being addressed. The sort of conservation laws Carroll is appealing to are only valid over locally flat regions of space-time. For the universe as a whole, neither momentum nor energy is even well-defined, much less conserved (MTW, 2017)—a fact that he’s not only aware of but has written about elsewhere himself (Carroll, 2010), yet now conveniently chooses to forget.3

It’s odd that Carroll manages to muddle so many metaphysical concepts as completely, and chronically, as he does. Unlike many scientists these days, he has a background in philosophy (having minored in it as an undergraduate) and is known for his thoughtfulness and attention to detail with metaphysical topics. He’s repeatedly, and rightly, called out many of his colleagues for their Philistine recklessness in these areas and with philosophy in general. If anyone should know better, it would be him.

Finally, it should also be noted that the history of thought on God’s nature isn’t quite as monolithic as I perhaps made it sound. In recent years, for instance, some theologians and philosophers of religion have questioned the notions of God as grounded personhood (as opposed to personality), His simplicity, and the claim that He’s timeless and unchanging. God, it’s argued, cannot be meaningfully omniscient and loving, as He’s presented in the Bible and Quran, unless He has attributes that manifest in a personality, not unlike ours, and He in some sense experiences time (although opinions as to whether His time maps onto the space-time of our experience, and if so, how). This school of thought, referred to by some as theistic personalism, has been particularly popular among advocates of presentism (the so-called “A-Theory” of time). It’s more notable advocates include Richard Swineburne, Alvin Plantinga, J.P. Moreland, and William Lane Craig.

Theistic personalism is a relatively late development in the history of Classical Theism and hasn’t gained widespread acceptance among theologians and philosophers of religion (Davies, 2004). The traditional arguments for the simplicity and timelessness of the God of Classical Theism as presented above are formidable and well-supported not only by metaphysics but the Abrahamic Scriptures as well. The apparent difficulties presented by a timeless God in changing history are not as difficult as they may seem at first blush either. Once we realize that if God is omnipresent throughout His created space-time, and interacting with it at every point according to His Will, He will appear to change from the standpoint of time-bound creatures like us, much the way a static landscape appears to change to the passengers of a car driving through it. Dispensing with all this simply to bring God more in line with our experience adds layers of arbitrary, and unnecessary metaphysical complexity that cry out for Occam’s Razor. As if that weren’t enough, it runs badly afoul of physics as well. The presentism that it most naturally fits has numerous issues, not the least of which are the difficulties of reconciling it with the Lorentz boost. While it is possible to make presentism work in a relativistic framework (Copan & Craig, 2004), the match ain’t exactly made in Heaven and IMHO at least, creates far more problems than it solves. Nevertheless, theistic personalism does have its place in modern theological discourse, and it has been ably defended by its proponents (Moreland & Craig, 2003).

There… Now that all the fine print is out of the way, let’s return to our seven-axiom argument for the existence of God. At this point, several things should be readily apparent.

1)   God is not “a god”

When Atheists (or more commonly, New Atheists) speak of "a god or gods" what they invariably have in mind are demigods—minor deities of the sort one finds in ancient mythologies. These are the disembodied space and time-bound magical spirits central to their narrative. In The God Delusion Richard Dawkins (2008) states that,

"I have found it an amusing strategy, when asked whether I am an atheist, to point out that the questioner is also an atheist when considering Zeus, Apollo, Amon Ra, Mithras, Baal, Thor, Wotan, the Golden Calf and the Flying Spaghetti Monster. I just go one god further."

The problem with this is obvious—the “gods” he names bear no resemblance whatsoever to the God of Classical Theism. In Greek mythology, Zeus had a family tree like us. He was the child of the Titans Chronos and Rhea, and they were, in turn, descended from the primordial Greek deities (Wikipedia, 2016). Like the rest of the Greek pantheon, not only was he a time-bound spirit, he was earth-bound as well and "lived" at a physical location (Mt. Olympus). In fact, as often as not, such demigods were deified human rulers. Case in point, the Akkadian ruler/gods Gilgamesh and Naram-Sin who respectively ruled during the late Third and early Second Millennia BC (Armstrong, 2015).

God on the other hand (note the capital “G”), is the ground of all being and personhood. He is neither space and time-bound nor an instantiation—there is no general class of things called "grounds of all being" of which He can be said to be one example among many. The very claim that there could be more than one such ground is inherently self-contradictory. It’s no accident that the Abrahamic religions are all monotheistic. And as the creator of all else that exists—including the very space-time manifold whose geometry is, per general relativity, related to the mass-energy and momentum it contains—calling Him a demigod amounts to claiming that He's bound by His own creation, and dependent on it for His existence. That, my friends, is patently absurd. Saying that God is "a god” isn't merely wrong, it's a category error.

Interestingly, the distinction we find today between the anthropomorphic personified God of televangelist’s sermons and children’s picture Bibles, and the God of Classical Theism was every bit as true in Aristotle’s day as well. Then, as now, philosophers distinguished between Everyman’s bearded, gray haired Zeus who threw thunderbolts from Mt. Olympus, and the classical theistic "Zeus" (or more properly, Greek primordial God) of formal thought. If this were the 4th Century BC, New Atheists like Dawkins would be out in front of the Athens Peripatetic school in togas beating their well-inflated chests about "a zeus or zeus'es," and Aristotle would be the one biting his tongue and doing whatever could be done to educate them. Some things never change… ;-)

2)   God is not a hypothesis

Science doesn’t deal in “facts” (at least not as most people understand that word). More correctly, it deals with data. One begins with reproducible measurements of some observed phenomena (e.g. – the power density spectrum of the cosmic microwave background, or tracks emerging from particle collisions in a cloud chamber). One or more hypotheses are formed to account for them, and the most viable of these are developed into formal theories from which the outcomes of further, yet untested observations can be predicted. In the case of physics, this generally means a set of differential equations and boundary conditions, a Lie algebra that embodies an expected symmetry, or the like. Failure of a theory’s predictions is its null hypothesis and counts as evidence against it. If further experiments yield the predicted outcomes, confidence in the theory grows, and if not, suspicion does. In this sense, hypotheses that make no testable predictions cannot meaningfully be called scientific.4

Enter our axioms 1) through 7). Though all are based on observation, and scientific illustrations could be given for them, they cannot be called “data” in any scientifically meaningful sense. How does one create a “dataset” to quantify concepts like act and potency, and use it to validate a ground of all being and personhood and the contingency of the universe? What they are, is a set of metaphysical axioms about the underlying ontic nature of the universe, and God (again, note the capital “G”) isn’t a hypothesis we postulate to account for them—He’s a formally reasoned conclusion derived from them.

Alright, before anyone blows a gasket, let me be clear about what I mean. No, I am not saying that the existence of God can be logically/mathematically proven. If it were that easy Atheism wouldn’t be a worldview worth discussing, and its proponents wouldn’t include some of the finest minds in history. What I am saying is that it’s a different sort of argument than the traditional data -> hypothesis -> test methodology science relies on. Claiming that there’s no evidence for God, as opposed to "a god or gods," is like claiming that there’s no “evidence” for “an equation or equations” called the Mean Value Theorem of Calculus. The Mean Value Theorem isn’t a hypothesis—it’s a formal proof that begins with certain axioms (e.g. – a continuous manifold, monotonic everywhere differentiable functions, etc.). The extent to which one accepts those axioms is the extent to which one accepts the conclusion. Likewise, to reject that conclusion is to reject the axioms it begins with.

Which brings us to the next point…

3)   Atheism is not a null hypothesis

Finally, we arrive at New Atheism's most beloved get-out-of-jail-free card—the belief that it's merely the rejection of Theism, and as such, a null hypothesis that needs no defense. Sam Harris (2008) minces no words when he states that,

“’Atheism’ is a term that should not even exist. No one ever needs to identify himself as a ‘non-astrologer’ or a ‘non-alchemist.” … Atheism is nothing more than the noises people make in the presence of unjustified religious beliefs.”

A New Atheist friend and colleague once put it to me even more starkly on social media,

“An Atheist is one who rejects the claims made by theists. An Atheist is simply a person who is not a theist. Atheism is not in itself a claim, and as such, simply cannot be false. Only claims can be proven false; a lack of claim cannot be said to be false. How can I be wrong when I say 'you haven't presented a compelling argument for your case'?” (My emphasis)

Clever, aren’t we? Don't state your claims directly, frame them as a rejection of someone else's… then conveniently excuse yourself from any responsibility for a proper defense of them, and set the standard of proof however high it needs to be to protect you, infinitely if necessary. Sleight of hand like this isn’t just bread-and-butter for New Atheists of course. Creationists and climate change skeptics rely heavily on it as well. Denial... it ain't just a river in Egypt anymore! ;-)

To be fair, this would be valid if we were postulating the activity of demigods in the created order as one possible explanation for some phenomenon. If my fishing buddy insists that the nibble I just had was a trout, I’m under no obligation to defend my skepticism when we both know the pond is full of bass and catfish as well. The burden of proof is on him to produce evidence for his “trout” theory as opposed to a bass or catfish one. But as we’ve seen, that’s not what’s happening here. We aren’t offering any “god hypothesis” to account for something in the natural world, whether it be trout in a pond or anything else. We’re formally demonstrating that a set of metaphysical axioms requires His existence. Atheists like Harris and my friend aren’t rejecting belief in “a god or gods”—they’re rejecting the metaphysical axioms that lead to the God of Classical Theism. That cannot be done in a vacuum without committing oneself to some, or all, of the following counter-axioms;

8)   The universe is a brute fact. Science may reveal its countless subtleties and underlying unities, but ultimately it just has the contingent features it does rather than an infinite number of other possibilities. There is no reason why... it just is that way.

9)   Per 8), the beginning of the universe's existence (13.73 billion years ago) is also a brute fact. There is no reason why... it just created itself from nothing.

10)   There is no such thing as causality—only events unfolding in certain ordered ways. “Causality” is just a concept we use to describe the appearance of mechanism between bits of stuff (what I referred to above as "interactions"), but ultimately those events are, to use David Hume's term, "loose and separate." They have no inherent relationship to each other.

11)   Matter does not actually possess any inherent properties or essential natures of the sort that could be described in terms of essence or potency (as I defined them above). Reality is ultimately just "bits of stuff" mechanically interacting according to mathematical laws expressed in terms of parameters that give the appearance of such. [“Um, ‘interactions’ and ‘laws’…? Didn’t you just say in 10) that…?” “Silence Dorothy! Pay no attention to that man behind the curtain...!”]

12)   The rationality of the laws of nature—that those "loose and separate" events between bits of stuff happen to unfold according to what physicist Eugene Wigner called "the unreasonable effectiveness of mathematics—is also a brute fact. There is no reason why... it just is that way.

13)   "Loose and separately" ordered bits of stuff are blind, and as such the universe ascribes no objective value or purpose. Everything in it, including us, is a byproduct of random, meaningless accidents—what Richard Dawkins called "blind, pitiless indifference" (Dawkins, 1996). Thus, morality is either nihilistic or entirely subjective.

14)   Alternately, if objectively normative moral values do exist—yours, mine, or anyone else's—then they too are brute facts. There is no reason why... they just are what they are. [“But my goodness gracious… isn’t it marvelous how nicely they align with mine…?”]

15)   Consciousness and personhood are illusory. To again use David Hume's term, we're just "bundles of percepts" in bodies made up of bits of stuff behaving according to deterministic laws. [“Um, ‘deterministic’…? Didn’t you say in 10) that…?” “Silence Dorothy! Pay no attention to that man behind the curtain...!”] "You" or "I" are concepts we use to describe our experience of the neural activity in our brains, and how it affects our perceptions and behaviors. Beyond that, we are no more “persons” in the sense of being freely empowered, intentional, and possessing rational agency than an email server is (analytic philosophers refer to this viewpoint as eliminative materialism).

16)   Though we are accidentally evolved "bundles of percepts," our perceptions and reasoned thoughts are reliable sources of knowledge of the deepest inner workings of the universe and ourselves.

Notice that these aren’t mere “rejections” of anything. Like 1) through 7), they’re positive metaphysical assertions about the ontic foundations of the universe, and as such, they have rational consequences. We can reject belief in mythological demigods, invisible dragons, or the Flying Spaghetti Monster if we like. But we cannot reject the God of Classical Theism without committing ourselves to a fully developed and properly defended philosophy of Materialism, any more than we can reject belief in light without accepting belief in darkness—which is of course, precisely what every Atheist philosopher of any repute in history has labored to produce. David Hume, Friedrich Nietzsche, Bertrand Russell, Antony Flew… these and many other luminaries devoted their lives to producing materialistic philosophies of nature, mind, and ethics based on some, or all of the above counter-axioms, and published countless influential works in the process (Hume, 2000; 2017; Nietzsche, 2000; Russell, 1967; 2017; Flew, 2005 to name a few).

According to Harris and my friend, all of that was a waste of time—what these and countless other luminaries should’ve been doing, was belittling televangelists and suicide bombers on social media and in TED talks to like-minded audiences. They, of course, knew better. Those who insist that there’s no evidence for “a god or gods” are merely demonstrating that they don’t even understand the question, much less have a properly thought out answer for it.5

A reporter once presented the late Samuel Shenton, then president of the Flat Earth Society, with a photograph of earth taken by the Apollo 13 astronauts from roughly 150,000 miles distance. Shenton stared long and hard at it, after which he began to nod. “Yes,” he finally said… “It is easy to see how the untrained eye could be fooled by that picture!” Well-trained eyes are becoming an increasingly important part of the modern intellectual landscape… particularly in secular communities that wear their claims to “reason” and objectivity like golden tiaras. But as I said in my last post, if our only tool is a hammer then sooner or later everything will look like a nail. Though some would deny it (sincerely, I believe), to many in these communities, science is no longer a discipline. It has become a religion in its own right—Scientism, the sacred Oracle whose mighty outstretched hand no question of earth, sky, heart, or soul can elude. Its practitioners are no longer experts, but authorities—high priests of the goddess Reason, whose metaphysical pronouncements are every bit as authoritative as the theistic fundamentalist dogmas they, often rightly, deride.

Nowhere is this more true than with physics—a discipline that not only knocks on the door of many metaphysical questions, but immerses itself in counterintuitive mysteries that at times seem almost magical, and higher mathematics that to the guy on the street are every bit as arcane as ancient hieroglyphics… so much so that a term has even been coined for it: physics envy. And human nature being what it is, once a scientist has been elevated from mere expertise to the august status of High Priest, he/she becomes an authority not only in their own field, but in beer brewing, Elizabethan poetry, personal lubricants, or any other topic for which it’s their whim to have an opinion. Anymore, hardly a week goes by that I don’t see yet another news story extolling Stephen Hawking’s latest complaints and/or warnings about society, international politics, or the impacts of technology on the future of humanity—as though expertise in quantum cosmology qualifies him to speak to any of those topics. [That isn’t Hawking’s fault of course. Scientists rarely ask for the deification so glibly bestowed on them by a credulous public.]

Unfortunately, there’s one big problem with all this… Like it or not, science is a discipline, not an Oracle. A powerful discipline to be sure, and one that has rolled back the mysteries of the universe like no other, but a discipline nonetheless, and for damn sure, no more either. And like all other disciplines, it is, and always will be, but one tool among many. As such, it lends itself to many but not all questions, and the experts who wield it are fallen mortals every bit as subject to their own hopes, fears, and human limitations as we are. It’s the height of naivete and outright hubris to pretend that we can cleanse it of our own limitations and treat it like a magic wand that can answer every question, meet every moral, spiritual, and existential need, and endow our existence with purpose… and we pay a steep price when we do. The philosopher Alfred North Whitehead once said,

“Scientists, animated by the purpose of proving they are purposeless, constitute an interesting subject for study.”

True that.

Footnotes

1)   I’m not knowledgeable enough about Hinduism to speak with any authority about it, but its concept of Brahman as the Absolute appears to bear some similarity to the God of the Abrahamic traditions. If so, then including it in this list would raise the tally of humanity that embraces some version of the God of Classical Theism to nearly 70%.

2)   There is one version of the cosmological argument that does presume that the universe had a beginning—the Kalam cosmological argument whose most notable proponent is William Lane Craig. However, it isn’t based on time-ordered causality either. The Kalam argument differs from the traditional one in that it contains two additional premises: Whatever begins to exist has a cause; and that this cause must be transcendent because (per Parmenides) the universe cannot efficiently cause itself. But like the traditional cosmological argument, it takes this cause to be essentially-ordered as well.

3)  Conservation of energy is suspect even for a flat universe. In this case, the global energy of the universe can be derived from the Poisson equation, which has no solution for an unbounded fluid. There is one, and only one case in which the universe can be said to have a well-defined global energy, and that is if it’s closed, in which case, a global definition of energy/momentum flux (gravitationally equivalent to Gauss’ Law) would require it to be zero.

4)  Interestingly, some physicists and philosophers are now beginning to question this, and their reasons are rather surprising. In recent years, multiverse models based on eternal inflation and the so-called string landscape have in the eyes of many physicists, become “the best game in town” for a “theory of everything” that could potentially resolve many issues in physics and cosmology. The inflationary framework accounts beautifully for a few cosmological conundrums that would otherwise be inexplicable (e.g. – the “flatness" problem, and the uniformity of the cosmic microwave background). But in the absence of a viable candidate for the inflaton (as of this writing), the scalar potential/s in inflationary models are flexible enough that for the time being at least, validating the framework has largely proven to be a whack-a-mole exercise. For every model that’s been observationally ruled out, more have sprung up. Likewise, while string theory has led to much progress in many areas, it has also proven excessively flexible—so much so that since its inception more than 40 years ago, it has yet to make a single testable prediction. Furthermore, the scale on which it’s real nuts and bolts are expected to reveal themselves requires testing at energies that will never be accessible to us (Woit, 2007). For all intents and purposes, this renders string landscape multiverse models virtually untestable… even in principle. However, in spite of these problems, they offer two really big carrots that in addition to their other strengths have proven irresistible to many physicists: a) In conjunction with anthropic arguments, they currently offer the only workable explanations of fine tuning that are based solely on physics; and b) Though vulnerable to some formidable arguments that the universe had a beginning, eternal inflation does offer at least some hope for avoiding a creation event. Technically, “eternal” inflation is a reference to future-eternal inflation and thus a bit of a misnomer. A past-eternal universe would run afoul of the BGV theorem; there are a few ways to get around it, although the best of them are contrived to say the least.

The bottom line is that as of this writing, the string landscape/eternal inflation multiverse offers the only path forward for cosmology that doesn’t smack of a Creator. Given the theistic alternatives, it’s little wonder that many Atheist physicists (most notably Sean Carroll) are willing to accept these limitations and argue that it’s time to dispense with testable predictions in science. If a theory is “elegant” (in their view) and at least fits observation, it is de-facto true. Likewise, it also comes as no surprise that many of the strongest opponents of this movement (known as Post-Empiricism) are Christians like George Ellis (Ellis & Silk, 2014).

Ironically, the shoe is now on the other foot. Atheists who for so long have (often rightly) accused religious believers of clinging to comfortable dogmas without evidence, are now the ones insisting that science should be divorced from it. When their backs are against the wall (and to their credit IMHO), they prove to be every bit as mortal as people of faith. And like us, they cherish their worldviews enough that they’ll occasionally struggle for their preservation even to a fault.

5)   Antony Flew is a particularly telling case in point. Often referred to as the Father of 20th Century Atheism, he was arguably the most important Atheist philosopher of his age. His seminal work God and Philosophy (2005), which was originally published in 1966, almost single-handedly shaped the direction of Atheist thought and scholarship during his lifetime. Shortly before his death in 2010, he shocked the secular world when he set aside his life’s work and said that based on reason and evidence, he could no longer deny the existence of God (Flew & Varghese, 2008). Flew didn’t conclude with a God who is personal, as in the Bible and Quran, nor did he embrace any major religion. But his God did bear a striking similarity to the God of Classical Theism, and he gave a particularly deferential hat-tip to… Christianity.

Needless to say, this dealt New Atheists a narcissistic injury which they still haven’t recovered from to this day. The reaction was immediate, and what one would expect. Despite his life’s work, Flew was promptly branded an apostate to the True Faith and excommunicated. Dawkins (2008) fumed about his “tergiversation” (as though using the biggest and most impressive word he could find in a crossword puzzle would somehow convert bullshit into a valid argument). Others resorted to smear campaigns (up to and including accusing him of senility), and intellectual cross-burnings that would make even the flock of Westboro Baptist Church blush. The one thing that was not, and to this day has not been produced, is a properly researched and soundly defended critique of his stance.

Perhaps New Atheists are as offended by religion as they are because they have more in common with blindly dogmatic religious fundamentalists than they’re prepared to admit. Few people evoke as much hate as those who hold a mirror up to us that we don’t want to face.

References

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Dawkins, R. (2008). The God Delusion. Mariner Books; Reprint edition, ISBN-10: 0618918248; ISBN-13: 978-0618918249. Available online at www.amazon.com/God-Delusion-Richard-Dawkins/dp/0618918248/ref=sr_1_1_title_1_pap?s=books&ie=UTF8&qid=1408044395&sr=1-1&keywords=god+delusion. Accessed July 11, 2017.

Ellis, G., & Silk, J. (2014). Scientific method: Defend the integrity of physics. Nature, 516(7531). Available online at www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535. Accessed July 11, 2017.

Feser, E. (2010). The last superstition: A refutation of the new atheism. St. Augustines Press; 1St Edition edition (December 10, 2010). ISBN-10: 1587314525; ISBN-13: 978-1587314520. Available online at www.amazon.com/Last-Superstition-Refutation-New-Atheism/dp/1587314525/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=1499974707&sr=8-1. Accessed July 13, 2017.

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Feser, E. (2015). Neo-scholastic Essays. St. Augustines Press; 1 edition (June 30, 2015). ISBN-10: 1587315580; ISBN-13: 978-1587315589 Available online at www.amazon.com/Neo-Scholastic-Essays-Edward-Feser/dp/1587315580/ref=pd_sim_14_3?ie=UTF8&dpID=51vOUR5k8eL&dpSrc=sims&preST=_AC_UL320_SR214%2C320_&psc=1&refRID=MP3S70WMRDF7N9VQNPMA. Accessed July 15, 2017.

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Flew, A., & Varghese, R. A. (2008). There is a God. HarperOne; unknown edition (November 4, 2008). ISBN-10: 0061335304; ISBN-13: 978-0061335303. Available online at www.amazon.com/There-God-Notorious-Atheist-Changed/dp/0061335304/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=1500661815&sr=1-1. Accessed July 21, 2017.

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Hume, D. (2017). An enquiry concerning human understanding. CreateSpace Independent Publishing Platform (July 1, 2017). ISBN-10: 1461180198; ISBN-13: 978-1461180197. Available online at www.amazon.com/Enquiry-Concerning-Human-Understanding/dp/1461180198/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=1500660885&sr=8-3. Accessed July 21, 2017.

Hume, D. (2000). A treatise of human nature. Oxford University Press; New Ed edition (February 24, 2000). ISBN-10: 0198751729; ISBN-13: 978-0198751724. Available online at www.amazon.com/Treatise-Human-Nature-Oxford-Philosophical/dp/0198751729/ref=sr_1_13?ie=UTF8&qid=1500660885&sr=8-13&keywords=david+hume. Accessed July 21, 2017.

Martin, C. F. (1997). Thomas Aquinas God and Explanations. Edinburgh University Press; 1 edition (June 30, 1997). ISBN-10: 0748609016; ISBN-13: 978-0748609017. Available online at www.amazon.com/Thomas-Aquinas-Explanations-Christopher-Martin/dp/0748609016/ref=sr_1_1?ie=UTF8&qid=1500142014&sr=8-1&keywords=Thomas+Aquinas+God+and+Explanations. Accessed July 15, 2017.

Misner, C. W., Thorne, K. S., & Wheeler, J. A. (MTW). 2017. Gravitation. Princeton University Press. ISBN-10: 0691177791; ISBN-13: 978-0691177793. Chap. 20.2. Online at www.amazon.com/Gravitation-Charles-W-Misner/dp/0691177791/ref=sr_1_1?ie=UTF8&qid=1514324449&sr=8-1&keywords=gravitation. Accessed Dec. 26, 2017.

Moreland, J. P., & Craig, W. L. (2003). Philosophical foundations for a Christian worldview. IVP Academic; unknown edition (April 28, 2003). ISBN-10: 0830826947; ISBN-13: 978-0830826940. Available online at www.amazon.com/Philosophical-Foundations-Christian-Worldview-Moreland/dp/0830826947/ref=sr_1_1?ie=UTF8&qid=1460753368&sr=8-1&keywords=Philosophical+Foundations+for+a+Christian+Worldview. Accessed July 17, 2017.

Nietzsche, F. (2000). Basic Writings of Nietzsche. Modern Library; Modern Library edition (November 28, 2000). ISBN-10: 0679783393; ISBN-13: 978-0679783398. Available online at www.amazon.com/Writings-Nietzsche-Modern-Library-Classics/dp/0679783393/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=1500661604&sr=1-7. Accessed July 21, 2017.

Oderberg, D. S. (2008). Real essentialism. Routledge; 1 edition (January 30, 2008). ISBN-10: 041587212X; ISBN-13: 978-0415872126. Available online at www.amazon.com/Essentialism-Routledge-Studies-Contemporary-Philosophy/dp/041587212X/ref=sr_1_2?ie=UTF8&qid=1500142092&sr=8-2&keywords=Thomas+Aquinas+God+and+Explanations. Accessed July 15, 2017.

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Russell, B. (2017). The problems of philosophy. CreateSpace Independent Publishing Platform (April 21, 2017). ISBN-10: 1545507635; ISBN-13: 978-1545507636. Available online at www.amazon.com/Problems-Philosophy-Bertrand-Russell/dp/1545507635/ref=mt_paperback?_encoding=UTF8&me=. Accessed July 21, 2017.

Wikipedia. (2016). Greek primordial deities. Available online at en.wikipedia.org/wiki/Greek_primordial_deities. Accessed July 17, 2017.

Woit, P. (2007). Not even wrong: The failure of string theory and the search for unity in physical law. Basic Books; Reprint edition (September 4, 2007). ISBN-10: 0465092764; ISBN-13: 978-0465092765. Available online at www.amazon.com/Not-Even-Wrong-Failure-Physical/dp/0465092764/ref=mt_paperback?_encoding=UTF8&me=. Accessed July 16, 2017.

discipline

Posted in Metaphysics, Theology | 94 Comments

It's been a while since I've done one of these...

My bookmarks folder wasn't backed up when my laptop was stolen in March, so I lost a bunch of links, but I remembered some of the really cool stuff from before:

♦  It turns out that if you expose a synthetic diamond to radioactivity, it generates an electrical current.  Diamond is also pretty good at shielding certain kinds of radioactive rays.  So scientists at the University of Bristol are proposing to convert radioactive waste into diamond batteries, as shown in this video.  The batteries generate a very small amount of power, but would last for thousands of years, and would be safe to use e.g. inside of humans as pacemakers.  So apparently that sci-fi trope about using diamonds to generate power will be right after all!

♦  A searchable database of classical oaths, which I found from the author Jo Walton's website.

I've thought for a long time that the curriculum about Facts vs. Opinions harms critical thinking far more than it hurts it.  Is something a "fact" (rather than an "opinion") because it is objectively true?  Or decisively proven?  Because it is uncontroversial to a certain community, or can be used in an essay (aimed at a particular audience) as ammunition to support a conclusion?  Because it has to do with tangible, physical reality, rather than being a normative judgement like morality or aesthetics?

(For example, the Resurrection of Jesus is a fact in the sense that it is claimed to be about objective physical reality, it is a fact in the sense that it actually occurred, but it is certainly not an opinion shared by everybody and when talking to people outside of the Church, it is indeed the sort of opinion which requires backing up with other, less controversial, facts.  Admittedly, as St. N.T. Wright says [pdf lecture], this is kind of a category-bending "fact", but there are plenty of other examples I could have used as well.)

"Well, you can't expect elementary school students to understand subtle distinctions like the ones you've just distinguished!"  But these are completely different meanings of the word, related only by metaphorical similarity!  That's like saying that you shouldn't expect children to understand the fine distinction between breaking a glass and breaking the law.

And now for some bookmarks on the new laptop:

♦  Math with Bad Drawings, a blog by a math teacher sharing math [facts?/opinions?]

♦  Did you know that the world's richest dog inherited his wealth from another dog?

♦  Meet St. John Mitchell, the clergyman who in addition to many other scientific accomplishments wrote the first paper about black holes, entitled by the impressively long title:

"On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose. By the Rev. John Michell, B. D. F. R. S. In a Letter to Henry Cavendish, Esq. F. R. S. and A. S."

♦  A blog post about some recent developments in black hole information theory, which happens to mention my work with some guys at Harvard about how to make a traversable wormhole!

♦ If you want to make your own black hole, check out this astonishingly black paint, which you can buy for a reasonable price.

♦  I've also been profiled by a journalist at HubPages (St. Joel Furches).  Oh, and I won a prize a while back.

♦  The fake history of Giordano Bruno, martyr for "Science!"?

♦  A sermon by a Coptic priest with a more legitimate claim than Cosmos to speak for martyrs.

♦  Speaking of dealing with grief over death, here is a tearjerking interview with a woman about coping with life after her son committed suicide.  I listened to it on Good Friday this year.  (Note: this is a Catholic radio show, so Protestant viewers may need to screen out all the remarks about how being Catholic is so very Catholic and have we mentioned that we're Catholic?)

Blog post on the same site: A Meditation On The Shocking Idea That Maybe Were Actually Not Just Lazy Whiners.

♦  Deconstructing the Documentary Hypothesis.  (Again, Roman Catholic site with various other polemics I don't endorse, but we're pretty much on the same team when it comes to the Old Testament having a basis in historical reality.)

♦  As for the New Testament, here's your periodic reminder that there are really easy ways to distinguish the historically authentic texts about Jesus from the rest.

♦  Why are women underrepresented in philosophy and should we care?  A statistical analysis of the academic ladder as it relates to gender politics.

My own private sources tell me that there is blatant, severe (and often illegal) discrimination in favor of women in academic philosophy, to the point where sometimes a woman with mediocre talents and a single publication in a mid-ranked journal, can win out in a competition with a brilliant male researcher with over a dozen publications in top journals.

♦  My Bionic Quest for Boléro, a story about what it takes to get a deaf person able to appreciate classical music again.  I highly recommend you listen to the musical piece in question while reading the article.

♦  Here is what a low-trust society looks like: Poor Russian Families Berate a Store Owner for Handing Out Free Bread.  It's also an image or an icon of how human beings treat God.  So now you know what it looks like from the other side.

## "The Glimmer"

“The Glimmer”
by Aron C. Wall

We used to think it was about individual particles,
and that the measuring apparatus was the same as before.
Then the War began, and it became personal;
each of us needing to roll dice,
and consult the railway tables,
To see what new home could become our destination;
or whether, if we could stay, home would remain home.
Some of us—secretly, but entangled with the rest—
dropped the sun on our new-home's enemies.
These histories decohere,
but you can still see the glimmer in each raindrop,
winking and saying:
“You won't believe it,
not even if someone tells you,
but life is quantum, not classical.”

—Holy Saturday, 2017

## Interpreting the Quantum World II: What Does It Mean?

In the first installment of this series, we immersed ourselves in the quantum realm that lies beneath our everyday experience and discovered a universe that bears little resemblance to it. Instead of the solid, unambiguously well-behaved objects we’re familiar with, we encountered a unitary framework ($\hat U$) in which everything (including our own bodies!) is ultimately made of ethereal “waves of probability” wandering through immense configuration spaces along paths deterministically guided by well-formed differential equations and boundary conditions, and acquiring the properties we find in them as they rattle through a random pinball machine of collisions with “measurement” events ($\hat M$). This is all very elegant—even beautiful… but what does it mean? When my fiancé falls asleep in my arms, her tender touch, the warmth of her breath on my neck, and the fragrance of her hair hardly seem like mere probabilities being kicked around by dice-playing measurements. The refreshing drink of sparkling citrus water I just took doesn’t taste like one either. What is it that gives fire to this ethereal quantum realm? How does the Lord God breathe life into our probabilistic dust and bring about the classical universe of our daily lives (Gen. 2:7)? We finished by distilling our search for answers down to three fundamental dilemmas:

1)  What is this thing we call a wave function? Is it ontologically real, or just mathematical scaffolding we use to make sense of things we don’t yet understand?

2)  What really happens when a deterministic, well-behaved $\hat U$ evolution of the universe runs headlong into a seemingly abrupt, non-deterministic $\hat M$ event? How do we get them to share their toys and play nicely with each other?

3)  If counterfactual definiteness is an ill-formed concept, why are we always left with only one experienced outcome? Why don’t we experience entangled realities?

Physicists, philosophers, and theologians have been tearing their hair out over these questions for almost a century, and numerous interpretations have been suggested (more than you might imagine!). Most attempt to deal with 2), and from there, back out answers to 1) and 3). All deserve their own series of posts, so let me apologize in advance for only having time to do a fly-by of the more important ones here. In what follows I’ll give an overview of the most viable, and well-received interpretations to date, and finish with my own take on all of it. So, without further ado, here are our final contestants…

Copenhagen

This is the traditionally accepted answer given by the founding fathers of QM. According to Copenhagen, the cutting edge of reality is in $\hat M$. The world we exist in is contained entirely in our observations. Per the Born Rule, these are irreducibly probabilistic and non-local,and result in classically describable measurements. The wave function and its unitary history $\hat U$ are mere mathematical artifices we use to describe the conditions under which such observations are made, and have no ontic reality of their own. In this sense, Copenhagen has been called a subjective, or epistemic interpretation because it makes our observations the measure of all things (pun intended :-) ). Although few physicists and philosophers would agree, some of the more radical takes on it have gone as far as to suggest that consciousness is the ultimate source of the reality we observe. Even so, few Copenhagen advocates believe the world doesn’t exist apart from us. The tree that falls in the woods does exist whether we’re there to see and hear it or not. What they would argue is that counterfactuals regarding the tree’s properties and those of whatever caused it to fall don’t instantiate if we don’t observe them. If no one sees the tree fall or experiences any downstream consequence of its having done so, then the question of whether it has or not is irreducibly ambiguous and we’re free to make assumptions about it.

Several objections to Copenhagen have been raised. The idea that ontic reality resides entirely in non-local, phenomenologically discrete “collapse” events that are immune to further unpacking is unsatisfying. Science is supposed to explain things, not explain them away. It’s also difficult to see how irreducibly random $\hat M$ events could be prepared by a rational, deterministic $\hat U$ evolution if the wave function has no ontic existence of its own. To many physicists, philosophers, and theologians, this is less a statement about the nature or reality than the universe’s way of telling us that we haven’t turned over enough stones yet, and may not even be on the right path.

For their part, Copenhagen advocates rightly point out that this is precisely what our experiments tell us—no more, no less. If the formalism correctly predicts experimental outcomes, they say, metaphysical questions like these are beside the point, if not flat-out ill-formed, and our physics and philosophy should be strictly instrumentalist—a stance for which physicist David Mermin coined the phrase “shut up and calculate".

Many Worlds

One response to Copenhagen is that if $\hat U$ seems to be as rational and deterministic as the very real classical physics of our experience, perhaps that’s because it is. But that raises another set of questions. As we’ve seen, nothing about $\hat U$ allows us to grant special status to any of the eigenstates associated with observable operators. If not, then we’re left with no reason other than statistical probability to consider any one outcome of an $\hat M$ event to be any more privileged than another. Counterfactuals to what we don’t observe should have the same ontic status as those we do. If so, then why do our experiments seem to result in discrete irreducibly random and non-local “collapse” events with only one outcome?

According to the Many Worlds (MWI) interpretation, they don’t. The universe is comprised of one ontically real, and deterministic wave function described by $\hat U$ that’s local (in the sense of being free of “spooky-action-at-a-distance”) and there’s no need for hidden variables to explain $\hat M$ events. What we experience as wave function “collapse” is a result of various parts of this universal wave function separating from each other as they evolve. Entangled states within it will be entangled while their superposed components remain in phase with each other. If/when they interact with some larger environment within it, they eventually lose their coherence with respect to each other and evolve to a state where they can be described by the wave functions of the individual states. When this happens, the entanglement has (for lack of a better term) “bled out” to a larger portion of the wave function containing the previous entanglement, and the environment it interacted with, and states are said to have decohered. Thus, the wave function of the universe never actually collapses anywhere—it just continues to decohere into the separate histories of previously entangles states that continue with their own $\hat U$ histories, never interacting with each other again. As parts of the same universal wave function, all are equally real, and questions of counterfactual definiteness are ill-formed.

The advantages of MWI speak for themselves. From a formal standpoint, a universe grounded on $\hat U$ and decoherence that’s every bit as rational and well-behaved as the classical mechanics it replaced, certainly has advantages over one based on subjective hand grenade $\hat M$ events. It deals nicely with the relativity-violating non-locality and irreducible indeterminacy that plague Copenhagen as well. And for reasons I won’t get into here, it also lends itself nicely to quantum field theory, and Feynmann path integral (“sum over histories”) methods that have proven to be very powerful.

But its disadvantages speak just as loudly. For starters, it’s not at all clear that decoherence can fully account for what we directly experience as wave function collapse. Nor is it clear how MWI can make sense of the extremely well-established Born Rule. Does decoherence always lead to separate well-defined histories for every eigenstate associated with every observable that in one way or another participates in the evolution of $\hat U$? If not, then what meaning can be assigned to probabilities when some states decohere and others don’t. Even if it does, what reasons do we have for expecting that it should obey probabilistic constraints?

And of course, we haven’t even gotten to the real elephant in the room yet—the fact that we’re also being asked to believe in the existence of an infinite number of entirely separate universes that we can neither observe, nor verify, even though the strict formalism of QM doesn’t require us to. Physics aside, for those of us who are theists this raises a veritable hornet’s nest of theological issues. As a Christian, what am I to make of the cross and God’s redemptive plan for us in a sandstorm of universes where literally everything happens somewhere to infinite copies of us all? It’s worth noting that some prominent Christian physicists like Don Page embrace MWI, and see in it God’s plan to ultimately gather all of us to Him via one history or another, so that eventually “every knee shall bow, and every tongue confess, and give praise to God (Rom. 14:11). While I understand where they’re coming from, and the belief that God will gather us all to Himself some day is certainly appealing, this strikes me as contrived and poised for Occam’s razor.

In the end, despite its advantages, and with all due respect to Hawking and its other proponents, I don’t accept MWI because, to put it bluntly, it’s more than merely unnecessary—it’s bat-shit crazy. According to MWI there is, quite literally, a world out there somewhere in which I, Scott Church (peace be upon me), am a cross-dressing, goat worshipping, tantric massage therapist, with 12” Frederick’s of Hollywood stiletto heels (none of that uppity Victoria’s Secret stuff for me!), and D-cup breast implants…

Folks, I am here to tell you… there isn’t enough vodka or LSD anywhere on this lush, verdant earth to make that believable! Whatever else may be said about this veil of tears we call Life, rest assured that indeterministic hand grenade $\hat M$ events and “spooky action at a distance” are infinitely easier to take seriously. :D

De Broglie–Bohm

Bat-shit crazy aside, another approach would be to try separating $\hat U$ and $\hat M$ from each other completely. If they aren’t playing together at all, we don’t have to worry about whether they’ll share their toys. Without pressing that analogy too far, this is the basic idea behind the De Broglie-Bohm interpretation (DBB).

According to DBB, particles do have definite locations and momentums, and these are subject to hidden variables. $\hat U$ is real and deterministic, and per the Schrödinger equation governs the evolution of a guiding, or pilot wave function that exists separate from particles themselves. This wave function is non-local and does not collapse. For lack of a better word, particles “surf” on it, and $\hat M$ events acting on them are governed by the local hidden variables. In our non-local singlet example from Part I, the two electrons were sent off with spin-state box lunches. All of this results in a formalism like that of classical thermodynamics, but with predictions that look much like the Copenhagen interpretation. In DBB the Born Rule is an added hypothesis rather than a consequence of the inherent wave nature of particles. There is no particle/wave duality issue of course because particles and the wave function remain separate, and Bell’s inequalities are accounted for by the non-locality of the latter.

There’s a naturalness to DBB that resolves much of the “weirdness” that has plagued other interpretations of QM. But it hasn’t been well-received. The non-locality of its pilot wave $\hat U$ still raises the whole “spooky action at a distance” issue that physicists and philosophers alike are fundamentally averse to. Separating $\hat U$ from $\hat M$ and duct-taping them together with hidden variables adds layers of complexity not present in other interpretations, and runs afoul of all the issues raised by the Kochen-Specker Theorem. We have to wonder whether our good friend Occam and his trusty razor shouldn’t be invited to this party. And like MWI, it’s brutally deterministic, and as such, subject to all the philosophical and theological nightmares that go along with that, not to mention our direct existential experience as freely choosing people. Even so, for a variety of reasons (including theories of a “sub-quantum realm” where hidden variables can also hide from Kochen-Specker) it’s enjoying a bit of a revival and does have its rightful place among the contenders.

Consistent Histories

As we’ve seen, the biggest challenge QM presents is getting $\hat U$ and $\hat M$ to play together nicely. Most interpretations try to achieve this by denying the ontological reality of one, and somehow rolling it up into the other. What if we denied the individual reality of both, and rolled them up into a larger ontic reality described by an expanded QM formalism? Loosely speaking, Consistent Histories (or Decoherent Histories) attempts to do this by generalizing Copenhagen to a quantum cosmology framework in which the universe evolves along the most internally consistent and probable histories available to it.

Like Copenhagen, CH asserts that the wave function is just a mathematical construct that has no ontic reality of its own. Where it parts company is in its assertion that $\hat U$ represents the wave function of the entire universe, and it never collapses. What we refer to as “collapse” occurs when some parts of it decohere with respect to larger parts leading, it is said, to macroscopically irreversible outcomes that are subject to the ordinary additive rules of classical probability. In CH, the potential outcomes of any observation (and thus, the possible histories the universe might follow) are classified by how homogeneous and consistent they are. This, it’s said, is what makes some of them more probable than others. A homogeneous history is one that can be described by a unique temporal sequence of single-outcome propositions, such as, “I woke up” > “I got out of bed” > “I showered” … Those that cannot be, such as ones that include statements like “I walked to the grocery store or drove there” are not. These events can be represented by a projection operator $\hat P$ from which histories can be built, and the more internally consistent they are (per criteria contained in a class operator $\hat P$), the more probable they are.

Thus, in CH $\hat M$ is not a fundamental QM concept. The evolution of the universe is described by a mathematical construct, $\hat U$ that can be interpreted as decohering into the most internally consistent (and therefore probable) homogeneous histories possible for it to. The paths these histories take give us a framework in which some sets of classical questions can be meaningfully asked, and other can’t. Returning to our electron singlet example, CH advocates would maintain that the wave function wasn’t entangled in any real physical sense. Rather, there are two internally consistent histories for the prepared electrons that could have emerged a spin measurement: Down/Up, and Up/Down. Down/Up/Up/Down isn’t a meaningful state, so it’s meaningless to say that the universe was “in” it. Rather, when the entire state of us/laboratory/observation is accounted for, we will find that the universe followed the history that was most consistent for that. There is no need to discriminate between observer and observed. Decoherence is enough to account for the whole history, so $\hat M$ is a superfluous construct.

CH advocates claim that it offers a cleaner, and less paradoxical interpretation of QM and classical effects than its competitors, and a logical framework for discriminating boundaries between classical and quantum phenomena. But it too has its issues. It’s not at all clear that decoherence is as macroscopically irreversible as it’s claimed to be, or that by itself it can fully account for our experience of $\hat M$. It also requires additional projection and class operator constructs not required by other interpretations, and these cannot be formulated to any degree practical enough to yield a complete theory.

Objective Collapse Theories

Of course, we could just make our peace with $\hat U$ and $\hat M$. Objective collapse, or quantum mechanical spontaneous localization (QMSL) models maintain that the universe reflects both because the wave function is ontologically real, and “measurements” (perhaps interactions is a better term here) really do collapse it. According to QMSL theories, the wave function is non-local, but collapses locally in a random manner (hence, the “spontaneous localization”), or when some physical threshold is crossed. Either way, observers play no special role in the collapse itself. There are several variations on this theme. The Ghirardi–Rimini–Weber theory for instance, emphasizes random collapse of the wave function to highly probably stable states. Roger Penrose has proposed another theory based on energy thresholds. Particles have mass-energy that, per general relativity, will make tiny "dents" in the fabric of space-time. According to Penrose, in the entangled states of their wave function these will superpose as well, and there will be an associated energy difference that entangled states can only sustain up to a critical threshold energy difference (which he theorizes to be on the order of one Planck mass). When they decohere to a point where this threshold is exceeded, the wave function collapses per the Born Rule in the usual manner (Penrose, 2016).

For our purposes, this interpretation pretty much speaks for itself and so do its advantages. Its disadvantages lie chiefly in how we understand and formally handle the collapse itself. For instance, it’s not clear this can be done mathematically without violating conservation of energy or bringing new, as-yet undiscovered physics to the game. In the QMSL theories that have been presented to date, if energy is conserved the collapse doesn’t happen completely, and we end up with left-over “tails” in the final wave function state that are difficult to make sense of with respect to the Born Rule. It has also proven difficult to render the collapse compliant with special relativity without creating divergences in probability densities (in other words, blowing up the wave function). Various QMSL theories have handled issues like this in differing ways, some more successfully than others, and research in his area continues. But to date, none of the theories on the table offers a slam-dunk.

The other problem QMSL theories face is a lack of experimental verification. Random collapse theories like Ghirardi–Rimini–Weber could be verified if the spontaneous collapse of a single particle could be detected. But these are thought to be extremely rare, and to date, none have been observed. However, several tests for QMSL theories have been proposed (e.g. Marshall et al., 2003; Pepper et al., 2012; or Weaver et al., 2016 to name a few), and with luck, we’ll know more about them in the next decade or so (Penrose, 2016).

Conclusion

There are many other interpretations of QM, some of which are more far-fetched than others. But the ones we’ve covered today are arguably the most viable, and as such, the most researched. As we’ve seen, all have their strengths and weaknesses. Personally, I lean toward Objective Collapse scenarios. It’s hard to believe that something as well-constrained and mathematically coherent as $\hat U$ isn’t ontologically real. Especially when the alternative bedrock reality being offered is $\hat M$, which is haphazard and difficult to separate from our own subjective consciousness (the latter in particular smacks of solipsism, which has never been a very compelling, or widely-accepted point of view). Of the competing alternatives that would agree about $\hat U$, MWI is probably the strongest contender. But for reasons that by now should be disturbingly clear, it’s far easier for me to accept a non-local wave function collapse than its take on $\hat M$. Call me unscientific if you will, but ivory towers alone will never be enough to convince me that I have a cross-dressing, goat-worshipping, voluptuous doppelganger somewhere that no one can ever observe. Other interpretations don’t fare much better. Most complicate matters unnecessarily and/or deal with the collapse in ways that render $\hat M$ deterministic.

It’s been said that if your only tool is a hammer, eventually everything is going to look like a nail. It seems to me that such interpretations are compelling to many because they’re tidy. Physicists and philosophers adore tidy! Simple, deterministic models with well-defined differential equations and boundary conditions give them a fulcrum point where they feel safe, and from which they think they can move the world. This is fine for what it’s worth of course. Few would dispute the successes our tidy, well-formed theories have given us. But if the history of science has taught us anything, it’s that nature isn’t as enamored with tidiness as we are. Virtually all our investigations of QM tell us that indeterminism cannot be fully exorcized from $\hat M$, and the term “collapse” fits it perfectly. Outside the laboratory, everything we know about the world tells us we are conscious beings made in the image of our Creator. We are self-aware, intentional, and capable of making free choices—none of which is consistent with tidy determinism. Anyone who disputes that is welcome to come up with a differential equation and a self-contained set of data and boundary conditions that required me to decide on a breakfast sandwich rather than oatmeal this morning… and then collect their Nobel and Templeton prizes and retire to the lecture circuit.

The bottom line is that we live in a universe that presents us with $\hat U$ and $\hat M$. As far as I’m concerned, if the shoe fits I see no reason not to wear it. Yes, QMSL theories have their issues. But compared to other interpretations, its problems are formalistic ones of the sort I suspect will be dealt with when we’re closer to a viable theory of quantum gravity. When we as students are ready, our teacher will come. Until then, as Einstein once said, the world should be made as simple as possible, but no simpler.

When I was in graduate school my thesis advisor used to say that when people can’t agree on the answer to some question one of two things is always true: Either there isn’t enough evidence to answer the question definitively, or we’re asking the wrong question. Perhaps many of our QM headaches have proven as stubborn as they are because we’re doing exactly that… asking the wrong questions. One possible case in point… physicists have traditionally considered $\hat U$ to be sacrosanct—the one thing that above all others, only the worst apostates would ever dare to question. Atheist physicist Sean Carroll has gone so far as to claim that it proves the universe is past-eternal, and God couldn’t have created it! [There are numerous problems with that of course, but they’re beyond the scope of this discussion.] However, Roger Penrose is now arguing that we need to do exactly that (fortunately, he’s respected enough in the physics community that he can get away with such challenges to orthodoxy without being dismissed as a crank or heretic). He suggests that if we started with the equivalence principle of general relativity instead, we could formulate a QMSL theory of $\hat U$ and $\hat M$ that would resolve many, if not most QM paradoxes, and this is the basis for his gravitationally-based QMSL theory discussed above. Like its competitors, Penrose’s proposal has challenges of its own, not the least of which are the difficulties that have been encountered in producing a rigorous formulation $\hat M$ along these lines. But of everything I’ve seen so far, I find it to be particularly promising!

But then again, maybe the deepest secrets of the universe are beyond us. Isaac Newton once said,

“I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”

As scientists, we press on, collecting our shiny pebbles and shells on the shore of the great ocean with humility and reverence as he did. But it would be the height of hubris for us to presume that there’s no limit to how much of it we can wrap our minds around before we have any idea what’s beyond the horizon. As J. B. S. Haldane once said,

"My own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose." (Haldane, 1928)

Who knows? Perhaps he was right. God has chosen to reveal many of His thoughts to us. In His infinite grace, I imagine He’ll open our eyes to many more. But He certainly isn’t under any obligation to reveal them all, nor do we have any reason to presume that we could handle it if He did. But of course, only time will tell.

One final thing… Astute readers may have noticed one big elephant in the room that I’ve danced around, but not really addressed yet… relativity. Position, momentum, energy, and time have been a big part of our discussion today… and they’re all inertial frame dependent, and our formal treatment of $\hat U$ and $\hat M$ must account for that. There are versions of the Schrödinger equation that do this—most notably the Dirac and Klein Gordon equations. Both however are semi-classical equations—that is, they dress up the traditional Schrödinger equation in a relativistic evening gown and matching handbag, but without an invitation to the relativity ball. For a ticket to the ball, we need to take QM to the next level… quantum field theory.

But these are topics for another day, and I’ve rambled enough already… so once again, stay tuned!

References

Haldane, J. B. S. (1928). Possible worlds: And other papers. Harper & Bros.; 1st edition (1928). Available online at www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=Possible+worlds%3A+And+other+papers. Accessed May 17, 2017.

Marshall, W., Simon, C., Penrose, R., & Bouwmeester, D. (2003). Towards quantum superpositions of a mirror. Physical Review Letters, 91 (13). Available online at journals.aps.org/prl/abstract/10.1103/PhysRevLett.91.130401. Accessed June 9, 2017.

Pepper, B., Ghobadi, R., Jeffrey, E., Simon, C., & Bouwmeester, D. (2012). Optomechanical superpositions via nested interferometry. Physical review letters, 109 (2). Available online at journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.023601. Accessed June 9, 2017.

Penrose, R. (2016). Fashion, faith, and fantasy in the new physics of the universe. Princeton University Press, Sept. 13, 2016. ISBN: 0691178534; ASIN: B01AMPQTRU. Available online at www.amazon.com/Fashion-Faith-Fantasy-Physics-Universe-ebook/dp/B01AMPQTRU/ref=sr_1_1?ie=UTF8&qid=1495054176&sr=8-1&keywords=penrose. Accessed May 16, 2017.

Weaver, M. J., Pepper, B., Luna, F., Buters, F. M., Eerkens, H. J., Welker, G., ... & Bouwmeester, D. (2016). Nested trampoline resonators for optomechanics. Applied Physics Letters, 108 (3). Available online at aip.scitation.org/doi/abs/10.1063/1.4939828. Accessed June 9, 2017.

Posted in Metaphysics, Physics | 24 Comments

## Interpreting the Quantum World I: Measurement & Non-Locality

In previous posts Aron introduced us to the strange, yet compelling world of quantum mechanics and its radical departures from our everyday experience. We saw that the classical world we grew up with, where matter is composed of solid particles governed by strictly deterministic equations of state and motion, is in fact somewhat “fuzzy.” The atoms, molecules, and subatomic particles in the brightly colored illustrations and stick models of our childhood chemistry sets and schoolbooks are actually probabilistic fields that somehow acquire the properties we find in them when they’re observed. Even a particle’s location is not well-defined until we see it here, and not there. Furthermore, because they are ultimately fields, they behave in ways the little hard “marbles” of classical systems cannot, leading to all sort of paradoxes. Physicists, philosophers, and theologians alike have spent nearly a century trying to understand these paradoxes. In this series of posts, we’re going to explore what they tell us about the universe, and our place in it.

To quickly recap earlier posts, in quantum mechanics (QM) the fundamental building block of matter is a complex-valued wave function $\Psi$ whose squared amplitude is a real-valued number that gives the probability density of observing a particle/s in any given state. $\Psi$ is most commonly given as a function of the locations of its constituent particles, $\Psi\left ( \vec{r_{1}}, \vec{r_{2}}... \vec{r_{n}} \right )$, or their momentums, $\Psi\left ( \vec{p_{1}}, \vec{p_{2}}... \vec{p_{n}} \right )$ (but not both, which as we will see, is important), but will also include any of the system’s other variables we wish to characterize (e.g. spin states). The range of possible configurations these variables span is known as the system’s Hilbert space. As the system evolves, its wave function wanders through this space exploring its myriad probabilistic possibilities. The time evolution of its journey is derived from its total energy in a manner directly analogous to the Hamiltonian formalism of classical mechanics, resulting in the well-known time-dependent Schrödinger equation. Because $\left | \Psi \right |^{2}$ is a probability density, its integral over all of the system’s degrees of freedom must equal 1. This irreducibly probabilistic aspect of the wave function is known as the Born Rule (after Max Born who first proposed it), and the mathematical framework that preserves it in QM is known as unitarity. [Fun fact: Pop-singer Olivia Newton John is Born’s granddaughter!]

Notice that $\Psi$ is a single complex-valued wave function of the collective states of all its constituent particles. This makes for some radical departures from classical physics. Unlike a system of little hard marbles, it can interfere with itself—not unlike the way the countless harmonics in sound waves give us melodies, harmonies, and the rich tonalities of Miles Davis’ muted trumpet or Jimi Hendrix’s Stratocaster. The history of the universe is a grand symphony—the music of the spheres! Its harmonies also lead to entangled states, in which one part may not be uniquely distinguishable from another. So, it will not generally be true that the wave function of the particle sum is the sum of the individual particle wave functions,

$\Psi\left ( \vec{r_{1}}, \vec{r_{2}}... \vec{r_{n}} \right ) \neq \Psi\left ( \vec{r_{1}} \right )\Psi\left ( \vec{r_{2}} \right )... \Psi\left ( \vec{r_{n}} \right )$

until the symphony progresses to a point where individual particle histories decohere enough to be distinguished from each other—melodies instead of harmonies.

Another consequence of this wave-like behavior is that position and momentum can be converted into each other with a mathematical operation known as a Fourier transform. As a result, the Hilbert space may be specified in terms of position or momentum, but not both, which leads to the famous Heisenberg Uncertainty principle,

$\Delta x\Delta p \geqslant \hbar/2$

where $\hbar$ is the reduced Planck constant. It’s important to note that this uncertainty is not epistemic—it’s an unavoidable consequence of wave-like behavior. When I was first taught the Uncertainty Principle in my undergraduate Chemistry series, it was derived by modeling particles as tiny pool ball “wave packets” whose locations couldn’t be observed by bouncing a tiny cue-ball photon off them without batting them into left field with a momentum we couldn’t simultaneously see. As it happens, this approach does work, and is perhaps easier for novice physics and chemistry students to wrap their heads around. But unfortunately, it paints a completely wrong-heading picture of the underlying reality. We can pin down the exact location of a particle, but in so doing we aren’t simply batting it away—we’re destroying whatever information about momentum it originally had, rendering it completely ambiguous, and vice versa (in the quantum realm paired variables that are related to each other like this are said to be canonical). The symphony is, to some extent, irreducibly fuzzy!

So… the unfolding story of the universe is a grand symphony of probability amplitudes exploring their Hilbert space worlds along deterministic paths, often in entangled states where some of their parts aren’t entirely distinct from each other, and acquiring whatever properties we find them to have only when they’re measured, many of which cannot simultaneously have exact values even in principle. Strange stuff to say the least! But the story doesn’t end there. Before we can decipher what it all means (or, I should say, get as close as doing so as we ever will) there are two more subtleties to this bizarre quantum world we still need to unpack… measurement and non-locality.

Measurement

The first thing we need to wrap our heads around is observation, or in quantum parlance, measurement. In classical systems matter inherently possesses the properties that it does, and we discover what those properties are when we observe them. My sparkling water objectively exists in a red glass located about one foot to the right of my keyboard, and I learned this by looking at it (and roughly measuring the distance with my thumb and fingers). In the quantum realm things are messier. My glass of water is really a bundle of probabilistic particle states that in some sense acquired its redness, location, and other properties by the very act of my looking at it and touching it. That’s not to say that it doesn’t exist when I’m not doing that, only that its existence and nature aren’t entirely independent of me.

How does this work? In quantum formalism, the act of observing a system is described by mathematical objects known as operators. You can think of an operator as a tool that changes one function into another one in a specific way—like say, “take the derivative and multiply by ten.” The act of measuring some property $A$ (like, say, the weight or color of my water glass) will apply an associated operator $\hat A$ to its initial wave function state $\Psi_{i}$ and change it to some final state $\Psi_{f}$,

$\hat A \Psi_{i} = \Psi_{f}$

For every such operator, there will be one or more states $\Psi_{i}$ could be in at the time of this measurement for which $\hat A$ would end up changing its magnitude but not its direction,

$\begin{bmatrix} \hat A \Psi_{1} = a_{1}\Psi_{1}\\ \hat A \Psi_{2} = a_{2}\Psi_{2}\\ ...\\ \hat A \Psi_{n} = a_{n}\Psi_{n} \end{bmatrix}$

These states are called eigenvectors, and the constants $a_{n}$ associated with them are the values of $A$ we would measure if $\Psi$ is in any of these states when we observe it. Together, they define a coordinate system associated with $A$ in the Hilbert space that $\Psi$ can be specified in at any given moment in its history. If $\Psi_{i}$ is not in one of these states when we measure $A$, doing so will force it into one of them. That is,

$\hat A \Psi_{i} \rightarrow \Psi_{n}$

and $a_{n}$ will be the value we end up with. The projection of $\Psi_{i}$ on any of the $n$ axes gives the probability amplitude that measuring $A$ will put the system into that state with the associated eigenvalue being what we measure,

$P(a_{n}) = \left | \Psi_{i} \cdot \Psi_{n} \right |^{2}$

So… per the Schrödinger equation, our wave function skips along its merry, deterministic way through a Hilbert space of unitary probabilistic states. Following a convention used by Penrose (2016), let’s designate this part of the universe’s evolution as $\hat U$. All progresses nicely, until we decide to measure something—location, momentum, spin state, etc. When we do, our wave function abruptly (some would even be tempted to say magically) jumps to a different track and spits out whatever value we observe, after which $\hat U$ starts over again in the new track.

This event—let’s call it $\hat M$—has nothing whatsoever to do with the wave function itself. The tracks it jumps to are determined by whatever properties we observe, and the outcome of these jumps are irreducibly indeterminate. We cannot say ahead of time which track we’ll end up on even in principle. The best we can do is state that some property $A$ has such and such probability of knocking $\Psi$ into this or that state and returning its associated value. When this happens, the wave function is said to have “collapsed.” [Collapsed is in quotes here for a reason… as we shall see, not all interpretations of quantum mechanics accept that this is what actually happens!]

Non-Locality

It’s often said that quantum mechanics only applies to the subatomic world, but on the macroscopic scale of our experience classical behavior reigns. For the most part this is true. But… as we’ve seen, $\Psi$ is a wave function, and waves are spread out in space. Subatomic particles are only tiny when we observe them to be located somewhere. So, if $\hat M$ involves a discrete collapse, it happens everywhere at once, even over distances that according to special relativity cannot communicate with each other—what some have referred to as “spooky action at a distance.” This isn’t mere speculation, nor a problem with our methods—it can be observed.

Consider two electrons in a paired state with zero total spin. Such states (which are known as singlets) may be bound or unbound, but once formed they will conserve whatever spin state they originated with. In this case, since the electron cannot have zero spin, the paired electrons would have to preserve antiparallel spins that cancel each other. If one were observed to have a spin of, say, +1/2 about a given axis, the other would necessarily have a spin of -1/2. Suppose we prepared such a state unbound, and sent the two electrons off in opposite direction. As we’ve seen, until the spin state of one of them is observed, neither will individually be in any particular spin state. The wave function will be an entangled state of two possible outcomes, +/- and -/+ about any axis. Once we observe one of them and find it in, say, a “spin-up” state (+1/2 about a vertical axis), the wave function will have collapsed to a state in which the other must be “spin-down” (-1/2), and that will be what we find if it’s observed a split second later as shown below.

But what would happen if the two measurements were made over a distance too large for a light signal to travel from the first observation point to the second one during the time delay between the two measurements? Special relativity tells us that no signal can communicate faster than the speed of light, so how would the second photon know that it was supposed to be in a spin-down state? Light travels 11.8 inches in one nanosecond, so it’s well within existing microcircuit technology to test this, and it has been done on many occasions. The result…? The second photon is always found in a spin state opposite that of the first. Somehow, our second electron knows what happened to its partner… instantaneously!

If so, this raises some issues. Traditional QM asserts that the wave function gives us a complete description of a system’s physical reality, and the properties we observe it to have are instantiated when we see them. At this point we might ask ourselves two questions;

1)  How do we really know that prior to our observing it, the wave function truly is in an entangled state of two as-yet unrealized outcomes? What if it’s just probabilistic scaffolding we use to cover our lack of understanding of some deeper determinism not captured by our current QM formalism?

2)  What if the unobserved electron shown above actually had a spin-up property that we simply hadn’t learned about yet, and would’ve had it whether it was ever observed or not (a stance known as counterfactual definiteness)? How do we know that one or more “hidden” variables of some sort hadn’t been involved in our singlet’s creation, and sent the two electrons off with spin state box lunches ready for us to open without violating special relativity (a stance known as local realism)?

Together, these comprise what’s known as local realism, or what Physicist John Bell referred to as the “Bertlmann’s socks” view (after Reinhold Bertlmann, a colleague of his at CERN). Bertlmann was known for never wearing matching pairs of socks to work, so it was all but guaranteed that if one could observe one of his socks, the other would be found to be differently colored. But unlike our collapsed electron singlet state, this was because Bertlmann had set that state up ahead of time when he got dressed… a “hidden variable” one wouldn’t be privy to unless they shared a flat with him. His socks would already have been mismatched when we discovered them to be, so no “spooky action at a distance” would be needed to create that difference when we first saw them.

In 1964 Bell proposed a way to test this against the entangled states of QM. Spin state can only be observed in one axis at a time. Our experiment can look for +/- states about any axis, but not together. If an observer “Alice” finds one of the electrons in a spin-up state, the second photon will be in a spin-down state. What would happen if another observer “Bob” then measured its spin state about an axis at, say, a 45-deg. angle to vertical as shown below?

The projection of the spin-down wave function on the eigenvector coordinate system of Bob’s measurement will translate into probabilities of observing + or – states in that plane. Bell produced a set of inequalities bearing his name which showed that if the electrons in our singlet state had in fact been dressed in different colored socks from the start, experiments like this will yield outcomes that differ statistically from those predicted by traditional QM. This too has been tested many times, and the results have consistently favored the predictions of QM, leaving us with three options;

a)  Local realism is not valid in QM. Particles do not inherently possess properties prior to our observing them, and indeterminacy and/or some degree of “spooky action at a distance” cannot be fully exorcised from $\hat M$.

b)  Our understanding of QM is incomplete. Particles do possess properties (e.g. spin, location, or momentum) whether we observe them or not (i.e. – counterfactuals about measurement outcomes exist), but our understanding of $\hat U$ and $\hat M$ doesn’t fully reflect the local realism that determines them.

c)  QM is complete, and the universe is both deterministic and locally real without the need for hidden variables, but counterfactual definiteness is an ill-formed concept (as in the "Many Worlds Interpretation" for instance).

Nature seems to be telling us that we can’t have our classical cake and eat it. There’s only room on the bus for one of these alternatives. Several possible loopholes have been suggested to exist in Bell’s inequalities through which underlying locally real mechanics might slip through. These have led to ever more sophisticated experiments to close them, which continue to this day. So far, the traditional QM frameworks has survived every attempt to up the ante, painting Bertlmann’s socks into an ever-shrinking corner. In 1966, Bell, and independently in 1967, Simon Kochen and Ernst Specker, proved what has since come to be known as the Kochen-Specker Theorem, which tightens the noose around hidden variables even further. What they showed, was that regardless of non-locality, hidden variables cannot account for indeterminacy in QM unless they’re contextual. Essentially, this all but dooms counterfactual definiteness in $\hat M$. There are ways around this (as there always are if one is willing to go far enough to make a point about something). The possibility of “modal” interpretations of QM have been floated, as has the notion of a “subquantum” realm where all of this is worked out. But these are becoming increasingly convoluted, and poised for Occam’s ever-present razor. As of this writing, hidden variables theories aren’t quite dead yet, but they are in a medically induced coma.

In case things aren’t weird enough for you yet, note that a wave function collapse over spacelike distances raises the specter of the relativity of simultaneity. Per special relativity, over such distances the Lorentz boost blurs the distinction between past and future. In situations like these it’s unclear whether the wave function was collapsed by the first observation or the second one, because which one is in the future of the other is a matter of which inertial reference frame one is viewing the experiment from. Considering that you and I are many-body wave functions, anything that affects us now, like say, stubbing a toe, collapses our wave function everywhere at once. As such, strange as it may sound, in a very real sense it can be said that a short while ago your head experienced a change because you stubbed your toe now, not back then. And… It will experience a change shortly because you did as well. Which of these statements is correct depends only on the frame of reference from which the toe-stubbing event is viewed. It’s important to note that this has nothing to do with the propagation of information along our nerves—it’s a consequence of the fact that as “living wave functions”, our bodies are non-locally spread out across space-time to an extent that slightly blurs the meaning of “now”.  Of course, the elapsed times associated with the size of our bodies are too small to be detected, but the basic principle remains.

Putting it all together

Whew… that was a lot of unpacking! And the world makes even less sense now than it did when we started. Einstein once said that he wanted to know God’s thoughts, the rest were just details. Well it seems the mind of God is more inscrutable than we ever imagined! But now we have the tools we need to begin exploring some of the way His thoughts have been written into the fabric of creation. Our mission, should we choose to accept it, is to address the following;

1)  What is this thing we call a wave function? Is it ontologically real, or just mathematical scaffolding we use to make sense of things we don’t yet understand?

2)  What really happens when a deterministic, well-behaved $\hat U$ symphony runs headlong into a seemingly abrupt, non-deterministic $\hat M$ event? How do we get them to share their toys and play nicely with each other?

3)  If counterfactual definiteness is an ill-formed concept and every part of the wave function is equally real, why do our observations always leave us with only one experienced outcome? Why don’t we experience entangled realities, or even multiple realities?

In the next installment in this series we’ll delve into a few of the answers that have been proposed so far. The best is yet to come, so stay tuned!

References

Penrose, R. (2016). Fashion, faith, and fantasy in the new physics of the universe. Princeton University Press, Sept. 13, 2016. ISBN: 0691178534; ASIN: B01AMPQTRU. Available online at www.amazon.com/Fashion-Faith-Fantasy-Physics-Universe-ebook/dp/B01AMPQTRU/ref=sr_1_1?ie=UTF8&qid=1495054176&sr=8-1&keywords=penrose. Accessed June 11, 2017.

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