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.