Tagged: quantum mechanics

Time In Two Dimensions

R.N. Carmona

Lately, I have been thinking a lot about time, both on a personal level and on a philosophical one. Setting aside all of my thoughts on the kind of freedoms and privileges I would need to truly own my time, the phenomenon of time occupies my thoughts, in many ways from the mundane to the complex. When I was younger and far less patient, I would grow incensed having convinced myself that I picked the wrong bus out of the two that showed up at roughly the same time because the other bus eventually drove past mine. As I got older and my philosophical tendencies started to take root ever deeper, I started to notice how whenever the other bus drove by the bus I was on, it would never get too far ahead. In fact, it would arrive at my stop less than a minute before mine did.

So came my idea of virtual simultaneity. From there, I would imagine a parallel me, a sort of ghost, who in another universe got on the other bus and I would imagine how far ahead of me he would be on his walk toward my building. I would then speed up so that I would catch up to my parallel on my way home as means to feel better about not having been on the bus that arrived earlier. This is how I think about time, in a very intimate sense. Nothing stops me in my tracks like an article about time. My mind could be furtherest from time and from philosophy more generally, reading fan theories about a show I am into or looking up the latest sports scores, and when scrolling, an article about time shows up and I am immediately in that headspace. This was the case two days ago when I read Musser’s article “A Defense of the Reality of Time.”

Time is one of the most difficult phenomena to apprehend in the universe. It is as elusive as it is seductive. It is safe to say that no one has won over this lover’s heart. No one has seduced her enough to understand all of her mysteries and secrets. It is because of this that I am often discouraged to write anything about time, despite growing confidence in my philosophical capacities. But just then, Musser said something that got the gears of my mind running.

“Well, what if time had two dimensions?” As a purely algebraic question, I can say that. But if you ask me what could it mean, physically, for time to have two dimensions, I haven’t the vaguest idea. Is it consistent with the nature of time that it be a two-dimensional thing? Because if you think that what time does is order events, then that order is a linear order, and you’re talking about a fundamentally one-dimensional kind of organization.

Musser, George. “A Defense of the Reality of Time”. Quanta Magazine. 16 May 2017. Web.

What if the critical error we continue to make is thinking of time as one-dimensional? What if time has more than one dimension, just like space does? A cursory look at Superstring Theory (ST) will begin to sound exactly like me in a footrace with parallel me. Parallel or possible worlds emerge from the fifth and sixth dimensions of ST. If it were possible to see the fifth dimension, we would be able to take note of similarities and differences between the world we occupy and a parallel world. Perhaps this is what our imagination does. If a runner gets a cramp in her calf a few meters from the finish line, she may envision herself winning the race in a world in where she did not get injured. Perhaps we do, in fact, see the fifth dimension, but I digress.

In the sixth dimension, one would be able to see the universe as it was at the beginning and an array of possibilities. One would, for instance, see universes in where the rate of entropy is lower or higher than in ours. If Boltzmann was correct, and time emerges from basic probabilities, then we would see universes in where .000000001 nanoseconds do not equal a second, but instead, .0.000000001515 nanoseconds equal a second, implying that time moves slightly slower in that universe than it does here. This is to say nothing about the arrow of time, which could move in the opposite direction (see Cartwright, John. “We may have a spotted a parallel universe going backwards in time”. New Scientist. 8 Apr 2020. Web. and De Chant, Tim. “Big Bang May Have Created a Mirror Universe Where Time Runs Backwards”. Nova. 8 Dec 2014. Web.).

In the seventh dimension, one may find themselves in the mirror universe on the other side of the Big Bang, in where the arrow of time travels backwards. The eighth dimension would give one access to exotic universes, with initial conditions so far from our own. In the ninth, one would possess the power to compare and contrast every possible world from worlds very much like our own to worlds decidedly unlike ours. Finally, the tenth dimension exhausts every possibility.

The fact of the matter is that we simply do not fully comprehend our own universe and so, we can be gravely mistaken about time. If one considers ST, and not necessarily whether the theory is true, but rather what the theory can teach us, one quickly notices that ST’s dimensions have consequences for time that are arguably more important than their ramifications for space. If ST is the case or if something close to it is true, time is ultimately nonlinear and therefore, not one-dimensional. So let us walk through what two-dimensional time might look like. First, imagine that the ancestors of homo sapiens in the far off future have invented time machines. If they can travel to and fro in time, time is still one-dimensional. In two dimensions of space, one can move horizontally and vertically. So then the question arises, what would it mean for time to move vertically?

Prior talks about a quasi change or “what is common to the flow of a literal river on the one hand…and the flow of time on the other” (Oaklander, Nathan. Adrian Bardon ed. “A-, B- and R-Theories of Time: A Debate”. The Future of the Philosophy of Time. New York: Routledge, 2012. 23. Print.). Rivers, in our world, do not rise, but they do fall. Setting aside evaporation, which does speak to water traveling upward, for time to flow vertically downward, we can imagine a powerful waterfall. Though this is completely new territory and may look like a new way of thinking about time, anyone who has ever thought about the past as something long dead and inaccessible implies that the flow of time travels vertically downward, forever making the past impossible to re-experience directly. For instance, Emery, et al. write: “According to presentism, only present objects exist. More precisely, presentism is the view that, necessarily, it is always true that only present objects exist. Even more precisely, no objects exist in time without being present” (Emery, Nina, et al. “Time”. Stanford Encyclopedia of Philosophy. 2020. Web.). Presentists therefore, believe that objects in the past are in a state of oblivion, but if Temporal Parts Theory (TPT) is correct, then objects and events in the past are annihilated and their corresponding intervals of time are also annihilated. A brief review of TPT is in order.

The Temporal Parts Theory of Identity (hereon TPT) is derived from the notion of time being, in some sense or to some degree, like space. One can think of, for instance, a linear timeline depicting the years all 46 U.S. Presidents held office. Or one can think of the x-y axis used in physics. Time is represented by the x-axis whilst space is represented by the y. Or one can think of a space-time diagram containing two axes representing space and another to represent time. These sorts of considerations have led some philosophers and scientists to ask whether time is a dimension. According to some accounts, time is the fourth dimension. Time, however, is not always analogous to space. D.H. Mellor discussed these disanalogies at length. He, for instance, concluded that there is no spatial analogue for our feeling of the passing of time. We cannot, in other words, attribute the passing of time to spatial changes (Mellor, D. H. Real Time II. London: Routledge, 1998. 95-96. Print.).

With respect to parts, however, time and space are analogous. Theodore Sider explains:

Temporal parts theory is the claim that time is like space in one particular respect, namely, with respect to parts. First think about parts in space. A spatially extended object such as a person has spatial parts: her head, arms, etc. Likewise, according to temporal parts theory, a temporally extended object has temporal parts. Following the analogy, since spatial parts are smaller than the whole object in spatial dimensions, temporal parts are smaller than the whole object in the temporal dimension. They are shorter-lived.

Sider, Theodore. “Temporal Parts”. 2008. Web. 

Consider, as an example, the b-moments in Friedrich Nietzsche’s life. Friedrich Nietzsche’s birth on October 15, 1844 is one b-moment and his death on August 25, 1900 is another. The dates of both represent distinct b-times. On TPT, he is spread out from October 15, 1844 to August 25, 1900. If we were to depict him in a space-time diagram, his parts on our diagram will depict his temporal parts. If we were capable of watching Nietzsche in his infancy, we will be observing a temporal part, then another that resembles it, and then another. If one were to watch infant Nietzsche long enough, his later temporal parts will be slightly bigger than the previous ones. That is to say that Nietzsche is no longer an infant; he is now, for instance, a toddler. So on our space-time diagram, Nietzsche grows the further we move away from his birth. It is also worth noting that temporal parts have spatial parts and vice versa. Nietzsche’s hand, like Nietzsche himself, persisted within the interval of time his life occupies. The parts he was comprised of will also be represented on our space-time diagram.

Nietzsche, therefore, has spatio and temporal parts, so if presentism were correct, the interval of time represented by the ~54 years Nietzsche lived would enter oblivion. The flow of time, as it pertains to Nietzsche’s life, ends and yet, continues. Perhaps a better analogy (though in actuality, this is time moving in three dimensions), presentists seem to imagine that time is like a river, at least on the surface, but within it are whirlpools in where intervals of time meet their end. With difficulty, therefore, one can imagine time in more than one dimension even if one is not convinced of presentism. Consider instead the growing blocking theory (GBT). On GBT, the present and the past are real and the future becomes real when the present edge meets it. Similarly, on the moving spotlight theory (MST), only objects within the spotlight are considered present though objects on the peripheries still exist (Emery, Ibid.). How might two-dimensional time look like under GBT or MST?

For simplicity’s sake, I will consider GBT. Since presentists deny the spatio-temporal parts of the past and thus, bury the past, we can imagine that for presentists, time moves to the right on the x-axis (that is, along the first quadrant of the axis) and also downward on the y-axis (along the fourth quadrant). Growing block theorists, on the other hand, since they believe in the future emerging at the present edge, see time moving in the same direction as presentists on the x-axis, but moving along the y-axis in the opposite direction, upward in the first quadrant. In other words, if the death of temporal parts is a downward movement, the birth of temporal parts is an upward movement.

To pursue a brief tangent, not all theories of time think of time as a line. Eternalists see time in one dimension, but their view of time is more in keeping with a circle. Emery, et al. state:

One version of non-presentism is eternalism, which says that objects from both the past and the future exist. According to eternalism, non-present objects like Socrates and future Martian outposts exist now, even though they are not currently present. We may not be able to see them at the moment, on this view, and they may not be in the same space-time vicinity that we find ourselves in right now, but they should nevertheless be on the list of all existing things.


Another eternalist conception that has been entertained can be called recurrentism. Nietzsche probably explains it best:

What if some day or night a demon were to steal after you into your loneliest loneliness and say to you: “This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence—even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again, and you with it, speck of dust!”

Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: “You are a god and never have I heard anything more divine.” If this thought gained possession of you, it would change you as you are or perhaps crush you. The question in each and every thing, “Do you desire this once more and innumerable times more?” would lie upon your actions as the greatest weight. Or how well disposed would you have to become to yourself and to life to crave nothing more fervently than this ultimate eternal confirmation and seal? 

Nietzsche, Friedrich W, and Walter Kaufmann. The Gay Science: With a Prelude in Rhymes and an Appendix of Songs. New York: Vintage Books, 1974. 373. Print.

On the cosmological interpretation of eternal return (see here), eternalism simply is the idea that time is like a circle. There is a sense in which recurrentism is already implied and though eternalists are usually not committed to the idea of time literally repeating itself, if Socrates and Martian outposts exist, then time and causation are a loop. This implies that some future event will jumpstart the Big Bang and every event in the universe will play out in identical ways all over again. This is precisely the sort of thinking entailed in the presentist’s response to eternalism. Heather Dyke explains:

According to this argument, any theory that assigns ontological privilege to the present moment while also recognizing the existence of non-present times faces an insurmountable problem: it is unable to account for our knowledge that we are located in the present. If anything is certain, surely our knowledge that we are present is! But if past times exist as well as the present time, what is to say we are not located in one of those past times, mistakenly believing ourselves to be present? We might insist that our experience of presentness is so compelling that it must be veridical. But what about Queen Elizabeth I’s experience of presentness? That’s pretty compelling too, yet she is in the past, so her experience misleads her. Perhaps our experience misleads us too.

Dyke, Heather. Presentism and eternalism. Time, metaphysics of, 2011, doi:10.4324/9780415249126-N123-2. Routledge Encyclopedia of Philosophy, Taylor and Francis.

We tend to give the present an ontological status greater than that of the past and the future. It appears that the only escape we have is the idea of spatio-temporal oblivion. Queen Elizabeth I is not somewhere in the past under the mistaken impression that she and not us is present. Time, therefore, probably does not have one dimension. Forward implies backward and up implies down, so any linear or circular view of time runs into problems of recurrence and all sorts of time-related paradoxes like the well-known Grandfather Paradox. Without straying too far in quantum mechanics, all of this is already implied in Bell’s Theorem: “Most models of nature are reversible in time; we can run the basic equations backwards in time as easily as forwards in time. This implies that theories with causality forwards in time must also have causality backwards in time; this was ignored by Bell” (t’Hooft, Gerard. “Time, the Arrow of Time, and Quantum Mechanics”. Frontiers. 29 Aug 2018. Web.).

Especially for people high on the idea of the universe being conscious or that there is a god(s), the universe would therefore offer us clues to help us better understand time. Think of the notion of space and time changing places within a black hole. Going back to the paradigm, namely the four-dimensional concept of space-time, time would then have three dimensions and space would have one. As Pösel explains:

Only outside the cylinder does the intersection with a plane at constant height (“at constant time” as seen from the outside) correspond to a snapshot. Inside the cylinder, time and space have switched places. Inside, the intersection image doesn’t show a snapshot – it shows something much more weird: a caleidoscopic combination of many different times. After all, inside, time is not the axial, but the radial coordinate, and all the different distances from the “center” which you see in the sketch correspond to different moments in time. Instead of the spatial structure of the black hole, the sketch shows a strange mix of space and time!

Pössel, Markus. “Changing places – space and time inside a black hole”. Einstein Online. 2010. Web.

I would highly recommend getting a handle of Pössel’s illustrations if you would like to better understand how time and space trade places within a black hole. For our purposes, the fact that this happens in a black hole might offer a clue. Perhaps the lesson to be learned from the inner workings of blacks holes is that time has more than one dimension. Maybe the relativity of time inhered in General and Special Relativity has to do with the fact that time is superimposed or even supervenes on space in a different way relative to one’s direction in space. In other words, time has a horizontal behavior, so to speak. It has a slightly different vertical behavior. Further still, it has another behavior along curved or edged spaces within the dimension of depth. On Earth, we commonly move as though we lived in two-dimensions, so thinking of moving in a third dimension is difficult to conceptualize. We would have to travel in space to get a better idea of how the effects of gravity, over long distances, look like traveling along a curved surface. Or, we can simply think of the difference between Mario on Super Nintendo versus Mario on the Nintendo Switch. When Mario performs any movements in the depth dimension, or to add to our x- and y-axes, a z-axis, he is now covering diagonal domains analogous to the width of a cube, for instance.

To exhaust a well-known example, time moves faster at higher altitudes, the further one is from the Earth’s center. This might be suggestive of time behaving differently along the vertical axis. This also readily explains the relative experiences of someone falling into a black hole and another person seeing this happen. Recall the following:

1. The light coming from the person gets redshifted; they’ll start to take on a redder hue and then, eventually, will require infrared, microwave, and then radio “vision” to see.

2. The speed at which they appear to fall in will get asymptotically slow; they will appear to fall in towards the event horizon at a slower and slower speed, never quite reaching it.

3. The amount of light coming from them gets less and less. In addition to getting redder, they also will appear dimmer, even if they emit their own source of light!

4. The person falling in notices no difference in how time passes or how light appears to them. They would continue to fall in to the black hole and cross the event horizon as though nothing happened. (“Falling Into a Black Hole Sucks!”ScienceBlogs. 20 Nov 2009. Web.)

If the observer never quite sees the faller fall into the back hole while the faller notices no difference in the passage of time and ultimately, crosses the event horizon, time here can be taking on a different behavior along the z-axis, in the dimension of depth along a curved plain. The 3:1 relation of space-time can be simplified with a 3:3 relation which is virtually the same as 1:1 or colloquially, one-to-one. To my mind, if simplicity is the aim, then this is our next recourse. ST was borne out of an attempt to condense the three dimensions of space into one dimension. That unfortunately did not work, at least not as intended. We should therefore attempt to think of time in three dimensions and see how this might help the project of unifying physics.

Ultimately, our theories of time, along with physics, may be impeded by the idea of one-dimensional time. Maybe it is time for us to begin thinking about the behavior of time in two or three dimensions. ST already shows that there are peculiarities about time across multiple dimensions, implying further that the ten dimensions of ST are not dominated by space. In other words, it is not that nine out of the ten dimensions belong to space and still one to time. There could be a disproportion, like a space-time ratio of 6:4, but if ST entails a few dimensions of time, we should begin conceptualizing how time behaves in a multi-dimensional setting. This might help us to finally unravel all of her mysteries and secrets. Until then, I leave you with a mind-bending interpretation of what happens inside of black hole from Christopher Nolan’s “Interstellar.”

A Refutation of Bruce Gordon’s “Argument From The Incompleteness of Nature”

By R.N. Carmona

Before setting out to formulate Gordon’s “Argument From The Incompleteness of Nature,” a general note is in order. After years of dealing with the more common arguments for God, e.g., the Kalam Cosmological, Moral, Fine-Tuning, Teleological, Ontological arguments, I began to notice that such arguments collapse when the complexity of the facts are analyzed. For instance, P1 of the Moral Argument states that “If God does not exist, objective values and duties do not exist.” This has proved to be the most controversial premise of the argument, but analyses of what is meant by objective, values, and duties lead us in directions where we can apprehend morality along these lines without God being necessarily involved. What I’m noticing now about more complex Theistic arguments is that they collapse when the simplicity of the facts are put on the table, i.e., when simple considerations are taken into account. This also applies to Gordon’s argument. To see what I mean, it will be necessary, first and foremost, to frame Gordon’s argument.

G1 “Quantum mechanics reveals a genuine ontological indeterminacy and incompleteness present in nature” (Gordon, Bruce L.. The Necessity of Sufficiency: The Argument From The Incompleteness of Nature. Two Dozen (or so) Arguments for God: The Plantinga Project, Edited by Walls, Jerry L. & Dougherty Trent. Oxford: Oxford University Press, 2018. 420. Print.)

G2 “Since all physical cause-and-effect relations are local, however, the completeness of quantum theory implies the causal-ontological incompleteness of physical reality: the universe is shot through with mathematically predictable non-local correlations that, on pain of experimental contradiction, have no physical explanation” (Gordon, 421)

G3 “Quantum theory raises fundamental questions about the coherence of material identity, individuality, and causality that pose a prima facie problem for naturalistic metaphysics” (Gordon, 423)

G4 (By way of inference) it is probable that all naturalistic interpretations of quantum mechanics contain conceptual shortcomings (Gordon, 423-429)

GC1 Therefore, “a theistic variant of the Copenhagen interpretation brings metaphysical completion to quantum theory so as to resolve the fundamental puzzle” (Gordon, 423)

GC2 Therefore, “God’s existence and continuous activity is the best explanation for the reality, persistence, and coherence of natural phenomena, and the account of divine action best meeting this explanatory demand is a form of occasionalist idealism” (Gordon, 436)

Gordon also condenses his argument as follows:

Now, in quantum physics we are confronted with a situation in which material causality falls irremediably short of explanatory demand, for there is no collection of physical variables jointly sufficient to the explanation of irreducibly probabilistic quantum outcomes. On pain of postulations to the contrary refuted by experimental violations of Bell inequalities, an ontological gap exists in the causal structure of physical reality that no collection of material causes can be offered to fill. So if a prior commitment to metaphysical naturalism constrains us, no non-naturalistic (transcendent) explanation is available to bridge this gap, and we must embrace the conclusion that innumerable physical events transpire without a sufficient cause, that is, for no explanatorily sufficient reason. In short, Copenhagen orthodoxy, framed in a purely physical context, entails a denial of the principle of sufficient reason (PSR) understood as the general maxim that every contingent event has an explanation. (425)

Right away, one can see how G1 through G3 hold insofar as scientific ignorance remains the case. But first, it will be useful to take note of what motivates Gordon to think that there is any truth to these premises. His primary motivations are informed by what he thinks is the inability of physicists to solve the measurement problem and that, at least from what he interprets is a fault of naturalism, quantum interpretations violate the Principle of Sufficient Reason (PSR) and/or are metaphysically implausible. If Gordon can draw his conclusions by way of induction, by ruling out particular interpretations yet to be offered on the basis of the shortcomings of six more general interpretations, then a naturalist has more warrant to rule out Theism by way of induction, by highlighting the many failures of Theism to square with scientific facts and its many more failures to offer sound philosophical arguments. God was once a local deity, intimately involved in matters far more mundane than quanta. It was widely believed that God created the Earth, not via the gradual work of physical laws, but as intimately as a potter forms his vase. Christians of the past even set out to prove God’s involvement in the world. Donald Prothero gives us a prime example:

Other geologists and paleontologists followed Cuvier’s lead and tried to describe each layer with its distinctive fossils as evidence of yet another Creation and Flood event not mentioned in the Bible. In 1842, Alcide d’Orbigny began describing the Jurassic fossils from the southwestern French Alps and soon recognized 10 different stages, each of which he interpreted as a separate non-Biblical creation and flood. As the work continued, it became more and more complicated until 27 separate creations and floods were recognized, which distorted the Biblical account out of shape. By this time, European geologists finally began to admit that the sequence of fossils was too long and complex to fit it with Genesis at all. They abandoned the attempt to reconcile it with the Bible. Once again, however, these were devout men who did not doubt the Bible and were certainly not interested in shuffling the sequence of fossils to prove Darwinian evolution (an idea still not published at this point). They simply did not see how the Bible could explain the rock record as it was then understood.

Prothero, Donald.  Evolution:  What the Fossils Say and Why it Matters.  New York:  Columbia University Press, 2007. 56-57. Print.

Going over the litany of examples throughout history is not necessary because Theism’s lack of explanatory success informs the behavior of today’s Theists. Therefore, it suffices to point out that Theists have gone from asserting that God is intimately involved in every aspect of reality, in addition to positing that the Bible renders an infallible account of many historical events, including a global flood, to relegating God to the outskirts of human knowledge where the refulgence of science remains unfelt, as hidden somewhere before the Big Bang, active solely in quantum phenomena that evade the experiences of even the most devout believers, and as grounds for some explanation of human consciousness that allows for the continuance of consciousness after death, i.e., a philosophy of mind that entails the existence of the soul, e.g., Cartesian dualism, Aristotelian hylomorphism, panpsychism. Gordon’s argument is a prime example of this retreat to the far reaches of scientific ignorance, hoping with all his might that he will find God at the fringes of reality. If naturalism has pushed Theism this far, then it is safe to say that Theism is teetering on the edge, that any argument Theists put forth now are highly likely to fail, and that it is only a matter of time before Theism plunges into the abyss.

Before exposing glaring issues with Gordon’s conclusion, I will go over issues with his analysis of the many worlds interpretation (MWI) and the Ghirardi-Rimini-Weber spontaneous collapse interpretation (GRWI). Then I will provide an overview of two interpretations that circumvent the measurement problem and one of its entailments, the observer effect. Prior to that, there are already issues with his analysis of the PSR that sound suspiciously like Plantinga’s EAAN or worse, Lewis’ Argument Against Naturalism. Gordon states:

Suppose, among all of the events that happen in the universe, there are countless many that happen without cause or reason. If this were true, we would have no principled way of telling which events were caused and which were not, for events that appeared to have a cause might, in fact, lack one. Our current perceptual states, for example, might have no explanation, in which case they would bear no reliable connection to the way the world is. So if the PSR were false, we could never have any confidence in our cognitive states. (425)

It is important to note that scientists are only concerned about causes inasmuch as they have explanatory power. If a cause does no explanatory work, then it does not help them to get a better understanding of a given phenomenon. Think of Nancy Cartwright’s $1,000 bill descending in St. Stephen’s Square. Scientists simply do not care to arrive at a model that accurately predicts where the bill will land and more precisely, about its exact movements through the air prior to landing. This particular example, that involves any number of difficult to quantify variables, e.g., bird droppings hitting the bill on the way down, dust particles slightly changing the bill’s trajectory, wind speeds, does not help scientists better understand drift, free fall, etc. Physicists already have general principles that help them understand how, for instance, a basketball succumbs to the magnus effect. A disposition of the ball, in particular its shape, makes it susceptible to this effect whereas the dispositions of the bill guarantee that it will drift wildly during the entirety of its descent to the ground.

Any event appearing to be caused does not immediately invite scientific scrutiny. Only events that do explanatory work or are suspected of having some explanatory power over a given effect, specifically in relation to a theory or model, are worth examining. In any case, it does not follow from the possibility that the PSR is false that our perceptual states have no explanation or cause. Therefore, that we can have no confidence in our perceptual states is completely non sequitur. Neuroscientists, cognitive scientists, and psychologists have done plenty of work to show that our perceptual states do have explanations, regardless of whether the PSR is true or not. Thus, if the PSR turns out to not be the case, our perceptual states are not among events lacking a cause or an explanation.

A general note of relevance is in order. Gordon’s citations are mostly decades old, which any peer reviewer in philosophy would immediately be suspicious of. Of the Many Worlds Interpretation, Gordon states: “So which way of building the universal wavefunction is to be preferred? This difficulty, known as the “preferred basis problem,” reveals that the branching process itself is completely arbitrary from a mathematical standpoint and therefore, from the abstract point of view presupposed by the MWI, not reflective of any physical reality” (427). Setting aside the non sequitur, “not reflective of any physical reality,” his primary authority informing this statement, namely David Wallace in 2003, no longer considers preferred basis to be an issue. Gordon would know that if he had read Wallace’s 2010 paper “Quantum Mechanics on Spacetime I: Spacetime State Realism,” in where he states:

We might sum up the objection thus: wave-function realism requires a meta-physically preferred basis… This objection is probably most significant for Everettians, who generally regard it as a virtue of their preferred interpretation that it requires no additional formalism, and so are unlikely to look kindly on a requirement in the metaphysics for additional formalism. Advocates of dynamical-collapse and hidden-variable theories are already committed to adding additional formalism, and in fact run into problems in QFT for rather similar reasons: there is no longer a natural choice of basis to use in defining the collapse mechanism or the hidden variables. We are not ourselves sanguine about the prospects of overcoming this problem; but if it were to be overcome, the solution might well also suggest a metaphysically preferred basis to use in formulating a QFT version of wave-function realism.

Wallace, David, and Christopher G. Timpson. “Quantum Mechanics on Spacetime I: Spacetime State Realism.” The British Journal for the Philosophy of Science, vol. 61, no. 4, 2010, pp. 697–727. https://arxiv.org/pdf/0907.5294.pdf. Accessed 1 Feb. 2021.

Lev Vaidman, Professor at the School of Physics and Astronomy in Tel Aviv, corroborates this: “due to the extensive research on decoherence, the problem of preferred basis is not considered as a serious objection anymore” (Vaidman, Lev, “Many-Worlds Interpretation of Quantum Mechanics”, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), Fall 2018, https://plato.stanford.edu/archives/fall2018/entries/qm-manyworlds/).

Gordon raises a second difficulty for the MWI: “The second difficulty lies in its treatment of quantum probabilities” (Ibid.). Worse than using outdated sources is Gordon’s misrepresentation of a source that actually disagrees with his statement. Simon Saunders, in “Chance in the Everett interpretation,” actually states: “To conclude: there is no good reason to think EQM is really a theory of over-lapping worlds. If questions of overlap of branches are to be settled by appeal to the underlying mathematics, in terms of vector space structure, then there is at least one natural mereology in terms of which worlds that differ in some feature, since orthogonal, are non-overlapping” (Saunders, Simon (2010). Chance in the Everett interpretation. In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory & Reality. Oxford University Press.). Saunders attempts to “solve the problem without introducing additional structure into the theory” (Vaidman, Ibid.) and yet Gordon tells his reader to “see Saunders et al. 2010 for extensive polemics regarding it” (Ibid.). This is an egregious level of malpractice that can only be explained by his desperation to prove his belief in God.

Turning now to his analysis of GRWI, the prospects for his argument do not improve. Gordon states of GRWI: “The problem is that it cannot be rendered compatible with relativity theory or extended to the treatment of quantum fields in this form” (Ibid.); “the theory remains radically non-local and has the additional drawback of eliminating the possibility of particle interactions and thus any physics of interest” (Ibid.); and “there are no versions of the theory in which the collapse is complete, with the consequence that all “material” objects have low- density copies at multiple locations, the presence and effect of which linger forever in the GRWI wavefunction” (Ibid.). The first and third concerns are not an issue for GRWI. The first issue simply restates the more general difficulty physicists have had with reconciling quantum mechanics and general relativity; this would then be an issue for the entire enterprise of quantum mechanics, so we would essentially be tossing the bath water, baby and all! The third issue is an appeal to ignorance. That there is currently no version of GRWI offering a collapse that is complete does not mean that scientists ought to give up on the search for a version containing a complete collapse. This leaves the second concern, which is addressed in Tejinder Singh’s 2018 paper “Space and Time as a Consequence of GRW Quantum Jumps,” where he deploys GRWI to solve the measurement problem. Singh states:

This classical metric is in turn produced by classical bodies, according to the laws of general relativity. And classical bodies are themselves the result of GRW localisation. Thus it is not reasonable to assume space to exist prior to the GRW quantum jumps. Rather, it seems quite intuitive that space results from GRW collapses taking place all over the universe. Space is that which is between collapsed objects. No collapse, no space. This also helps us understand why the GRW jumps take place in space: it is because space in the first place is created because of these jumps.

Singh, Tejinder. “Space and time as a consequence of GRW quantum jumps.” TZeitschrift für Naturforschung A73 (2018) 923. https://arxiv.org/pdf/1806.01297.pdf. Accessed 1 Feb. 2021.

Singh considers Hilbert space as more fundamental than classical space, so these GRW jumps occurring in Hilbert space give rise to the classical fabric of space we are accustomed to. He posits that the wave function is contingent on the configuration space where the particle moves through time, to potentially infinite degrees of freedom. This then results in a complete collapse of the wave function. Gordon’s hasty conclusion no longer holds if Singh has succeeded in offering a version of GRWI containing a complete collapse of the wave function.

This is setting aside the fact that Gordon overlooked what many consider an updated or even upgraded version of MWI, namely the Many Interacting Worlds Interpretation (MIWI). The MIWI differs from the MWI in that all quantum phenomena are the result of an inter-universal repulsive force acting on worlds in close proximity to one another, thus explaining any dissimilarity between them. Michael Hall, et. al. conclude that the MIWI can reproduce quantum interference phenomena, in addition to offering advantages with respect to computational modeling. They note that on the de Broglie–Bohm Interpretation, the wave function denoted by Ψ, even when it is a very large value allows computer modeling to focus on high density regions in configuration space, specifically regions where calculation errors have to be corrected to analyze convergence given norms of angular momentum (see Hall, Michael J. W., Deckert, Dirk-André, and Wiseman, Howard M.. Quantum Phenomena Modeled by Interactions between Many Classical Worlds. Physical Review X, 2014; 4 (4) DOI: 10.1103/PhysRevX.4.041013).

There is also the Lindgren-Liukkonen Interpretation (LLI), championed by two quantum physicists that take Ockham’s Razor seriously. Given this, their quantum interpretation is a statistical interpretation that solves the observer effect. In other words, there is no logical reason, to their minds, why the results of a measurement are dependent on an observer. They dispense with the notion of a conscious observer changing the result of measurements. The LLI shows that any epistemological and ontological issues that stem from the uncertainty principle are solved given that the uncertainty principle is a fixed property of stochastic mechanics (see Lindgren, Jussi and Liukkonen, Jukka. The Heisenberg Uncertainty Principle as an Endogenous Equilibrium Property of Stochastic Optimal Control Systems in Quantum Mechanics. Symmetry, 2020; 12 (9): 1533 DOI: 10.3390/sym12091533

Gordon not only failed to rule out enough interpretations of quantum mechanics to make his conclusion more likely, but he failed to rule out the best defenses of, at least, two of the interpretations he is skeptical about. The larger issue for Gordon is that even if he managed to rule out say, twenty interpretations in quantum mechanics, his conclusion simply does not follow and if it did, there are simple considerations that render it untenable. Recall: “God’s existence and continuous activity is the best explanation for the reality, persistence, and coherence of natural phenomena, and the account of divine action best meeting this explanatory demand is a form of occasionalist idealism” (Gordon, 436). It follows from this that God’s existence and continuous activity is the best explanation for the reality, persistence, and coherence of viruses, diseases, natural disasters, and pretty much any undesired consequence a Theist can imagine. Clearly, Gordon does not want to admit these natural phenomena into his conclusion, choosing instead to special plead for any cases he thinks suit his argument. In other words, one of his concerns fits better on his foot: Suppose, among all of the events that happen in the universe, there are countless many that happen without God’s continuous activity, e.g., pretty much all the bad stuff. If this were true, we would have no principled way of telling which events were caused by his activity and which were not, for events that appeared to have been caused by God, in fact, were not. It is far more probable therefore, that God has no hand in any event in the natural world, not even granting a retreat into the quantum realm.

Ultimately, if a Theist wants to continue to assert that God has a hand in the unification of quantum and classical phenomena, they need to take a different route than Gordon has. Gordon severely undermines his own project by using outdated sources, being completely unaware of the fact that one of the authors of one of his primary sources changed their mind and actually proved the opposite of what seemed to lend a hand to Gordon’s argument, and overlooking a number of interpretations that may provide a stable and complete collapse of the wave function, thus solving quantum paradoxes, like the measurement problem and related observer effect. More damning to such arguments is that if a personal, loving deity saw fit to retreat to the far reaches of metaphysical reality, then he can have no desire to be known or detected by even people who are hopelessly devoted and attached to him. Quanta lies so far outside of the everyday experience of human beings that the idea that God is asking us to pursue him into the microcosms of the quanta is, quite frankly, nonsensical. It makes more sense that retreats like Gordon’s, into profoundly metaphysical territory, has everything to do with Theism’s failure to square with science, in addition to offering philosophical arguments or proofs that are sound or, at the very least, cogent and without controversy. This is precisely the prognosis for Theism and the relentless advances of science and philosophy, closely in tow, do not look poised to provide any remedy. Gordon’s argument, while complex, completely collapses in the face of simple considerations, which is a happy irony given his claims about the quantum wave function.