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Finding God’s Dice


When most people think of Albert Einstein’s contribution to physics, the theory of relativity is what comes to mind, and rightly so. What most don’t realize is that his Nobel Prize was actually awarded for explaining the photoelectric effect, a result which contradicted the classical understanding of light and helped lead to the development of Quantum Mechanics. Despite his major contributions to its development, Einstein was famously uncomfortable with the way randomness and uncertainty became so integral to the understanding of that new theory, often summed up in his quote, “God does not throw dice.”

This objection, however offhand it may seem, resonated with many physicists of the time. The glory of classical physics was how neat and tidy everything was. It offered the promise of determinism: if we could know perfectly the state of the universe at one moment and the laws that govern it, we could extrapolate forwards and backwards perfectly as far as we like. Despite the recognition that this ideal was well nigh impossible, there was comfort in the promise, and each step we took at least brought us closer to that perfection. The claim was that perfect knowledge of the natural world, the sort that is attributed to God, would ultimately be expressed in a deterministic mathematical formula.

The difficulty that Quantum Mechanics presented for Einstein and many others, physicists and non-physicists alike, is that the best picture of the physical world that it allows seems partial and incomplete. It implied that it is not just practically difficult but theoretically impossible to completely describe the current state of the world, let alone extrapolate forwards or backwards as we please. As bad as the loss of “perfect” knowledge of the world was for physicists, it further called into question the nature of God’s knowledge of the world. If some aspect of the natural order was inherently uncertain and unknowable what does this imply for God? Is God’s knowledge subject to this randomness, is he simply reacting to the whims of nature?

The image of God awaiting the results of a chance outcome is rightly viewed as absurd, but the solution was not a recovery of classical determinism. Even independent of the results of Quantum Mechanics, that view was philosophically flawed, and the attempt to understand God’s knowledge using it was even more so.

If physics could actually give us a complete description of the now and from that extrapolate forwards and backwards, then the past, present and future are logically the same and all equally “present.” In a sense, nothing “new” ever happens because everything is subject to absolute necessity. Every effect is completely defined by its cause, a picture of the world that is arguably static rather than dynamic, detracting from the very notion of time. There are a host of subtle problems this raises about necessity and contingency and what it even means to be a cause, but the most obvious difficulty with this view is that it leaves no room at all for free human activity.

Additionally, thinking of God’s knowledge in this way cripples the idea of His providence. If everything in nature simply happened necessarily based on what came before, it would seem reasonable to say that God’s knowledge is just the perfect working out of the complicated physics problem of the universe. As creator He knows how all things will work together and His providence simply becomes this human kind of foresight and His governance simply becomes setting things up to run perfectly. The danger inherent in this is to see God as the external Architect who only works on and understands the world on a natural level, more powerfully and perfectly than we ever could perhaps, but still on a natural level.

It took many years and much experimentation and calculation before the reality of the quantum world sunk in. Physicists eventually became comfortable with the success of Quantum Mechanics and settled into a new status quo that accepted a randomness and indeterminism underlying physics. Even those who sought alternative interpretations of Quantum Mechanics that might save determinism recognized that they had to bring in other phenomena that destroyed the crisp, clean classical worldview. Unfortunately, the damage done to the understanding of causality and of God’s providence by classical determinism remains.

Even if the natural world “throws dice” in its most fundamental interaction, this may simply be a physical manifestation of the inherent contingency of all material things. This idea would not have been so foreign to Aristotle and St. Thomas Aquinas, who saw both necessary and contingent causes in the world around them. More importantly, this loss of absolute necessity does not threaten God’s absolute knowledge of the created order, for his knowledge is not limited to the particular mathematical and formal descriptions that we are able to develop in the sciences. God’s providence, His wise ordering of everything to its proper end, is above every natural cause. The certainty of God’s knowledge does not limit his power to create natural objects that can act in a truly contingent way. Einstein was right that “God does not throw dice,” but He knows perfectly the natural order that He created to do just that.
This article first appeared on DominicanaBlog.com, an online publication of the Dominican Students of the Province of St. Joseph who live and study at the Dominican House of Studies in Washington, DC. It was written by Br. Thomas Davenport, O.P., who entered the Order of Preachers in 2010. He graduated from Stanford University with a PhD in Physics.
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Dominicans of the Province of St. Joseph

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The Order of Preachers, known also as the Dominican Order, was founded by St. Dominic in 1216 with the mission of preaching for the salvation of souls. With contemplative study serving as a pillar of Dominican religious life, the Order continues to contribute to the Catholic synthesis of faith and reason, following the example of such Dominican luminaries as St. Albert the Great and St. Thomas Aquinas. The Friars of the Province of St. Joseph administer Providence College in Providence, RI and serve as teachers and campus ministers in several colleges, universities, and seminaries in addition to serving as pastors, chaplains, and itinerant preachers. Follow the Dominican students at their blog, DominicanaBlog.com.

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  • Danny Getchell

    What act of creation would be greater and more worthy of respect?

    (1) To build a complete model of the city of London in Legos - carefully hand-placing blocks to define every street, every building, every vehicle.

    (2) To invent a single Lego which was capable of duplicating itself, modifying the design of the duplicates as needed, and which internalized the plan to replicate the same model of London - without the need for the ultimate designer to touch a single block after the first one.

    • I vote for (2).

    • Jim (hillclimber)

      But under (2), the Logos of the Legos (yes, I am proud of myself) is present during the building of London. The Logos has an intimate relationship with the Legos that persists during the building.

      You didn't exactly say whether the activity of your auto-building Legos in (2) is completely pre-determined, or whether the Legos have some freedom in how they build themselves, albeit subject to a strict grammar of construction. I would pick (2), but modified to give the Legos some sort of free response, and modified further so that the original inventor hovers lovingly over the Legos, somehow guiding the Legos back on track (while never violating the Logos of the Legos) when they misuse their freedom.

      • Elson

        Just too...(2) much expected of a creative commenter.

      • Danny Getchell

        modified further so that the original inventor hovers lovingly

        That's exactly the "God's providence" line of thought in the article which I intended to dispute. Not wanting to hijack this into yet another problem-of-evil thread, but it's precisely the lack of historical evidence for that "loving guidance" which is my support for a wind-it-up-and-let-it-go God.

        As I have said here before, it's entirely possible that we live in a universe created by God to be a perfect simulacrum of a universe in which He does not exist. Fits the arguments from logic, as well as observed reality.

        In closing, I tip my hat to you for "Logos of the Legos" :-)

    • I vote for (2) as well, but I don't think it leads to deism. In the example of a London made of legos, the Designer could walk away after making and programming the first block. However, in the lego scenario there is no chance involved. That is the point of the article: classical physics doesn't allow for chance and quantum mechanics is all about chance. In other words, with quantum mechanics no thing has to be the way that it is. Considering the great number of factors involved for the development of intelligent life it screams for something more than a deist conception of God to me.

  • Elson

    I am not exactly sure what points that SN is trying to make with this article. Is it's purpose to somehow make the concept of "god" more credible and the deterministic effects on free will less credible?

    Quotes from Stephen Hawking
    "Our search for understanding will never come to an end, and that we will always have the challenge of new discovery. Without it, we would stagnate"/b>

    "One could calculate probabilities, but one could not make any definite predictions. Thus, the future of the universe is not completely determined by the laws of science, as Laplace thought. 'god' still has a few tricks up his sleeve."



  • Quantum mechanics is in some ways friendlier to determinism than classical mechanics.

    Ironically, quantum mechanics is one of the best prospects for a genuinely deterministic theory in modern times! ( http://plato.stanford.edu/entries/determinism-causal/#QuaMec )

    Although it is the case that, on the quantum mechanical level, future events cannot generally be determined from previous events, knowledge of the space of probabilities (the Hilbert space) at any time gives perfect knowledge of the space of probabilities into the future and into the past, assuming that quantum mechanics perfectly respects unitarity.

    Even if quantum mechanics does not respect unitarity, quantum mechanics has to reduce to classical mechanics for large objects, and there is no evidence of which I'm aware that our brains function on the quantum level. Our brains could very well be deterministic classical systems, their future states determined to sufficiently high accuracy from past states.

    • TomD123

      I think at the current level of understanding in neuroscience that this is not entirely clear. For one, I think that Roger Penrose argued that perhaps brains could function at the quantum level...at least parts of the brain. I believe he put forward the possibility that various cytoskeletal components could operate on that level.

      • At the very least it is possible. The notion of brain determinism crushing free will extrapolates wildly into unknown causes and effects. It is simply saying that the material cause totally determines the material effect. It is assumed human thoughts, feelings and decisions are nothing more than that so free will is done. The theory readily admits some of the cause and effect relations may not even have been speculated on yet. So what? It is just a matter of time. If you add in the quantum level then it is not a, "So what?"

        • GCBill

          Well, brain-based libertarian free will requires not only an indeterminate QM theory, but a stochastic mechanism that is sensitive enough to be affected by quantum variations. And furthermore, for the indeterminacy to be meaningful (not merely random), you need a person's thoughts to constrain the way in which the "randomness" unfolds at higher levels.

          I judge it to be possible, but I certainly wouldn't bet on it actually being true. There's a reason metaphysical libertarians tend to align themselves with dualism more often than not.

          • TomD123

            1) Indeterminism in QM right now is the leading interpretation
            2) Catholics are a sort of dualist...even though not Cartesian dualists.
            3) Indeterminist QM does not entail free will, nor does no QM entail no free will. It is just that indeterminist QM provides a nice opening for free will. I suggest the latter part of Dr. Stephen Barr's Modern Physics, Ancient Faith for a discussion on this issue

          • 1) Is it? Which specific interpretation is the leading interpretation?

            2) Ok.

            3) I don't think it helps much with free will unless there is some evidence that the brain operates at a regime where quantum effects dominate. As far as I know, there is none. I'm not a neuroscientist, though.

          • TomD123

            1) I was under the impression that the Copenhagen interpretation was inherently only probabilistic, but I am no physicist and am open to correction.
            3) Yeah, and right now, I think that it is not clear. Some, like Penrose who I mentioned above, have suggested that quantum effects could play a role in certain neural structures.

          • 1) I don't know. That's why I asked. GCBill's link suggests you are correct. The article has Copenhagen at 42%, followed by information-theoretical at 24% and Everett at 18%. (see http://arxiv.org/pdf/1301.1069v1.pdf , Q12)

        • But quantum effects may not matter much for how the brain works. Classical mechanics may do just fine.

          • Yes, but you need that as an additional premise to arrive at determinism. It is a statement about science that science is nowhere close to proving. That is that classical mechanics can explain ALL brain activity. We are a long was from fully explaining everything the brain does.

          • It is true that no one knows for sure. But, as far as I know, neuroscientists have not yet needed to concern themselves with quantum physics. Maybe this will change. Until then, it seems reasonable to treat the brain as a purely classical system.

          • David Nickol

            Yes, but you need that as an additional premise to arrive at determinism.

            I am not sure what difference it makes—at least to those of us who lean strongly toward materialism—if the brain can be completely explained by classical mechanics or if quantum mechanics must be brought into it. Now and then I have seen speculation that the brain may be subject to quantum effects, and that that (somehow) can be used as an explanation of how determinism is false and "free will" can exist. But I can only imagine that "freeing up" the brain in this manner—exempting it from determinism—couldn't account for "free will." It would just add an element of true randomness to the working of the brain, not some kind of special power to make "free" choices.

            It is a statement about science that science is nowhere close to proving.

            Science doesn't prove statements about science. And of course science has not "proven" that quantum effects don't enter into the baking cupcakes. It seems to me that good neuroscientists will make the working assumption that the brain can be explained by classical mechanics until they bump up against something that classical mechanics can't explain, which may be never.

            It seems to me that it may very well be the case that believers in things spiritual (like souls) may be clinging to the mind/brain as yet another "gap" which only theology, not science, can explain and will have to keep retreating a bit every time neuroscience advances.

  • It implied that it is not just practically difficult but theoretically impossible to completely describe the current state of the world

    That's not quite right. The math that describes how quantum measurements and experiments work is extremely well confirmed, but what physical phenomena might underly the math is open to multiple interpretations. Future experiments may be able to discriminate between these possibilities, but for now all we can say is that we don't know whether a complete description of the world is in principle possible. The Copenhagen interpretation has the character you describe, but, for example, de Broglie–Bohm theory does not.

    Even those who sought alternative interpretations of Quantum Mechanics that might save determinism recognized that they had to bring in other phenomena that destroyed the crisp, clean classical worldview. Unfortunately, the damage done to the understanding of causality and of God’s providence by classical determinism remains.

    For once, I think an SN author is underselling theism! The Copenhagen interpretation may have won out historically simply because of the fame of its founders and the way that it appears to postulate as little as possible beyond what we observe. Nevertheless, there are some who argue that more rigorous concern for Occam's Razor would, in this unusual case, strongly favor the Everett interpretation. For those who dislike the Everett's pure-wave ontology, de Broglie-Bohm theory is very similar but conserves the intuition that particles are also real. In any case, the evidence upon which we might later make a decision between interpretations doesn't yet exist. Thus it's premature to say classical deterministic causality is undermined.

    I have to wonder if we have here another example of what atheists see as a major failing of theism: the tendency to rush to judgment on the basis on inadequate evidence.

  • Jim (hillclimber)

    I think our knowledge of pseudo-random generators is relevant here as well. Good pseudo-random numbers, far from being evidence of disorder, are evidence of extremely subtle order. It takes some good mathematics to make highly unpredictable sequences of pseudo-random numbers. By extrapolation, we could reasonably infer that the truly unpredictable sequences in nature are in fact evidence of a very sophisticated, and not-at-all-arbitrary, underlying logos.

  • GCBill

    Physicists eventually became comfortable with the success of Quantum
    Mechanics and settled into a new status quo that accepted a randomness
    and indeterminism underlying physics. Even those who sought alternative
    interpretations of Quantum Mechanics that might save determinism
    recognized that they had to bring in other phenomena that destroyed the
    crisp, clean classical worldview.

    If recent polls of working physicists are any indication, this is wrong. There is no "majority view" of QM even nearly a century after its foundation. Does this not significantly undermine the major concern this article sets out to address (and ultimately claim in favor of theism)? There's a significant "chance" that the universe might still not play dice after all, in which case the proposed "problems" and "solutions" here are moot.

    Furthermore, I'm skeptical of the claim that deterministic views of QM have to bring in "other phenomena." At a recent World Science Fair presentation, Sean Carroll made a convincing case that the (deterministic) Everett interpretation follows from a single equation. From my understanding, that's actually an improvement over the more popular Copenhagen interpretation, which requires assumptions about the functioning of reality not contained within the linked equation. If this is right, then we should prefer Everett to Copenhagen all else being equal.

  • Peter

    All laws in the universe are constant, even the uncertainty principle. There are no circumstance where it does not apply. It applies everywhere all the time, just like the other laws of nature.

    For the uncertainty principle to be truly uncertain, truly indeterministic, it would have to apply randomly, so that there would be times and place it did apply and times and places it did not, and these times and places would alter randomly.

    However, that is not the case. The uncertainty principle is constant; it is always in force, everywhere. There are no laws which apply at random in God's universe for, if there were, God would lose control of his creation.and it would not evolve as he intends.

    • Unless you believe in God, in which case things like, gravity, the laws of motion, and so on are more like house rules you give to children that can be suspended and re-written on a whim and all matter can be created out of nothing through sheer will. Except for that, all laws of the universe are constant.

      • Peter

        If God chooses to momentarily suspend the laws of nature as in, say, miracles, then they are the opposite of random. Furthermore, matter created out of nothing does not necessarily contradict the laws of nature and is consistent with our current scientific hypotheses.

  • I think this is a fascinating piece thanks. I think it puts forth a pretty interesting problem for theists. It the universe is deterministic, there is no free will. Humans must have free will on Christian theology, therefore it can't be deterministic. However, if it is indeterminite, god can't be all knowing. God knows everything, therefore it can't be indeterminate.

    I'm not sure that the author has explained away this problem. I think he just says, god can know everything and there be free will because he's god. He's beyond all that.

    • For a theist perhaps; for a deist definitely, but for the Jew or Christian there is no problem presented by the universe being indeterminate. God's omniscience is not based on knowledge of how everything works nor is His knowledge related to time. The Christian understanding of God's transcendence and being eternal makes His knowledge not a differing degree from our, but wholly other than ours. This is what people like Stephen Hawking seem to not appreciate when they say we'll know the mind of God when we discover the unifying theory/law of all things and are able to explain the great mysteries such as the big bang and black holes. I do not at all think it is unreasonable to think it possible for us to attain such knowledge (though I find it highly unlikely). However, all we will have done is be able to explain the processes of the universe in it's entirety and make more accurate predictions. There would still be other questions beyond our reach.

    • Ararxos

      You are wrong. God knows our choices which are determined by us, He doesn't chose for us.


  • There is the Conway/Kochen Free Will Theorem that asserts the free will of quantum entities. See