A “Laplace’s Demon” for the Age of Quantum Uncertainty

Paradoxes derived from the classic thought experiment shed light on fate, free will, and the fundamental structure of reality

I have always been fascinated by parables of fate and free will, because when done properly they are timeless. The “moral” of these stories is never some minor ethical quandary but a metaphysical truth which applies to all of us, always and forever.

In an ancient parable from the Babylonian Talmud, a man sees Death in a Baghdad market place. When death makes a “threatening gesture,” he takes off toward Samarra to escape. Death later confesses that she didn’t make a threatening gesture at all, but a jolt of surprise.

“I was astonished to see him in Baghdad,” she says. “Because I have an appointment with him tonight in Samarra.”

The moral found here in “The Appointment in Samarra” — as well as in Oedipus Rex, 12 Monkeys, and a myriad of other stories throughout history —is that fate always wins. It is, by definition, inevitable. Our efforts to avoid what has been predestined only bring us more assuredly towards the same end we aim to avert.

Predestination further entrenched itself in our philosophy as the Enlightenment and the advent of modern science gave rise to an increasingly clockwork view of the universe. At one time, philosophers wondered whether free will was compatible with an omniscient God; now they wondered whether free will was compatible with a universe which evolves according physical laws.

This “clockwork” view of the universe — and the scientific optimism which accompanied it — was neatly enshrined by Pierre Simon Laplace in 1814, in a thought experiment we now refer to as “Laplace’s Demon.”

Laplace wrote:

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

The reader might be inclined to take this supposition for granted. After all, it is essentially an extrapolation from our common sense notions of cause and effect. If we could aggregate all the “causes” prevailing at a single instant of time, and if we knew the laws which governed the evolution of all physical processes, predicting the future would be a simple matter of solving some complicated mathematical equation with an immense number of variables.

This is all rooted in the assumption that we live in a universe which is deterministic and fundamentally comprehensible. If that’s the case, it leaves little room for “free will” in the conventional sense of the term. If your thoughts and decisions arise from physical processes and their accompanying laws — if you are part of the clockwork, so to speak — you ever have the freedom to determine your own fate? Presumably not, but an interesting paradox arises when when we add a new element to Laplace’s thought experiment, and this paradox calls our assumption of a deterministic universe into question.

Imagine that Laplace’s fortune-telling, super-intelligent entity (the “Demon”) is capable of communicating its knowledge to other, less intelligent entities who exist in the same universe. If the Demon is a part of the same universe it is analyzing and not merely an outsider looking in, then there is no reason to object to this possibility. To visualize this as easily as possible, let’s imagine that the Demon can create a video representation depicting specific parts of the future it has predicted. What would happen if you sat in front of the TV and were invited to watch thirty seconds ahead into your own future? Remember, we are assuming that the Demon really is infallible. It possesses what we might call the “algorithm of reality,” and its mathematical predictions cannot be wrong. Whatever the Demon predicts, and whatever you might choose to do after viewing this prediction, reality will unfold in exact accordance with the prediction.

Herein lies the paradox. The Demon must be right, but it can’t be right.

Let’s say you are shown a video of yourself and asked to re-enact everything you see yourself doing in the video. Maybe you could give a decent approximation of what you saw, but wouldn’t you mistime a breath, or say something with a slightly different inflection, or blink one moment too soon? Could you ever re-enact the video with a degree of accuracy so perfect that not even a single atom deviated from the reality you saw?

Even with the explicit intention of fulfilling the predicted future, a test subject would be like an imperfect actor reading from a script. Even the slightest complexity — a blink, a lifted finger, a sigh — would make the prediction virtually impossible to re-enact exactly, and yet is must be re-enacted if the Demon is truly infallible. That’s not even considering the obvious alternative: what if the test subject is told specifically not to do what they see on the video? How can the Demon possibly be right?

The only rational outcomes occur when we eliminate all circumstances in which the human test subject has the autonomy to affect the future. If the predictions are perfect, the human subject must be powerless to deviate from them, but this powerlessness necessitates particular physical conditions that affect either the human’s comprehension of the circumstances or their ability to act upon those circumstances.

One can imagine the human subject seeing a future in which they have fainted, then they promptly faint from the anxiety. One can imagine the subject closing their eyes, refusing to look at the monitor, then inadvertently and unknowingly re-enacting the predictions. One can imagine them seeing a future so distant that they eventually forget the prediction altogether or simply fail to notice when the predicted future arrives. One can imagine the test subject being some animal, a rabbit for instance, watching the video and not recognizing itself there, and thus remaining oblivious to the fact that it is re-enacting what it is seeing. One cannot, however, imagine a human subject looking at the monitor, seeing themselves move about in a rationally-directed, autonomous way, then fulfilling or diverting that prediction through a deliberate decision. The paradox eliminates all physical circumstances that would allow for human autonomy, artificially funneling reality into a finite number of results wherein the test subject either lacks comprehension or the ability to physically act at a normal capacity.

The quality and specificity of the foreknowledge is relevant to the paradox. If the Demon merely told you, “In thirty years, you’re going to marry a red-headed woman,” it would not be hard to imagine that in thirty years you might meet a red-headed woman and say, “Damn, good call Demon!” then make the decision to go through with marrying her. But if the Demon gives you much more thorough information, things become increasingly complicated. Imagine the Demon shows you exactly what you will be experiencing for the next five minutes— everything you will be seeing, feeling, hearing, thinking, etc. In nearly every conceivable circumstance, having this insight into your forthcoming thoughts would invalidate the chain of cause and effect which led to those same thoughts. In order to have identical thoughts and experiences two times in five minutes, we have to imagine that, in the intervening five minutes, something would occur to erase your memory of the foresight or mentally incapacitate you in some way. To the extent that the future is unknown or undetermined, we are free, and to the extent that it is known or determined, we are powerless.

So what does this say about the nature of free will? It depends whether we accept the Laplacian premise that we live in a deterministic universe where, with a perfect set of mathematical tools, the future might be predictable. In that case, the thought experiment suggests that nature “abhors free will” in the same manner that it “abhors a vacuum.” Reality conforms to prevent any situation in which free will may influence a fated outcome. However, the peculiarity of the possible results would lead us to accept the “existence” of the paradox — which is to say, free will must have a tangible influence on reality, because it has engendered the paradox which reality is overtly avoiding. The paradox, in this case, is like a rock embedded in the stream of possible circumstances—if we can see the stream ebbing around the rock, doesn’t that imply the rock has some measure of existence?

After sufficient scrutiny, paradoxes are often revealed to be the result of flawed or contradictory assumptions. For example, the famous paradox of an immovable object meeting an unstoppable force is resolved when one realizes that one or the other notion is possible, but the two are not co-possible. If there is such thing as an immovable object, there cannot be such thing as an unstoppable force. This is arguably the case here as well, in that a future-predicting intelligence seems incompatible with a universe in which free will exists.

It is worth noting, however, that in the paradox we created, we did not have to ascribe any magical or unproven properties to free will — we simply had to imagine the normal human reaction to a particular stimulus. We could just as easily call this version of free will “biological, rational decision-making,” with no need for desperate appeals to spirituality, and the paradox would still occur, which suggests that the flawed assumption lies elsewhere.

The crucial assumption — the unproven or magical assumption that creates the paradox — is that there could possibly exist an infallible intelligence which could predict the future of a finite or infinite space, but rejecting this premise, it seems, is tantamount to rejecting determinism.

Determinism claims “all events are determined by preexisting causes.” If that’s true, we need to be able to understand and quantify fundamental energy (or some fundamental thing or event) in order to define those “preexisting causes.” We also need to have a mathematically definable law (some fundamental rule) in order for those causes to “determine” future events in any verifiable way.

“The apple hit the ground because it fell from the tree” may be a cause-and-effect statement, but it is several layers of subjectivity removed from the fundamental level which would truly justify determinism. If we can’t comprehend fundamental energy or mathematically express fundamental laws of physics, then we have no way of expressing what a “cause” truly is or how it “determines” a particular outcome, and determinism becomes a matter of faith.

It is fitting, then, that the deterministic philosophy behind “Laplace’s Demon” has already been cast into doubt by the rise of quantum physics, which upended our traditional outlook on cause and effect. Decades of research have proved again and again that “particles” — once thought of as indivisible building blocks of matter — only appear as singular, self-contained entities in the moment we directly measure or observe them. The rest of the time they are smeared across space in the form of a “probability wave,” which is a decidedly indeterminate phenomenon by all appearances.

Before we detect them at a specific location, particles do not have definite positions. The “probability wave” (defined by Schrödinger’s Wave Function) determines the positions where a particle is most likely to be found, and we consider the particle’s present state a superposition of all of these possible positions until the moment when the particle is detected and the probabilistic wave function “collapses” into a single position.

This “probability wave” is not merely an abstract notion. It is considered real and the source of the wave distribution of particle impacts in the double-slit experiment, but we have no sure-fire way of conceiving of the physical embodiment of the wave function. We have no way of understanding what it actually signifies beyond the observable results it produces. The mathematical framework of quantum theory is universally accepted as an accurate description of subatomic phenomena, but in more than eighty years physicists have not been able to reach any consensus regarding the metaphysical, deterministic basis of its most crucial facet, the probability wave.

Does the probabilistic wave function mean that the universe is truly random and indeterminate at a fundamental level, or is the randomness merely an idiosyncrasy of our subjective perspective on the universe? We know that a slot machine, for instance, is “random” from the perspective of someone pumping coins into it, but it’s not random at all when we take it apart and examine the gears or programming that make it give one result or another. What if the reality we’re seeing only appears random and indeterminate because there is a higher, determinate perspective we have no access to?

This, essentially, is the stance of the so-called “Many Worlds” interpretation of quantum physics, which was first posited by the physicist Hugh Everett in 1957. In Everett’s formulation, the wave function never “collapses” when an observer measures a particle position. Every plausible particle position genuinely exists, to be measured by separate observers in separate branches of the universe. For each observer, the resulting measurement appears completely random, but only because they are seeing a single data point of a wave that is distributed across a litany of different branches of reality. The branching produces the subjective impression of randomness, but there is no randomness involved on a fundamental level. The wave-function is a real wave spread across separate branches of the universe and not in itself a function of probability.

As satisfying and “cool” as the Many Worlds interpretation may be, there is no way to prove it. We have no way of putting one foot in one branch and one foot in another so that we might send a message “sideways” between universes. We may permanently be stuck in this state of uncertainty, in a subjectively indeterminate reality with a potentially determinate one underpinning it. But while we cannot prove that reality is deterministic or “branching” in the Everettian sense, we have ample reason to believe something almost equally profound:

In order to be deterministic, reality must be branching.

I say this, first of all, because Everett’s interpretation is the only logically sound, strictly deterministic interpretation of quantum mechanics, but there is also another Laplacian thought experiment and paradox which seem to suggest the very same conclusion.

Return again to our previous thought experiment, but this time replace the human test subject with a simple computer program. This computer can see, but it only has two functions: it may activate a red light or a blue light. It is programmed such that, at a certain preordained moment, it must randomly activate either the blue light or the red light, but if at this moment it happens to see a blue light elsewhere, it will trigger the blue light. If it sees a red light, it will trigger the red light.

Just like the human test subject from before, this computer will be made to watch a video of its own future. If it sees that its future self has activated the blue light, it will promptly activate the blue light and fulfill the prediction, or vice versa with the red light. This time, there is no challenge in “re-enacting” the video because the computer’s actions are limited to the flipping of a switch at a pre-programmed time. It is a binary “choice” affording only two possible futures. The switch will be flipped, one way or the other, at the exact moment indicated by the prediction and by the computer’s own programming. The light-up computer is powerless to do anything else but what it is predicted and programmed to do.

An interesting new paradox arises, similar to the backwards causation of the Newcomb Paradox. If the sole impetus for showing either blue or red is the Demon’s prediction of the future, then there is no other initial cause which the Demon might factor into that prediction. Whether the Demon predicts the computer to show blue or red, it will still be correct, because the light-up computer is programmed to follow whatever it sees, and it possesses no auxiliary abilities which would otherwise influence the results. If blue or red predictions are both equally valid, what makes the Demon predict one or the other?

At a glance, this invites us to imagine that the Demon possesses free will in the purest sense of the term. The Demon literally curates the future through its prediction, making a choice between two distinctly plausible eventualities. But there’s a hitch: for this ideal situation to exist in the first place, there cannot be two plausible outcomes to a situation that ultimately has only one outcome. This would be a decidedly indeterminate reality, which would be incompatible with the deterministic logic underpinning the Demon’s initial existence and purpose.

It seems that the only deterministic solution to this new paradox is to dissolve the fictional distinction between “plausible” and “actual.” In a truly deterministic universe, to say that there are two plausible outcomes is to say that there are two outcomes that both transpire and are both equally real. In other words, reality branches. The Demon doesn’t have to pick between the red and the blue alternate realities. It reveals both, just in parallel branches.

In order to logically exist, Laplace’s Demon must operate in an Everettian, “Many Worlds” reality, and we have gotten back to where we ended our discussion of quantum physics. If reality is deterministic, we can almost assuredly say it is branching. It’s the only satisfactory picture of quantum mechanics and the only satisfactory solution to the “blue and red” paradox.

All that being said, we still don’t know if our universe is truly deterministic, and we are not likely to find out one way or the other. If it is not, then it will never be fully comprehensible, and it would be fair to say that theoretical physics is a largely futile endeavor.

But since an indeterminate reality is diametrically opposed to human reason, it seems to me that the only rational response to this logical quandary is to make the a priori supposition that it is deterministic, and therefore branching, and then we follow that supposition down whatever rabbit hole it might lead us to.

In the meantime, thanks for following me down this one.

Post-script:

The arguments made in this article clearly rely upon a complicated logical lattice-work. If you have any questions about my assertions, don’t hesitate to ask. If you feel that I have committed a logical fallacy in the argument or that I have overlooked important details, please don’t hesitate to comment below. If I’ve made an error, I’d be glad to address it, and if it’s a contentious point, I’d love to debate!

Essayist, Fiction Writer, Occasional Humorist

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