Why am I, as a Hegelian philosopher, so fascinated by quantum mechanics? What we find in quantum physics is something that is usually considered an exclusive feature of the symbolic universe, namely a self-reflective move of including one’s (the observer’s) own subjective position into the series of observed phenomena. Recall Hegel’s famous infinite judgment “Spirit is a bone.” How does it work? Instead of arguing (from the safe distance of an observer) that spirit cannot be reduced to a bone, it begins by endorsing the claim “spirit is a bone,” the reaction to which (of us, observers) is shock: we experience this claim is blatant nonsense, as radical self-related negativity… but it is only through experiencing the nonsense/negativity of this statement that we arrive at Spirit because “spirit” is such a self-relating negativity which encompasses me in my subjective stance.

What has this to so with quantum mechanics? Let’s dive directly in medias res. The fact that a particle – say, an electron – takes all possible paths when it travels from point A to point B means that this particle splits and interacts with itself, not just with other surrounding particles. One should not miss the Hegelian “speculative” echo of this formulation: what appears as the interaction of elements external to each other turns out to be the interaction of one element with itself. The ultimate consequence of this approach was brought out by Richard Feynman in his classical paper from 1949 where he introduced his notion of positron as being actually an electron running backward in time. The trade-off enacted by Feynman is: if we accept running backward in time, the whole image gets simplified, one element suffices.

“In the approximation of classical relativistic theory the creation of an electron pair (electron A, positron B) might be represented by the start of two world lines from the point of creation, 1. The world lines of the positron will then continue until it annihilates another electron, C, at a world point 2. Between the times t1 and t2 there are then three world lines, before and after only one. However, the world lines of CB, and A together form one continuous line albeit the “positron part” B of this continuous line is directed backwards in time. Following the charge rather than the particles corresponds to considering this continuous world line as a whole rather than breaking it up into its pieces. It is as though a bombardier flying low over a road suddenly sees three roads and it is only when two of them come together and disappear again that he realizes that he has simply passed over a long switchback in a single road.”

I am, of course, not qualified to judge the scientific validity of this line of thought; all I am saying is that, from my Hegelian standpoint, it works perfectly. What I especially appreciate in it is that what appeared to be another positive element of reality (positron) is grasped as something which differs from its opposite only because of its different temporal line. And, to risk a jump to another domain altogether, is this not also a proper way to reject the dualism of good and evil? The good God himself “turns back in time,” becomes evil (the Old Testament god of wrath and fury) and then turns to goodness (to love) only when it is born in/as a man in Christ.

How should reality be structured so that such paradoxes become possible? To explain the present state of a physical system, the usual scientific approach needs two elements: the original situation (boundary conditions) and the laws that determine the evolution of the original situation into its present state. Relying on Wheeler and others, Hertog[1] adds a third element, observership (an observer who is not just a passive witness but focuses attention on some parts of the observed state by way of asking questions and in this way regulates, directs even, the evolution of a system, even when we are dealing with the past evolution): “The triptych evokes the idea that this grand question /of the origins of the universe/ retroactively draws into existence those few branches of cosmological history that have properties that are being observed. Observership in quantum cosmology /…/ is an indispensable part of the continual process through which physical reality – and physical theory, we argue – come about.” (188-9)

Quantum cosmology thus involves

“a subtle backward-in-time element. One doesn’t follow the universe from the bottom up – forward in time – because one no longer presumes the universe has an objective observer-independent history, with a definite starting point and evolution. Quite the contrary, built into the triptych is the counterintuitive idea that in some fundamental sense /…/ history at the very deepest level emerges backward in time. It is as if a constant flux of quantum acts of observation retroactively carves out the outcome of the big bang, from the number of dimensions that grow large to the types of forces and particles that arise.” (189)

The first thing to add here is that the temporality in quantum processes is double: the backward movement (a recent “collapse” retroactively changes/reconstructs the past) has to be supplemented with a no less paradoxical forward movement in time. John Wheeler, the “archetypal physics-for-poets physicist,” complicated things further and imagined a delayed-choice experiment: the experimenter decides whether to leave both slits open or to close one off after the electron has already passed through the barrier—with the same results. The electrons seem to know in advance how the physicist will choose to observe it. (This experiment was carried out in the early 1990s and confirmed Wheeler’s prediction.)

If we read the history of the cosmos bottom-up, then the enigma of the improbability of intelligent life on Earth remains unresolved: how was it possible that our cosmos (which existed billions of years before life on Earth emerged) is composed in such an extremely improbable way that life on Earth is possible? The answer that imposes itself is, of course, God and teleology: some higher force had to direct the evolution of the cosmos in the direction of the possibility of intelligent life… But in the top-down approach the probability distribution “is of no significance because ‘we’ have already measured that we live in a universe with three large dimensions of space.”(199) Or, as Lacan would have put it, a letter always arrives at its destination not because of some hidden teleology guaranteeing this outcome but because “destination” is retroactive: the destination of a letter is contingent, but the point at which a letter contingently arrives IS its destination.

But Hertog makes here a step further which I find problematic: he says that biologists can also “use this knowledge /arrived at through backward-in-time reasoning/ to influence future branchings.” So, it is not only that “at the quantum level, the universe engineers its own biofriendliness”(255); it is also that “scientists are starting to envisage hypothetical laws and then engineer systems in which they emerge”(261), and this means we (humanity) are at the “dawn of a new era, the first of its kind in the history of Earth, and perhaps even of the cosmos, in which a species attempts to reconfigure and transcend the biosphere it has evolved in. Echoing Hannah Arendt, from merely undergoing evolution, we are transitioning toward engineering it and, with it, our humanities.” (263)

I think this idea misreads Arendt’s intention: when she emphasizes our (humanity’s) finitude and groundedness in Earth, Arendt speaks as a Heideggerian for whom the very idea of “engineering evolution and, with it, our humanness” is the danger we are confronting today: when we engineer nature, inclusive of our own nature, humanness is over because by definition it cannot be engineered. Rather, we are thrown into it, and Arendt’s Heideggerian point is that our relationship to reality as an object of engineering is rooted in a certain disclosure of the meaning of Being which stands for utter self-destructive nihilism, the idea that “the courage of our questions and the depth of our answers would allow us to navigate planet Earth safely and wisely into the future.” (266)

Furthermore, I find utterly problematic the vision of a smooth passage from spontaneous/unpredictable quantum collapses to having an overview of superpositions and then deciding for one among them that fits our interests:

“Taking a quantum view, the myriad of paths forking off into the future are in a sense already out there, as a landscape of possibilities. Some futures may even appear rather plausible. We should learn from the past, though, that chance constantly interferes, leading history to take unexpected twists and turns.” (264)

However, freedom is not unpredictable contingency but a “freely” imposed necessity, the act of decision which cannot be reduced to its causes, while a quantum collapse is by definition a point at which chance interferes. Furthermore, if our unsurpassable finitude means anything at all, it means precisely that we a priori cannot acquire “a clear global vision” of our predicament: to do this we would have, as it were, to step on our own shoulders and look at ourselves from outside. Top-down approach means that our evolution has already collapsed into our present state and we cannot see in advance which superpositions are contained as non-collapsed in our present state.

The notion of finitude could also be given a different spin. A simple but convincing idea circulated recently in some media: since there is a limited number of sounds that can be used to compose a song, and since millions of songs were already written, it is practically impossible today to avoid plagiarism – basically all possible songs were already written. Does the same hold also for philosophy? Are all basic philosophical stances already formulated? However, the paradox here is that the experience of the space of songs as potentially infinite is grounded in our very finitude – only if it were possible to step out of our finitude and grasp the space of possible songs from an external view, would we be able to see its finitude. Infinity is thus strictly a category rooted in our finitude – as in quantum mechanics in which the multiplicity of superpositions appears infinite precisely because we cannot step out of ourselves and grasp the totality of the universe “objectively.”

Here the notion of hologram enters: “The latest incarnation of holography envisions that everything in the four dimensions we experience is in fact a manifestation of a hidden reality located on a thin slice of spacetime.”(212) Plato’s vision is turned on its head: “everything there is to know about strings and gravity in a four-dimensional anti-de-Sutter universe can be encrypted in quantum interactions of ordinary particles and fields lying entirely in the three-dimensional boundary surface. The surface world would function as a kind of hologram /…/ It is almost as if you could learn everything about the interior of an orange by meticulously analyzing its skin.” (225) However, does the holographic cosmology not tend to reduce the parallax tension to the classic duality of the true basic reality of a hologram and the standard reality of our expanding universe?

“If, as holographic cosmology posits, the surface of our observations is in some sense all there is, then this builds in the backward-in-time operation that is the hallmark of top-down cosmology. Holography tells us that there is an entity more basic than time – a hologram – from which the past emerges. The evolving and expanding universe would be output, not input in a holographic universe.” (243)

How far can we go in this direction? John Wheeler is famous for proposing the phrase “the it from bit”: “every it – every particle, every field of force, even the spacetime continuum itself – derives its function, its meaning, its very existence entirely – even if in some contexts indirectly – from the apparatus-elicited answers to yes-or-no questions, binary choices, bits.” Is this formula not the ultimate scientific version of the fundamental ontological premise of Western metaphysics: whatever exists in reality (any “it”) results from some “bit,” from a cognitive logical matrix? If we follow this path, we end up in a new version of idealism, the timeless network of qubits out of which “it,” our reality, emerges, so that the ultimate reality “may be better thought of as a mathematical realm that can inform physics but need not exist as such” (247):

“quantum information inscribed in an abstract timeless hologram of entangled qubits forms the thread that weaves reality. /…/ It is as if there is a code, operating on countless entangled qubits, that brings about physical reality.” (244-5)

This basic reality of qubits is at the same time in the past and in our future, since we are not yet able (not just to discover but simultaneously) to create it: holography “places the true origin of the universe in the distant future, because only the far future would reveal the hologram in its full glory.” (245)

What remains here of the Darwinian insight that “not the laws as such but their capacity to change and transmute would have the final word” (246)? What remains of the idea of overcoming “the separation between law-like dynamics and ad hoc boundary conditions as a fundamental property of nature” (80)? Or, as Hawking put it, for the classic physical science,

“theoretical physics will have achieved its goal when we have obtained a set of local dynamic laws. They would regard the question of the boundary conditions of the universe as belonging to the realm of metaphysics or religion. But we shall not have a complete theory until we can do more than merely say that things are as they are because they were as they were.” (82)

The only alternative to this idealist vision (or, rather, its necessary supplement) is a self-limitation, i.e., the claim that “we are living in a patch of spacetime, surrounded by an ocean of uncertainty about which, well, we must remain silent.” (247) So there is a boundary to (our) cosmos, the boundary which does not reside in its outer limits but is implied by the very position in which we find ourselves as observers and from which, in a top-bottom approach, we reconstruct the cosmos. This would have been the quantum cosmology version of the Hegelian infinite judgment: the entire external cosmos equals (or is correlative to) the observer’s eye.

What these counterintuitive thoughts imply is that philosophy returns with a vengeance in today’s quantum physics. The old question not just ignored but outright prohibited by Bohr and the Copenhagen orthodoxy (what is the ontological status of wave functions?) is today answered by the claim that quantum waves describe “the world at some kind of preexistence level” (88) since what exists in/as our reality is only the outcomes of the collapse of the quantum superpositions. At this preexistence level, particles “follow all possible paths when they move from one point to another” (90): in a double-slit experiment, “individual electrons follow not one but every possible path from the gun to the screen. One path takes the electron through the left slit, another through the right, back out through the left, into a U-turn, and through the right slit once more.” (91)

(Could we not say the same also about how a subject’s sexual identity is formed? It (mostly) “collapses” into a particular form (gay, hetero man, lesbian…), but to understand how this form emerged we have to accept that the subject enacted all possible forms, and that these “superposed” forms continue to echo in the final form.[2]) Alenka Zupančič wrote: “In theatre, we start with ‘repetitions,’ for rehearsals are called repetitions, and we end up with la première, with the first (performance or the first night). Repetitions do not repeat some first occurrence but, rather, lead up to it.”[3] Can we say, in a similar way, that wave superpositions are like theatrical repetitions which prepare he (back)ground for the premiere in their collapse?

Such paradoxes surprisingly induced Hawking (who otherwise despised philosophy) to return to it: “We need a new philosophy for cosmology.” (167) “/…/ a proper quantum outlook /onto the universe/ will lead to a different philosophy of cosmology in which we work from the top down, backward in time, starting from the surface of our observation.” (175) Can we apply the top-down approach to universe itself, so that it has multiple pasts? Hawking’s final answer is yes – the premise of his new philosophy is that we should abandon the idea that “the universe has a global classical state. We live in a quantum universe so it should be described by a superposition of histories a la Feynman, each with its own probability.” (174) Or, to quote Hertog’s paraphrase:

“we should adopt a full-blown quantum view not just of what’s happening within the universe – the wave functions of particles and strings and so forth – but of the cosmos as a whole. /…/ we should think of the universe as a superposition of many possible spacetimes. So a quantum universe is uncertain even on the very largest scales, on scales well beyond our cosmological horizon like those associated with eternal inflation. And that large-scale cosmic fuzziness puts a bomb under the eternal background that the multiverse aficionados assume exists.” (174)

This means that we shouldn’t imagine the Big Bang as a singularity that then explodes but as a primordial fuzziness in which time bends into space (130), or, as Hertog quotes Wagner’s Parsifal, “I hardly move, yet far I seem to have come. You see, son, here time becomes space /zum Raum wird hier die Zeit.” (72) Or, to quote Hertog, “in the very early universe, quantum effects would have blurred the very distinction between space and time, causing them to suffer a bit of an identity crisis, with intervals of time sometimes behaving like intervals of space and vice versa.” (94) The singularity at the bottom of the classical universe, that event without a cause that seemingly put the beginning outside science, is therefore replaced by “a smooth and rounded quantum origin complying with the laws of physics everywhere.” (95)

The fact that there is no pure singularity of the absolute beginning where all the laws of nature break down implies a further radically counterintuitive conclusion: there is no zero-level at which things (or, rather processes) just happen without being is some sense observed. Even the remotest past is retroactively generated by an observer: “What matters is not what is most probable in the theory but what is most probable to be observed. Cosmological histories that don’t produce observers don’t quite count when we compare our theories to our observations.” (127) However, are there different universes for different observers? How do we locate ourselves in this multitude of observers? “Einstein showed that gravity is a manifestation of warped spacetime. Holography goes further and postulates that warped spacetime is woven from quantum entanglement.” (235) In what precise sense do entanglements occur only for observers?

Let’s begin with the notion of entropy, a concept that is most commonly associated with a state of disorder, randomness, or uncertainty. Entropy is central to the second law of thermodynamics, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium, where the entropy is highest. A consequence of the second law of thermodynamics is that such processes are irreversible. In 1928, Arthur Eddington endeavored to explain the nature of timeorder, and the universe in terms of entropy: “If you take a pack of cards as it comes from the maker and shuffle it for a few minutes, all traces of the original systematic order disappears. The order will never come back however long you shuffle. There is only one law of nature – the second law of thermodynamics – which recognizes a distinction between the past and the future. Its subject is the random element in a crowd. A practical measure of the random element which can increase in the universe but never decrease is called entropy.” In this way Eddington offers a thermodynamic explanation of time’s arrow: a direction of time emerges from irreversible growing entropy.

Along these lines, Carlo Rovelli claims that time is an effect of our ignorance: we cannot see it all, we cannot access a total view of reality: “if I could take into account all the details of the exact, microscopic state of the world, would the characteristic aspects of the flowing of time disappear? Yes. If I observe the microscopic state of things, then the difference between past and future vanishes.”[4] Why? Because the changes regulated by physical laws are “symmetric between future and past.” (30) Again, why? Because of the growing entropy from the past to the future: “The entire difference between past and future may be attributed solely to the fact that the entropy of the world was low in the past.” (125) However, entropy (growing disorder) appears only if we measure a starting point as that of order – “every configuration is particular, every configuration is singular, if we look at all of its details.” (29) Rovelli evokes here a short science-fiction novel (co-authored by Alain Connes and two of his friends) in which Charlotte, the protagonist, “manages to have for a moment a totality of information about the world, without blurring. She manages to ‘see’ the world directly, beyond time,” (123) and when she is gradually returning to our blurred image of reality, she falls back into time. But does quantum indeterminacy not imply that reality is in itself blurred, “muddled,” so that the limitation of our observations is grounded in the incompleteness of reality itself? Rovelli generally opposes “our confused fantasies about the supposed freedom of the future,” (48) but he himself wrote: “The intrinsic quantum indeterminacy of things produces a blurring which ensures – contrary to what classic physics seemed to indicate – that the unpredictability of the world is maintained even if it were possible to measure everything that is measurable.” (123) And, to risk even a step further, does this “unpredictability” not point – not towards freedom but – towards some kind of openness of the future?

This unpredictability means the unpredictability of the collapse of a wave function, and the big problem that haunts the entire history of quantum physics is: how does this collapse happen? In the multiple-worlds interpretation of the quantum mechanics, the ontological gap between quantum waves and our ordinary reality disappears: there are only quantum waves with all their superposed versions actualized. Based on this insight, Sean Carroll postulated that from an (impossible) objective view, we could give a full deterministic description of reality; the problem is only that we would not know to which of the multiple worlds we belong, i.e., where we (observers) are located in this multitude of worlds. Is this not the problem with the Cartesian cogito? The subject reduced to a pure observer has no place in mechanically-determined external reality, and it exists as subject only if it has no place in it. Lacan knew this when he wrote that modern science is based on the foreclosure of the subject… How to resolve this paradox? Again, we should posit that the objective view which would give a full deterministic description of reality is not only inaccessible to us because of our finitude (because we are part of reality), but – much more radically – because reality is in itself not all, because it doesn’t exist as a totality with no immanent barrier.

Rovelli knows this, which is why he defines reality as a multiplicity of worlds each of which is rooted in the point-of-view of a particular observer – there is no “independent” reality. Rovelli is also right to reject the idea that this multiplicity implies a version of the many-worlds interpretation of quantum oscillations; however, he seems to get caught in the traditional philosophical paradox when he argues that “it is impossible for a system to have information about itself because it requires it to stand in a particular correlation to itself and this is not possible. It is not a new idea that quantum mechanics cannot describe the observers.” (102) So if “in RQM /relational quantum mechanics/ it does not make sense to claim that the whole universe is in a state of entanglement because, by being part of it, we cannot interact with it by definition,” (104) do we not here stumble upon the old problem—is a set a part of itself?—in a new guise? Are we not back at the well-known liar paradox? If my statement “I am always lying” is true, then this statement itself is a lie since it implies that I am not always lying, etc. Lacan offer a solution here, distinguishing between the content of an enunciation and the subjective stance of enunciation implied by it: “I am always lying” can correctly render my experience of my entire existence as inauthentic, as a fake. However, the opposite also holds: the statement “I know I am a piece of shit” can in itself be literally true but false at the level of the subjective stance it pretends to render since it implies that, by saying it, I somehow demonstrate that I am NOT fully “a piece of shit,” that I am honest about myself… But have these psychological finesses anything to do with the quantum universe?    

If, as Rovelli repeatedly claims, there is no object, no element of reality, which is not observed, if objects exist only in relation to an observer, as relative to that observer, then the fact that “it does not make sense to claim that the whole universe is in a state of entanglement” means that one should abandon the very notion of the “whole universe.” This doesn’t imply that there is something outside the universe – it’s just that the universe cannot be totalized since, to do this, an external observer is needed. The non-totalizability of the universe thus implies a negative limit (boundary), a limit outside which there is nothing. So I, as a part of the universe, can claim that there is nothing in the universe that is not entangled and that, located at this boundary, I am this nothing. I cannot be just a part of the universe: the whole world “collapses” in me as an observer, i.e., in one of its parts.

To put it in yet another way, when RQM posits that quantum events exist only in interactions and that the character of each quantum event is only relative to the system involved in the interaction, so that different observers can give different accounts of the actuality of the same physical property, i.e., when it claims that the occurrence of an event is not something absolutely real or not, but is only real in relation to a specific observer, are these and similar claims universally true (true independently of any observer) or are they also valid only in relation to a specific (human) observer? The only way to assert their universal validity without presupposing a global external observer is to base such universal claims on an immanent limitation or boundary of reality itself.

This limitation brings us to the first conclusion of special relativity theory: there is no global simultaneity, no NOW that encompasses the entire universe. If you observe with a telescope a person on a planet four light years from the Earth, what you see is what she was doing four years ago on that planet. So, can you say that she is doing now on that planet what she will be doing for years after you (in your now) observe her from the Earth? No, because four years after you have seen her through the telescope, in her time, “she might already have returned to Earth and could be ten terrestrial years in the future (measured by the Earthly time).” (39) So between my past – the events that happened before what I can witness (in my) now – and my future – the events that will happen after my now – “there is an interval that is neither past nor future, and still has a duration. It is an expanded present (15 minutes on Mars, millions of years in the Andromeda galaxy…).

There is, nevertheless, an aspect of time that has survived the demolition of the Newtonian theory of time: the world is nothing but change; it is not a collection of things, it is a collection of events. These events are “in a where but also in a when. They are spatially but also temporarily delimited: they are events.” (87) The only limitation is that “we cannot arrange the universe like a single orderly sequence of times”(99): “In the world, there is change, there is a temporal structure of relations between events that is anything but illusory. It is not a global happening. It is a local and complex one which is not amenable to being described in terms of a single global order.” (100)

If the “true reality” of fields and waves is out of time and space, then time and space are in some basic sense illusory. However, isn’t the underlying scheme of basic reality and illusory appearances false in the same way as its opposite, the gradual progress towards higher forms? What pushes this pre-ontological quantum space towards collapses and/or towards our common reality must be some immanent impossibility, a “barred One,” or some “boundary” (beyond which there is nothing – a boundary which coincides with its Beyond, i.e., which is itself inaccessible) in the basic quantum space itself.

To go back to our main line, the fundamental theory of the world “does not need a time variable: it needs to tell us only how the things that we see in the world vary with respect to each other.” (103-4) OK, but “the things that we see in the world” are always perceived by us as things that exist in space and time:

“From our perspective – the perspective of a creatures who make up a small part of the world – we see the world flowing in time. Our interaction with the world is partial, which is why we see it in a blurred way. To this blurring is added quantum indeterminacy.” (169)

I detect here a certain ambiguity: the first factor (the limitation of our perspective) makes the world appear blurred to us, so that we can still imagine how from a complete global perspective the world is not blurred, but the quantum indeterminacy makes it blurred IN ITSELF. This brings us back to entropy: the illusion of a single line of the flow of time is (to simplify things to the utmost) the outcome of the fact that we all (humanity) share the same perspective of living in a world of growing entropy. Entropy also explains why we remember the past and not the future: it is not simply because the future didn’t yet happen but because the flow of time is based on the growing entropy – entropy was lower in the past, and (what appears from OUR standpoint) as the greater order of things in the past leaves traces in our present. Since our future is based on growing disorder, it cannot leave traces to us: “The fact is that the origin of our sensation of being able to act freely in the world, choosing between different futures, even though we are unable to act upon the past.” (144-145)

A further problem I see here is: if every encounter/interaction counts as observation, does this not mean that collapses are infinite since entities are processes of change existing only in interaction with others? For Rovelli, an entity is exposed to multiple interactions and in every interaction it “collapses” into a different determined object (into a different eigenstate) – in itself, this object is just a mess of quantum wave oscillations. But, again, if collapse occurs in all encounters, even between two particles, not just in observations in any narrower sense, then collapses happens all the time continuously, trillions of trillions, more than particles – they are in no way exceptional Events. So was Sabine Hossenfelder right when she wrote that our universe is basically deterministic, with just small margins of uncertainty at the subatomic level which do not affect the larger-scale reality?

If every interaction counts as observation that causes a collapse, and if things exist only in their interrelations, does this not mean that all that exists are determined “collapsed” objects? “The world is like a collection of interrelated points of view. To speak of the world ‘seen from outside’ makes no sense because there is no ‘outside’ to the world.” (109) We thus arrive at the problem of Wigmer’s Friend: does the observation of the all of interaction of an object with its observer imply that collapses can also be superposed, that an object/event X contains a multiplicity of collapses, not only because it interacts with multiple “observers” but because this interaction itself is observed by multiple agents? To quote Rovelli again: “Each part of the world interacts with a small part of all the variables, the value of which determines ‘the state of the world with regard to that particular subsystem’.” (136) So, again, the world is like a collection of interrelated points of view, each of which is in some sense universal since it renders the entire world from a singular point of view.

But, again, what counts as an observation? Relying on Gödel’s incompleteness theorems and quantum physics, Roger Penrose maintained that consciousness is not computational, that it cannot be explained on the model of a computer, and claimed that we have to evoke another more fundamental dimension to account for it. Gödel’s theorems are concerned with the limits of provability in formal axiomatic theories. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. The second theorem, an extension of the first, shows that the system cannot demonstrate its own consistency. From a Hegelo-Lacanian standpoint, a different solution imposes itself: what if, staying with Gödel, we posit that there is no need to go beyond because consciousness is grounded in a deadlock of computation, that it is an effect of computation stumbling upon a limit (a limit beyond which there is nothing)? Is there not a vague homology between this idea and Heidegger’s point (in his analysis of our everyday use of things in Sein und Zeit) that we become fully aware of tools only when they malfunction? I use a hammer thoughtlessly relying on my practice and habitudes, but I become aware of it when, say, its weighted “head” detaches itself from a long handle after I swing it too strongly?

Penrose draws on the basic properties of quantum computing: bits (qubits) of information can be in multiple states – for instance, in the “on” or “off” position – at the same time. These quantum states exist simultaneously – in a “superposition” – before coalescing into a single, almost instantaneous, calculation. Quantum coherence occurs when a huge number of things – say, a whole system of electrons – act together in one quantum state. What has this to do with our consciousness? Penrose refers here to Stuart Hameroff’s idea that quantum coherence happens in microtubules, protein structures inside the brain’s neurons. Microtubules are tubular structures inside eukaryotic cells (part of the cytoskeleton) that play a role in determining the cell’s shape, as well as its movements, which includes cell division – separation of chromosomes during mitosis. Hameroff suggests that microtubules are the quantum device that Penrose had been looking for in his theory. In neurons, microtubules help control the strength of synaptic connections, and their tube-like shape might protect them from the surrounding noise of the larger neuron. The microtubules’ symmetry and lattice structure are of particular interest to Penrose. He believes that “this reeks of something quantum mechanical”:

“what’s going on in the brain must be taking advantage not just of quantum mechanics, but where it goes wrong. It’s where quantum mechanics needs to be superseded.” So we need a new science that doesn’t yet exist? “That’s right. Exactly.”[5]

There are three problems with this account. First, a large majority of scientists reject Hameroff’s idea of microtubules as quantum devices. Second, although Hameroffs’ notion of microtubules is materialist (it describes what goes on in our brain), his overall view is idealist (to put it bluntly, he thinks consciousness is an immaterial spiritual substance), while “Penrose is an atheist who calls himself ‘a very materialistic and physicalist kind of person,’ and he’s bothered by New Agers who’ve latched onto quantum theories about non-locality and entanglement to prop up their paranormal beliefs.”[6] However, Penrose also seems to oscillate with regard to this point, claiming that proto-consciousness is everywhere:

“An element of proto-consciousness takes place whenever a decision is made in the universe. I’m not talking about the brain. I’m talking about an object which is put into a superposition of two places. Say it’s a speck of dust that you put into two locations at once. Now, in a small fraction of a second, it will become one or the other. Which does it become? Well, that’s a choice. Is it a choice made by the universe? Does the speck of dust make this choice? Maybe it’s a free choice. I have no idea.”[7]

And in some passages, Penrose goes to the end of this road and draws the idealist conclusion: “Somehow, our consciousness is the reason the universe is here.”[8] We thus find ourselves at the opposite end of Ravelli for whom “observation” which collapses a quantum superposition has nothing to do with consciousness since it occurs in any material interaction of different particles.

So how to navigate between these two extremes? Of special interest are here attempts to define the modes of cognition which do not involve any conscious self-awareness, not even the one that is sometimes attributed to highly developed animals. In an overview of the existing literature, Michael Marder convincingly argues that “plants are res cogitantes extendentes”: “plants are constantly extending their cognition through the active extension of their bodies, and, with it, their functional cognitive apparatuses. And beyond that, plants also actively extend their cognitive process to the environment they are constantly engaged with and which houses a wide array of their biochemical substances.” Such an anti-Cartesian approach (rejecting the ontological distinction between res cogitans and res extensa) has nothing whatsoever to do with any New Age vitalist obscurantism – it remains firmly in the space of scientific materialism.

Third problem: where precisely does consciousness enter here? Is it the space of superpositions as such or does it designate the moment of collapse, of a choice when, “in a small fraction of a second, it will become one or the other”? From a Lacano-Schellingian standpoint an immediate counter-argument imposes itself: but why the identification of (free) decision with consciousness? Are basic decisions not unconscious? What is missing in Penrose’s mental space in which there are physical processes and consciousness is thus simply the Freudian unconscious. This is also why we should abandon the option that superpositions are unconscious, while consciousness enters at the moment of decision which causes the collapse of superpositions: decisions are unconscious, consciousness just takes note of them.

The price Matteo Smerlak and Rovelli are ready to pay for this relational view[9] is that they reject the predominant view, according to which the violations of Bell’s theorem provide a proof of non-locality, and claim that their version of RQM enables us to save locality: “it is not necessary to abandon locality in order to account for EPR correlations. From the relational perspective, the apparent ‘quantum non-locality’ is a mistaken illusion caused by the error of disregarding the quantum nature of all physical systems.” First, what is locality? “We call locality the principle demanding that two spatially separated events cannot have instantaneous mutual influence. We will argue that this is not contradicted by EPR type correlations, if we take the relational perspective on quantum mechanics.” The basic axiom of RQM is that physical reality is

“formed by the individual quantum events (facts) through which interacting systems (objects) affect one another. Quantum events are therefore assumed to exist only in interactions and (this is the central point) the character of each quantum event is only relative to the system involved in the interaction. /…/ different observers can give different accounts of the actuality of the same physical property. This fact implies that the occurrence of an event is not something absolutely real or not, but it is only real in relation to a specific observer. Notice that, in this context, an observer can be any physical system. /…/ The preferred Copenhagen observer is relativized into the multiplicity of observers, formed by all possible physical systems, and therefore it no longer escapes the laws of quantum mechanics.”

In the EPR situation, we have precisely such a case: each of the two entangled particles is measured by a separate observer (A and B), so that

“A and B can be considered two distinct observers, both making measurements on α and β. The comparison of the results of their measurements /…/ cannot be instantaneous, that is, it requires A and B to be in causal contact. More importantly, with respect to A, B is to be considered as a normal quantum system (and, of course, with respect to B, A is a normal quantum system). /…/ this does not mean that B and A cannot communicate their experience. In fact, in either account the possibility of communicating experiences exists and in either account consistency is ensured. Contradiction emerges only if, against the main stipulation of RQM, we insist on believing that there is an absolute, external account of the state of affairs in the world, obtained by juxtaposing actualities relative to different observers.”

In this precise sense, Smerlak and Rovelli distance themselves from Einstein while pointing out that “Einstein’s original motivation with EPR was not to question locality, but rather to question the completeness of QM, on the basis of a firm confidence in locality”:

“RQM is complete in the sense of exhausting everything that can be said about nature. However, in a sense RQM can be interpreted as the discovery of the incompleteness of the description of reality that any single observer can give: A can measure the pointer variable of B, but the set of the events as described by B is irreducibly distinct from the set of events as described by A. In this particular sense, RQM can be said to show the “incompleteness” of single–observer Copenhagen QM. Then Einstein’s intuition that the EPR correlations reveal something deeply missing in Copenhagen quantum mechanics can be understood as being correct: the incompleteness of Copenhagen QM is the disregard of the quantum properties of all observers, which leads to paradoxes as the apparent violation of locality exposed by EPR.”

How does this line of argumentation account for the fact that, in the case of entangled particles, if A measures the spin of one of the particles, he can know what the spin of the other particle is without even waiting for a message from B who will measure this spin? Or, more modestly, how can he know what any other observer who will measure the spin of the other particle will see?

If we universalize relationality and define every part of reality as depending on an observer (so that the same part of reality not only appears different but is different for different observers), do we not get stuck in a rather flat global view akin to the first feature of dialectical materialism formulated by Stalin: every entity is caught in a complex network of relations, things do not exist alone in separation from each other… Or, to complicate things further: when A and B interact, are they BOTH not at the same time observers of the other and observed by the other? So why do we even need an external observer who registers the interaction? Do the two interacting particles not already observe each other?

A naïve but correct philosophical counterpoint arises here: if everything is relative, if it is what it is only relationally, with regard to an observer, does this entire network not float in the air? In order not to collapse into itself, does this network not need to rely on some form of Absolute? The answer is: yes, but this Absolute is not some reality-in-itself beyond all observations. It can only be a negative foundation: the LIMIT itself, a limit beyond which there is nothing. In the same way as, in structuralism, differentiality can only function through a pure difference, in quantum relationality the fact that every entity is grounded in being observed implies that not everything can be observed, but this unobservable is not an external not-observed positive reality; it is the limit of observation itself.

It is in this sense that “RQM is realist about the existence of quantum entities, even though it is antirealist about the wave function”: wave function superpositions are just an instrument for calculating probabilities as they appear to an observer of a quantum entity, not part of the observed reality… Here we stumble upon the basic philosophical question: when we claim that a theory should fit reality, WHAT do we mean by this reality? When asked about an underlying quantum world, Bohr allegedly answered: “There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.” So all we are effectively dealing with are parts of our everyday reality: numbers on the screen of a measuring apparatus, etc. But is such a view not all too easy? It is difficult to avoid the question: why do QM predictions hold? (QM is the most successfully tested theory in the history of science.) Even more, wave superpositions are not just possibilities: the point of quantum mechanics is that possibilities have AS SUCH an actuality and influence the outcome – in some cases, the only way to account for a measuring is to assume that a particle took all possible superposed paths. Or, as Nikki Weststeijn put it in a concise way:

“In RQM the wave function is understood as a book-keeping device that tracks what will happen upon the next interaction. It encodes any previous interaction that A has had with system S and allows A to predict the state of S with respect to A in the future.”

It is thus “a bookkeeping device instead of a representation of a real physical quality.” However, is it necessary for RQM that the wave function does not represent any real physical quantity? “If we say that the wave function does not represent a real physical quantity, the question then remains what the underlying physical quantity is that in some way gives rise to the wave function.” In short, “in order to give a coherent interpretation, RQM should take the wave function to represent a real physical quantity, albeit a relative quantity.”[10]

The collapse of superpositions effectuated by a measurement asserts the duality of quantum reality and ordinary reality. Do all the paradoxes displayed by the measurement of quantum processes not impose a rather obvious conclusion: beyond/beneath our ordinary spatio-temporal reality there is (not a timeless spiritual domain but) another level of reality where the laws of our spatio-temporal reality do not apply (where a particle can take many paths simultaneously, where two entangled particles can be in contact instantaneously, faster than the speed of light, etc.)? This duality is not complementary (in the traditional sense of the term) since it concerns two totally incompatible levels of reality – the two levels are related like the two dimensions of a parallax. Here, Lacan’s logic of non-all can be of some use: our ordinary reality forms an All grounded in an exception (the observer who causes the collapse of superpositions), while quantum reality requires no exception, yet it is for that very reason not-all, and the impossibility that makes it non-all pushes the network of superpositions towards collapse. So what if, in order to grasp this duality, we use Lacan’s difference between the two forms of assertion: an X exists or there is (something of) X (il y a de…)? Lacan’s examples: “la Femme n’existe pas” (the Woman doesn’t exist”) and “il n’y a pas de grand Autre” (there is no big Other). The second negation is stronger: although the Woman doesn’t exist, there is (something of) the women… Similarly, a single reality that arises through the collapse of a wave superpositions exists while there are superpositions which do not properly exist.

Rovelli’s pluralistic and perspectivalist view of QM is best rendered by the following this quite striking quotation: “if we want to get a true idea of what a point of space-time is like we should look outward at the universe…The complete notion of a point of space-time in fact consists of the appearance of the entire universe as seen from that point.”[11] The determination between a subsystem of the universe and the universe itself is perfectly symmetrical: it is true that the nature of such a local subsystem (“space-time point”) depends on the way it interacts with, or “reflects”, the universe from its particular perspective (and this seems a partial concession to monism), but in RQM there is no Leibnizian “monad of the monads” because “the cosmos can only be described from some local physical system. The problem with priority monism is that it concentrates exclusively on the dependence of a part on the whole, neglecting completely the converse type of dependence.” This converse dependence (all in a part) is crucial.

Muciño, E. Okon and D. Sudarsky’s essay “Assessing Relational Quantum Mechanics” deals with the general ambiguity problem that affects standard quantum theory when deprived of special roles for measuring devices or observers: “within RQM, the breakdown of unitarity is not brought about by mysterious quantum jumps. Instead, it is a consequence of the fact that it is impossible to give a full description of an interaction in which one is involved.” This is a truly ingenious solution: wave collapse happens because of the impossibility of a full description that would include the observer measuring a quantum state. So, in a properly dialectical tension, waves collapse locally because they cannot collapse globally.


[1] See Thomas Hertog, On the Origin of Time, London: Penguin 2023. Numbers in brackets that follow indicate the pages of this book.

[2] I owe this thought to Jacqueline Rose.

[3] Alenka Zupančič, The Odd One In: On Comedy, Cambridge: MIT Press 2008, p. 171.

[4] Carlo Rovelli, The Order of Time, London: Penguin 2019, p. 30. Numbers in brackets that follow indicate the pages of this book.

[5] Quoted from Roger Penrose On Why Consciousness Does Not Compute – Nautilus.

[6] Quoted from op.cit.

[7] Quoted from op.cit.

[8]  Quoted from op.cit.

[9] See 0604064.pdf (arxiv.org). Non-assigned quotes that follow are from this source.

[10] Weststeijn, op.cit. One should thus not confuse the pre-ontological Real-in-itself implied by the quantum theory (a Real composed of quantum processes) with the pre-ontological Real that we find in Lynch’s or Tarkovsky’s films (an impenetrable density which ultimately remains fantasmatic/imaginary.

[11] Barbour J. (1982), “Relational concepts of space and time”, Brit. J. Phil. Sci. 33, p. 265.