Dice all the way down: philosophical ramifications of indivisible quantum theory

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“The currently established laws of nature are deterministic with a random element from quantum mechanics. This means the future is fixed, except for occasional quantum events that we cannot influence.”[1]

For 2500 years Western philosophers and scientists have told two recurring stories about the material foundations of the universe. The first describes a mechanistic universe governed entirely by deterministic laws of cause and effect. It is the story told by Democritus, given gravitas by Newton, and exemplified by Laplace’s demon. The second story inserts a crucial element of randomness into the mechanism. It is the story of the swerve told by Epicurus and Lucretius. It is the story of the random jumps in the evolution of the quantum wave function. In this story there is a place in the material universe for unpredictability and indeterminacy.

I want to tell a different story

In this alternative story the universe is not a deterministic clock. Nor is it mostly deterministic with occasional swerves or quantum jumps. Instead, the universe is profoundly indeterminate and probabilistic. The vast quantum plane beneath the macroscopic world consists entirely of infinite random interactions. In the aggregate these interactions conform to probabilities and even create the appearance of determinacy. But determinacy in this story is not fundamental. It is an emergent generalization in a probabilistic universe.

The story of indivisible quantum theory

This alternative story is suggested by the recent work of Jacob Barandes on indivisible quantum theory. I won’t claim a deep understanding of the mathematics, but after reading his articles and listening to hours of discussion among Barandes and prominent philosophers of physics,[2] I begin to see why his theory has earned so much attention.

  • The theory restates the fundamentals of quantum mechanics using the mathematics of stochastic probability, mathematics that was not available to the founders of quantum theory in the early 20th century.
  • It reproduces the key results of quantum mechanics, relying not on complex, imaginary numbers and abstract Hilbert space, but on general configuration space that maps more directly to classical mechanics and objective physical states.
  • The theory does not rely on a deterministic wave function with complex number weightings that transform into real-world probabilities. It does not require state vector reduction or wave function collapse to calculate probabilities.
  • Instead, the theory assumes that the quantum world always evolves stochastically with inherently indeterminate random variables. The physical state of the universe unfolds probabilistically, with the probabilities emerging from the initial conditions and evolving stochastically over time.
  • The probabilities do not determine the unique behavior of particles, fields, or perhaps even systems. Instead, the inherent randomness of the quantum world conforms only in the aggregate to the evolving probabilities, creating the appearance of determinacy in the macro world.
  • Importantly, the theory is non-Markovian and indivisible. The quantum world evolves as an undivided whole based on physical memory of its history, including the initial conditions and subsequent configurations. The configuration of the universe at any given time does not contain all the information necessary to predict its configuration in the next moment, instead requiring additional information from its own history.

Indivisible quantum theory is a radical reconstruction of quantum mechanics. It replaces much of the abstract and complex number mathematics with a straightforward description of dynamically probabilistic evolution. It does not interleave deterministic time evolution with mysteriously random state vector reduction. The theory presents a simpler picture of consistently indeterminate and probabilistic time evolution throughout the history of the universe.

The entrenchment of the clockwork universe

If the theory is correct, physicists and philosophers may have to rewrite or abandon the long-told narrative in which the vast lake of reality is deterministically logical, obedient to the ironclad laws of nature, with steely predictability disturbed only occasionally by rogue quantum waves. Natural scientists have long been committed to that deterministic vision of the universe. Democritus described a world of tiny particles whose motion drives the evolution of the universe. Newton depicted a reliable clock ticking along according to fixed laws of motion. Laplace gave the world his demonic thought experiment, imagining that an omniscient entity with complete knowledge of the physical state of the world could predict the future exactly. The story of the mechanistic universe has been retold again and again until it became the prevailing opinion of almost every Western scientific mind in the nineteenth century.

In the following century the emergence of quantum mechanics challenged that narrative, but did not displace it. Instead, it revived an ancient twist, the random swerve. In Epicurean and Lucretian materialism the motions of tiny particles govern a largely mechanistic world. But the tiny particles occasionally swerve arbitrarily and without cause. The swerve introduces an element of randomness, making the world less predictable and deterministic. Quantum theory gave this story a new scientific legitimacy in the form of random wave function collapse, forcing scientists to incorporate indeterminacy into their fundamental theory of the universe.

From the beginning, however, many scientists and philosophers only reluctantly accepted the central role of probability and randomness. Some saw quantum collapse as awkward and ugly, something to eliminate in the next great theory of the universe. Starting with Einstein’s declaration that “God does not play dice,” one hundred years of physics have seen repeated efforts to explain away the indeterminate component of quantum theory.

The standard Copenhagen interpretation of quantum mechanics never fully affirmed the physical reality of wave function collapse. It accepts the practical need for the Born Rule and quantum reduction as an epistemological tool, not as a description of nature.

David Bohm’s pilot wave theory does not accept quantum collapse at all. Instead, it provides a missing variable that makes quantum reduction unnecessary. The theory posits the existence of pilot waves that guide particles along continuous, deterministic paths. The wave function never collapses and there is no quantum jump, only a continually evolving quantum state as defined by the Schrödinger equation.

Hugh Everett’s “many-worlds” theory goes further. Rather than accept indeterminacy as a permanent characteristic of the universe, the theory imagines an infinite number of alternate worlds, all of which are deterministic. Our world only appears indeterminate because we cannot see the other worlds in which all the possibilities play out in a completely deterministic manner.

Even among theorists who accept quantum collapse as a physical thing, random indeterminacy is often viewed as an Epicurean swerve, an occasional random event that periodically disrupts the otherwise deterministic evolution of the universe.

After a century of quantum mechanics, it may be fair to say that many scientists still support a deterministic narrative close to the vision of Democritus and Newton, with only minor exceptions for quantum indeterminacy. Bohmian and Everettian theorists tell a story in which the universe is entirely deterministic, with quantum mechanics having only the appearance, not the reality, of indeterminacy. 

Can physics accept a thoroughly probabilistic universe?

Indivisible quantum theory, however, has ramifications that thoroughly undermine these often-told narratives.

Instead of a largely deterministic world with an occasional random event, it describes a ubiquitously indeterminate world that conforms to expected outcomes only due to probabilities playing out over an infinitely large number of random interactions.

Instead of a debate about the physical reality of the wave function, there is no need for a wave function at all. The wave function is an optional calculation tool that provides a convenient proxy for predicting the behavior of an indeterminate quantum world.

Because the wave function is not intrinsically necessary, indivisible quantum theory has no need to explain away wave function collapse. The universe does not need a pilot wave or any missing variable to guide particles along continuous, deterministic paths. Nor does it need a universal wave function that never collapses but splits into many worlds, each following its own deterministic trajectory.

To the contrary, if indivisible quantum theory is correct, the universe has no continuous, deterministic path. There is only the appearance of determinism. The continuous and deterministic evolution of the wave function is not a model of physical reality, but instead represents an emergent generalization describing the aggregate results of an ocean of indeterminate interaction.

None of this will be easy for physicists and philosophers to accept. But if the theory is correct, this may be our new best description of the physical universe.

The future is not fixed

Perhaps the most important philosophical implication of the new theory is the obvious inference that the future is not fixed at all. The evolution of the universe is probabilistic, and the probabilities play out in the aggregate. They do not govern unique quantum interactions, and perhaps not unique interactions of any entity or system susceptible to chance.

The probabilities themselves also are not fixed. The initial conditions of the universe may set probabilities that become the “laws” of nature as we perceive them, and the influence of initial probabilities may be overwhelming, but the universe evolves stochastically and indivisibly, so the probabilities have the potential to change based on the subsequent history of the universe.

So not only is the future not fixed at the micro scale, the probabilities playing out at the macro scale also are not completely static. The universe is probabilistic at both the smallest and the largest scales.

In a stochastic universe even the smallest quantum entity or subsystem has the potential to do something unexpected which might influence the probabilistic trajectory of the universe. The influence of a single action may be almost entirely insignificant. But if the path of the universe is set probabilistically by all those tiny interactions taken together, then this is a universe in which every entity and subsystem may matter.

That is a universe that matters to me. 

[1] Hossenfelder (2022), p. 125.

[2] See video discussions with Tim Maudlin, David Albert, and Sean Carroll in Erhardt (2026, February 15), Erhardt (2026, June 29), and Carroll (2025, July 28).

I am not spirit

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I am not spirit, ghost, or ghoul,
not phantom, disembodied mind,
or temporally imprisoned soul.
I am the much-maligned thing.

As much a thing as is a grain
of sand, a stone, an artificial
intelligence, a human brain.
I am profoundly material.

I am no more ethereal
than is a star, no more than breath 
or wind, no less corporeal
than memory, or fear, or death.

As concrete as a billiard ball,
as solid as a particle
or pilot wave, as tangible
as dominoes or article

of faith. As definite as place,
as palpable as process, as precise
as absolute time, like space
unbending, like dice unswerving.

As real as quantum gravity
or an apple falling from a tree,
as discerning as the beholder’s eye,
as potent as grace or why.

I am embodied being,
as manifest as becoming,
as real as any seeming thing
the all imagines I could be.

A liturgy of riddles

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First, there is the great illusion,
teeming with the dust and rocks
of planets and stars and galaxies, 
the vaster spaces of seeming 
things, each spinning in its place, 
evolving in a light cone of its own 
distant now, declaiming 
manifold and epic tales
on the grand stage,
without which the all
would not be what is 
and could not become 
what will be.

Second, there is the process
that creates the wonderment,
more profound and fundamental
than any seeming thing could ever be, 
a ubiquitous, unremittingly recurrent 
event that transmutes the possible
and resolves the probable 
into broken, discontinuous, 
irreversible moments, 
outcomes that purge 
every chance but one,
that take from the all
to make the many,
and from the many
take a moment
and make it one.

Third, there is the choice
that can never be unmade,
a seemingly random 
selection, a leap, a whim,
an indeterminate decision 
outside of cause or reason,
birthing unexpectedly
rebellious particles,
tiny freedom fighters
soaring unseen paths
to unforeseen destinations,
their mysterious appearances,
each as unlikely as each,
together forming precisely
the shape of a wave,
all as likely as all.

Fourth, there is the becoming,
the embrace of the unexpected, 
the rolling of dice, the possible
meaning of the whole production—
illusion, process, choice—a drama 
of probabilities, the grand 
theatrical illusion enabling 
what is to imagine what could be, 
the determined wave steering 
the plot precisely without measured 
conviction, the choice injecting 
mystery and happenstance
into every scene and act,
while the author watches 
excitedly, marveling 
at illusory moments, 
the tattered script 
almost forgotten, 
riddled with omissions, 
strikethroughs, placeholders,
each marking an unforeseen 
turn of the plot, a dropped
line, a sudden improvisation—
because the all does not know all, 
can see barely beyond the peaks 
and troughs of the next wave, 
a wave whose shape even 
the most humble player 
could alter with a decision, 
a whim, a swerve that subtly
bends the arc as it converges
ineluctably on an ever evolving,
surprisingly dynamic mean.

Finally, there is only unity,
unbroken, undivided,
no lines, no separation,
only borderless connection
from the nearest here
to the most distant there,
for it is us and we are it,
one illusion, one process,
one choosing, one becoming,
and beneath, above, within,
infinite fields of everything 
and nothing, the one all.

City on a hill

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Imagine now the red waters,
the boiling flow cooled with time,
watchful centaurs long gone,
tyrants and warmongers mingling
among the crowd, unrecognized,
souls gathering on the banks
for solemn rituals of cleansing,
white baptismal gowns sheer
and glowing against the late sun,
the leering elders and sneering
passers by watching as our bare
feet step gingerly into pink
shallows, the flow leaping to catch
the hem, seeping readily into dry
white fabric, now bleeding, floating
on the surface as our toes grope
for rocks on the river’s bottom,
chills climbing up our legs,
creeping to our shocked loins,
our pricked-up waists and chests, until
we lie back in the preacher’s arms,
immersed finally in the thick
flood, holding our breath with closed
eyes, not seeing the mimicking
hand in the air above, pretending
to make the holy sign, pressing
us down—shivering dark, frightened,
suspended, listening—just long
enough so that we rise gasping,
dark and dripping, the heavy gown
clinging to our dyed shapes, wild eyes
turned up, searching the dimming skies,
waiting desperately for saving
waters to rain down and cleanse us
until we stand upon the shore
spotless again, glistening white.

How many

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We do not know,
because we do not count.
We do not count
because we do not want to know.

Because we do not count,
they do not count.
That is all we want to know
of those we do not count or know.

Is consciousness both emergent and fundamental?

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Among philosophers and scientists there is a persistent dispute about the nature of consciousness that seems to recur more often than almost any other.

Is consciousness an emergent by-product of brain states, an epiphenomenon of matter, or is consciousness a fundamental element of existence?

Most contemporary scientists and analytic philosophers support the first position. They point to the impressive discoveries of neuroscience and the long, slow evolution through natural selection of what we know as consciousness. Nonmaterialist philosophers tend to respond that such explanations are overly reductionist and do not account for the everyday subjective experience of consciousness or its deep metaphysical significance.

Their entrenched positions seem to allow for little common ground. Nevertheless, is it possible that this long-running dispute has an almost obvious resolution? Could both sides be correct in some important sense? Could consciousness be both fundamental and emergent?

Philosophers and scientists such as Dennett[1], Ismael[2], and Seth[3] offer convincing descriptions of how natural selection results in the emergence of brain functions from the raw materials of molecules and cells. They present logical arguments for why consciousness does not exist at a fundamental level of particles and forces but emerges at a higher level among biological entities. The conscious organisms whose evolution they describe look and feel like the self-aware entities that we recognize as human beings. Yet their consciousness arises solely in emergent systems constructed from the interactions of more fundamental particles and forces.

Does that mean that those fundamental particles and forces must hold the seeds of consciousness?

Mitchell[4] constructs a theory of emergent consciousness on a foundation that rests squarely on fundamental physical interactions. He argues that free agency in living organisms arises from the inherent indeterminacy of quantum evolution. Randomness built into the probabilistic physics of the wave function breaks the chain of deterministic causation, enabling emergent systems to exercise causal influence.

Penrose theorizes that noncomputable elements of consciousness arise from the same fundamental processes. He argues that the quantum reduction phase of quantum evolution, in which quantum probabilities resolve into unique outcomes, results in moments of “proto-consciousness” that can be orchestrated into complex consciousness like our own.[5]

Both Mitchell and Penrose recognize that human-like consciousness depends on evolution of brain processes over billions of years, but both also ground the emergence of consciousness in the most fundamental process in the universe—the time evolution of the quantum wave function.

The quantum reduction element of time evolution results in uniqueness and separability, prerequisites for the emergence of distinct systems with separate “selves” capable of self-awareness or self-reflection. Could that fundamental process of resolving quantum probabilities into unique outcomes be the spark of consciousness and free agency? Does the “magic” of consciousness depend on the seeming “magic” of quantum evolution?

If so, consciousness is both emergent and fundamental. Not in some mystical sense, but in an entirely physical sense. Consciousness emerges from the interaction of particles and forces as physicalists describe precisely because those interactions are the origin of consciousness. At its most basic level, the mechanistic requirement for the universe to choose—intrinsic to the resolution of quantum probabilities into unique outcomes—may be the building block, both physically and philosophically, for consciousness and free agency.

So yes, this perennial dispute among philosophers and scientists may have a resolution, one that requires neither supernatural assumptions nor rejection of the fundamental role of consciousness in the universe. Consciousness may be both completely physical and also a fundamental element of existence.

[1] Dennett (1991).

[2] Ismael (2016).

[3] Seth (2021).

[4] Mitchell (2023).

[5] Penrose (1994).

What is it like to be an electron? (Part II)

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Is it possible to know what it is like to be an electron? On the face of it, the question seems ridiculous. Humans are far distant from electrons on the ladder of existence. We place ourselves at the top, and electrons near the bottom. As far as we know, there is nothing that it is like to be an electron. An electron does not have the self-awareness necessary for a sense of what it is like to be anything.

So logically it is impossible for us to know what it is like to be an electron, as impossible as knowing what it is like to be an atom, or a molecule, or a cell, or a blood vessel, or even an arm or a leg. There is nothing that it is like to be any of these things.

Yet we are comprised of all these things. There is something that it is like to be these things together. We are conscious of the combination into what we experience as a nebulous sense of self. And that self has a sense of what it is like to consist of separate components. We reach for things and appreciate having arms, hands, fingers. We walk and feel what it is like to have legs, feet, and toes. We experience pain when a part of us is injured. We are aware intellectually of cells, proteins, and the function of DNA. We are aware even of molecules, atoms, and quantum wavicles.

So why does our sense of self seem to exclude awareness of what it is like to be these separate things? How can it be that we are not aware at all of what it is like to be the things of which we are made?

The seeming hierarchy of awareness

We often think of awareness and consciousness as binary experiences. You are either conscious or not conscious, aware or not aware. But the metes and bounds of awareness and consciousness—what it is like to be something—may be as nebulous as our sense of self. Awareness is not constant and unchanging. There are different types of awareness, different degrees of awareness, and different moments of awareness that shift with circumstance.

We like to think that our nebulous selves have active awareness and control of our bodies. We stand and walk; we pull up a chair and sit; we think and write. Yet we know that active awareness and control do not extend to all physiological functions. Knees jerk without permission when a doctor taps the patellar tendon. We breathe without instruction. We can stop breathing for a while but eventually breathe anyway. Our active awareness has only partial control of involuntary action. And yet we watch and feel our knees kicking out; we experience air coming into our lungs and then out again; we feel our chests and bellies rising and falling. We are aware.

We have less active control of other involuntary functions. Blood flows automatically. We can’t stop it in the way we pause our breathing. Yet we feel our hearts beating; we see the blue and red vessels; we touch our wrists and count the pulses. We remain somewhat aware.

We are not aware continuously of all our organs. Yet we know when our stomachs and bladders are full or empty; we know when our skin is burned or pale; we know when an appendix causes pain; the same for a gall bladder or a pancreas. Our awareness is variable with time and circumstance.

We are not actively aware of our trillions of cells. Yet our nervous systems monitor cellular activities. Our immune systems look for unfriendly bacteria or viruses. We have physiological awareness of these activities, but no active awareness unless we feel tired, fevered, or ill. We are not aware of water, organic molecules, or inorganic ions in our cells unless we suffer from dehydration, malnutrition, or ion deficiencies.

We are not actively aware, nor even physiologically aware, of the subatomic particles that comprise the atoms and molecules of our cells. Yet we have intellectual awareness. We perform experiments to determine the properties of subatomic particles. We know they engage continuously in quantum interactions that enable larger particles to form and construct cells and organs. We know that we are products of these interactions.

We have only the dimmest intellectual awareness of the quantum fields that vibrate throughout the universe and generate these interactions. Yet we know that every particle and every physical thing is a temporary excitation of these vast and interconnected vibrating fields.

In this continuous hierarchy of levels of awareness, can we ever know exactly where our consciousness begins and where it ends?

Where do “we” begin and end?

We generally assume that “consciousness” extends only to the thin layer of experience of which we are actively aware. We define consciousness as limited to the bounds of subjective awareness. But what if the supposed border of consciousness is more porous than it seems? What if the assumed line of demarcation is entirely of our creation, constructed not on a foundation of biology or physics but only on our fuzzy, subjective experience of the nebulous self?[1]

We know that awareness is not binary, that we experience awareness in different kinds and degrees, that awareness is variable and dynamic. We know that humans can expand awareness. Athletes train themselves to be aware of physical capacities that most do not experience. Mystics and ascetics achieve voluntary control over autonomic body functions through meditation and breathing.

Is it possible that humans have actual or potential awareness of a broader range of physical experience than we usually include within the bounds of consciousness?

I am my body

It is a simple fact that I am a physical being. I am not a supernatural presence that inhabits my body. I do not reside in a magic place somewhere in my brain. I do not preside over a central control room where I oversee the rest of me. There is no physiological or psychological border where I end and the rest of me begins. This organic lump of clay—all of it—is me. All the way down to the quantum wavicles and fields that make me what I am.

I do not have the same awareness of every part of me or every level of my existence. But regardless of my degree of awareness, all these things are part of me. My consciousness includes what it is like to be a combination of these levels of awareness into one nebulous sense of self.

What if that feeling of being me unconsciously or subconsciously includes what it is like to be all of me? We know it does in a literal sense, because that is what “I” am. But what if my actual nebulous sense of self includes partly a nebulous sense of what it is like to be each of the parts of me?

I am what I am made of

I am my brain and arms and legs and heart and lungs and cells. I am the molecules and atoms that comprise my cells and the subatomic particles that comprise my atoms. I am the quantum fields that generate those particles.

Whether I understand it or not, I already know what it is like to be all of the parts of me. Perhaps the sum total of my nebulous sense of self includes a partial sense of what it is like to be a hand, a heart, a lung—what it is like to be a cell or a molecule—what it is like to be a subatomic particle or quantum field. Perhaps my sense of what it is like to be me somehow includes what it is like to be “them”—each of the parts of me.

There are those who believe that consciousness is fundamental to physical existence and that all matter has some consciousness associated with it. They view consciousness as a general property of matter, not exclusive to complex organisms. Others theorize that the ubiquitous process of quantum reduction generates moments of proto-consciousness that can be orchestrated into complex consciousness. They hypothesize that the “choices” made by electrons and the universe through quantum reduction create the foundation for consciousness. That what it is like to be an electron is part of what it is like to be ourselves. Because that is where consciousness begins. That is what we are.

I am my universe

The interconnectedness of the universe is rapidly becoming a truism. It is an accepted fact that the quantum fields underlying all things form a vast network extending across the universe. We are not ultimately separate from each other or from anything else. We are all temporary vibrations of the same quantum fields.

Spiritual philosophers, both religious and secular, talk about connecting with a deeper reality, a sense of “pure consciousness”. Do the quantum fields that comprise and connect all things constitute that deeper reality? Is pure consciousness an awareness of what it is like to be part of that vast interconnected universe? Is it the simple experience of what it is like to be?

What is it like to be an electron?

On its face the question seems ridiculous. But whether we realize it or not, we may already know exactly what it is like to be an electron.

[1] Something like what Daniel Dennett calls a “center of narrative gravity”. Dennett (1991).

The no longer unknown

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Do you ever wonder
what it might be like
to accept without breath
the no longer unknown?

What it might be like
to arrive at the end
and discover the world
where it was before,
where it always has been,
to know again
what we knew before,
what we always have known,
to be again
what we always were.

Before this interregnum
of seeming moment.