Written for the equation-averse.
Quantum mechanics and consciousness, from zero.

Quantum mechanics is a theory written not in "words" but in "equations." This is where many people give up, but the math you actually need comes down to just three things at the advanced high-school / introductory-college level: complex numbers, vectors, and probability. In this chapter we explain each of them intuitively, focusing strictly on what they are used for in quantum mechanics.

① Complex numbers — "numbers in two dimensions"

A complex number is a number written in the form \(a + bi\), using \(i\) (the imaginary unit), the number whose square is −1. In humanities terms, think of complex numbers as extending the "one number line (the real numbers)" into "a plane (a two-dimensional map)."

The magnitude of a complex number \(z = a+bi\) is computed as \( |z| = \sqrt{a^2+b^2} \). In quantum mechanics, the most important point — coming up in a later chapter — is that the square of this magnitude, \(|z|^2\), corresponds to "probability." (Keep this in mind.)

② Vectors and "state space"

A vector is a quantity that has direction and magnitude. On a map, picture an arrow like "3 km northeast from Shinjuku." High school covers two- and three-dimensional vectors, but the vectors used in quantum mechanics can have hundreds, thousands — sometimes infinitely many — dimensions. Even so, the rules for working with them (addition, multiplication, computing length) stay exactly the same.

③ Probability — dice and "weights"

Probability expresses how "likely" an event is, as a number from 0 to 1 (0% to 100%). The probability of rolling a 1 on a die is 1/6. Probability in quantum mechanics uses the same mathematical framework — but the decisive difference is that it takes the stance that "the die has no predetermined outcome before it is thrown" (more on this from Chapter 4 onward).

To grasp how strange quantum mechanics is, you first need to know the common sense it broke. That is the worldview of classical mechanics (Newtonian mechanics).

Newton's world: a clockwork universe

In the classical mechanics that Newton established in the 17th century, once you know an object's position and velocity, all of its subsequent motion can be predicted perfectly. Throw a ball and its trajectory can be calculated exactly by formula; in principle, if you knew "the state of the universe at this very instant," everything forever after would be determined. This is called determinism.

The tacit assumptions about "reality"

Classical physics rests on assumptions that we intuitively believe:

• Realism: things exist "there" in a definite state even when no one is observing them (the moon is there even when nobody looks).
• Locality: what happens in one place cannot instantaneously affect a distant place (information travels no faster than light).
• Determinism: given the initial conditions, the future is uniquely determined.

Quantum mechanics confronts us with phenomena that cannot be explained without giving up at least one of these three assumptions (in most interpretations, several). This is the reality behind the claim that "quantum mechanics defies common sense."

The gateway to every quantum mystery is the nature of "waves." Recalling the ripples on a pond, let's pin down two phenomena unique to waves.

Wave basics: crests and troughs

A wave is a phenomenon in which "crests" and "troughs" repeat periodically across space and time. Sound is a wave of air pressure; light is a wave of electromagnetic fields. What distinguishes waves from particles (balls) is that they are spread out and can overlap with one another.

Interference: waves reinforcing and canceling

The double-slit experiment (the classical picture)

Cut two narrow slits in a wall, place a screen beyond them, and send waves through: stripes (an interference pattern) appear on the screen. This happens because the waves passing through the two slits overlap, producing places where they reinforce (bright stripes) and places where they cancel (dark stripes). This apparatus will appear again and again as the "star of the show" when we explain quantum strangeness in the coming chapters. For now, just remember this: overlapping waves make stripes.

Diffraction: waves bend around obstacles

When a door is slightly ajar, you can hear voices from the next room even around the corner of the hallway. That is because sound waves "bend around" the edges of obstacles — a property called diffraction. Particles (marbles) cannot bend around an obstacle; waves can. This "difference between particles and waves" is the theme of the next chapter.

At last we reach the heart of quantum mechanics. In the early 20th century, scientists fired minuscule particles — electrons — at a double-slit experiment. Common sense said that electrons are like tiny marbles: each should pass through one slit or the other, and the screen should show two bands.

The idea of "superposition"

To explain this result, physicists introduced the concept of superposition. Until it is observed, the electron is not decided as "went through the left slit" or "went through the right slit"; it is in a state in which both possibilities exist simultaneously. This "both at once" part is where everyday intuition breaks down completely.

Observation turns the wave back into a particle

Curiously, the moment you try to check with a detector which slit the electron actually passed through, the interference pattern vanishes and the electrons form two bands, like marbles. Merely trying to look makes the wave behavior disappear. What this act of "observation" brings into quantum mechanics is examined in depth in Chapter 7.

The mathematical tool that describes the "superposition" from the last chapter is the wave function, written \(\psi\) (psi, a Greek letter). The wave function is like a "map" that assigns a complex number — the kind you met in Chapter 1 — to every point in space.

The wave function as a map of possibilities

The Born rule: \(|\psi|^2\) gives probability

In Chapter 1 we promised that "squaring the magnitude of a complex number relates to probability." Here it is. The wave function \(\psi\) itself is a complex number (and cannot be observed directly), but the square of its magnitude \(|\psi|^2\) gives the probability density of finding the particle at that location. It is called the "Born rule," after the physicist who proposed it.

The Schrödinger equation: the "law of motion" for the wave function

Just as Newton's equation of motion \(F=ma\) determines a ball's trajectory in classical mechanics, in quantum mechanics the Schrödinger equation determines how the wave function \(\psi\) changes over time. The equation itself belongs to a university physics course, but for our purposes the following understanding is enough.

Many people have heard the phrase "Heisenberg's uncertainty principle." But this is not a limit that arises because our instruments are crude; it is a fundamental limit built into the universe itself.

Position and momentum: you cannot know both

The uncertainty principle states that a particle's "position" and "momentum (≈ velocity × mass)" cannot be known simultaneously and to arbitrary precision. The more precisely you try to pin down the position, the greater the uncertainty in the momentum — and vice versa.

Why it must be so: the nature of waves

A common misunderstanding

This is the point that draws the most attention from those who want to connect quantum mechanics with consciousness. Let's take our time with it.

Collapse of the wave function

As we saw in Chapter 5, the Schrödinger equation evolves the wave function smoothly and deterministically. Yet the instant a measurement is made, the wave function suddenly "jumps" to the single observed outcome. This is called collapse of the wave function. That a special, non-deterministic leap occurs only at the moment of measurement is one of the greatest unsolved problems in quantum mechanics — the famous measurement problem.

What is "measurement"? — and does consciousness have anything to do with it?

In the early formulations of quantum mechanics (von Neumann and others), what "measurement" actually means — and where the quantum system ends and the "observer" begins — was left ambiguous. This is the historical reason the speculation arose that "consciousness collapses the wave function." In the mainstream modern understanding among physicists, however, the story is far more mundane.

There is more than one interpretation

Whether "collapse actually happens" is itself a matter of disagreement among physicists. Here are the main positions.

Which interpretation is correct has not been settled experimentally in physics to date. This is an important fact: the claim that "consciousness is involved in the measurement problem" rests on a decided minority position among the many interpretations.

"Quantum entanglement" is the other phenomenon frequently invoked in arguments linking quantum mechanics to consciousness. Einstein disliked it, calling it "spooky action at a distance."

What entanglement is

When two particles are "entangled," the moment one is measured and its result is fixed, the state of the other is instantly determined in a correlated way, no matter how far apart they are. For instance, if the spins (something like the direction of their rotation) of two particles are entangled, the instant you measure one and find it "up," the other is invariably "down."

Bell's theorem and its experimental verification

In 1964, the physicist John Bell proved mathematically that "if reality is local (no instantaneous influence across distance) and particles possess definite properties before measurement (realism), then measurement outcomes must satisfy a certain inequality." Subsequent experiments — notably those by Aspect, Clauser, and Zeilinger, honored with the 2022 Nobel Prize in Physics — confirmed with high precision that this inequality is violated. In other words, experiment has shown that we must give up locality or realism (or both).

It does not "transmit information instantaneously"

Decisively important in debates about quantum physics and consciousness, yet rarely touched on in popular explanations, is the concept of decoherence. The strongest objection to "quantum brain theories" comes from here.

Superpositions are fragile

A quantum superposition (see Chapter 4) is an extremely delicate state. The moment it interacts even slightly with the surroundings (air molecules, photons, thermal vibrations), the information of the superposition "leaks" into the environment almost instantly, and the system effectively becomes classical (no longer superposed). This process is called decoherence.

Can the brain maintain quantum superpositions?

In a 2000 paper, the physicist Max Tegmark compared the timescales of neuronal firing in the brain with the timescales over which decoherence occurs, and estimated that in a warm, wet, complicated environment like the brain, quantum superpositions are lost in roughly 10^-13 to 10^-20 seconds — orders of magnitude faster than neural activity (on the order of milliseconds). In other words, "superpositions are destroyed instantly, before they could ever be used for the brain's information processing." This is the physics community's most powerful rejoinder to quantum brain theories.

To evaluate arguments that connect quantum physics and consciousness, you also need basic knowledge of how the brain works. Here we cover the minimum on how neurons (nerve cells) operate.

Neurons: electrically powered communication cells

The human brain contains roughly 86 billion neurons, each wired (at synapses) to several thousand others on average. Neurons carry information as electrical signals (action potentials), and at synapses they pass the signal to the next cell mainly through chemicals (neurotransmitters).

What microtubules are

Essential to understanding the Orch-OR theory are microtubules. These are tubular protein structures about 25 nanometers in diameter found inside every cell, neurons included; they serve as the cell's "scaffolding" and also act as rails for transporting material within the cell. Orch-OR claims that quantum computation takes place inside these microtubules — a claim examined closely in Chapter 13.

The brain's information processing is considered fundamentally classical

In the mainstream understanding of neuroscience today, the brain's information processing (memory, learning, perception, and so on) is well understood as electrochemical processes explainable in terms of classical mechanics. To be sure, at the molecular level quantum mechanics is at work (all chemistry — chemical bonds, enzyme reactions — rests on quantum mechanics), but it is important to note that this is an entirely different matter from the claim that "the brain's higher information processing itself works like a quantum computer."

The word "consciousness" actually refers to different things depending on who is doing the arguing. To avoid confusion, here is the philosopher David Chalmers's famous distinction.

The "easy problems" and the "hard problem"

"Easy" here does not mean simple — it means "in principle solvable within the existing framework of science (explanation in terms of function and information processing)." The "hard problem," by contrast, is the charge that no matter how much you pile up explanations of physical processes, the gap never closes on why "subjective feeling" accompanies them.

Why "quantum mechanics" gets called in to explain consciousness

Because the hard problem is so hard, some researchers concluded: "a deterministic, mechanical framework like classical mechanics can never explain consciousness — the clue must lie in a theory that is fundamentally probabilistic and inseparable from observation, like quantum mechanics." That is the motive behind the quantum brain theories covered in the next chapter.

Building on the previous eleven chapters, let's map the psychological and logical structure of why so many people — experts and laypeople alike — are drawn to connect quantum mechanics with consciousness.

The surface resemblances

• Both seem exquisitely sensitive to "observation": in quantum mechanics, observation (apparently) settles the outcome; consciousness, too, changes experience when attention turns toward it.
• Both seem to escape determinism: quantum mechanics is inherently probabilistic, and human beings feel that they possess "free will."
• Both rank as science's most "inexplicable" puzzles: the measurement problem is the greatest riddle in physics, and the hard problem of consciousness the greatest in philosophy. Hence the intuition: "two mysteries must be connected."

But none of this is logical "proof"

Why it is still seriously researched

That said, quantum biology (quantum effects in photosynthesis, quantum entanglement in migratory birds' magnetic sensors, and so on) exists as a solid, peer-reviewed research field showing that quantum effects really do play functional roles in some life processes. In this context, the hypothesis that "something similar may be happening in the brain" is not dismissed out of hand as unscientific. The issue is that between "possible in principle" and "demonstrated" lies a great distance. The next chapter looks concretely at the flagship theory, Orch-OR.

The most systematic and famous theory linking quantum physics and consciousness is Orch-OR (Orchestrated Objective Reduction), proposed by the physicist Roger Penrose (awarded the 2020 Nobel Prize in Physics — though for his black-hole research, not for Orch-OR) and the anesthesiologist Stuart Hameroff.

The theory in outline

1. Inside the microtubules introduced in Chapter 10, quantum superposition states form.
2. Those superpositions collapse spontaneously after a certain time through a gravitational effect Penrose proposes on his own ("objective reduction," OR, grounded in quantum gravity) — independent of any external observation.
3. Because this collapse occurs in an orchestrated fashion across the entire microtubule network, each discrete unit of experience — a "moment" of consciousness — is born.
4. The repetition of this process generates the stream of consciousness that feels continuous.

Why the theory looks attractive

Orch-OR does not rest on the loose analogy that "quantum mechanics and consciousness resemble each other." It specifies a concrete biological structure (microtubules), a concrete physical mechanism (Penrose's own quantum-gravity theory), and a concrete correspondence ("the instant of collapse = the unit of consciousness"). It is one of the few falsifiable (testable) quantum theories of consciousness, and precisely because of that specificity it has been taken seriously as a subject of debate, setting it apart from the many vague "quantum spirituality" claims.

Precisely because Orch-OR is concrete and testable, it has drawn many concrete rebuttals. For a balanced picture, here are the main criticisms.

Criticism 1: The decoherence timescale problem (see Chapter 9)

The most powerful criticism comes from the physicist Max Tegmark. As noted above, in a warm, wet environment like the brain, quantum superposition was estimated to be lost orders of magnitude faster than neural activity — on the order of a trillionth of a second or less. Hameroff and colleagues have pushed back on this calculation, citing the ordered structure of water molecules inside microtubules and shielding effects from the surrounding proteins; but as of 2024, direct experimental evidence for these protective mechanisms remains limited.

Criticism 2: No known evolutionary reason for the brain to "use" quantum effects

Even if some quantum effect does exist in the brain, showing that it is functionally used for information processing or for generating consciousness is a separate, high hurdle. Between "it is there" and "it causes consciousness" sits a logical leap.

Criticism 3: The explanatory gap remains unfilled

There is also the philosophical objection that even if every piece of the Orch-OR mechanism were correct, it still would not answer the hard problem itself (see Chapter 11): why should quantum-gravity-induced collapse in microtubules be accompanied by subjective experience (qualia)? Substituting a quantum mechanism for a classical one leaves the core mystery — why subjectivity should dwell there at all — untouched.

Positive material: indirect support from related fields

Nor is it flatly denied. Since 2013, discoveries in neighboring fields — research on anesthetic mechanisms involving microtubules, and demonstrations of quantum effects in quantum biology (photosynthesis, birds' magnetic sense) — have given Orch-OR's supporters genuine encouragement. Note, however, that these demonstrate "quantum biology exists," not that "Orch-OR is correct."

Chapter 15 — well done for getting here. To close, here is a "checklist" for judging claims for yourself, without swallowing them whole, whenever you pick up a book or article about quantum mechanics and consciousness.

A checklist for reading critically

• Check whether the word "quantum" names a concrete mechanism or is used merely for atmosphere.
• Check whether the phrase "observation creates the outcome" smuggles in consciousness (Chapter 7: modern physics doesn't need it).
• Check whether the decoherence problem is squarely addressed (beware books that discuss quantum effects in the brain without it).
• Spot any reliance on the "both are mysterious, so they must be related" move (the appeal to ignorance).
• Ask whether the claim is falsifiable — whether some experiment could, in principle, show it wrong.

The fun of this field lies in its unanswered questions

Neither the measurement problem in quantum mechanics nor the hard problem of consciousness has been settled, even by humanity's best minds. That is precisely why they captivate so many people — and there is nothing dishonest about that in itself. What matters is not to mistake "we don't understand it yet" for "so I am free to pick whichever conclusion I like." What remains unknown can be held as unknown, with honesty and lasting curiosity.

For further study (advanced references)