Shuichiro Ogawa
日本語

Notes · updated 2026-07-19

If Light Is a Particle, Matter Must Be a Wave

Sometimes only the correct shape of the question is fixed, before any evidence is in.

In 1924, de Broglie’s doctoral thesis predicted the existence of a phenomenon no one had yet measured. Light had long been believed to be a wave, yet the physics of the day already accepted that it also behaves as a particle (the light quantum). Only one side was granted. Then, he wrote, matter, long believed to be particulate, must likewise behave as a wave1. He closed the symmetry with a single equation: a particle carrying momentum p is accompanied by a wavelength λ. There was not yet a single experimental confirmation.

Three years later, that prediction was confirmed without being aimed at. Davisson and Germer, in the middle of a different experiment firing electrons at a nickel crystal, saw electrons draw the same diffraction pattern as X-rays2. Electrons were interfering as waves. A symmetry closed by inverting a one-sided asymmetry was later filled in by measurement. This is not an isolated anecdote. Physics keeps, as a method, the practice of using symmetry as a heuristic for theory construction3.

What happens if this move is carried straight into human learning and expertise? The method is this. Take one asymmetry that the learning sciences grant on only one side, and invert it to close the symmetry. The blind spot lies on the unclosed opposite side.

The Asymmetry the Learning Sciences Grant on Only One Side

First, write out the granted side precisely.

The learning sciences and expertise research depict development as acquisition. The novice lacks knowledge and skill, builds them up through practice, and becomes an expert. The direction is one-way, and the quantity increases monotonically. The central hypothesis of expertise research, formulated by Ericsson, Krampe, and Tesch-Römer, states this direction explicitly. Their monotonic benefits assumption holds that an individual’s level of expertise is a monotonic function of the amount of deliberate practice accumulated in the domain4. Those who start earlier will always reach a higher level for the same amount of practice. Expertise is depicted as a climb along a single axis of practice time, without turning back.

Under this picture, every reverse-direction phenomenon carries a negative sign. Unlearning is forgetting, regression is degradation, and an expert returning to the novice state is damage. A skill fading through disuse, or an acquired routine ceasing to work in a new situation, is treated as a failure to be avoided. What ought to be measured is accumulated practice and stacked-up ability, not knowledge that has been let go.

This asymmetry is inscribed deep in the instruments that measure learning. Degrees, credentials, years of experience, the number of items mastered. What educational institutions and assessments count is, in every case, the quantity of acquisition. On these scales, unlearning has no graduation. From inside an instrument that measures only acquisition, the structure of letting-go is hard to see from the outset.

Here is a side not yet inverted.

Invert It, and Unlearning Becomes a Developmental Stage

Invert it.

What principled reason divides acquisition and unlearning into ascent and degradation? Both are processes that reconfigure the relation between agent and environment. Acquisition writes a new mapping; unlearning dissolves an existing one. But when the environment changes, a mapping that was once correct becomes a wrong mapping in the new environment. Then dissolving it is not degradation but a step of adaptation to the changed environment. As Hedberg observed in the context of organizational learning, understanding involves both learning new knowledge and discarding obsolete and misleading knowledge5.

From this step follows a consequence that steps down from privileging acquisition. Unlearning is a developmental process symmetric in structure to learning. What is denied here is not the proposition that unlearning carries no loss. What is denied is the proposition that development is one-directional acquisition and that every reverse change is degradation. Unlearning can carry development forward with the same standing as acquisition. Escaping fixation, adapting to change, and undoing mistaken automatization can happen only through letting-go. [evidence level: author's inference]

From here a consequence about expertise continues. Expertise is not the top rung of a one-way ladder. Expert and novice are not two points fixed at the ends of a ladder but frame-relative states. Just as the speed of a body takes a value only once a reference frame is specified, expertise becomes expertise only once an environment (task structure, tools, constraints) is specified. When the environment changes, the same routine turns from expertise into liability. That is, expertise is reversible, and its reversal is not another name for degradation but a developmental direction that can have a pedagogy of its own. [evidence level: author's inference]

This has the same shape as de Broglie’s step. It inverts the “development is monotonic acquisition, the reverse is degradation” that learning research grants on one side, and closes the symmetry. What appears on the closed side is an ontology of reversible, frame-relative expertise.

Why This Blind Spot Is Structurally Invisible

Granting that the inversion is correct, why does the mainstream overlook it? The reason is not that researchers lack attention. It is that the very purpose of the instruments measuring learning renders this inversion structurally invisible.

Educational institutions exist to certify acquisition. A degree certifies the accumulation of completed coursework, a credential the passing of mastered items, years of experience the accumulated time. Every such instrument builds in, as a condition of its operation, the premise of monotonic acquisition. Reversibility and frame-relativity deny this premise. So from inside an institution whose purpose is to measure acquisition, the developmental structure of unlearning is in principle invisible.

As Kuhn showed, during normal science researchers assume the paradigm to be correct and refine details, without questioning the framework itself6. The paradigm of expertise research wears the ontology of a monotonic climb before it measures any quantity of acquisition. The question that doubts that ontology lies outside the instrument’s design spec. This structure is precisely what makes the blind spot a blind spot. [evidence level: author's inference]

Scattered Phenomena Bundle Under One Ontology

Whether an inversion is productive is decided by what it explains. The ontology of reversible, frame-relative expertise bundles, under a single figure, phenomena that have been treated separately.

First, the Einstellung effect. What Luchins showed in 1942 with the water-jar problem was that people keep repeating a once-successful solution method even where a simpler solution is available7. Bilalić, McLeod, and Gobet showed, through the eye movements of chess masters, that this effect works precisely on experts8. Masters who had found one solution reported they were looking for a better one, while their gaze kept tracking features tied to the first solution. The mainstream sees this as a cognitive bias mixed into expertise. Invert it, and this is the very state of expertise fixated to a particular frame; dissolving that fixation is a step of the developmental process called unlearning.

Second, design fixation. What Jansson and Smith showed in 1991 was that designers shown an example whose flaws were made explicit carried the example’s features, flaws and all, into their own designs, novices and experts alike9. A once-acquired frame narrows the space of new design. The mainstream sees this as an obstacle to creativity to be avoided. Invert it, and fixation is the underside of the frame that expertise acquired; if we can design an unlearning that lets go of that frame, this is not the removal of an obstacle but a reversible operation of expertise.

Third, negative transfer. That prior knowledge is misapplied in a structurally similar new task and impedes learning is something cognitive psychology has observed repeatedly10. The mainstream sees this as interference mixed into new learning. Invert it, and negative transfer is the phenomenon of expertise that was correct in the old environment turning into liability in the new; a contrastive unlearning targeting that liability gives the outline of a symmetric pedagogy.

Fourth, deskilling. What Braverman argued in 1974 in labor-process theory was the process by which division of labor and standardization strip skill from workers step by step11. Here is a phenomenon in which expertise is let go institutionally. The mainstream sees this as the degradation of skill by capital. This note is not concerned with labor control, but deskilling shows at scale that expertise is dismantled by changes in external conditions, and that serves as circumstantial evidence that expertise is not an irreversible accumulation.

These four the mainstream has processed separately, as degradation, interference, and obstacle mixed into the climb. Invert them, and they are not degradation but different faces of one phenomenon, the reversibility of expertise. And the logic that bundles the four comes down to one thing. If development is not one-directional acquisition, the premise that every reverse change is degradation does not hold. [evidence level: circumstantial]

Stating a Falsifiable Prediction

So far this is ontology, and as such it cannot be falsified. De Broglie’s step could be science because it carried a falsifiable prediction, electron diffraction. The ontology of reversible expertise, to earn the same standing, must predict something that the picture of monotonic acquisition cannot in principle explain.

There are two predictions.

First, deliberate unlearning interventions improve adaptation to a changed environment more than “learning more.” Compare an intervention that explicitly dissolves the old frame with one that stacks new knowledge on top, on an adaptation task in a changed environment. If the picture of monotonic acquisition is correct, adaptation is always a function of acquired quantity, and letting-go should have no effect of its own. So if the unlearning group significantly outperforms the acquisition group, the picture that treats acquisition alone as development is falsified. [evidence level: author's inference]

Second, expertise shows measurable negative transfer, and a symmetric pedagogy can be designed to target it. Place experts in a new environment where their expertise turns to liability, and compare a contrastive intervention dissolving the old frame with ordinary additional learning. If expertise is an irreversible accumulation, the intervention dissolving the old frame should have no effect of its own. So if contrastive unlearning outperforms additional learning, the irreversibility of expertise is falsified. [evidence level: author's inference]

The ground that these are not fantasy is that one side of the break has already been measured. The Einstellung effect and design fixation carved out experimentally that expertise is tied to a particular frame and works to disadvantage outside that frame. This is the “light quantum.” What the symmetry announces is the prediction that, in the reverse direction, an intervention that dissolves the frame should produce measurable gains. This is the “matter wave.” The one-sided fixation has already been measured, and only the effect measurement of the reverse-side unlearning intervention remains as the unfilled side. [evidence level: circumstantial]

Where the Novelty Is, and Where It Is Not

The more attractive an inversion looks, the more strictly the boundary with prior work must be drawn. Much of this note’s claim already exists in part.

The concept of unlearning itself is prior work in organizational learning. Hedberg set the origin point in 1981 (cited above5), and Rushmer and Davies in 2004 discussed individual unlearning in three types: fading, wiping, and deep unlearning12. These treat unlearning finely as a deliberate process. But none of them go as far as an ontological promotion of unlearning to a developmental stage symmetric with learning; they stay within a frame that takes acquisition as primary and unlearning as its auxiliary.

A pedagogy of unlearning is also prior work. In the context of professional education, a “pedagogy of unlearning” has been proposed that treats unlearning as an iterative, always-in-process undertaking13. This discusses pedagogical procedures specific to unlearning. But that proposal does not formulate unlearning as a developmental stage symmetric with acquisition; it treats it as a process incidental to professional learning.

That pedagogy reverses with expertise is also prior work. The expertise reversal effect, formulated by Kalyuga, Ayres, Chandler, and Sweller in 2003, showed that instructional methods effective for novices turn ineffective or harmful for experts14. This is the closest existing finding to this note: the optimal pedagogy reverses with the level of expertise. But this effect sits within cognitive load theory and concerns a reversal of instructional design, namely that novice-oriented scaffolding becomes redundant for experts. The ontological inversion that expertise itself is reversible and frame-relative, and the promotion of the unlearning that dissolves expertise to a developmental direction, are not included here.

That expertise turns to liability is also prior work. The Einstellung effect (cited above78), design fixation (cited above9), negative transfer (cited above10), and the “curse of expertise” in which experts overrate their explanatory ability15 each point out the negative side of expertise individually. But these are reported as individual phenomena of fixation or overconfidence, and are not bundled under one ontology.

With the above in view, this note’s novelty is strictly limited to the following three points.

First, the ontological inversion. Beyond the existing frame that treats unlearning as an auxiliary process of organizational learning or a reversal of instructional design, it promotes unlearning to a developmental stage symmetric with learning, one that carries development forward with the same standing as acquisition. Second, the reversibility of expertise. It takes expert and novice not as points fixed at the ends of a ladder but as frame-relative states, and formulates expertise as a reversible quantity. Third, the bundling. It bundles the scattered phenomena of Einstellung, design fixation, negative transfer, and deskilling under a single ontology of reversible, frame-relative expertise.

And these three points are not established facts. They are a falsifiable hypothesis awaiting a confirming experiment that compares whether deliberate unlearning interventions outperform “learning more.” [evidence level: author's inference]

The Same Heuristic Lights Two Sibling Asymmetries

The same move lights two asymmetries outside acquisition and unlearning as well. Both are touched on only briefly.

One is the asymmetry between discovery and loss of knowledge. Research and education take as default the direction in which knowledge is discovered and accumulated, and treat the direction in which knowledge is lost as accident. But if discovery and loss are symmetric, loss too should have a structure of its own. The sibling note undiscovery-knowledge-loss inverts this asymmetry.

The other is the asymmetry between addition and subtraction in creation. Design and creative work take adding elements as the default of creation, and see removing as the cleanup of finishing. But if addition and subtraction are symmetric, subtraction too should have a creativity of its own. The sibling note subtractive-creativity-design inverts this asymmetry.

What the three notes share is the impulse to question, from its underside, the figure that takes only the ascending direction of acquisition, accumulation, and addition as development. It resonates, at a distance, with the view that placed learning within the relation between organism and environment16. When that relation changes, former expertise ceases to be expertise. The view that expertise is a state rather than a destination remains placed on the underside of that figure.

One Question Left Open

De Broglie’s symmetry closed with electron diffraction. This note’s symmetry has not yet closed.

That expertise fixates to a particular frame has already been measured by the Einstellung effect and fixation research. Then, in the reverse direction, an unlearning that dissolves the frame should produce measurable gains, the symmetry announces. But announcing and showing are different. How to design a deliberate unlearning intervention, how to compare adaptation in a changed environment with additional learning, and how to target expertise’s negative transfer are left to the design of a comparative experiment. If confirmed, the picture of development as monotonic acquisition is falsified. If not, the picture that development is after all a one-way climb survives.

Which way it falls has not yet been measured. In that single fact of being unmeasured lies this hypothesis’s right to be a hypothesis.

References

Sources for the method, and works whose existence was confirmed as evidence for each claim, are given with DOI/URL. Items whose bibliography is unconfirmed or whose full text was not reached are marked [pending primary verification].

Method (symmetry completion as heuristic)

  • de Broglie, L. (1924). Recherches sur la théorie des quanta. Doctoral thesis, University of Paris. (Direct access to the original PDF is [pending primary verification]; the argument and submission date are confirmed across multiple secondary sources.)
  • Davisson, C. & Germer, L. H. (1927). The Diffraction of Electrons by a Crystal of Nickel. Physical Review 30(6):705–740. https://doi.org/10.1103/PhysRev.30.705
  • Stanford Encyclopedia of Philosophy. Symmetry and Symmetry Breaking. https://plato.stanford.edu/entries/symmetry-breaking/
  • Kuhn, T. S. (1962). The Structure of Scientific Revolutions. University of Chicago Press.

The granted asymmetry (monotonic acquisition)

  • Ericsson, K. A., Krampe, R. Th., Tesch-Römer, C. (1993). The Role of Deliberate Practice in the Acquisition of Expert Performance. Psychological Review 100(3):363–406. https://doi.org/10.1037/0033-295X.100.3.363

Scattered phenomena the inversion bundles (reversibility of expertise)

Limiting the novelty (boundary with prior work)

Sibling asymmetries

  • Gibson, J. J. (1979). The Ecological Approach to Visual Perception. Houghton Mifflin.

Pending primary verification

Items whose bibliography is unconfirmed, or whose full text was not reached, are collected here.

  • de Broglie (1924): direct access to the original PDF (argument and submission date consistently confirmed across multiple secondary sources).
  • Macdonald (2002): full-text detail (bibliography confirmed; abstract-only access. The claim that it does not promote unlearning to a symmetric developmental stage rests on the abstract).

Footnotes

  1. de Broglie, L. (1924). Recherches sur la théorie des quanta. Doctoral thesis, University of Paris, submitted 25 November 1924. It extended the wave-particle duality of light to matter and gave a relation linking momentum and wavelength. Direct access to the original PDF is [pending primary verification] (the argument and submission date are consistently confirmed across multiple secondary sources). ↩

  2. Davisson, C. & Germer, L. H. (1927). The Diffraction of Electrons by a Crystal of Nickel. Physical Review 30(6):705–740. https://doi.org/10.1103/PhysRev.30.705 Demonstrated electron diffraction and confirmed (initially unintentionally) de Broglie’s matter-wave hypothesis. ↩

  3. Stanford Encyclopedia of Philosophy, “Symmetry and Symmetry Breaking.” https://plato.stanford.edu/entries/symmetry-breaking/ An overview of how symmetry functions as a heuristic for classification, constraint on theory form, unification, and explanation (“symmetries have an important heuristic function”). ↩

  4. Ericsson, K. A., Krampe, R. Th., Tesch-Römer, C. (1993). The Role of Deliberate Practice in the Acquisition of Expert Performance. Psychological Review 100(3):363–406. https://doi.org/10.1037/0033-295X.100.3.363 Proposes the monotonic benefits assumption, treating expertise as a monotonic function of accumulated deliberate practice. ↩

  5. Hedberg, B. (1981). How Organizations Learn and Unlearn. In P. Nystrom & W. Starbuck (Eds.), Handbook of Organizational Design (pp. 3–27). Oxford University Press. The origin point of organizational unlearning theory: knowledge grows and simultaneously becomes obsolete as reality changes, and understanding includes both learning and unlearning. ↩ ↩2

  6. Kuhn, T. S. (1962). The Structure of Scientific Revolutions. University of Chicago Press. That normal science takes the paradigm as given and refines details without questioning the framework itself. ↩

  7. Luchins, A. S. (1942). Mechanization in Problem Solving: The Effect of Einstellung. Psychological Monographs 54(6):i–95. https://doi.org/10.1037/h0093502 Demonstrated with the water-jar problem that a successful solution method is repeated even where a simpler solution exists. ↩ ↩2

  8. Bilalić, M., McLeod, P., Gobet, F. (2008). Why Good Thoughts Block Better Ones: The Mechanism of the Pernicious Einstellung (Set) Effect. Cognition 108(3):652–661. https://doi.org/10.1016/j.cognition.2008.05.005 Showed via chess masters’ eye movements that the first solution biases attention and hides better solutions. ↩ ↩2

  9. Jansson, D. G. & Smith, S. M. (1991). Design Fixation. Design Studies 12(1):3–11. https://doi.org/10.1016/0142-694X(91)90003-F Demonstrated across four experiments that both novices and experts carry an example’s features into new designs even when its flaws are made explicit. ↩ ↩2

  10. Negative transfer is the phenomenon in which prior learning is misapplied in a later similar task and becomes an impediment; explicit contrastive analysis is a known mitigation. For a review see Perkins, D. N. & Salomon, G. (1992). Transfer of Learning. International Encyclopedia of Education (2nd ed.). Pergamon. https://jaymctighe.com/wp-content/uploads/2011/04/Transfer-of-Learning-Perkins-and-Salomon.pdf ↩ ↩2

  11. Braverman, H. (1974). Labor and Monopoly Capital: The Degradation of Work in the Twentieth Century. Monthly Review Press. The origin of labor-process theory, arguing the stepwise deskilling of workers through division of labor and scientific management. ↩

  12. Rushmer, R. & Davies, H. T. O. (2004). Unlearning in Health Care. Quality and Safety in Health Care 13(Suppl 2):ii10–ii15. https://doi.org/10.1136/qshc.2003.009506 Classifies individual unlearning into fading (gradual decay), wiping (deliberate replacement), and deep unlearning (radical break). ↩

  13. Macdonald, G. (2002). Transformative Unlearning: Safety, Discernment and Communities of Learning. Nursing Inquiry 9(3):170–178. https://doi.org/10.1046/j.1440-1800.2002.00150.x Discusses unlearning as a transformative process advancing within safe spaces and communities. (Bibliography confirmed; access to full text is abstract-only.) ↩

  14. Kalyuga, S., Ayres, P., Chandler, P., Sweller, J. (2003). The Expertise Reversal Effect. Educational Psychologist 38(1):23–31. https://doi.org/10.1207/S15326985EP3801_4 Formulates from cognitive load theory the effect whereby instruction effective for novices becomes ineffective or harmful for experts. ↩

  15. Fisher, M. & Keil, F. C. (2016). The Curse of Expertise: When More Knowledge Leads to Miscalibrated Explanatory Insight. Cognitive Science 40(5):1251–1269. https://doi.org/10.1111/cogs.12280 Demonstrated that expertise unduly raises confidence in explanatory ability, which is then betrayed when an actual explanation is offered. ↩

  16. Gibson, J. J. (1979). The Ecological Approach to Visual Perception. Houghton Mifflin. Formulated perception within the relation between organism and environment, the ecological approach. ↩

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