The Einstein Gap

Sungchul Ji, Ph.D.
Emeritus Professor of Theoretical Cell Biology, Rutgers University
with conceptual and editorial assistance from ChatGPT

Quantum mechanics may be the most successful predictive theory ever created.

It predicts atomic spectra, chemical bonding, lasers, semiconductors, superconductivity, and the extraordinary correlations observed between entangled particles.

Again and again, experiment agrees.

And yet a surprisingly simple question remains:

What kind of reality produces these quantum phenomena?

Nearly a century ago, Albert Einstein recognized that successful prediction and understanding physical reality are not necessarily the same thing.

I propose calling the distance between these two achievements the Einstein Gap:Einstein Gap = the gap between successful quantum prediction and an agreed
account of the underlying physical reality.

This is not Einstein’s terminology. It is a term proposed here for a problem whose historical roots reach directly back to Einstein.

And Richard Feynman, decades later, expressed essentially the same difficulty in unusually candid language [1].

1. Feynman’s remarkable admission

In his 1983 workshop Quantum Mechanical View of Reality at the Esalen Institute [1], Feynman began to say that quantum mechanics allows physicists to calculate and understand nature—then immediately corrected himself.

His point was striking: quantum mechanics allows extraordinarily successful calculation, while understanding “real nature” remains elusive.

This distinction can be represented simply:

Prediction (What will happen) is not = Ontology (What reality makes it happen)

Physics possesses the left-hand side to extraordinary precision.

The Einstein Gap concerns the right-hand side.

2. Einstein saw the problem early

In 1935, Einstein, Boris Podolsky and Nathan Rosen [2] published one of the most consequential papers in modern physics. Its title was itself a question:

“Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”

Their answer was no.

EPR argued that if quantum mechanics were a complete description, peculiar consequences followed for two systems that had interacted and then separated. Their conclusion was that the wavefunction did not provide a complete description of physical reality.

Niels Bohr immediately disagreed. He argued that the EPR criterion of physical reality contained an ambiguity and defended quantum-mechanical complementarity as providing, within its proper domain, a complete description.

Thus, already in 1935, the central divide was visible:Quantum formalism = ? complete description of reality.

Einstein said, in effect: not necessarily.

Bohr replied, in effect: the demand itself misunderstands quantum phenomena.

The Einstein Gap had appeared.

3. Then came Bell

For decades, the dispute could easily appear philosophical.

Then John Bell transformed part of it into mathematics.

Bell showed that theories satisfying a particular locality condition, together with additional assumptions, impose constraints upon correlations between measurements made on spatially separated systems.

These are Bell inequalities [3].

Quantum mechanics predicts circumstances in which those inequalities are violated.

For a pair of spin -1/2 particles in the singlet state, quantum mechanics predicts the correlation

E(a,b) = −cosθ_ab​,

where θ_ab​ is the angle between Alice’s and Bob’s measurement orientations.

Experiments agree with the quantum predictions.

So we arrive at an extraordinary situation:Bell-local model ⟶ Bell constraints
Quantum mechanics ⟶ violations possible ​
Experiment​ ⟶ violations observed

Bell therefore greatly narrowed the range of possible explanations. A theory satisfying the conditions used to derive the relevant Bell inequality cannot reproduce all the quantum predictions. Importantly, Bell’s theorem does not eliminate every hidden-variable theory; nonlocal approaches such as de Broglie–Bohm theory [4] remains possible.

But Bell did not tell us uniquely what reality is.

And therein lies the Einstein Gap.

4. Prediction is not necessarily explanation

This distinction is essential.

Quantum mechanics does not fail at entanglement.

It succeeds spectacularly.

It gives us the probabilities and correlations that experiments subsequently observe.

The unresolved problem is different:Why does nature possess precisely this quantum structure?

What is the wavefunction?

Does it represent something physically real?

Does measurement cause a physical collapse?

Do all possible outcomes occur?

Are particles guided by additional variables?

Are quantum states fundamentally relational?

Is a quantum event produced by a transaction?

Or are we asking for an underlying reality that quantum mechanics tells us cannot be described in classical terms?

These questions lead to very different interpretations.

5. Possible bridges across the Einstein Gap

There is no shortage of candidates.

The Copenhagen family of interpretations [5] emphasizes quantum formalism, measurement context and complementarity. From this perspective, demanding a classical underlying picture may itself be misguided.

Bohmian mechanics supplies definite particle configurations and a guiding dynamics. It restores an explicit ontology, but at the price of nonlocal structure.

Everett’s relative-state or Many-Worlds approach removes fundamental collapse. The universal quantum state evolves continuously, with different outcomes represented in different branches.

Objective-collapse theories instead propose that collapse is a genuine physical process.

Relational approaches make relations between physical systems central rather than assigning an observer-independent quantum state in the traditional way.

Transactional approaches interpret quantum processes through relationships between emitters and absorbers.

These approaches differ dramatically in what they claim reality consists of, even where they reproduce the same standard quantum predictions.

That is perhaps the clearest expression of the Einstein Gap.

6. Could the problem be geometrical?

There is another possibility worth considering.

Perhaps part of our difficulty arises because we continue trying to imagine quantum reality primarily in terms of objects located in spacetime.

Suppose Alice has one particle and Bob another:A B.

Spacetime physics tells us beautifully how separate events and objects are situated geometrically.

I have recently called this broad perspective the Geometry of Shapes (GOS).

But entanglement asks us to consider something else:A ⟷ B.

For an entangled state,

Ψ_AB /= Ψ_A ⊗ Ψ_B

The state of the whole cannot be represented simply as independent quantum states of its parts.

Perhaps, therefore, the missing language is partly a Geometry of Relations (GOR).

The distinction would be:GOS/Geometry of Shapes/geometry within which things relate

​​GOR/Geometry of Relations/geometry generated by relations themselves​

This does not mean ordinary spacetime geometry is non-relational—it certainly is relational. Nor does Bell’s theorem prove GOR.

Rather, GOR asks whether certain phenomena require us to treat the relation itself as part of the fundamental structure, rather than attempting to reconstruct everything from independently possessed properties of separated objects.

7. From relations to higher-order relations

This possibility leads naturally toward simplicial geometry.

A line can represent a relation between two vertices.

A triangle can represent an irreducible three-way relation.

A tetrahedron can represent a four-way relation.

A 5-cell [6], or hypertetrahedron, can represent a five-way relation.

Thus:

S1 ​→ S2​ → S3 ​→ S4​ →⋯

can be viewed, with suitable definitions, as an ascent toward increasingly higher-order relational organization.

Category theory suggests an analogous movement at a more abstract level:objects → morphisms → functors → natural transformations.

The common intuition is:things → relations →relations among relational structures.

Perhaps the Einstein Gap is telling us that the ontology of quantum mechanics cannot be reconstructed entirely from the first term—things.

Perhaps relations deserve equal ontological status.

8. S5 → S4: a speculative possibility

This brings us to a more speculative proposal.

Suppose an entangled quantum state is represented metaphorically by a higher-order relational geometry, which I call S5, the hypertetrahedral level.

The experimentally observed world of definite events is represented by S4, the tetrahedral level.

Quantum measurement could then be pictured asS5 ⟶ S4.

I have also introduced an intermediate Dynamic Body-Centered Tetrahedron (BCT) to represent mediation between the two levels:S5 ⟶ Dynamic BCT ⟶ S4.

The interpretation would be:

(S5/relational quantum state/ possibilities) ​→

(Dynamic BCT/measurement interaction/mediation) →​

(S4/observable event/actuality​)

Elsewhere I have called this direction a Reverse Tagore Transition, because it reverses the metaphorical S4→S5 transition I have associated with passage from manifest reality toward a larger unknown relational domain.

But the important point here is not the terminology.

It is the possibility that the Einstein Gap might be a dimensional or relational gap:observable reality ↔ a richer relational structure underlying it.

9. But can this become physics?

Here we must draw a firm boundary between metaphor and theory.

WritingS5 → BCT → S4

does not explain entanglement merely because the diagram is suggestive.

A physical theory must reproduce numbers.

For the singlet experiment, for example, a successful geometrical theory would have to recoverE(a,b) = −cosθ_ab​.

Better still, it should derive the quantum probability rule rather than insert it by assumption.

And ideally it should make at least one prediction distinguishing it from existing quantum theory.

Thus we can identify three stages:Metaphor → mathematical model → experimentally distinguishable theory.

At present, GOR and S5 → BCT → S4 belong primarily to the first stage, with the possibility of developing the second.

Recognizing that limitation does not weaken the proposal. It tells us exactly what must be done next.

10. Perhaps Einstein’s question is still with us

The extraordinary story can therefore be summarized:Einstein (Is QM complete?​) → ​Bell (What does locality permit?) ​→​Experiment (Nature violates Bell inequalities)​

Quantum mechanics survives magnificently.

But Einstein’s deeper question does not simply disappear.

Bell taught us that one attractive classical answer cannot work under Bell’s assumptions.

Experiments confirmed that lesson.

What remains unsettled is the ontology.

That is what I propose calling the Einstein Gap:Einstein Gap
successful prediction <------------------------>​ understanding physical reality.

Perhaps Copenhagen tells us that the gap should not be crossed in the classical way.

Perhaps Bohm crosses it with nonlocal hidden variables.

Perhaps Everett dissolves it by abandoning unique collapse.

Perhaps relational or transactional interpretations redefine what lies on the other side.

Or perhaps a future Geometry of Relations will show that we have been trying to describe an intrinsically relational reality with an ontology too strongly centered on separate objects.

We do not yet know.

And that may be precisely the point.

Nearly a century after EPR, physics can predict some of nature’s strangest phenomena to astonishing precision. Yet the question Einstein helped place at the center of quantum foundations remains:What is the reality that our extraordinarily successful equations are describing?

The Einstein Gap is a name for the distance between having the right answer to the experiment and knowing what kind of world makes that answer true.

References:
[1] Feynman, R. P. (2018). Quantum Mechanical View of Reality. https://www.google.com/search?q=The+1983+Esalen+workshop%2C+Quantum+Mechanical+View+of+Reality%2C+a+November+1983+workshop+at+the+Esalen+Institute%2C+Big+Sur%2C+California%2C&rlz=1C1GCEA_enUS1187US1196&oq=The+1983+Esalen+workshop%2C+Quantum+Mechanical+View+of+Reality%2C+%0A%0Aa+November+1983+workshop+at+the+Esalen+Institute%2C+Big+Sur%2C+California%2C&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCjQ4NjI4ajBqMTWoAgCwAgA&sourceid=chrome&source=chrome.rb&ie=UTF-8#fpstate=ive&vld=cid:e7ac01c3,vid:72us6pnbEvE,st:0
[2] Einsterin-Podolsky-Rosen paradox. https://en.wikipedia.org/wiki/Einstein%E2 https://en.wikipedia.org/wiki/5-cell %80%93Podolsky%E2%80%93Rosen_paradox
[3] Bell test. https://en.wikipedia.org/wiki/Bell_test
[4] De Broglie-Bohm theory. https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory
[5] Copenhagen interpretation. https://en.wikipedia.org/wiki/Copenhagen_interpretation
[6] 5-cell. https://en.wikipedia.org/wiki/5-cell