If quantum reality is relational, the line between physics and mathematics becomes difficult to defend.
Quantum mechanics has never suffered from a lack of success.
It predicts the behavior of the microscopic world with astonishing precision
and sits underneath technologies we use every day. What it has never produced
is anything like comparable agreement about what its success means. Nearly a
century after its arrival, physicists can work with the theory while holding
radically different ideas about the reality it describes.
One serious attempt to make sense of that reality is called Relational Quantum Mechanics. The framework begins with an unsettling proposal: the properties
of a physical system may not belong to that system alone. A quantity such as
spin does not simply sit inside an electron, fully determined and waiting for
someone to look. A property has no definite value on its own. The value emerges
when two systems interact, and its silhouette is drawn by the relation between
them.
This is not the claim that human consciousness manufactures
reality. In relational quantum mechanics, an observer can be a detector,
another particle or the surrounding environment. The important event is not a
mind looking at the world. It is one part of the world encountering another.
The framework was first developed in the 1990s by the
theoretical physicist Carlo Rovelli. His proposal rejects the idea of a single, observer-independent
state containing every fact about a system. Instead, physical facts arise
between systems. The world remains real, but its facts do not necessarily
assemble into one absolute inventory that exists from every possible point of
view.
At first, this may sound like a strange new account of
properties rather than a threat to objects. Perhaps the electron still exists
independently; only its properties become relative during interactions. But the
word properties conceals a problem. What is an object once everything
through which it can be described, identified or distinguished has been removed
from it?
One answer is that something remains: a bare physical
substance that has properties without being reducible to them. This gives the
object a protected core. Yet a core with no mass, position, state, behavior or
relation to anything else is difficult to distinguish from an empty word. It
does no explanatory work beyond giving the properties somewhere grammatical to
land.
Another answer has a long history in philosophy. According
to bundle theories, an object is not a hidden substance carrying its properties; it
is the organized bundle of those properties. There is no apple underneath its
color, shape, weight, texture, taste and the ways it behaves. The apple is not
necessarily reducible to the properties we happen to notice, but neither is
there an additional, propertyless apple hiding behind them.
If that is right, relational quantum mechanics may be saying
more than it initially appears to say. If a particle is nothing over and above
the properties and behavior that make it identifiable, and those properties are
entirely relational, then there may be no independent particle left once the
relations are removed. The particle becomes a stable role within a structure
rather than a little object that first exists and later enters into
relationships.
Physics is not the only discipline to have made the
self-contained object look unstable. Phenomenology approached it from the
opposite direction. For Edmund Husserl, an object is never given to us all at once. We see one side of a
table while anticipating sides we cannot see; we recognize it as the same table
across different angles, distances and moments. The object arrives as a unity
held together through a changing flow of appearances.
Phenomenology does not prove that physical reality is made
of relations. It is concerned with how things appear and acquire meaning in
experience, not with issuing a final inventory of the universe. Still, it
reveals something relevant: even the ordinary object is not presented as a
naked core underneath its qualities. Its unity is achieved across perspectives,
expectations and time. Quantum mechanics now presses from the other side. If
the object is constituted relationally in experience while its physical
properties also become definite through interactions, the independent object is
squeezed from both directions.
An ancient Buddhist dialogue offers a less technical version of the same discomfort.
In the Milindapañha, the monk Nagasena asks King Milinda to identify the
chariot in which the king arrived. Is the chariot its wheels? Its axle? Its
frame, pole or yoke? None of those parts, taken alone, is the chariot. But no
separate chariot can be found floating beyond them either. The chariot is
simply the name given to the components when they are organized and functioning
in a particular way.
This does not make the chariot imaginary. It can carry a
king, break an axle and run over a foot. It is real at the level at which
people encounter and use it. What it lacks is a separate essence in addition to
its parts, arrangement and function. Remove enough of that organization and the
chariot does not travel elsewhere; the name simply stops applying.
A particle may be real in a similar sense. Our instruments
register localized events; our theories connect them with extraordinary
reliability. Calling the pattern an electron may be indispensable. But
indispensability does not tell us whether an electron is a tiny self-contained
thing or the name we give to a persistent structure of possible interactions. A
whirlpool is real, but it is not an additional substance placed inside the
water. Its identity lies in an organized pattern that temporarily holds.
Ontic Structural Realism pushes this possibility into an explicit view of
reality. Philosophers of physics including James Ladyman and Steven
French argue that modern physics gives us reason to rethink objects in
structural terms. Identical quantum particles do not behave like individually
labeled marbles: exchanging their labels does not necessarily produce a new
physical state. Entangled systems, meanwhile, possess a joint structure that
cannot be rebuilt from independent descriptions of each part.
None of this proves that objects do not exist. Quantum
mechanics supports several competing interpretations, and relational language
can be used without accepting the most radical metaphysics attached to it. A
moderate structural realist can say that objects and relations depend on one
another. Rovelli himself continues to speak of physical systems; he does not
simply erase everything the relations are supposed to relate.
But the radical possibility cannot be dismissed by pointing
at the noun particle. If the particle has no identity apart from the structure,
calling it an object may add nothing. It may be like calling one position in a
network a node: useful and perfectly legitimate, but not evidence for a small
piece of substance living underneath the connections.
Only now does the larger question come into view. Suppose
the relational account is right in its strongest form. Suppose fundamental
reality contains no self-standing objects, only structures within which the
appearances we call objects emerge. What remains of physics?
Relations remain. Symmetries remain. There are
transformations, probability distributions and rules governing how one possible
state leads to another. There are stable patterns and invariants. There are
equations.
What remains looks remarkably like mathematics.
We normally preserve a comfortable division between mathematics and physics. Mathematics describes possible structures; physics uses some of those structures to explain and predict the behavior of the world. The difference is not that each discipline governs a separate portion of reality. It is that physics is answerable to observation. Mathematical consistency may tell us what is possible, but only experiment can tell us how our universe behaves or determine the value of a physical constant.
In the conventional picture, then, physics occupies the
intersection between mathematics and observable reality. Mathematics supplies a
range of possible structures; observation identifies which of them correspond
to the behavior of our universe. Physics emerges at that intersection: not as
pure mathematics and not as uninterpreted reality, but as the mathematical
description of observable phenomena.
This distinction seems secure as long as observable reality
contributes something beyond its mathematical description. The equation is the
map; particles, fields and forces occupy the territory. But under the strongest
relational account, those entities no longer provide an independent material
content. What remains are relations, symmetries, transformations, probabilities
and laws: precisely the structure expressed mathematically. In an objectless
universe, what would the circle of observable reality add to the intersection?
Observation remains indispensable. It tells us which
mathematical structure describes our universe rather than another. But that is
an epistemic distinction: it explains how we identify the structure we inhabit.
It does not yet explain what makes that structure physical. If nothing
underlies its relations, saying that one mathematical structure is “realized”
in nature may simply rename the mystery. Realized in what?
One possible response is that physical reality contains
something mathematics alone cannot supply: not merely relations, but their
actual unfolding in time. A mathematical structure may represent change,
causation and the behavior of fire; but no fire burns merely by being
abstractly formulated.
However, this objection also postpones the problem. Is
actuality something added to the structure, or does it simply mean that this is
the structure experienced from within? And are time, change and causation
nonmathematical ingredients, or are they themselves relations within the
structure? If they are relations, invoking them does not restore an independent
physical substance. It simply adds more structure.
Under the objectless hypothesis, the conventional diagram
must therefore be redrawn. Observation still distinguishes our universe from
merely possible structures, but it no longer supplies a separate ontological
territory. Physics becomes the empirically identified region of mathematics
that we encounter from within.
The physicist Max Tegmark has defended the much stronger claim that physical reality is
itself a mathematical structure. His Mathematical Universe Hypothesis remains
highly controversial, and relational quantum mechanics does not entail it. But
the route considered here reaches Tegmark’s neighborhood without beginning from
his premise. It arrives by subtraction: remove the independent objects,
remove the substance beneath their properties, and ask whether anything
nonmathematical remains.
Physics would not disappear under this view. It would lose
one kind of priority. Mathematics would describe the possible structures;
physics would remain the empirical practice through which beings inside one of
those structures discover where they are. Experiments would still matter
because an inhabitant cannot deduce its address from the list of every possible
address.
The result is not that physics becomes useless or unreal. It
may become something stranger: mathematics conducted from the inside. The
physicist would not stand outside the structure and compare equations with an
independently furnished material world. The physicist, the instrument, the
measurement and the particle would all be patterns within the same structure,
and the physicist would learn about it through the relations available from
within.
This conclusion remains conditional. Relational quantum
mechanics may be incomplete; objects may possess intrinsic features that our
theories have not captured; physical actuality may resist every attempt to
reduce it to form. But if fundamental physics ultimately contains only
relations, and if its objects are nothing beyond stable positions within those
relations, then the question can no longer be avoided. Perhaps mathematics is
not merely the language in which physics is written. Perhaps physics is the name
given to mathematics when it is encountered from within.
---------------------
Selected sources
Rovelli, Carlo. "Relational Quantum Mechanics."
International Journal of Theoretical Physics 35 (1996): 1637-1678. https://arxiv.org/abs/quant-ph/9609002
Rovelli, Carlo. "The Relational Interpretation of
Quantum Physics." In The Oxford Handbook of the History of Quantum
Interpretations (2022). https://arxiv.org/abs/2109.09170
French, Steven, and James Ladyman. "Remodelling
Structural Realism: Quantum Physics and the Metaphysics of Structure."
Synthese 136 (2003): 31-56. https://doi.org/10.1023/A:1024156116636
Ladyman, James, Don Ross, Don Spurrett, and John Collier.
Every Thing Must Go: Metaphysics Naturalized. Oxford University Press, 2007. Oxford Academic book page
Husserl, Edmund. Ideas Pertaining to a Pure Phenomenology
and to a Phenomenological Philosophy, First Book. 1913; English translation,
1983. Internet
Archive scan.
The Questions of King Milinda, 3.1.1: "Individuality
and Name; the Chariot Simile." Translated by T. W. Rhys Davids. https://dhammatalks.net/suttacentral/sc2016/sc/en/mil3.1.1.html
Tegmark, Max. "The Mathematical Universe."
Foundations of Physics 38 (2008): 101-150. https://arxiv.org/abs/0704.0646
