Objectivity Between Perspectives

On Lorentz, measurement, and what objectivity means

Two physicists describe the same set of events, one of them aboard a craft moving rapidly relative to the other. They disagree about nearly everything one would first want to call a fact. They measure different lengths for the same rod, different times between the same two events, and if those events are spacelike separated they may even disagree about which came first. Yet they do not disagree about the physics. Translate one physicist's measurements into the other's by the Lorentz transformation and everything falls into place, and certain quantities turn out to be the same for both: the speed of light, and the spacetime interval that separates two events. What set their descriptions apart was perspective-dependent. What they shared was whatever survived the passage between their perspectives.

This small example carries, to my mind, a large idea, and the whole framework I work with rests on it. We tend to imagine the objective as what exists independently of any perspective at all—a view from nowhere, a gaze that sees the world without standing anywhere in it. But we have no such gaze, and physics does not require one. The objective turns out instead to be what survives translation between perspectives: not what is seen from above, but what remains when one moves from one perspective to another. And since it is precisely such passages that physics handles all the time, the observer's perspective is no obstacle standing between us and the world. It is, on the contrary, the point from which physical content can be determined at all.

Something about symmetry follows from this. If the objective is what is preserved under a change of perspective, then symmetry is not an assumption added to physics from outside but an expression of what objectivity means. This is what I mean by observer equivariance: the physical content of a law is preserved when the perspective is transformed. How far that principle reaches is something I return to below.

The observer in the various theories

It is worth looking more closely at what the word observer actually means in physics. In relativity an observer is a frame of reference, a set of rulers and clocks in a given state of motion. In gauge theory there is a related, though not identical, pattern: a choice of local description, a gauge, can be altered without altering the physical field. In quantum mechanics the observer usually appears through the measurement context, that is, through which quantity one chooses to measure. In every case what is at issue is a perspective, a definite standpoint from which something is described.

The same pattern recurs in each case. Different frames disagree about lengths and times but agree about the interval. Different gauge choices give different potentials but the same field. Different measurement contexts give different descriptions, but these descriptions are not arbitrary; they are constrained by the structure that relates the possible contexts to one another. The choice of perspective makes a visible difference to the description and none to the physics, and the objective is what remains once that difference has been factored out. This is why the observer is more than a technical detail. It is the point from which physics is formulated, and objectivity is what its various points have in common.

What happens, then, in a measurement?

The sharpest test of all this is measurement in quantum mechanics. Behind the usual answers lies a division that is rarely stated outright: a mind on one side, a reality on the other, and a dispute over which acts on which. The division is Cartesian, and two opposing camps share it. One holds that the particle makes up its mind only when someone looks, as though consciousness made the world real by regarding it. The other objects that the mind cannot act on matter at all. But both presuppose the very two sides they are quarrelling over, and the question of whether consciousness creates reality is already posed from within the division. The relational view does not begin there.

What happens in a measurement is that a relation acquires definite content. This does not mean that two finished things are joined together. The relation is what is primary, and what we call the particle and the apparatus acquire their determination only within it. The outcome was not hidden in advance, waiting to be uncovered; it is fixed in the relation and holds only with respect to it. This is what is real in the measurement, and it belongs to the structure rather than to anything that would precede the relation. We should not picture a finished reality on one side and a registering gaze on the other.

There is an old image in Leibniz that helps here, if one borrows it with care. Leibniz imagined that reality consists of windowless perspectives, which exchange no content with one another and yet mirror the same world, coordinated through what he called a pre-established harmony. The perspectives open no windows toward each other; they stand under a condition requiring their descriptions to hang together. Measurement is not a window opening between gaze and world, but a relation being bound under that condition. Harmony, but without causal exchange.

The collapse one usually speaks of then becomes something less dramatic. Before the measurement the description holds several possible determinations; afterward it is bound to the outcome that was actualized in the relation. That transition is not a second physical event on top of the first, but the perspective's bookkeeping of the fact that the relation has acquired definite content. The measurement adds nothing to the world through some special mental force, but neither is it a mere reading-off of a value that already lay finished behind the perspectives. The possible determinations belong to the structure; that one of them is the actual one holds only with respect to a perspective.

The perspective is therefore not a mere point of readout. It has a side of its own: the experiential, which belongs to the measurement and is not found in the shared structure as such but in the perspective itself. The objective is what several perspectives can share, but that there are perspectives at all, each with its own being, belongs to the picture just as much.

This is why different observers can have determined different things at once, since an outcome holds with respect to the relation it is determined in. That is the whole point of thought experiments like Wigner's friend. The trouble arises only if one believes that one of the outcomes must be the true one seen from nowhere; remove that vantage and the paradox dissolves. The question becomes instead whether the distinct relations are comparable—whether they translate into the same structure once all the registrations and interactions are counted in. This is no retreat into subjectivism. The perspectives are not arbitrary opinions about some underlying thing, but the binding points through which structure comes to be determined at all.

Here it is worth comparing with QBism, which my framework resembles in several ways. Both deny that the quantum state describes a collapse out in the world, and both take the first-person perspective seriously. In QBism, states and probabilities are tied to an agent's expectations about her own experiences, and so far I am with it; in that sense QBism takes hold of the perspective's own side. But QBism stops at the perspective. My framework begins there, and then asks what remains when perspectives are compared. Perspectives stand in definite relations to one another, and once one projects away what distinguishes them, something remains that no longer belongs to any single one of them but is shared and objective. The symmetry principle is what this projection preserves: it says that distinct perspectives are not sealed-off vantage points, and that the physical content is whatever the relations among them leave invariant. Without such a requirement, nothing distinguishes structural equivalence from arbitrary variation. With it, objectivity is not a view above the perspectives but the structure of how they hang together.

Symmetry as principle

The point is not merely philosophical. The same principle of invariance seems, moreover, to point toward several of quantum theory's apparently independent postulates: the squared probabilities of the Born rule, the constraints on which symmetries are admissible according to Wigner, and the uncertainty relations understood as a Fourier condition tied to translations of perspective. Three things usually postulated separately would then turn out to be expressions of one and the same idea. How the principle of invariance can support them is something I try to show in a more technical article: Observer Equivariance as an Interpretation of Quantum Theory.

The observer as ground

We began with two physicists who disagreed about lengths and times but agreed about the interval. What they shared was not a picture standing above them both, but what remained when one translated between their perspectives. The same figure has recurred all the way since. The objective is not a view from nowhere. It is what survives the projection from perspective to shared structure, and the observer's perspective is not an obstacle in front of the objective but the condition for its being determined at all.

But the two physicists are not merely points of readout. Each sees from somewhere, and seeing from a place has a side of its own that does not carry over into the shared structure. Reality has, in this picture, two faces: what the perspectives share, and the fact that there are perspectives at all, each with its own being. Physics speaks of the first and is silent about the second, but its silence is not a denial.

Where this points in turn I leave open. But this is the form I believe in. Objectivity lives between the perspectives, not above them, and each perspective still carries something of its own that does not dissolve into the shared. It is neither a world seen from nowhere nor a world enclosed within each gaze, but a structure that shows itself only between the perspectives from which it can be determined.