> This is a great way to express the historical aspect in physics-speak.

Well, it's 'worm theory' (Balashov's terminology[1]), which is one way of defining at objects in relativity (curvature is not necessary, so you can do this in Special Relativity too). It unfortunately still imposes all sorts of human chauvinism in terms of what an object is, and what a worldline (or worldtube, for "objects" that aren't strictly pointlike) is.

An alternative is to take fields (which take on some value at every point in spacetime) seriously, and declare that the universe-pervading fields on the background spacetime (curved or flat) are the only "objects". Then, if you find a characteristic pattern of field values that appears in a region of spacetime wherein its components obey some adjacency function, you can describe the pattern as a worm or as a 3d object evolving in time.

Let's consider a piece of flat 2d Lorentzian spacetime, with a single scalar field drawn as a 5x5 matrix:

1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1

Aha! A pattern! There's a characteristic value (the set of "1"s) that we want to treat as a 'worm', or worldline, of a single object represented as a "1" somewhere in space (at a given time). This means we have to slice our 2d spacetime into 1d spaces at different times.

Take the bottommost row as a spacelike 1-d hypersurface at some early time, then the next row up as a similar surface at a later time, and the next row up at an even later, and so forth. We won't lay down coordinates, and won't be precise about scale beyond "this is a small region of a larger spacetime".

Let's complicate the picture:

1 0 0 0 1
0 1 0 1 0
0 0 2 0 0
0 1 0 1 0
1 0 0 0 1

What's this? Well, like before it's just a scalar field on a patch of 2-d flat spacetime, with a different set of values.

But what's "happened" here under our slicing? Is one "1" always going left and the other always going right, and they just pass through each other? Or, alternatively, do they bounce off one another, with the "1" on the left scattering leftwards at t=3 and moving rightwards at t=4? The "1"s are indistinguishable, so it could be either! We need an interaction rule for the field, deciding when "1"s pass through each other and when "1"s bounce off each other.

We could complicate this further, by adding more fields (and more complicated fields, and interactions among the fields) on the same spacetime. Indeed, we could add all the fields (and their mutual interactions) of The Standard Model of Particle Physics. This requires specifying a set of values for each of the fields at each point in spacetime, everywhere throughout the spacetime. And indeed, the Standard Model, on flat spacetime, allows one to do exactly that.

Our conversation's Mona Lisa is in this way of thinking "just" a recognizable characteristic pattern of a vast number of values across several fields in a region of spacetime. But "recognizable" here is critical: it's not the theory picking out an object; it's a user of the theory first spotting a pattern and then deciding how that pattern evolves or moves, by fixing a gauge[2]. In the 4-d fields on 4-d spacetime block universe, there is no motion or evolution. We only get that by making choices that let one talk about what's past and what's future, and what's separated spatially within a 3d space at some time t.

When one does not have at hand all the values for all the fields across the whole of spacetime, one wants to fill in the blanks using already-known values and adjacency rules. The typical human only has access to a small range of observables, so is missing a lot of detail locally as well as knowledge about what's further away on her or his left, right, front, back, above, below, future and past. Fundamental theoretical physics to some extent is about finding useful rules that let one accurately fill in missing detail near to a point in spacetime, and about predicting the detail further away from that point. It's also about things like accurately connecting a crystallized blockworld formalism with a deterministic Hamiltonian formalism for the same spacetime with the same field content.

> I can't quite imagine how one could duplicate that

Original Mona Lisa is qualitatively characterized by some set of values that that "hang together" across a region of spacetime. One has to say pattern adjacent to Leonardo's studio and pattern adjacent to Louvre wall are "close enough to be the same". That requires deciding that many values in the spacetime between those are "noise". Cosmic microwave background photons, solar and cosmic neutrinos, and so on, don't "hang together" with the core painting pattern across such a large region. Also, one has to coarse grain somewhat, since the values of quark and gluon and electron fields at positions within the pattern (relative to something we pick out as it's centre, say) are far from the same at small scales over large spacetime regions.

Likewise, Original Mona Lisa and Duplicate Mona Lisa can only ever be "close enough", or "identical within the limits of our ability to measure, and deliberately ignoring measurable differences in position, orientation, ...".

Indeed, even comparing Original Mona Lisa complete-and-with-Leonardo and Original Mona Lisa complete-and-being-appreciated at the Louvre by President Macron, the painting at the latter point in spacetime has outgassed, dropped off flakes or chips, had environmental pollutants adsorbed onto it, and so on, and thus is not atomically the same.

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[1] Balashov, Y. (2002), "On stages, worms and relativity", in Callender, ed., _Time, Reality and Experience_, Cambridge University Press, pp. 223–252

[2] in the relativity sense, https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/ cf. https://en.wikipedia.org/wiki/Coordinate_conditions?oldforma...