He is trying to define it in a way that the people who he is interacting with here don't agree with.
It's a bit incongruous to point to an article that claims, "Arrangement is everything" (emphasis his), and then proceed to consider the arrangements of atoms in a painting without considering the arrangement of the painting with respect to other things, and especially not with respect to everything. At a chosen time coordinate, the painting and its replica (down to their subatomic constituents) occupy a non-overlapping range of coordinates in space. They are different because of the arrangement. Yet his argument is that they are the same because of arrangement (but only of the atomic components of each).
More importantly, at a time coordinate in which Leonardo da Vinci was alive and the original Mona Lisa painting existed, there was only one such painting -- any atomically perfect duplicate comes much later, and it's that arrangement in time that is important in your arguments, which I agree with.
More generally, otherwise-identical extended composite objects differ because the average of their components' worldtubes are essentially non-overlapping and diverge (or converge, depends on which way you want to think about timelike directions in this context) at different points in spacetime. In the case of our paintings the divergence happens at the tip of the paintbrush Leonardo da Vinci applied his completing stroke with, versus in the Star Trek style replicator.
The value of these paintings are position-dependent, and history-dependent. Position and history (combined they are the worldline, or worldtube for extended objects) are degrees of freedom that does not vanish by physics tricks, although it is easy to neglect them when their effects are small, and neglecting them makes calculations much simpler. But the effect of position and history on the paintings' value is not small, or at least I think it would not be small for most assessors of value (although lisper claims he would value them equally).
This is a great way to express the historical aspect in physics-speak. That is, the object isn't just a spacelike thing at some particular time. It's a spacetime thing. I can't quite imagine how one could duplicate that.
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
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
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.
- --
[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...
Actually, it would. That is the definition of "exact atomic replica".
Did you read the article I linked to?
And really, "did you read" gets boring quickly.
> ... muster a counter-argument rather than simply proclaiming with no supporting evidence whatsoever that "it's still a replica and not the original."
It's you who are missing the point. One can have supporting evidence about which is the original.
I mean, just consider the Mona Lisa. How do we know which of the many copies of that painting are the original? We arguably don't know that through any sort of measurement. Because Da Vinci and the early owners didn't have the technology to make necessary measurements. So what would we compare our results to? Maybe one could get at it through radiochemical dating, but even that's iffy.
Anyway, how we know which is the original is through the chain of custody. And that also applies to atomically exact copies.
Of course we do. We can, for example, carbon-date the wood that the original is painted on. We can do chemical analysis of the pigments. There are a lot of ways to distinguish a real Rennaissance painting from a modern copy. But (and this is the main point) only because the technology we have for making copies of paintings is not yet perfected. If we could make an atomically perfect copy of the Mona Lisa, it would be absolutely indistinguishable from the original.
"Absolutely"???
The painting is an off-axis bump on a slowly rotating roughly spherical planet; consequently it sheds gravitational radiation. The painting is effectively a rigid extended object, and thus the gravitational radiation has a corresponding characteristic mode depending on the painting's position and orientation. The mode propagates to infinity. Sure, it would take an ultra-super-hyper-advanced gravitational wave detector to pick it out at interstellar range, but it is possible in principle.
Before forgery: one Mona Lisa mode; after forgery: two Mona Lisa modes. The modes will differ because of different position and/or orientation on Earth. The position and orientation of the "original" has changed over time, pretty substantially; the latter's position and orientation is likely to change over time too. Anyone observing the relevant bits of Earth's gravitational radiation spectrum (over time, if you want to think of it that way) would be able to distinguish the two. Trouble if the buyers are already accomplished gravitational wave astronomers (we've just barely started) and keep detailed records.
I think it's easier to handwave an extremely tuned gravitational wave detector than an exact atomic duplicator or a device which determines that a pair of ~ 8kg paintings are atomically identical (especially one that does not render them atomically non-identical).
Well, lets look at the current state of the art with respect to each.
We can make non-destructive 3-D scans of objects, and we can image and manipulate individual atoms. We can fabricate 3-D structures with feature sizes a few atoms wide. That's not quite at the level of a 3-D atomic duplicator, but it seems to me to be well on the way. The machines that do these things are not yet household items, but they are not uncommon, and the technology is improving all the time.
By way of contrast, the state of the art in gravity wave detection lets us see nothing less energetic than the collision of two black holes, and there are two devices that can do this on the entire planet.
So a 3-D atomic duplicator seems much more plausible than a device that can track an 8kg object through a gravitational field at interstellar distances.
Of their surfaces. What about the internal components?
The Mona Lisa is many things but it is not very thin or flat.
There are pigments and bindings involved that are sensitive to protein structure, as well; it's not just the count of atoms (and subatomic components; there are metals involved too, and isotope ratios are fingerprints), or even their relative position sensu stricto that matters.
I'm not sure how you could go about non-destructively determining (for example) potassium radioisotope differences in the original painting's layers between the optical surface and the canvas.
> state of the art in gravity wave detection ... black holes
We can detect gravitational waves of much closer much smaller systems just fine, and did so about 105 years before Poincaré proposed them formally. It was almost eighty years later that they were cast into the current perturbative formalism though.
The amplitude isn't really the critical factor with LIGO. It's sensitive to a particular frequency band (~ Hz - kHz) that is far from that of a small off-axis bump on a planet (~ microHz). It would totally pick up a set of deadlift weights spun around by a dental drill, if you could make that work in practice. (The amplitude difference between the sites would exclude it as an astronomical signal; the final inspiral of binary black holes and neutron stars have enormous amplitude, but that falls off linearly with distance, and they are very very far away, so the amplitude difference between sites is basically nil).
> track an 8kg object through a gravitational field
Given that one knows a number of things about the object including rough position and its surrounding environment (notably one wants to know its background metric exactly, or at least the exact model metric for Earth and some subleading-order non-Mona-Lisa contributions to perturbations thereof), it gets much easier. For a painting it's not something we could do today even if we had a spaceborne observatory sensitive to the relevant bits of Earth's GW spectrum, but it is plausible that we could observe the GWs shed by Olympus Mons with current technology, for example. (It'd be expensive to build).
We have good lunar masscon data so can watch the GWs shed by those as the moon relaxes into a more spherically symmetric shape; we have decent masscon data for Earth so can in principle with today's technology watch seismic events using gravitational wave Earth observation (as opposed to astronomy) (earthquakes make Earth rounder and spin faster, so the remaining masscons shed even more gravitational radiation).
https://en.wikipedia.org/wiki/X-ray_microtomography
> We can detect gravitational waves of much closer much smaller systems just fine
So what? We're talking about interstellar commerce here.
> today's technology watch seismic events using gravitational wave Earth observation
Seismic events are many, many orders of magnitude more energetic than a painting being moved around.
Even if you had the technology, all it would take to foil it would be for the copy to move close to the original at any point in time.
(And I have to emphasize here that the point here is not that it would be easy to execute a deception. The point is that no sensible being could possibly care whether or not they have "the original" if they have to resort to such extreme measures to figure it out.)
Neat! But, can it work in principle to pick out the structure and arrangement and composition of molecules? (I'd guess yes, but am not sure).
> We're talking about interstellar commerce here
Interstellar distances are ~ pc distances; the GWs we are looking for with LIGO are >> Mpc or << pc with GRAIL/GOCE/GRACE and their follow-ons. These observatories are sensitive to sources at radically different distances, but since such sources are not what's under study (and in particular it is hard to correlate their GW signals with other observables), their signals are excluded.
One could build a GW observatory to study an exoplanet in pretty fine detail (down to whatever the appropriate word for its seismology would be); there are a lot of unknowns about exoplanets, but their mass quadrupoles are determinable independently, and GW observatories essentially just look for changes in mass quadrupoles. What's responsible for any given change is the hard part, after one has built the (distributed) observatory.
GRAIL II would have done exactly that for the moon and (it was hoped) for a couple of other objects in the solar system. GRAIL itself was an approximation of this broad technique for the moon.
> Seismic events are many, many orders of magnitude more energetic than a painting being moved around
Sure, amplitude-wise. They have very distinct frequencies though. The argument you want to advance is that there are lots of similar objects (8kg rectangles, roughly) that generate a lot of noise, and worse, some of them are in the same art gallery (and with similar orientation) as the subject of observation. Worst of all, picking it out if it never leaves the Louvre wall is implausibly difficult; but if it's moved around the gallery, and in particular, it's back does not always face the gallery wall it normally hangs on, that opens a lot of "technology will improve" arguments, such as you use with the "perfect copier".
> all it would take to foil it would be for the copy to move close to the original at any point in time
The emissions from a bump on a rotating sphere is strongly determined by the bump's position. I happily admit that you can contrive ever-greater screening, though, but the cat would be out of the bag that you were deliberately trying to frustrate distinguishing between the original and the copy.
Which rather raises the question, why? Why not just hang the copy and ship the original to the aliens as agreed?
> no sensible being could possibly care ... if they have to resort to such extreme measures
I think you have the ordering wrong; they might resort to such extreme measures because they care. Their valuation function might not be identical to yours (why the Mona Lisa rather than any other Earth painting? or any painting they could make locally, in the style of an arbitrary Earthling?).
Or, more pointedly, maybe when 'all you have to do is to try to define what "the same thing" actually means', you, other people, and aliens' efforts might lead to different definitions.
Well, yeah, they might. But I'm assuming the aliens understand physics, in which case only one definition makes sense. You can snooker the irrational and the ignorant into paying for anything regardless of what species they are.
On which note, I have this nifty bridge you might be interested in? It's available at a great price. And it is the original!
> ... It had been believed to have been painted between 1503 and 1506; however, Leonardo may have continued working on it as late as 1517. Recent academic work suggests that it would not have been started before 1513. It was acquired by King Francis I of France ...
So what we rely on here is custody records, all the way back to King Francis I. Also, why limit the discussion to modern copies? Again, from Wikipedia:
> A version of Mona Lisa known as Mujer de mano de Leonardo Abince ("Leonardo da Vinci's handy-woman") held in Madrid's Museo del Prado was for centuries considered to be a work by Leonardo. However, since its restoration in 2012 it is considered to have been executed by one of Leonardo's pupils in his studio at the same time as Mona Lisa was being painted.
Basically, it was a copy, painted at about the same time. Now imagine that King Francis I liked the Mona Lisa so much that he had one or more copies created. How would we know now which was the original? Only via records.
To ignore that would ignore the change of things over time in the meeting associated with them. Whoever has the original is the authority on the state of the original, the copies are copies derived from that Authority. They have context in meaning only because of that original.
Whoever owns that, owns the culture and the story behind the original. That is something one can purchase and it does have value even though there are no physical differences. The original will diverge from the copies if anything just because how it's capped and where it exists in the universe.
Say there was a pan galactic radiation blast of some kind. And the original. Slightly contaminated. That's part of its history now, the copies wouldn't have been similarly tainted. Just one example.
People value stories, and we work to maintain them in their continuity. That is what the original represents. It can be purchased it does have value. This is not a physical thing.
Would you pay a premium for "the original" of a digital image?
The difference lies in the state of the object. Over time, it will degrade, change, be impacted by it's environment.
A copy, can be thought of like both the photo and a physical object.
In the photo sense, a capture sufficient to exactly reproduce the object is no different from the photo. That's just data.
In the physical object sense, the moment a duplicate exists, it begins to diverge from the original, which makes the original an authority. Future copies will differ from prior ones.
From there, they would diverge.
Three things happen:
One, the data capture representing the object gets dated, and would represent the original at some point in time, not as it is today.
Two, the copy objects would also diverge from both the data and the original.
Finally, the stories related to the objects differ.
The original remains the authority on that particular object. For many things, nobody would care, and I agree with you on all of that.
However, you very seriously under estimate the value history and culture have. And you also are ignoring how a story becomes intertwined with a given object.
As an extreme example, one could say there was some war, and one of the copies of a famous painting was damaged in the war, but owned by someone who won that war at great personal cost.
Now, we've got the original, with historical value, and one copy in particular with value, both above and beyond that value any other copy may have.
For those interested in, perhaps involved in, that war, the relevance of that specific copy, with the damage marks on it, where it's at, who owns it, all differentiate that copy from all other objects.
Things that are exactly the same do not remain the same.
And where that is true, originals will have value above and beyond copies.
Consider this scenario: instead of scanning the object, sending the information to some remote location, and recreating the copy at the remote location, the copier works like this: you put an object in, and after some time two objects come out, each atomically identical to the original. Now you really can't tell which is which.
In the case of remote-copy you can tell the difference. But would an alien race really care enough to be willing to pay a lot more for "the original"?
There's actually a similar situation going on right now in the diamond market. DeBeers has spent a lot of money trying to convince people that natural diamonds are somehow better than artificial ones despite the fact that they are absolutely indistinguishable from one another (and so DeBeers is putting a lot of money into developing technology that can mark "authentic" diamonds). IMHO this is a pretty transparent scam, and people fall for it largely out of stupidity or ignorance of chemistry. I believe (or maybe "hope" is a better word here) that any society that can travel to the stars will have moved beyond such foolishness.
In other words, people aren't placing value in the arrangement of atoms, they're placing value in the context of how those atoms came to be arranged that way. The original object is a token of that context.