What's different is their history. Sure, one couldn't distinguish them through examination. But with authenticated chain of custody, they are distinguishable. In a word, metadata.
Suppose we wanted to sell "the original" Mona Lisa to an interstellar society. How would they be able to satisfy themselves that we had in fact sent "the original" and not a perfect copy? And given that there is no experiment that they could possibly perform whose outcome would be different, why should they care?
As far as the interstellar trade goes, they would need to trust the seller. Or trust third-party experts to authenticate it. That's all that any art buyer can do.
Regarding some particular release of Word, perhaps there is a disk somewhere containing the original compiled binary. I doubt that anyone has considered such stuff memorable, but who knows? Also, given how disk storage works, that arrangement of atoms wouldn't have persisted very long. So it's not such a useful distinction for software.
But that's the whole point: if you can make atomically perfect copies, then "the particular bunch of atoms Da Vinci put together" becomes meaningless. There is no such thing as "a particular bunch of atoms" in a world where the technology exists to make atomically perfect copies. "A particular bunch of atoms" is every bit as meaningless as "a particular bunch of bits", and for exactly the same reason: atoms, like bits, are actually states, not things.
Edit: Another issue is that objects aren't immutable. Let's say that we could make "atomically perfect copies". But those copies would remain "atomically perfect" only briefly. And then they'd be historically distinguishable. And OK, I borrowed that from Hoffstadter's I Am a Strange Loop.
Do you see people paying huge premiums for "the first instance" of a digital image?
It does if that person understands physics. If you can make an atomically perfect copy, then insisting on "the original" is just as silly as insisting on having "the original" of a digital image.
> You can't just arbitrarily claim something universally lacks meaning like that.
I am not "just claiming" it. I have cited an extensive argument in support of that position:
http://blog.rongarret.info/2015/02/31-flavors-of-ontology.ht...
Yes, is it unintuitive. But there are a lot of unintuitive things in physics that are nonetheless true.
This original and perfect copy stuff is mostly about status and the monkey-human desire to get to the top of hierarchies. Aliens might not care about that, but they might not care about anything we have.
And how exactly will that trust be built up? Keep in mind that it takes 8 years to do one round-trip communication to the closest star. The closest inhabited star will almost certainly take longer than a human lifetime to complete a round-trip.
Well, for starters, they might determine that there is no other version of the painting on Earth or nearby that is said to be "the original".
They could additionally investigate the chain of custody of "the original" as far back as is feasible. It's getting hard to fool investigators here-and-now about these sorts of things; a sufficiently advanced interstellar civilization could have all sorts of additional investigative tools at its disposal.
This is simply accepting the premise that aliens have a preference for the oldest purported original over the most recent exact forgery, or alternatively have a preference for not being deceived and if promised the original want the original. If they don't care about acquiring the original, then maybe the forgery doesn't have to be that exact. "It's so exact that they should not care" is simply shifting the "that exact" line around a bit; physics doesn't quite let you abolish "provenance". Or, more finely, having promised to deliver "the original", if the seller ships "a perfect copy", has the seller committed fraud?
This is all hypothetical anyway; we have no evidence for aliens of any sort, let alone ones that want to acquire a human artifact for whatever reason. Imagining aliens sharing our own peculiar preferences with respect to art, but not granting that individual humans have different peculiar preferences, is the real problem in this thread. I don't think imagining yet more Star Trek technology is especially enlightening, but at least it's a little interesting.
Small nit:
> If you take one atom and replace it with another
This is a bit sloppy; for your argument you want to replace it with an identical atom -- no swapping of isotopes etc. -- and in an identical state with respect to its neighbours. Already historians do studies of Cs, Sr etc. isotope ratios at various depths, to study the mid 20th century history of various artifacts. They are already quite good at determining on which continent a painting was displayed or stored (or fabricated) at various times during 1945-1963.
Arguendo, the technology exists to make a "perfect copy" of an object like the Mona Lisa painting that is _locally_ indistinguishable in principle from the original. Arguendo, interstellar art forgery is profitable use of this technology. Arguendo, the knowledge of the technology and its utility in forging art is unknown to to the aliens, even though they know about the Mona Lisa and want it (that is, the one "universally" believed to have been painted by Leonardo da Vinci) rather than some traditional form of copy (that is not as perfect). That is, they care about provenance, but have not been offered (and have thus not rejected) a "perfect" copy in your sense.
The issue here is that provenance relates to the worldlines of the constituents of the macroscopic painting and whether they all converged around Leonardo da Vinci, for instance, rather than not converging around Leonardo da Vinci, but converging around the forgery machine. Since humans do not see macroscopic objects as worldtubes, human physicists are continually at risk of falling prey to a sort of slicing/threading chauvinism. In particular, the risk is that we assume that since electrons have spacetime-position independent (and covariant) characteristics, only those characteristics matter in a system involving multiple electrons. (cf. ideally we want to avoid considering large numbers of small contributions).
Boiling that down a bit, I think you're arguing in this thread that we should only consider some "present" values surface (e.g. one in which the aliens begin a test of all the traits of the Mona Lisa painting with those they have come to learn through research) and that everyone can and will ignore the surfaces on one timelike side of that.
Take the spacelike hypersurface on which the perfect copy and the original both exist but the copy only exists in one of the adjacent spacelike hypersurfaces. I think you are essentially arguing that the only choices of gauge on that surface all throw away (as "redundant degrees of freedom") the information necessary to reconstruct hypersurfaces on the "no copy exists" side, forming an information horizon.
(Geroch has a few things to say about this sort of argument in various papers, given the mild assumption of hyperbolization, and there is a wider literature on the initial values / Hamiltonian formulation of General Relativity. To be clear, I don't think you necessarily need recourse to O(h^n), n > 1 effects to poke holes in a formalization that imposes information loss; you get it only from the causal structure of a Lorentzian manifold with a tiny handful of mild additional constraints, all of which are well supported experimentally.)
Accepting for the sake of argument that a perfect copy in your sense can be made, I'd agree in an instant that we do not have the in practice ability to distinguish between copy and original if we threw both into a tumble dryer and ran the latter inside a thick-walled lead box for a couple of hours. I'd accept that nature with its Gauss-Laws provides similar (partial[1]) screening of "provenance", even. However, I'm not sure I'm convinced that a sufficiently advanced alien society could not see through these in principle, given enough effort; here we could add yet more Star Trek technology in the form of transporters, scanners, extremely long range telescopes ("enhance!"), FTL travel, etc.
Finally, if neither party can see through these in practice, the salient point is that at least one forgery exists, as does an effort by the seller of the "original" Mona Lisa to make it maximally difficult to tell that that forgery is a forgery. Caveat emptor.
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[1] Distinguishing between information conserving systems and Hawking's semiclassical information-destroying black holes.
Really? And here I was thinking that the original paper was meant to be taken seriously. (Who is William Proxmire anyway?)
> for your argument you want to replace it with an identical atom -- no swapping of isotopes etc. -- and in an identical state with respect to its neighbours.
That's right, to the limits of what is measurable anyway.
> the knowledge of the technology and its utility in forging art is unknown to to the aliens
No, I'm assuming the aliens have this technology. So they have a choice: they can receive a scan of the original, from which they can construct an indistinguishable copy, for $X, or they can receive "the original" sent to them as a bundle of atoms for $Y, with Y>>X. There is no deception involved. My claim is simply that if the aliens have any sense at all they will choose the first option.
Does Homo economicus really exist? And even if it did, the ends optimized for are chosen subjectively, aren't they? If the aliens' goal is to possess the original fsvo original, that's their business. Just as it is the vendor's business to set the price of the original at $Y at a price of $X.
AFAICT you introduce "... as a bundle of atoms ..." here. Are you proposing that rather that to "actually ship" original or copy, rather than packaging up the original carefully to keep it intact on its journey, you ship a dust that the buyer can reassemble, IKEA-style ("Interstellar Kamprad")? (Even still, they may decide that destroying the original in this way is worth the price premium you're demanding above destroying the atomically-identical copy; who's to say?)
Finally, there is some circularity in you asking $X rather than $Y, Y >> X in this case -- if you don't see the difference yourself, why would you have priced them so differently, instead of charging either $X for both or $Y for both, and then randomly choosing to send the copy or the original at that price? For instance, "Because that is the price they are willing to pay? Because that is the price the market will bear?" involve some assumptions about your a priori market knowledge.
Not here. Not yet. But maybe somewhere.
But even here, no one pays a premium for "the original" of a digital image. Originals command a premium only in the absence of technology to make perfect copies.
He has an interesting wikipedia page. I can't for the life of me figure out why his campaign paid Krugman for this paper. Perhaps he gave the campaign (and it's anti-space-exploration platform) something they weren't expecting, and they had paid in advance. :-) More likely it was Krugman making a joke. There are several others in the paper.
Krugman's paper is interesting in arguing whose clock should be used for the calculation of compound interest and makes the perfectly reasonable argument that if a common frame of reference between the planet-bound sender and receiver is avaialble, that should be used, otherwise the receiver's (and certainly not a relativistically moving transport vessel). There's really not that much physics in it, which he cheerfully admits.
He also argues that the interest rates of the trading parties would equalize with trade. Again, perfectly plausible (and, it turns out, in the intervening decades that has essentially happened on Earth). He does have a relativistic take on this, though, doing roughly a Lorentz transform on interest rates. Maybe it partially anticipated the investment into low-latency/high-frequency trading that has been popular recently?
That's only because of current limitations of our technology. Did you read the article I linked to?