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Imagine a visiting alien accidentally spilled a bucket of inverse matter (a substance I made up just now) on the planet Earth and this stuff will annihilate with ordinary matter to produce neutrinos with perfect efficiency, erasing the earth.

Feeling remorseful the alien 4D printed the Earth in its exact state just seconds before the destruction took place, atom by atom.

How can we possibly tell that we are a copy of the original?

Additional information:

  • Satellites and sensors on Earth were returned to that exact moment.
  • This only affects the region of space up to the orbit of the moon.
  • The irresponsible alien simply retreats silently leaving no trace of its presence and action.
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    $\begingroup$ "The alien 4d printed the Earth to the exact state": The no-cloning theorem by Wootters, Zurek, and Dieks (1982) says they cannot. $\endgroup$ – AlexP Jan 5 at 11:13
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    $\begingroup$ @AlexP Every alien craft is equipped with WZD-compensators. $\endgroup$ – PTm Jan 5 at 11:34
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    $\begingroup$ @AlexP since they use made up inverse matter and that the no cloning theorem only matters for the fluff and not for the question itself, why bring it up? $\endgroup$ – Demigan Jan 5 at 11:58
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    $\begingroup$ Fun fact: if, instead of spilling a mere bucket of antimatter on Earth, the aliens somehow managed to completely annihilate the entirety of it, they'd be releasing 2. trillion more energy than is required to gravitationally unbind the Sun (AKA reduce it to an ever-expanding cloud of hydrogen and helium). Even though most of it misses the Sun, enough of it gets delivered to gravitationally unbind it anyways. Although, (somehow) using neutrinos instead of photons as the reaction product might be enough to keep the Sun in one place. $\endgroup$ – John Dvorak Jan 5 at 20:07
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    $\begingroup$ Arthur Dent is no longer on it. $\endgroup$ – endofline Jan 5 at 20:58
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Even the satellites and every sensors on Earth were returned to that exact moment and this only affects the entire region of space up to orbit of moon (...)

Everything above the Moon will seem to have changed position instantaneously in a very weird manner. All the signals picked up by the Deep Space Network will be coming from the wrong places. Solstices and equinoxes will happen at the wrong dates and times.

We might not be able to figure whether we have been teleported or whether we are a copy, but this will be a discussion that's way more popular dark matter vs. MOND.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Monty Wild Jan 9 at 1:07
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Even if the alien does not create a perfect copy of the quantum state, we will not know.

First, 99.99% of all people (possibly more) couldn't tell anyway if the copy wasn't quantum perfect. As long as the copy is perfect within maybe millimeter scale or so (say pico if you will), few will observe it at all, of those only few will notice, and of those who do, most will do it away.

Second, from inside a system, there is no way we could tell "truth" anyway. In order to notice that something has changed, we would have to have access to external information. That's true for every system. Luckily there's an entire universe around us, isn't there! While that solves the problem in theory, in practice things are much different.

Easily observed, or not that easily observed details such as the sun being not in sync with every clock on the planet, or stars "jumping" in the sky, or deep space radio signals having a hitch will not do.

Humans are excellent at denying truth, and they are even better at coming up with a plausible explanation when their beliefs are shaken. In fact, that's probably what humans are best at.

I've recently had the opportunity to observe this on a person with ischemic stroke. That person was motorically 100% functional, but cognitively entirely dysfunct. He had his tablet computer in his hands and was typing random characters and approx. 200 emotes (whatever the onscreen keyboard creates when you keep tapping randomly) into the email program's To: field (no network access, mind you). The person was deeply convinced of knowing what he was doing, and it was an important task (without being able to tell what).
A week and half later, that same person was, again, fully functional. Still, even today, he denies the externally observable truth, insisting on having done something orderly, and important (without being able to tell what). Is that man a liar? Well no. From his point of view, from what's stored inside his brain, that is indeed the exact truth. Even if you showed to him a video recording of what happened, then this couldn't be true. Because, well, that's obviously not what happened, the video must be fake.

Remember the famous garbage-guy scene from the "Voyage Home" Star Trek movie:

(strong wind, a garbage can gets flattened, a hatch opens out of nowhere, weird people come out of it, hatch closes and is gone)

Did you see that?!!
No. And neither did you, so shut up.

Worded differently, if your clock is wrong, then you should probably adjust it. If you just saw the stars jump in the sky, then you should igore it, or maybe see a neurologist. If the guy next do you saw the same thing, it's folie à deux. Or it was a reflection of, something that flew by. Weather balloon?
If the government's clocks are all wrong, then some stupid bureaucrat fucked it up. Or the global, uh, Bilderberger, conspiracy did it so they can, I don't know, whatever they're doing. Control your mind, steal your underpants, whatever.
And unluckily, the crazy explanation isn't even as unlikely as one would wish. For example, GPS being suddenly "wrong" is a thing that demonstrably happened during the Gulf wars. Aliens? Well no. Bush and Schwarzkopf.

Occam's Razor applies in its mundane (wrongly quoted) form: The simplest solution is always the correct one. Many people go even further, and turn it into: The least disturbing explanation is always the correct one.

So... if something is suddenly definitively weird, then the people observing it either made a mistake, or they're crazy. If there exist too many people worldwide having observed it, and hard, undeniable evidence exists so this solution can be ruled out, then alright, something did happen, but it was a perfectly normal natural phenomenon that we just don't understand yet.

No way has Earth with everybody on it been duplicated by aliens. Because, hey, that is just a crazy, stupid idea. Being external controlled by aliens? Duplicated? Go see a psychiatrist.

Whatever it was, it's most definitively something that happens naturally every few million years, we only just observed it for the first time, and we do not understand it yet. Some, whatever, interference shifting our space-time frame a bit. While we do not have an explanation at hand, we will work out a perfectly normal, non-disturbing explanation related to... black holes, or dark matter, or something.

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    $\begingroup$ I love this answer! Are we sure we're not actually the enslaved humans of "The Matrix"? Are you sure you're actually moving your hand in front of your eyes right now? You'll never know. $\endgroup$ – Simone Jan 7 at 9:57
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    $\begingroup$ "As long as the copy is perfect within maybe millimeter scale" Pretty sure that if the precision was one millimeter, all computers would break and everyone would die. $\endgroup$ – Tomáš Zato - Reinstate Monica Jan 7 at 10:46
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    $\begingroup$ If every single professional and hobbyist telescope suddenly pointed the wrong way, and pointed the wrong way in the exact same way, it won't be "did you see that? No? Okay nevermind." It would be "Hullo, I'm Scott Manley, and for the last two days, scientists have been puzzling over some very strange events in the sky." $\endgroup$ – Ghedipunk Jan 7 at 16:11
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    $\begingroup$ I disagree with every word of this answer. You seem to paint with this broad brush that only has the ability to assume people sweep things under the rug, and while that may be true about you, there is a full spectrum of people out there between seeing a star flash weirdly and assuming it is aliens to people who consider all possibilities. Having all scientific observatories, regardless of domain, SIMULTANEOUSLY notice a jump in time, by the same amount, is not something that the scientific community would just sweep under the rug. It wouldn't cause mass panic either, but it would be discussed. $\endgroup$ – Muuski Jan 7 at 17:19
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    $\begingroup$ @Muuski hey, do you have a better explanation of what's been happening at Tabby's, than a Dyson swarm under construction? And yes, it would be discussed - in the scientific community. The public would sweep it under the rug as shared psychosis, at least until some scientist spoke in the newspapers, "hey, we saw it too - and no, we don't have any idea what it was either" $\endgroup$ – John Dvorak Jan 8 at 14:59
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You can't.

Heraclitus, a Greek philosopher born in 544 b.c. said, “No man ever steps in the same river twice, for it's not the same river and he's not the same man.”

Though the Nile is never the same Nile Ramses saw, we still call it the Nile.

Replacement of molecules happens in every moment in almost every system, and we don't tell any difference.

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    $\begingroup$ Downvoting as this misses the larger frame of reference inherent in the problem. The replacement only happens on a planet-wide scale, so the rest of the observable universe would be (observably) different than we expect. Humans are much better at looking at large or distant things than small ones. We can't see individual molecules in a stream, but we can see distant stars and galaxies "jump" to a new position in the sky $\endgroup$ – D.Spetz Jan 6 at 15:16
  • $\begingroup$ @D.Spetz It still remains a philosophical issue, rather than a scientific one. Even if the scenario plays out the way it was asked, it's not clear that that is a "copy" in any meaningful sense. $\endgroup$ – John O Jan 6 at 15:33
  • $\begingroup$ @D.Spetz, I don't see how one can infer from "the stars have jumped in the sky" that "we have been copied! $\endgroup$ – L.Dutch - Reinstate Monica Jan 6 at 15:36
  • $\begingroup$ @L.Dutch-ReinstateMonica - unless someone was reading this thread while it happened! $\endgroup$ – colmde Jan 7 at 9:58
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Perhaps this helps?

In one of the Star Trek (TOS) novels (I forget which one: either Spock Must Die, or The Price of the Phoenix), they make reference to an organization within the Federation vehemently against the use of transporters for people.

The point was that transporters never technically "move" anything; they operate by destroying the item and rebuilding it elsewhere.

The problem with moving people was whether or not the copy had a soul. Hence the organization to stop it, however small a group they were, were freaked out about having everyone who ever went through a transporter possibly having been killed on the spot the very first time they used it.

So just as with this story, the issue in your case has to do with what "copy" means.

In that discussion one of the Enterprise crew pointed out:

"As Mr. Spock once said, 'A difference where there is no difference, is no difference.' "

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    $\begingroup$ This is an interesting insight - can you be more specific as to how this pertains to OP's scenario? What does Star Trek tell us about identifying copies? As it written, this post is an awesome comment and might work better in the comments section. Right now, it doesn't provide a direct answer. $\endgroup$ – Zxyrra Jan 6 at 2:47
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    $\begingroup$ @Zxyrra I think that it does. $\endgroup$ – Lightness Races in Orbit Jan 6 at 15:34
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    $\begingroup$ [...]the alien 4d printed the Earth to the exact state just seconds before the destruction took place atom by atom and how can we possibly tell that we are a copy of the original? "Direct" answers here are nebulous; we're talking about fiction most of the time. Hence a comment on what the need to discover the difference is (to them) seems more than apropos to me. If there was no need to discover the difference, why would the copied populace's question "are we the same" matter? $\endgroup$ – tgm1024--Monica was mistreated Jan 6 at 15:36
  • $\begingroup$ @tgm1024--Monicawasmistreated Ah, that makes more sense. $\endgroup$ – Zxyrra Jan 6 at 16:43
  • $\begingroup$ if a Star Trek-style transformer were possible, it would also be possible to copy without destroying the original. And given human nature, someone would be doing it, even if illegal. $\endgroup$ – WGroleau Jan 7 at 16:42

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