An advanced alien species clones me on the atomic level, lines me up exactly across myself, in a perfect mirrored room:
I stare at myself for a second. Then, as a soft “hi” escapes my mouth, I notice that my clone does exactly the same. Every motion, everything, is mirrored.
In this experiment, we assume a perfectly deterministic psychological state: eg, given the same conditions, a person will always do exactly the same. (scientifically, that makes most sense to me)
Together with my clone, I’m trying to devise how to escape this unfortunate situation: eg, how to untangle us mirroring each other’s motions.
The first idea we devise is to run into each other. We hope to apply Chaos Theory to the extent where both of us would fall in a slightly different way, and thus we would no longer be perfectly mirrored as such. But, if my understanding of physics is correct, our perfect opposing forces cause us to stumble and fall in perfectly mirrored ways.
For the second idea, I fetch a coin from my pocket. Just a coinflip won’t work: we’d apply the same pressure to both our coins, and they’d land in the same spot. The idea is to number each corner of the room, and to decide the corner we’re both going to through two coinflips. The corner we should go will be further away for one of us, thus breaking the mirror.
But, as we try to number the corners, we notice that we give the same number to opposite corners all the time. When I point at a corner, my mirrored self starts pointing at the opposite corner and giving it the same number.
I slump down to the ground. Will I be mirroring this perfect copy of myself for eternity? Or is there a way out?
As far as my understanding goes, in a deterministic framework, it is impossible to escape this scenario (eg, break the mirroring). In my opinion, determinism is separate from free will (eg free will is possible even when everything is deterministic). Am I correct or am I missing important things?
If you’re in a classical-physics simulation that’s guaranteed to have rotational symmetry, then yep, you stay mirrored.
In any messy real world setting (even ignoring quantum mechanics), chaos theory would indeed kick in pretty quickly—the thermal jostling of air molecules, or radiation from outside, would slowly lead to neurons firing at slightly different times.
But maybe the most sciencey way to unmirror yourselves is to suppose you have the ability to prepare and measure an entangled quantum state. E.g. suppose you meet in the middle and put the spin of a pair of atoms into the state |up,down>+|down,up>. This state is rotationally symmetric (for the nitpickers, I think I’ve implied the atoms have integer spin), so you can do this, but when you measure the atoms you’ll get opposite results.
With quantum, you can go further: even if you’re instantiated in a universe that starts out perfectly rotationally symmetric, as long as we’re not modifying physics to guarantee the symmetry is preserved over time, then the vastly overwhelming majority of quantum behavior will not have spurious correlation between rotationally symmetric positions, meaning that the rotational symmetry will almost instantly be lost at the nanoscale, and then it’s just some chaos away from having macroscopic effects. You can think about this under the many worlds interpretation: there’s a vanishingly small fragment of the wavefunction where every time an atom collides with another atom in one position, the quantum random portion of the collision’s outcome is exactly matched in the rotationally symmetric position. From the outside, this means that even picking which classical slice of the wavefunction is still symmetric requires you to specifically encode the concept of symmetry in your description of what slice to take. (I don’t quite know the quantum math necessary to write this down.) From the inside, it means an overwhelmingly high probability of nanoscale asymmetry, and from there it’s only chaos away from divergence.
I expect it would still take at least a few seconds for the chaos in your brains to diverge enough to have any detectable difference in motor behavior. If we were instead running the same trial twice rather than putting two instances in the same room across from each other, I’d expect it would take slightly longer to become a macroscopic difference, because the separate trials don’t get to notice each others’ difference in behavior to speed up the divergence.
Importantly, assuming many worlds, then the wavefunction will stay symmetric—for every classical slice of the wavefunction (“world”) where person on side A has taken on mindstate A and side B has mindstate B, there’s another world in which person on side A has mindstate B and vice versa. This is because if many worlds is correct then it’s a “forall possible outcomes”, and from the outside, it’s not “randomized” until you pick a slice of this forall. It’s unclear whether many worlds is physically true, so this might not be the case.
Can you symmetrically put the atoms into that entangled state? You both agree on the charge of electrons (you aren’t antimatter annihilating), so you can get a pair of atoms into |↑,↑⟩, but can you get the entangled pair to point in opposite directions along the plane of the mirror?
Edit Wait, I did that wrong, didn’t I? You don’t make a spin up atom by putting it next to a particle accelerator sending electrons up. You make a spin up atom by putting it next to electrons you accelerate in circles, moving the electrons in the direction your fingers point when a (real) right thumb is pointing up. So one of you will make a spin-up atom and the other will make a spin-down atom.
Well, I was going by the original post where you’re rotationally symmetric, not mirror-symmetric. But for mirror symmetry, pick the mirror plane to be the z direction, then you just make your spins either both +z or both -z.
Mirror symmetry is not rotational symmetry.
The post has been edited since my answer. See two comments below, or five answers below.
In our universe’s physics, the symmetry breaks immediately and your clone possibly dies, see https://en.wikipedia.org/wiki/Chirality
A very clever answer. Although I worry it might not actually carry through. My understanding is that chiral molecules react differently with other chrial molecules. So that if molecules A and B react to give C then the mirror of A reacts with the mirror of B to give the mirror of C.
So the clone might be immune to snake venom (yay!), but all kinds of everyday foods might effect them as if they were snake venom (boo!). But if the clone has (behind them) a whole mirror-world ecosystem then I think they are OK.
There is some particle physics stuff that is believed to break this symmetry intrinsically, without needing another Chiral thing to react with. [I find this really hard to believe, but apparently it is so]. So I suppose over a very long timescale some of those obscure particle interactions might break the symmetry.
Funny, I’d assumed (without really thinking about it) that it was a ROTATED copy, not a front-to-back transposition, even though the text actually said “mirror image”. A flipped copy would have a number of inconsistencies, like which hand it’s comfortable to extend in greeting, or even which side their shirt buttons on.
If this room is still on Earth (or on any other rotating body), you could in principle set up a Foucault pendulum to determine which way the rotation is going, which breaks mirror symmetry.
If the room is still in our Universe, you can (with enough equipment) measure any neutrinos that are passing through for helicity “handedness”. All observations of fusion neutrinos in our universe are left-handed, and these by far dominate due to production in stars. Mirror transformations reverse helicity, so you will disagree about the expected result.
If the room is somehow isolated from the rest of the universe by sufficiently magical technology, in principle you could even wait for long enough that enough of the radioactive atoms in your bodies and the room decay to produce detectable neutrinos or antineutrinos. By mirror symmetry the atoms that decay on each side of the room are the same, and so emit the same type (neutrino or antineutrino, with corresponding handedness). You would be waiting a long time with any known detection methods though.
This would fail if your clone’s half room was made of antimatter, but an experiment in which half the room is matter and half is antimatter won’t last long enough to be of concern about symmetry. The question of whether the explosion is mirror-symmetric or not will be irrelevant to the participants.
Assuming you’re somehow gravitationally/rotationally symmetrical as well, and that quantum uncertainty doesn’t matter, you are probably right. I strongly suspect that this pile of assumptions is not just infeasible, but impossible in our current universe.
I think the classic answer to the “Ozma Problem” (how to communicate to far-away aliens what earthlings mean by right and left) is the Wu experiment. Electromagnetism and the strong nuclear force aren’t handed, but the weak nuclear force is handed. Left-handed electrons participate in weak nuclear force interactions but right-handed electrons are invisible to weak interactions[1].
(amateur, others can correct me)
Like electrons, right-handed neutrinos are also invisible to weak interactions. Unlike electrons, neutrinos are also invisible to the other forces*[2]. So the standard model basically predicts there should invisible particles wizzing around everywhere that we have no way to detect or confirm exist at all.
Besides gravity
The premise seems like a hard ask, though if we assume precise control over all shapes on all ‘observable’ levels, I feel there is always background noise, radiation of different kinds, so when you are not in the same position there will be slightly different values reaching you.[edit: so when this reaches biological systems it will always affect them slightly. So you could probably just sit there, only if we are looking for an observable threshold you might be there a while depending on levels]
As a human, you react to what other humans do around you. Your reaction algorithms may not allow two copies of you to mirror each other.
The clone is not mirrored, so you are not in front of a mirror you, but a rotated you.
I don’t think (1) works like that. Because both our reaction algorithms would yield the same actions?
Regarding (2): I suppose for this to work, the clone should be mirrored as well? I guess the advanced aliens can do that.
Ok, let’s say the clone is mirrored.
For (1), think about this concrete toy example: say the first thing you do is raising your right hand. The mirror clone rises his left hand. Then say you have an instinctive reaction behaving in this way:
if I see a person raising his right hand, I repeat that movement.
if I see a person raising his left hand, I do nothing.
So the next thing you do is nothing, while the next thing the mirror clone does is raising his right hand, which differentiates you from the clone.
HOWEVER, I now realize I was wrong: the mirror clone’s notion of left-right is mirrored as well.
Maybe you could treat each other as two parts of the same system. It hurts to pull your hair out so suppose you had some scissors too. You could cut your hair, and scatter them on the floor. Wind is really sensitive to initial conditions (consider brownian motion) so suppose you blow the hair and you both decide to pick them up. Since you’re different distances to the hair strands you could break the symmetry?
Step outside of the room. You’ll see the world from different locations, symmetry will be broken. IDK why you’re interested in a situation that can’t happen, perfect sensory symmetry for long periods.
Free will is a contradiction in terms, so I don’t think it’s worth fussing over exactly that wording. What people ususally mean by free will is that their decisions truly affect the future. If you take “they” to refer to their brain state, this is pretty clearly true on that interpretation. I think other definitions of self are incoherent and that one is pretty straightforwardly what we mean by “me”, so I agree that “free will” in its common definition is compatible with determinism.
Just physically interact. Push each other around. You’ll be building up tiny differences, and those interactions will magnify those differences.
Also, smash the environment. I originally read you post as the room had mirrors for walls, and that’s what made me think of it.
I don’t think that your question is quite makes sense. The world is non-deterministic. There are macroscopic patterns that are generally symmetrical, but not at the deepest levels. For instance, there is the cosmic gravitational background, where space is sort of wobbling around because of the gravitational waves from other things in the universe moving about, similarly to ripples on a pond. Even if you controlled for everything in the room, you could not control for those differences. The only way for that room to be perfectly rotationally symmetrical, is if the universe is rotationally symmetrical relative to that room.
THEN you can talk about quantum field theory.
Given your clone is a perfectly mirrored copy of yourself down to the lowest physical level (whatever that means), then breaking symmetry would violate the homogeneity or isotropy of physics. I don’t know where the physics literature stands on the likelihood of that happening (even though certainly we don’t see macroscopic violations).
Of course, it might be an atom-by-atom copy is not a copy down to the lowest physical level, in which case trivially you can get eventual asymmetry. I mean, it doesn’t even make complete sense to say “atom-by-atom copy” in the language of quantum mechanics, since you can’t be arbitrarily certain about the position and velocity of each atom. Maybe saying something like “the quantum state function of the whole room is perfectly symmetric in this specific way”. I think then (if that is indeed the lowest physical level) the function will remain symmetric forever, but maybe in some universes you and your copy end up in different places? That is, the symmetry would happen at another level in this example: across universes, and not necessarily inside each single universe?
It might also be there is no lowest physical level, just unending complexity all the way down (this had a philosophical name which I now forget).