# How to break perfect symmetry? Having a conversation with a duplicate

You wake up and find yourself in a vast expanse of emptiness. As you look off into the distance you see a faint speck contrasting with the pale white expanse. Lacking anything better to do, you decide to head for it.

As you start walking, you feel that the distance between you is closing unusually quickly. It does not take you long to realize that the speck is moving towards you to. Before long, you begin to distinguish details. It is not a speck, but actually a person. You call out, but no response. Perhaps they did not hear you. As you get closer you decide to make another attempt. As you call you seem to hear something coming from the other person, and quickly quiet down.

They do the same. After a few false starts you decide to just keep walking towards them, as they begin to walk towards you. As you draw closer you begin to distinguish details, this person looks rather familiar. Suddenly it dawns on you: they look just like you. You start, and they stutter as well.

"The only way to straighten this out is by talking" you think, so you both decide to close the distance. As you draw closer you attempt to start a conversation, but every time you say something they say something too. You stop to let them continue, and the halt as well. Finally, you are face to face. It is almost like looking in a mirror. You turn to look at a different angle, and they turn as well. You say something and they do too. You walk around to your left, and they walk around to your right.

It is then that you realize that you are perfectly synchronized. Every time you try to speak, they say the same thing. Everytime you scratch your head, they do as well. You begin to wonder, if you are so well synchronized, surely the same thoughts are running through your head. You try to figure a way to break this symmetry, any way that you can actually hold a conversation with your other self. One where you are both not cutting off and falling silent.

How do you do it. How do your break a perfect mirror without outside help?

Edit: The universe isn't necessarily deterministic, at least I feel that it doesn't require it. But otherwise for all intent and purposes the 2 you/mes are mirrored down to the quantum level.

• Is it mirror symetry or rotation simery? That is, if it is mirror simetry I extend my hand the duplicate does so in such way that own hands touch. On the other hand * wink, wink * if it is rotation simetry I extend my and and I can touch its shoulder while the duplicate touches mine - also in rotation simetry we can shake hands. Commented Sep 25, 2016 at 7:41
• :) it's rotary, you could effectively walk circles around each other. Commented Sep 25, 2016 at 7:42
• So their initial state, including quantum states of the atoms in air are exactly the same right? Otherwise, they will drift apart slowly and after a while synchronization would break. Commented Sep 25, 2016 at 8:38
• I disagree with the close vote because this is not opinion-based. This is quite the opposite: the setup is quite clear and precise, and any valid answers will be of the sort "do this, then do this, then this, and voila". Commented Sep 25, 2016 at 11:02
• Well, I'd say you'll finally recognize that this is not a duplicate of you, but it is you, and you're in a space with unusual geometry. Commented Sep 25, 2016 at 12:20

# You let chance decide

You can do it, but you need some accessories. You need something like a coin, and something to stick them together with, let us say a chewing gum. So you each stick the gum to the coin, and then press the two coins together.

Then you jointly thrown the merged coins in the air, and let them fall.

The faces of the coin have an up and a down. The one of you who gets the "up" side pointed at them says "up", the other says "down".

And there you go, you have broken the symmetry.

Even if this universe is rotationally mirrored down to the last atom, this will break symmetry because of Heisenberg's Uncertainty Principle. Because even if you assume that the coin will be tossed up so perfectly mirrored that it does not even rotate, once it hits the floor the uncertainty principle adds sufficient amount of randomness to break the symmetry.

I cannot do this calculation myself, but my professor in physics at the university showed that the uncertainty principle makes the universe non-deterministic. She put it this way: make a lead pencil as perfectly sharp as you can, and balance it on its tip on a hard surface (and yes we are assuming Spherical Cow-conditions: vibration free surface, in a vacuum, with no forces except perfect gravity acting on the pencil once it is standing up). Even if you manage to get it there, the uncertainty principle will eventually nudge the pencil far enough out of balance to make it fall over. You can even determine the average time it will take for the pencil to fall over that way.

If the both sides were so perfectly mirrored that the coins always hit the floors at perfect symmetry and bounced straight up, ending up standing on its narrow side, then the Uncertainty Principle would be out of whack, and you have a universe that breaks the laws of physics, i.e. it is magic. If it is magic, well then that is the way it is and we cannot answer the question. But assuming normal laws of physics are in play, then we can break it this way.

Also note: the uncertainty principle will eventually make the copies diverge anyway, because of the butterfly effect. The coin toss just speeds up the process.

• Comments are not for extended discussion; this conversation has been moved to chat. Commented Sep 25, 2016 at 19:38
• If you both stuck two coins together with gum, the coins would mirror each other and would be showing the same face. You'd have to coordinate with your duplicate to pick up a single coin. Commented Sep 26, 2016 at 3:54
• @ApproachingDarknessFish Read the answer closely again. Commented Sep 26, 2016 at 4:02
• @MichaelKarnerfors Ah, clever. But what if the coins fall so that they're facing exactly sideways to both of you? Commented Sep 26, 2016 at 4:09
• @ApproachingDarknessFish Throw again until you get a result. Commented Sep 26, 2016 at 4:10

Since you and your duplicate are so in-tune, after some thought it occurs to both of you simultaneously that conversation is unnecessary - you already know exactly what each other would ask/say. As such, you both realise that the mirror is, in essence, already broken.

Staring at one another while deep in thought, it also occurs to you that it would be impossible to stay together - the moment you decided to start walking it is a certainty that your paths would diverge. As such, you resolve not to waste time on this and to devote your energies to exploring this strange landscape.

At the same exact instant, both of you make a sharp turn to your respective rights, and march off without so much as a backward glance. Good luck to me, then, you think with a slight smirk on your face, and off you go to an uncertain future ahead.

• To me this answer makes the most sense,as the OP didn't give any indication that the person and their duplicate will ever diverge Commented May 28, 2018 at 10:00

## Symmetry only in the persons

Let's say that the duplicate thinks exactly as I do. With that in mind deciding to follow the other is pointless... we cannot pretend to have the other escort to where they came.

We would have to consider some way to decide to distinguish ourselves. Perhaps "waiting a random time" won't work as we consider the same period of time equally random. We cannot just go cross paper scissors or toss a coin, because we both pick the same thing.

Now, unless we are saying that the universe has this kind of symmetry, there are going to be some environmental differences. If we can think of a way to give us Id based on the environment we could figure out an order...

For example, if we are on a planet we could use the brighter star on the sky to tell what side should go first. Perhaps there is none visible, or it isn’t clear on what side the star is. Then it is a matter of waiting until it does. Alternatively we could look at the terrain and find higher ground and use on whatever side it is to decide who goes first.

It should be noted that if we both think the same things, then we both consider these ideas in this order and use the same criteria to decide.

Can we roll dice and will they roll the same? This is an important question, because perhaps the dice we pick aren’t identical, they could eventually roll something different. Saying that if we both bring dice and both dice roll the same all the time is saying that the symmetry is not in us, but in the universe…

## Symmetry in the universe

Now, if we are in some sort of weird universe where this symmetry exists, things are different. Perhaps in this universe if you travel far enough you find this boundary from where it has another identical copy. This symmetry is complete, and covers all phenomena from background cosmic radiation to the movement of astral bodies.

And then there is another you. And that other you has lived in his region of the universe the same exact things as you, and so both have the same memories and same thoughts… ah, yes, if all the event has happened identically for both of us, this universe has no randomness and there is no free will. This universe is deterministic.

If you happen to find a solution to this version of the problem, then you would be showing that the universe is not deterministic. That would lead to spontaneous breaking of the symmetry and those symmetric regions of the universe would start to demerge by mere entropy.

If you stay with the deterministic universe, then there is no solution.

According to theories about symmetry breaking in physics you have explicit symmetry breaking and spontaneous symmetry breaking. In the former the laws of physics fail to remain invariant while in the later the ground state fails to be invariant.

If you're not interested in getting deep into theory, then you could play with a juxtaposition of the later to the mental space and follow a Zen-like tract where all is perception. If thought precedes intentional action as well as intentional response, then by not thinking and acting spontaneously it is possible for action to precede perception (since there was no mind the moment the action occurred making the perception of the action completely surprising to both parties, both perceiving independently as a surprise), but then you have to work out a way to communicate spontaneously with random words, vocalizations, movements or other actions which occur without forethought. Very difficult indeed, but perhaps this will lead you in a worth while direction.

Jump in air toward each other and physically grapple each other. One of you will end up on top of the other (unless the whole universe is symmetric). That one speaks first. You don't even have to agree to this up front because both of you will have the same idea.