Direct aftermath
First, I will assume that your aliens were friendly enough to avoid a huge chaos: no one is left in flying planes or on crash-landing areas. No one in cars, or in cars way, etc. Ships might be avoided for the same reason. So no one died in the event henceforth known as Duplication. Everyone has now a copy of him/herself separated seemingly randomly from a few centimeters away to the other side of the world.
I think the immediate questions would be (in general) along the lines of
- What happened? I had this strange feeling that something happened, and I can't explain it.
- Where am I? I was there, and now I'm here... wherever that "here" may be.
- Is it only me?1 Looking around, people's faces seem as puzzled, so whatever happened seemed to have affected everyone around me, until...
Before the first sync
I realised that there are some clones/copies/Doppelgänger/duplicata/whatever, I don't know how to put a name on it. How that happens depend on different cases. It might be that strange gut feeling I was having. Maybe, I witness two identical persons staring at each other where there were only one before. Maybe I am facing at myself without any mirror.
The reactions of most people would follow the usual steps
- Shock like "what?!", "who are you?" and the like. People would stand frozen on the spot. Those with no double to be seen will continue to look around to search for more cases or simply stare at how those react.
- Denial In particular, those facing their clone in public, we'll tend to deny the existence of their clones. "You're not real", etc. Those who don't see their clones will deny the strange feeling that they have.
- Anger if the clone can't be denied, it can surely be killed. So fight might broke out at that point, with both clones fighting in a way or another. Some will be killed. Also to be heard at that stage are the like of "How made that?" "Who is responsible?", military, government officials, police, banks, etc. may be attacked at that point, for taking the blame.
- Bargain Since it is hard to find a culprit, and the police members seem to be equally affected, then it might be a better idea to bargain. For those who aren't sure of their clone yet might consider saying: "Ok, to whoever did that, I see what you did there. I'll be a good boy, and you don't do it to me." The others will try to negotiate a turn back.
- Depression As some comments on previous answers show, there would be some depression part: "All secrents are left out of control: someone else knows them. For sure s/he is going to reveal it to everyone!" "I'll never be alone." "How are we to continue on living?" or maybe some more psychological issues. What happened to me? This person is going to kill me for sure, etc. Suicides may happen at this stage. This is an event too large to bare for a lot of people.
- Acceptance The acceptance of the whole thing will greatly differ from individuals to individuals as well as their own situation in the face of the Duplication. People facing their own clone, assuming they did not kill them or themselves in the previous stages, may kind of accept it as the appearance of a yet unkown twin brother. Those without clone in sight, might either follow their gut and assume that they too have a clone somewhere. And others might just ignore that feeling, and assume that for whatever reasons, some people got cloned.
It should be noted that news coverage would be highly disrupted as the people presenting them are themselves walking through the above steps, and futhermore aren't all at their workplace. Internet might be an interesting sources of news though, but not all have means to check it, transported far from home without even a phone in your pocket.
After the first sync
And then it came: "The First Sync". Also the called The Shock. Yes you were teleported somewhere else, yes some people, maybe you, yourself had twi brother or sister appearning out of nowere, otherwise you might have that strange feeling you, were cloned as well, but are just enable to see the clone. But on the whole, you were kept yourself. But then... a flash, and strange thoughts and memories start to appear in your brains. Scenes you cannot have seen yourself. Thoughts that are somewhat familiar but aren't exactly your own.
This will produce a lot of anxiety to everyone. By that time not all arrived at the acceptance step before. Therfore the reaction will depend on many factors, but we can explain a few cases.
- You accepted that, due to the Duplication, you have a twin just facing you. Somehow you always wanted to have a twin brother to see how that felt like. And after the Shock, foreign thoughts and memories came to you. But you can quite easily identify that those are from the other you facing yourself. So it is not only a cloning, you are linked to that person in front of you. No secret to keep from him/her, but none kept from you neither. That kind of a relief, if s/he were to spill your secrets, you'll know. You don't know how that happened, but there might be something to take from that.
- "Who am I, what am I doing?" were the thoughts that were haunting your mind before the Shock. And those strange depressing ideas seemed to have sprung from that flash. This is much more than you can take. Better end it there than living through that pain and anxiety.
- You accepted that somehow the Duplication created double of some people, but in yourself you have a feeling that you, too, have a double. But you are not sure. You sure can't seem to see him around. But then another flash. This time, it was shorter. But on the other hand, it was most stressing. But after the initial surprise, you realise that the new memories must come from that other you. Where could he be?
Slowly each will walk down the steps, and it will somehow be established that the Duplication created a double of each and everyone, and that some events may syncrhonise the thoughts. As the concept starts to spread, the second sync came in, which confirm the theory and established the fact that the synchronisation is something they will live by from now on.
The first month
The first month is the time of experiment. A great many people died due to fear, anxiety or psychological stress. I don't have any source for it, but we could assume that 10-30% of humanity died in the first days after the Duplication. Sometimes, only one of the double did, but at other times, both of them.
Nevertheless, the surviving ones are trying to re-establish a new life. Some are experimenting to see the limits of that strange effect. The synchronisation time is established with a great precision, so that people start to be expecting it. Some are travelling, looking for their doubles. Some engage in more frivolous experiments (foursome sex being one of them).
The lowered need for food per individual is found. So is the fact that somehow the food taken by one can be used by the other. Scientists start to study the communication between the two doubles, the sync process, the Duplication, etc.
Some young try to kill one double during a sync to experience death to the surviving double.
Some rules are established:
- Humans have become more efficient machines. Even those whose double have disappeared only need half food income as they had before.
- Thoughts, memories and ideas are synchronised every 387minutes and 17seconds.
- Physiological attributes (food, sleep, etc.) are also syncrhonised at the same time.
- Physical and biological events are not synchronised: the death of one double does not provoke the death of another, as stated in another answer, a cut will scar only one double. And consequently, a woman getting pregnant does not imply that her double will be as well.
It is a bit too early to tell, but it seems to indicate that the Duplication was a single event, and not a continuous. Namely the next generations won't have doubles (unless the event occurs again).
Society acceptance and evolution
The initial chaos is slowly brought under control. And people have gone back to work, the whole society is slowly going back to "normal", trying as best as possible to accomodate for the new individuals.
Legal
Politicians and lawyers will jump on scientific conclusions to produce some laws. Without covering the extend of all the laws, the humans are considered more like a moral person (like a company), which happens to be physically presented with two bodies. Due to the uniqueness of the moral person, everyone is responsible for the actions of his or her double. That might not be the best, but that was the easiest for most cases. Generally individuals are replaced by moral person.
Family and Relationships
The new laws have a strong incident on the family. Mariage is a contract between moral person, meaning that you are considered married to the same wife as your double. And you are also consider the father of your double's children. Affairs are exploding: you can be faithful and have an affair at the same time. And so can your wife. Non-married relationships becomes complex: A1 is with B1, when B2 is with C1 and C2 and A2 are together (when A, B, and C represents moral persons, and 1 and 2 their physical doubles). And it can get worst than that. The number of open relationships also increases due to the possibility of multiple relationships with synchronised minds. This creates resentment towards the laws, but conservatives refuse point blank to change it and some progressists also point out that the next generation will differ and that one should account for that. Nevertheless the traditionaly family view crumbles.
Work and Economy
Most people work because they need. Meaning, they work to get money to pay the rent/mortgage, for the food, etc. Food consumption does not increase, even worse, it has decreased due to the high mortality of the aftermath of the Duplication. Housing per moral person has increased, the amout of space is higher, regardless whether they choose to live together or not. Transportation, clothing, etc. costs all increase. However due to the increase of work force, the wages tend to be reduced. But nevertheless, few really work the typical 80 hours a week, most setting themselves to 55-60 hours per week. Different individual organise differently. Some work in shifts: one after the other for half a work day, some set that only one work on a precise day and the other relax, sleep, take care the house, or just enjoy free time (e.g. travel). Among those there are some who never changed turned, those who change everyday, or every month, etc.
Spiritual
Slowly, all the consequences of the Duplication are known. But the cause remains a mystery that continues to elude the scientists. The emotional stress of sharing a mind with what appears a foreigner lead many to what can be called a renewed Spiritual Spring. People go back to the usual religions, but new ones appear and gain some popularity. Those are often centered around a mythology which explain why (one of) the god(s) created the Duplication, and the message it meant.
I knew it would be long, but I didn't expect to be that long. I tried to limit to some points in each part only, but I think you can fill the blanks by yourself.
Thanks to all those who bore with me until this line :-)
1: Of course for people being alone, that step would limited, and they might have to move to identify the extend of that event. They may see their clone even before seeing anyone else.