Something that simply does not exist.
Plainly and simply: the concept of physical personal space does not exist in Russia. No extended hand rule. People around you, friends and total strangers alike will violate your personal space all the time.
On one hand in overpopulated cities like Moscow it is always crowded everywhere. In public places it is almost impossible to avoid physical contact with strangers. Public transportation is packed with people, crowds of pedestrians on streets, way too many customers in grocery shops, especially on weekends. On the other hand even in situations when there is plenty of space available, personal space is never minded and never respected. When you ask Russians about their personal space (личное пространство — lichnoe prostranstvo) they think about their apartment.
Here are some real (absolutely real, not exaggerated even a bit) situations to illustrate how it works in Russia.
You are in a grocery store. You are about to go to check out and every check-out has long lines. You wait for additional check-out to be open. Store clerk jumps between two cash registers as something is not working. You are not sure which check-out opens, so you wait. Another customer comes behind you and smashes your back with her shopping cart. You turn to complain. She angrily blames you for being too slow. Same might happen in the store isle, customers push you and hit you with their shopping carts and complain that you are talking too much space, or too slow or say nothing and just walk away.
You are standing on a street sidewalk. The street is empty, no one is around. You are talking on your cell phone. There is like two meters of empty sidewalk space between you and a curb. Another pedestrian, total stranger, walks towards you. She goes right at you, not making even a step to avoid hitting you. She approaches you, hits you with her bag as she passes you just a few inches away and continues walking. This happens all the time, people walking on streets would never take a step to part ways, they would smash you with their shoulder or bag. No one would ever apologies.
You are in subway. It is late and subway car is almost empty. You are standing in the corner, there is no one around and a bunch of seats available. Two passengers come in at a station. They do not pay attention to all the empty seats empty space available. They go right to where you stand, one of them stops like an inch away from you, almost touching you. They talk and pay no attention. Each time the train makes turn, or slows or shakes, that passenger leans on you. You complain and ask them to get away from you. They give you a strange look, and reluctantly move away.
You are in subway again. You are sitting on a corner seat, close to doors. There is just a handrail that separates you from the doorway. The handrail is close to your face, few inches away. Another passenger comes in and puts her butt onto that handrail. Her butt is real big. So when she stands this way, leaning her butt onto that handrail, her butt gets right into your face. You complain, but she complains back saying it is comfortable for her to stand there and she won’t move. You take out a ballpoint pen and poke her butt. She starts yelling at you.
There is a bunch of deep cultural reasons for this type of behavior, but suffice it to say — notion of physical personal space does not exists in Russian culture. In all the public places, offices, people will be getting real close to you — physically, touching you, pushing, often without any reason. What may seem as aggressive and disrespectful behavior, in reality is a norm, well tolerated in Russian culture.