> Yes, a thousand times yes you can put your seat back you gentle soul.
Overjoyed that I understand this, allow me to explain it to those who don't.
Seats on the Shinkansen [0] are bolt-upright by default. You basically have to recline them a little bit to be even vaguely comfortable.
Every person, every time, asks the person in the seat behind them whether it's okay to recline their seat by 5°.
The seat pitch on the Shinkansen is approximately 1 metre. There's a lot of room.
[0]: My line, anyway – the E5 series cars that run the Hayabausa service.