Is one allowed to wear a smartwatch on Shabbat?
A smartwatch tracks the heartbeat, so by walking you cause it to work. On motzei shabbat you can see results.
We can compare this situation to a situation the Mishnah Berurah brings in Siman 316 Seif 25. He says a person is not allowed to lock their house to protect his valuables on Shabbat while a deer is inside, even if they doesn't have any intention of trapping it.
It's called Psek Resha, which means if you have the intention to do something mutar (allowed), but it inadvertently causes you to do something asur (forbidden), it is asur. Certainly then, it is forbidden to trap the deer.
The Mishnah Berurah is quoted from the Ran and the Ritba, but the Rashba says if you don't have the intention of trapping the deer, you are allowed to close the door on Shabbat. The majority of Poskim follow the Ran and the Ritba.
At first glance you could say that in our situation it will be the same argument because he doesn't have the intention of monitoring his heartbeat with his watch, he just wants to know the time. The Ran and the Ritba would say it is forbidden, even if it is unintentionally or unwillingly. However, we can still argue and say that the Ran and the Ritba were only strict because the individual in the situation they commented on wanted to trap the deer, but the primary reason for locking the door is because they wanted to protect their belongings. Maybe if that person didn't want the deer to be trapped there, perhaps all would agree that the locking of the door would be permissible.
Similarly in Siman 340, the Rama says one is not allowed to cut a cake that has letters, because it is considered erasing, but the דגול מרבבה argues with the Rama and says that it is permissible. We can still say that over there is different, because it has two rabbinical decrees. He is erasing it in an abnormal way, and he is not erasing it with the intention to write something on it.
Similarly in this situation with the smartwatch, you can say there are two rabbinical decrees. First, because it is not actually writing since it records the heart rate in binary code. Second, you are indirectly causing it to happen. Even if we say that there is only one rabbinical decree, it is still psik resha dlo nicha le בדרבנן, that many are lenient.
All this only applies if the person had no intention of making any changes on their smart watch. However, if they want the heartbeat data, it is then forbidden.