"I'm still here, I'm just on my phone"

You're in the room. You're on the sofa next to them. Being present, you'd say, is about being there, and you're there.

There's a well-known piece of research on infants that tests this exactly. A parent plays with their baby, then, on a signal, keeps looking at the baby but goes still and unresponsive, then after a couple of minutes resumes. The parent never leaves. Babies hate it. They protest, look away, try to get the parent back, and take a while to recover when the parent does. Sarah Myruski and colleagues ran a version of this with fifty infants aged between seven months and two years, with one change. During the still phase, the mother used her phone. As in the standard version, the infants showed more negative feeling and less positive feeling while the mother was on the phone than during play, and made their most attempts to get her back during that phase. Infants whose mothers reported using their phones more often were less exploratory and less positive during the phone phase, and recovered less when their mothers came back.

The point of the original experiment was that a parent's presence isn't their body in the room. It's their responsiveness, and a face that's there but not answering is worse for a baby than an empty room might be, because it's a face that should answer and doesn't. The phone version says that's what a phone does to a face.

A baby is not your partner and this is one study. But I think the shape holds at every age. Being in the room while on the phone isn't a lesser form of presence. It's a distinct thing that the other person experiences as being with someone who isn't there, and the fact that you could be there, that your body is right here and your face is right there and it still isn't answering, is what makes it worse than the empty room. Nobody feels ignored by a person in another city.

So "I'm still here" is true of your body. The rest of you is at a distance the other person can measure, and they measure it by your face.