Terrorism changes the way we see the world. It sets out to set us on edge. Jonas Hassen Khemiri's play shows one flip-side of that – for some, terrorism changes the way the world sees them.

Based on a text written after Sweden's first suicide bomb, I Call My Brothers shows the world through a young Muslim man's eyes. He sees it staring back at him.

After two explosions have rocked the city – a car bomb – Amor (Richard Sumitro) spends the next day in town, running errands. Little things: catching up with friends on the phone, returning a drill to a hardware store. All of it comes to seem enormous: a Joycean everyday epic. He feels the whole city looking his way, practically patting him down with their eyes - a young muslim man in a backpack. In seeing how he's seen, Amor loses sight of himself.

Bombarded by phone calls and texts, Amor almost sits outside of himself anyway. His best friend Shavi (Jonas Khan) – his 'brother' – calls with updates on his young daughter's diet. Relatives check in from all over the world, and cold-callers guilt-trip him into animal rights donations. A school sweetheart Valeria (Nadia Albina) – his love is hopelessly unrequited – shuts him out for stalking her.

Sumitro changes for each encounter. A geek with a habit of ascribing friends chemical elements that reflect their personalities, Amor is himself a compound – street with strangers, shy with girls. He buddies up to a brown-skinned shop worker, and almost jumps two policemen talking to another Muslim. Khemiri asks who we identify with, and with whom we're identified.

For all the clumsiness of Tinuke Craig's production – too eager to mime out the day's events – Khemiri's play is artfully constructed. A criss-cross of memories and media, it conveys the tangled psychology of modern life – a mix of distance, dissonance and guilt. Designer Sadeysa Greenaway-Bailey boxes each actor in to perspex compartments – specimens on show, suspects on trial or patients in isolation – and Elena Peña picks their voices up via mic.

In this atomised world, Amor's identity splinters. Others' stares – or the stares he imagines – changes the way he sees himself and the way he carries himself around town. "Walk like a person that isn't thinking about walking," he thinks, as self-consciousness swallows him whole. The more he tries to shake off suspicion, the more suspicious he seems – even to himself.

That's what makes Khemiri's play so vital a watch – it's ardent in its empathy and acute in its accusations. In fact, it lets an audience damn themselves. We never find out anything about the bomber. "They say he looked like a…" Shavi tails off. "They say he was wearing a…" In leaving us to fill in the blanks, Khemiri invites us to sketch out a terrorist in our mind's eye. Who exactly do you picture? Exactly.

I Call My Brothers runs at the Gate Theatre until 3 December