When world leaders meet at pivotal points which change the history of the world, how does it feel to be there?  More importantly, how does it feel to be them? According to John Adams’ first opera, Nixon in China – or, at least, in Michael Cavanagh’s intelligent staging for Royal Swedish Opera – the answer veers between the banal and the weird, sometimes spilling over into downright surreal. The great men of our age talk in political platitudes, their features freeze into perfect smiles for the camera (this is an era before ubiquitous smartphone cameras), they can be aware of their importance, or can be sentimental or filled with self-doubt.

Faintly disturbing weirdness greets you from the moment you enter the hall, facing you with a giant wall of miniature Red Guard faces which are just slightly in motion. Designer Erhard Rom artfully mixes video projections and physical structures to make us feel like we’re in the middle of events, from Nixon staring out of his aircraft cabin, to the aircraft steps and the formal greetings on the tarmac, to the Great Hall of the People and the festivities elsewhere. We are always tracked by news cameras and suitably reverential crowds. The singers portray characters with precision: Nixon as the supreme machine politician, the down-home warmth of Pat Nixon, the urbane charm of Chou En-Lai, the strident menace of Chiang Ch’ing. Mao, by this stage in history, was downright batty, his utterances impossibly delphic, and the great man’s self-importance is surreally amplified by the trio of trouser-suited and bespectacled acolytes who move and echo his words like a jazz age backing trio (Mao and the Maoettes, perhaps).

But it’s the orchestral performance that makes this into a stunning three hours of opera. Lawrence Renes drives the orchestra hard and the insistent figures of the music get under your skin in much the same way as Philip Glass – but Adams’s score has hugely more variety than Glass and the music had me completely gripped at every twist and turn. There are various sections of Nixon which can drag – the libretto gets distinctly opaque during the political speeches, while the Peking Opera scene might have felt particularly lengthy – but the vibrance of the music and some superb dancing, choreographed by Arsen Mehrabyan, ensured that there was never a dull moment. And the set pieces came through with impact and humour, most notably the scene where Chiang Ch’ing announces that it’s time to “teach these motherf***ers how to dance” and she and the previously sedentary Mao set off into a disco routine.

While all the main singers showed attractive voices with good characterisation, the principal negative of the performance was that they virtually all struggled to make themselves heard above the orchestra, with the notable exception of Jeremy Carpenter as Chou En-Lai, whose warm baritone was strong enough to be always audible above the wash. As Mao, Michael Weinius gave us an open, clear tenor; as Nixon, Ola Eliasson gave perfect diction and attention to the nuances of the libretto. Hanna Husáhr’s Pat Nixon was beautifully sung, but there were problems with diction; Marianne Hellgren Staykov's Chiang Ch'ing was clear and exciting through most of her role, but couldn’t summon up the required decibels to nail her headline coloratura aria “I am the wife of Mao Tse-Tung”.

Nixon in China is a great opera because it makes us muse on a pivotal moment in history. Prior to Nixon’s visit to China, there was a sense that the Cold War was permanent, frightening and that World War III was only a matter of time: the US-China rapprochement was the first demonstration that some other outcome might be a possibility. It doesn’t really matter whether Adams and librettist Alice Goodman are being remotely accurate about the real events: the opera makes our imagination run riot as to what might have happened behind those closed doors. As Act III closes with the principals mawkishly considering their past and their legacy, we can join in that contemplation.

And that performance from the Royal Swedish Opera Orchestra turns Nixon in China into a real tour de force. There's one performance left: if you're in Stockholm, don't miss it.