Love is pain. That's the message of the Richard Burton–Elizabeth Taylor story | Jonathan Jones

Dominic West and Helena Bonham Carter as Richard Burton and Liz Taylor. Photograph: Gustavo Papaleo/BBC/PA

The modern world has a problem with love. How do we even imagine it, let alone live it? In Shakespeare's time people knew what love looked like. It meant a young man playing a lute or a lady listening to her lover's honeyed words from her balcony. Marriage was something else, a property arrangement. But in modern times, love and relationships, long-term partnerships versus short-term joy, are hopelessly confused as is witnessed by the tangled tale of those two famous 20th-century lovers, Richard Burton and Elizabeth Taylor.

In this photograph just released by the BBC, Dominic West and Helena Bonham Carter impersonate the great unhappy ones in a drama about the last time they ever worked together, in 1983, in a critically trashed stage tour of Noel Coward's Private Lives. The fact that this image feels like an event is proof that Burton and Taylor have now become a modern equivalent of the romantic couples of history and legend who Shakespeare celebrated. Perhaps for generations to come actors will compete to recreate the looks and emotional turbulence of Richard and Liz.

Love is pain. That's the message of the Taylor and Burton story. In this picture, the face of the actor personified by West is set in passion, a dangerous and unwieldy promise of pain to come, even as Bonham Carter looks happy and trusting beside him. At the moment the actual Burton and Taylor met in the early 1960s on the set of Cleopatra, the silkscreen paintings of Andy Warhol were entering their prime and "Liz" became one of Warhol's favourite icons to portray. His images of her, at the beginning of her relationship with Burton, are both sensual and painful – Warhol, poet of car crashes, sees disaster coming.

And so it was to be. The burden of the tale of Elizabeth and her Welsh Romeo is that love cannot survive in the modern world. Intense passion on the set of Cleopatra, divorce from their partners, a failed marriage, then another attempt – it's harrowing.

In all this, a suspicion of false coinage haunts the grand passion played out in public. They were both actors, after all. In this picture, seeing West and Bonham Carter playing these consummate performers, we are pointed towards the histrionic quality of the way Burton and Taylor played themselves.

From passionate pictures of them happy, so happy, together to their nightmarish evisceration of a rotten relationship in the film of Who's Afraid of Virginia Woolf?, Burton and Taylor acted out the extremes of modern love in public.

Their relationship was diamond and it was ash. The joy and bitterness were real, and also provided artistic material. Of course their love was not fake. Like any artist – like Picasso – they had to use their lives.

But love is an act as well as a reality. In Romeo and Juliet, young Romeo goes around brooding and waxing lyrical about love even before he sees Juliet – he fancies himself a lover, then becomes a lover.

In this picture, two actors who are not in love play two actors who were – and in doing so draw attention to the complex relationship of image and reality, acting and truth, in the art of love itself.

Modern times make that art more difficult, as Burton and Taylor found. Both famous when they met, they loved and fell apart in public. Perhaps it's a lesson for the social media age. Now (as Warhol prophesied) we are all celebrities to some extent. Everything can be shared. But look into the eyes of Helena Bonham Carter as Elizabeth Taylor. She so wants to be happy. Would a private love with no media and no fame and no pictures online have given her that dream?

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