The "impossible lives" of Greta Wells are impossible and multiple because she has the chance to experience living as herself in three different eras.

As a fantastical premise goes this isn't necessarily the most unusual or most original, but Greer, with three excellent novels behind him including the moving and thoughtful The Story Of A Marriage, knows how to make this a memorable and special tale.

Greta's story is primarily about loss and the opportunity for second chances. It is 1985 in New York, exactly a year since her twin brother, Felix, died during the height of the Aids crisis, and her long-term lover, Nathan, left her for another woman. She is caught in a deep depression, unable to "move on", and so she books a series of sessions with Doctor Cerletti, who is a specialist in electro-convulsive therapy.

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Intended to spark her back into life, instead these treatments take her back to the past and to two other ­possible lives, one in 1918 and the other in 1941. These dates are key: one is the end of the First World War, and the other just before the US's entry into the Second World War. In other words, they are crossover points, moments at which the world changed or was about to. It is also relevant that Greta and Felix are both of German descent: their insistence that they are both Americans isn't always heard in these eras, strengthening both twins' sense that they are, and always will be, outsiders.

In these two other eras, Greta finds that nothing has essentially changed about the people she loves, but that the times have of course inflicted themselves on individuals. So Felix is still homosexual but cannot live openly with his lover, Alan, the way he would in 1985. In both 1918 and 1941, he is married to a woman called Ingrid and conducting an illicit affair with Alan on the side. Greta also discovers that in 1918 she has a young lover, Leo, who will die of Spanish flu, the pandemic a mirror of the 1980s Aids crisis, felling young people all over the country. Does this help her ­understand Nathan's betrayal better? For in 1918, he is still unfaithful to her.

Greer's time-travelling story of love and loss will inevitably be compared to Audrey Niffenegger's The Time Traveller's Wife, which is surely the only reason his publishers, Faber, have chosen to cover his serious and complex novel in pale green with pink lettering and a woman in a yellow-patterned summer dress carrying a pink-spotted umbrella walking into a blazing sun. It speaks of 'chick-lit', and those led to expect a light read will be sorely disappointed.

Greer can be melancholy but he is always insightful and thought-provoking, and while his novel shares a similar compelling quality in the "what if you could..." premise to ­Niffenegger's bestseller, his understanding of loneliness, of the awareness we are essentially alone in the world without those family members, lovers and friends who make it bearable, pierces and haunts. "When you were little, was this the person you dreamed of becoming?" is a refrain throughout the book, and the loss of what we might have become had our lives gone in other directions, had we lived in other times, permeates his tale.

Part of this is due to Felix's ­sexuality, but also to Greta's discovery that in her other worlds she has a child, a little boy. He is a ghostly presence, as is the daughter she discovers she is carrying after a night of passion with her 1918 lover, Leo. Was this the road not taken in 1985 she has secretly regretted?

Greer seems to see a biological imperative here, a reflection of the way that Felix was pressurised by previous eras to live a certain way. Deny your homosexuality to yourself because of society; deny your longing for a child to yourself because of a career.

It's a controversial point in its conservative assessment of women's lives but Greer knows better than to leave it there. Greta will make an informed choice about the era she lives in permanently. True to the spirit of the book, his heroine doesn't opt for the conventional route.