Prof Stephen Hawking, who will narrate a journey through history with an emphasis on scientific discoveries at the Paralympic opening ceremony Press Association

Those behind the Paralympic opening ceremony have revealed it will feature Sir Ian McKellen, Prof Stephen Hawking, and the "world's biggest apple crunch" as part of a "unique and extraordinary piece of work about challenging our perceptions".

Stephen Daldry, who is overseeing all four Olympic ceremonies, said the ceremony – titled Enlightenment and directed by Jenny Sealey and Bradley Hemmings – was very different from the Olympics ceremonies.

"If Danny Boyle's was very much about two revolutions and popular culture and Kim Gavin's was very much about a symphony of British music, then what you will get from Jenny and Bradley is something very different," said the Billy Elliot director.

Sealey, the director of the country's leading disability theatre company, said she and Hemmings were feeling "very slightly nervous, terrified and excited" about the ceremony, which had been a "phenomenal journey".

Following a flypast by a disabled pilot with an organisation called Aerobility just before 8.30pm, the show will open with Hawking, who Sealey described as "the most famous disabled person alive".

Sealey said Hawking would narrate "the most exquisite journey" through history, with an emphasis on the scientific and cultural advances of the 18th century. An opening "big bang" will feature 600 volunteers with umbrellas spreading out from the centre of the stadium in a "spectacular" opening sequence.

As with Boyle's opening ceremony, the theme of the Tempest will be explicitly woven through the narrative. Shakespeare's character Miranda provides the eyes through which the 80,000-strong audience in the stadium and millions more on television will see the show.

"She sees everybody but she doesn't judge. That is fundamental to our personal and political ethos," said Sealey.

"Our Prospero is Sir Ian McKellen – he sends her on her way and she's always there but she has to make that journey of discovery on her own.

"Don't look down at your feet, look up at the stars. If you're not curious, you might as well give up."

She said that ethos had rippled out through the 3,000 volunteers in the show. They include 42 disabled performers who have trained from scratch in circus skills.

The organisers face a challenge in holding the attention of viewers while the majority of the 4,200 competing athletes file into the stadium, a process that takes place following the entry of the Queen into the stadium and is likely to take an hour and a half.

After speeches by the Locog chairman, Lord Coe, and the International Paralympic Committee president, Sir Philip Craven, the show will continue.

It will include a depiction of "an exciting and dangerous storm of ideas", including a "giant whale" and an aerial ballet featuring the disabled dancer David Toole and the 42 volunteers.

Hemmings said the performance, to a rendition of the Antony Johnson song Bird Girl by 16-year-old singer Birdy, was an emotional highlight of the show.

Giant inflatable apples will "play with gravity" in all sorts of ways, at which point the crowd and those watching on television will be invited to take part in the "world's largest ever apple crunch".

"We create a hadron collider in the stadium. Extraordinary and transformational understandings arise. In the same way the hadron collider changes our perception of the universe, so the Paralympic Games changes our perceptions in a very different and very human way," said Hemmings.

Ian Dury's song Spasticus (Autisticus) and a version of Marc Quinn's giant sculpture of a pregnant Alison Lapper, which was displayed on the fourth plinth in Trafalgar Square, will also feature during a "moment of celebratory anarchy".

At the conclusion of the show, Hemmings promised: "Miranda takes to the air and breaks a glass ceiling that descends over the whole stadium. The resolution of the lighting of the cauldron is going to be extremely spectacular and like nothing you've seen in previous ceremonies."

Given the prevalence of umbrellas in the ceremony and the Tempest theme, organisers hope they are not tempting fate. The already delayed Paralympic torch relay, which began in Stoke Mandeville on Tuesday night and is already running an hour and a half late, might see its route altered if forecast heavy rainstorms impede its progress before its arrival at the stadium.

Asked about the involvement of Atos, which has angered disability rights campaigners by sponsoring the Games at the same time as carrying out controversial tests to determine whether disability benefit claimants are "fit to work", Sealey said a boycott was the wrong approach.

"There is one part of Atos doing that and there is another part that is all about communicating and promoting the Games. If we decided just to boycott the Paras, because the disability movement has had so many battles, we would just be forgotten about and fade away all over again," she said.

"The Paras are monumentally important to remind people that we are here and we have rights. Our whole production is about rights and reasons."

Daldry defended the fact that less had been spent on the Paralympic opening ceremony than the Olympic opening ceremony, saying they were of a different scale. He refused to say how much the Paralympics ceremony had cost, beyond saying that half of the £81m budget had been shared across all four ceremonies to provide the infrastructure and the spectacular "pixels" that turn the seating bowl into a video screen.