Friday, February 27, 2015

Interstellar - Inspirational Science

"We're still pioneers, we've barely begun. Our greatest accomplishments cannot be behind us, because destiny lies above us." - astronaut Cooper, Interstellar.

I was excited to go and see Interstellar, but coming out of the theatre after watching the film, I was walking on air. It had begun to snow for the first time this winter in Leuven, and as the snow flakes floated gently down on me, I experienced, to borrow Milan Kundera's words, an unbearable lightness of being. I felt the joy of science and space exploration washing over me - I've always been excited about this stuff, but this film has influenced and inspired me as no other film has, and re-kindled within me, my childhood love for physics.

Without giving too much away about the film, the basic plot is as follows: In the near-future, planet Earth has become uninhabitable for mankind, and the protagonist, astronaut Cooper (played by Matthew McConaughey), supported by a surviving, skeleton staff from NASA, blasts off in the direction of a black hole to explore 3 planets in its vicinity that have been deemed suitable as candidates for supporting future human life. The trouble is, these planets are many million light years away, with no known technology to get there. So Cooper and his fellow astronauts journey through a worm-hole, a short-cut through the fabric of space-time to get to Gargantua, the black hole around which their candidate planets orbit.

Caltech physicist Kip Thorne was the consulting scientist in the film, and for once, Hollywood has taken great care to get the physics right. I'm going to be taking this opportunity (and the inspiration - while it lasts) to write about some of the physics in the film. 

One of the most visually stunning effects in the film is the view of the black hole Gargantua, as Cooper and his crew approach it. A black hole is a collapsed star of such high density and gravitational pull that nothing, not even light can escape from it, and consequently, it itself is invisible. However, stars and other inter-galactic matter in its vicinity are constantly being sucked into it, and as their hot gases spiral down the vortex into the centre of the black hole, they leave behind a tell-tale, brightly glowing disk, called an accretion disk. It is this disk that is seen as an indicator of the presence of a black hole, and has actually been visually confirmed by the Hubble Space Telescope.

Now, what would this accretion disk look like, as you approach a black hole?

Artist's impression of an accretion disk around a super-massive black hole [source]

Artists' impressions of black holes show the accretion disk orbiting the black hole's shadow, flattened along its equatorial plane. 

Light no longer travels in straight lines around a black hole - its intense gravitational pull bends light towards it - this phenomenon is called gravitational lensing [source]

Interstellar's Visual Effects team Double Negative (they won a special effects oscar for their efforts), instead of relying on previous artistic impressions, took Kip Thorne's advice and used Einstein's equations of General Relativity to simulate what a black hole would look like, from up close.

Einstein's General Relativity equations define the curvature of space-time around a black hole - the more massive a black hole, the more this curvature and the more the gravitational lensing, or bending of light due to the black hole's gravity. 

Gravitational lensing bends light from behind the black hole over 
and under the black hole [source]


Using these equations for their computer generated renderings of the black hole, the team from Double Negative found that if you're near and just above or below the equatorial plane of the black hole, you will see light from the accretion disk behind it curve up and around its bottom and top. This will mean that in addition to the ring of the accretion disk along the black hole's equatorial orbit, you will see a ring along its polar orbit. 

The secondary, tertiary and higher order images of 
gravitationally-lensed stars behind a black hole​ [source]

Some of these light rays will spin around the black hole a few times before they escape and reach your eyes, which will lead to secondary and and higher order images of the gravitationally-lensed stars behind the black hole, with the black disk at the centre (whose edges coincide with the Event Horizon, from where light cannot escape). 

A spinning black hole like Gargantua drags space around it into 
whirls and eddies [source]
A spinning black hole like Gargantua would also drag the space around it into a whirl, and this produces eddies of light and a much more complicated pattern of gravitationally lensed stars behind it. Along the accretion disk itself, as light approaches and then recedes away from an observer, it would appear bluer, and then redder along the approaching and receding sides, due to an effect called the Doppler Shift. The Doppler Effect is a physical phenomenon that changes the apparent frequency of a wave (light in this case) as it approaches an observer - the crests of the waves approaching you appear bunched together (higher frequency - blue) compared to the crests of the waves moving away from you (lower frequency - red). The same effect was observed by Edwin Hubble (after whom the space telescope is named) with galaxies - they seem to be more red-shifted (moving faster) the further away they are from us, indicating that the universe is expanding. In fact, Einstein had predicted this using his equations of General Relativity, but was so shocked at what his equations were telling him, that he decided to put in a "fudge factor" to account for this perceived anomaly. His theoretical predictions of an expanding universe were later confirmed by the astronomical observations of Hubble.

 Blue and red Doppler shifts seen along the approaching and receding 
sides of the accretion disk [source]

Back at Double Negative, the blue and red, Doppler-tinged accretion disk and some of the more complicated star patterns were deemed too complicated for a movie audience (already overwhelmed by a booster-dose of physics) to digest, and so they decided to slow down the spinning of the black hole a little bit (to tone down the Doppler shifts) and give it a slightly more anaemic accretion disk. If you were to strictly follow the laws of physics, Gargantua needed to be spinning faster to have a planet - Miller's planet (the first planet that the crew explores) so close to it and not break the speed of light barrier. The whirl of space (dragged along by a rapidly spinning Gargantua) means that the speed of Miller's planet, relative to the speed of whirling space around the black hole is still under the speed of light. 

And why does Miller's planet need to be so close to Gargantua?

Just as the immense gravity of a black hole curves space around it, it also slows down time, a phenomenon called time dilation, again a consequence of Einstein's General Relativity. 
Space and time are connected - scientists use the hyphenated space-time to describe this. The more "bendy" space is, slower the clock ticks and this effect is really pronounced in the vicinity of a gravitational heavy-weight like a black hole. 

Cooper's crew loses 7 years of Earth-time for every hour spent on Miller's planet, an important story element, and this would only be possible if the planet was very close to the gravitational tipping point of no return, the Event Horizon of Gargantua. 

The final result from the Double Negative effects team is the rainbow of fire effect that you see in the film, a spectacular visualization of what a black hole (or more accurately the space around it) would really look like. 

Gargantua and Miller's planet, as seen in the film [source]

You'll find more details about the visual effects of the film in this video. And for those who want to dive into the equations, here are the links to the published journal and book:

The Science of Interstellar, Kip S. Thorne, 2014.

No comments:

Post a Comment