电影《源代码》（Source Code）

Jim Kakalios on the Quantum Mechanics of Source Code

by Sean

Jim Kakalios of the University of Minnesota has achieved internet demi-fame — he has a YouTube video with over a million and a half views. It's on the science of Watchmen, the movie based on Alan Moore's graphic novel. Jim got that sweet gig because he wrote a great book called The Science of Superheroes — what better credentials could you ask for?

More recently Jim has written another book, The Amazing Story of Quantum Mechanics. But even without superheroes in the title, everything Jim thinks about ends up being relevant to movies before too long. The new movie Source Code features a twist at the end that involves — you guessed it — quantum mechanics. Jim has applied his physicist super-powers to unraveling what it all means, and was kind enough to share his thoughts with us in this guest post.

——————————————————————-

There is an interesting discussion taking place on the internets concerning the ending of the newly released film SOURCE CODE, that suggests that the film concludes with a paradox. I believe that any such paradox can be resolved – with Physics!

This entire post is one big honkin' SPOILER, so if you want to read about the final twist ending of a film without having seen said film – by all means, read on, MacDuff!

In SOURCE CODE, Jake Gyllenhaal plays US helicopter pilot Colter Stevens, whose consciousness is inserted into another man's body (Sean Fentress, a school teacher in Chicago) through a procedure that requires a miracle exception from the laws of nature (involving quantum mechanics and "parabolic calculus" – by the way, there is no such thing as parabolic calculus). Thanks to some technobabble (or as Q-Bert on Futurama would describe it – weapons grade bolognium) Colter's mind can only enter Sean's body in the last eight minutes of Sean's life. As Sean is sitting on a city bound Chicago commuter train, on which a bomb will explode at 7:58 AM, killing everyone aboard, the goal is for Colter to ascertain who planted the bomb. He cannot stop it from exploding, he is told, because that has already happened. He cannot affect the past, but he can bring information obtained in the past back to his present time. Learning the identity of the bomber would enable the authorities to prevent the detonation of a threatened second "dirty atomic" bomb is downtown Chicago.

While the above can be discerned from the movie trailer, what I am going to discuss next involves the actual ending of the film, and if you do not want this ending spoiled, you should stop reading now.

Colter learns that the reason his last memory is being attacked in his helicopter in Afghanistan is that he in fact died in the crash. His mangled body is kept artificially alive, and his brain can be activated, and sent to inhabit the body of Sean Fentress (who happens to be a neurological match). At the end of the film, after multiple failed attempts, Colter manages to identify the bomber. Providing this information to Col. Goodwin (a military officer played by Vera Farmiga) and Prof. Rutlidge (the great Jeffrey Wright), the scientist who designed the Source Code project, the terrorist is caught before he can set off the second bomb, but after, of course, the first bomb on the Chicago train explodes.

It is left somewhat vague as to whether Colter is going to parallel realities, a la the Many World's interpretation of Quantum Mechanics, or whether he is engaging in a quantum/ neurological simulation. If the former (which seems to be borne out by the ending) then this would tie into notions of time travel being explored in the context of quantum gravity. That is, if one could time travel into the past, you need not fear any Grandfather paradox (what if you killed your ancestor – preventing your birth, but then you would not be able to travel back in time to ice Grandpa). Some physicists argue that time travel is only possible via parallel realities. You do not go back in time in your own reality, but to an alternate Earth's past. You can thus kill as many grandparents as you have bullets, remaining safe in your own timeline. In any event it is assumed that the bomber is the same person every time Colter enters the Source Code.

While everyone is celebrating the capture of the bomber, the first successful trial of the Source Code project, Colter convinces Goodwin to send him back one last time, to try to save the passengers on the train. At the end of the eight minutes, he convinces Goodwin to terminate his life support, allowing him to die in actuality, as the world and his father believe happened months ago in Afghanistan. Needless to say, he manages to stop the first bomb from exploding on the train, hands the bomber to the authorities, and kisses his love interest just as the eight minute mark is reached. We see Goodwin make good on her promise and end his life support at that moment, at which point she is arrested my the military police for acting against Rutlidge's instructions.

On the train however, Sean/Colter is still alive after the kiss. The film implies that he goes on to live happily ever after in Sean's body, with Colter's mind, while Colter's deformed body remains at the Nellis laboratory on life support. As the bomb never went off on the Chicago train – there was no reason to activate Coulter and send him into the Source Code, and the project awaits its first true trial by fire. Thus it is indicated that we are witnessing two alternate realities – one where Goodwin is arrested after pulling the plug on Colter following the successful application of the Source Code, and the other where Sean/Colter is still alive, where the Source Code project has not been activated.

Among the many discussions I've noted on the web about the ending of this film, I wish to address two particular issues that are being debated by the Hive Mind. In the film's final reality, where the bomb does not explode on the train – does Colter's consciousness reside in two places at once? And, what happens to Sean Fentriss' consciousness in this final reality?

Reasonable people may reach different conclusions concerning these two points. As I am a physics professor – I will tell you the RIGHT answers!

(1) In the final reality – Colter is NOT consciousness in two places at once. He is awake and aware in Sean's body and at the same time his damaged body is in the Nellis lab – IN A NON-CONSCIOUS STATE. He is not awake and aware in the lab at Nellis, he can not initiate motion or form an independent coherent thought. He is in essence brain dead, kept artificially alive until there is a time and need for him to be activated (if there is a terrorist attack).

Even if he is activated – this would NOT influence or affect Colter in Sean's body, as it would take place in Sean/Colter's FUTURE. Remember he was sent back to Chicago at 7:50 AM – the bomb exploded at 7:58. Time progresses forward for both Sean/Colter and Nellis/Colter at the same rate. This was why Goodwin and Rutlidge were upset about how many trials it was taking – for each trial burned up a minimum of eight minutes, and brought the second explosion closer to happening.

What you are doing and thinking now is not affected by what you will be doing and thinking several hours from now. Do you know what you will be thinking about several hours from now (ok – for the guys this is an easy one). Nellis/Colter may not be activated for weeks/months/years later. But even if he is – Sean/Coulter can live his life, unaffected by what is happening in his future. There is no paradox, for Colter in Sean's body is only awake and conscious at one point in time. Colter is NOT like Schrodinger's cat, in two different conscious states simultaneously, as they are separated in time.

(2) What happened to Sean's consciousness? Here there is a potential problem. Basically I believe Sean is dead. When Colter's mind jumps into his body, it over-writes Sean's consciousness. Rutlidge probably knows this, and ignores the ethical issues. Sean will be dead when the bomb explodes after all, and Rutlidge believes that cannot be changed. By sending Colter into Sean's body, he robs Sean of the last eight minutes of his life. As Sean is unaware that a bomb will explode, killing him and everyone on board, he would not do anything extraordinary in those eight minutes. Rutlidge probably believes that it is acceptable to sacrifice the last eight minutes of one man's life in order to save millions of lives if they can prevent the second bomb blast in downtown Chicago. Every time Coulter enters the Source Code at 7:50 AM, he essentially kills Sean. Sean will die in every reality where Colter does not enter the code, and he will also die in all N – 1 realities where he does – so this is an ethical problem of order 1/N where N goes to infinity.

Alternatively, Sean may be alive in Colter's damaged body – but there was no suggestion that something like that was happening. Here I'm taking the Quantum Leap analogy too literally. (There is a wonderful tip of the hat to Quantum Leap – listen carefully to Coulter's Dad).

Sorry this is so long. Never ask a professor a simple question – you always get a lecture in reply!