A Christmas Closed-Timelike-Curve: Could the story of Scrooge actually happen in a quantum universe?
By Maria Violaris, PhD student at the University of Oxford
Traveling backwards and forwards in time is a common trope that appears often in science fiction. However, as we enter the holiday season, I find myself contemplating a famous time travel story rooted in a very different genre — specifically, a piece of Victorian era morality literature by Charles Dickens. And as usual, I’m doing it from the perspective of quantum mechanics.
Have you guessed the story I’m talking about? That’s right! It’s “A Christmas Carol,” the tale of the grumpy, selfish Ebenezer Scrooge who receives visits from ghosts of the past, present and future on Christmas Eve. Scrooge emerges from his experience a changed and newly generous man, but I can’t help but wonder, could the fantastical story of Scrooge really happen in a universe with quantum time-loops?
In the latest installment of the Quantum Paradoxes video series on the Qiskit YouTube channel, I investigate the possibility that time-loops — more commonly known to physicists as “closed-timelike-curves” — may in fact be consistent with quantum mechanics. In this blog post, I apply my findings from that video to make sense of the story of “A Christmas Carol”.
A Christmas paradox
Let’s first consider the visit from the Ghost of Christmas Past. The ghost takes Scrooge to observe various happy scenes from his past. Scrooge does not interact with his past self, and his past self does not see him at all.
This experience begins to change Scrooge’s outlook on life, so it has an effect on Scrooge’s future behaviour. However, there’s no paradox here. It is fully self-consistent for Scrooge to invisibly observe his past self, and then have that experience change his own future actions. In fact, this process isn’t too different from something most of us do just about every day. Like anyone else, Scrooge is simply reflecting on his past memories, and changing his actions as a result.
Next, the Ghost of Christmas Present takes Scrooge to see some scenes from the present day. No time-travel here, so all is good!
Now for the most interesting case: Scrooge receives a visit from the Ghost of Christmas Yet-To-Come. The ghost takes Scrooge to a scene that occurs after his death, where he sees that his death is celebrated rather than mourned, and also observes the tragic fate of a sick child, Tiny Tim. Seeing this future is the final straw for Scrooge to change his ways. He wakes up on Christmas morning as someone kind, generous and compassionate.
Here’s the paradox: If Scrooge changed his ways because he saw a bleak future, then the bleak future will never happen. If the bleak future never happens, it will never cause Scrooge to change his ways!
Self-consistency is key
The paradox we run into with our friend Ebenezer shares many similarities with the “Grandfather Paradox,” the idea that someone who goes back in time and kills their grandfather will never exist to go and kill their grandfather in the first place. These paradoxes can be solved in quantum mechanics using a “consistency condition,” which is a constraint that ensures everything makes logical sense in a time-loop. If someone goes into a time-machine, they must be in the same state as when they come out of the time-machine, and this limits the range of actions they can perform. If you go back in time, you physically will not be able to kill your own grandfather.
With that in mind, we can resolve the paradox of Scrooge changing his ways. Consider a modified story, where the Ghost of Christmas Yet-to-Come shows Scrooge a bright and happy future. In this future, Scrooge is a kind and generous man. Seeing how much happiness he can bring about by being kind and generous, present-day selfish Scrooge is inspired to change his ways. He becomes kind and generous as well, leading to the bright and happy future he was shown by the ghost, with no logical contradiction.
Is everything all well and good now? Not quite. There’s another, more subtle time-travel paradox hidden in this modified story, called the Knowledge Paradox. Imagine I travel forward in time to read this blog post, copy it from my future self, and then post it, making it the blog post that my past self would eventually copy. This is logically consistent, but where did the knowledge of the ideas in the blog post come from?
Our Scrooge scenario is similar. Sure, Scrooge can see his kind future self and become a kinder person as a result. That is perfectly self-consistent. But where did Scrooge’s knowledge of the positive impacts of being kind come from? This Knowledge Paradox has not yet been solved in quantum mechanics, so I cannot quite finish the quantum modification of Scrooge in this blog post.
Who knows? Perhaps this Christmas Eve I will be visited by a Ghost of Christmas Yet-to-Come, one who will show me a future Qiskit video where the Knowledge Paradox has been resolved. I will then come back to the present, and make a new Qiskit video resolving the Knowledge Paradox with quantum circuits, which turns out to be the one I saw in the future…
Until that happens, be sure to check out the current version of the video where I investigate this topic on Qiskit YouTube. You can also dive into the accompanying Jupyter notebook, which will show you how to simulate closed-timelike-curves as a quantum circuit. And of course, whether you are spending the festive season watching videos, reading Victorian morality tales, or reflecting on the past, present and future, best wishes for the holidays and everything yet to come!
