Quantum Time Travel

Is there a way to avoid paradoxes and travel through time... in the quantum realm?

Hey Nerds! I’m Abi, a physicist in the last year of my PhD at the University of Oxford. My research is related to atomic and laser physics and particle acceleration in plasma. I talk about the science of scifi and explain speculative physics across my social media channels. Come join the nerd revolution!

You might be familiar with the concept of quantum weirdness, the idea that how we interact with the universe is different for objects on a quantum scale; the wave-particle duality of light, the paradox of superposition, the spooky action of quantum entanglement. 

All of this quantum weirdness centres around objects in space. But our universe is made up of space-time. Intricately linked through our perception of cause and effect. An underlying rule in all that we know, causality. Even with all the strangeness of quantum mechanics, causality holds true.

Or does it. 

To really understand this weird concept, we have to start with what we know about time, specifically the arrow of time. 

The arrow of time

Time itself is a measurement tool. A way for us to calculate the rate of change in something. The unit of time is the second and it’s calculated using cesium atoms, specifically it’s the time it takes for a cesium-133 atom to undergo 9,192,631,770 cycles of microwave radiation, absorption and emission. But the flow of time, the flow of processes, doesn’t have one specific definition. Instead we talk about the arrow of time and how we describe that arrow depends on the context. 

The psychological arrow of time is the way that we perceive time, we see it as flowing in one direction, we remember our past, we experience our present and we cannot know our future. This is our perception of time. But physical processes also have an arrow of time. 

The second law of thermodynamics says that in an isolated system the amount of disorder, the entropy, will increase over time. This process is irreversible and so the increase in entropy gives time a direction. A cup of hot coffee will cool down as time progresses forward. 

The universe has been expanding since the big bang and as this expansion progresses, it gives us a sense of the cosmological arrow of time. The universe began in a state of low entropy and as it expands this entropy increases. The direction of expansion provides a direction to cosmological time. 

But most significantly, in our universe, we experience events in a specific order, this is causality. If you push an object over, it falls after you push it, not before. Causality is a fundamental aspect of our human experience and of the universe. Everyday we see examples of cause preceding effect. 

Whatever the process, whatever you feel about the ‘reality of time’, it’s this asymmetry, this one-way direction, that we describe as the ‘arrow of time’. But can the same be said about quantum time? 

Well..

Quantum Time

For all the time I've dedicated to ridiculing the physics in Ant Man. Was he actually right? 

In science we write equations to describe different processes and interactions. In classical physics, time flows one way and our equations and observations match that. As Gerard T’Hooft put it : ‘time is the order in which our models for nature predict, prescribe or explain events.’ To describe an event we have to specify an order, a direction of time. 

When it comes to quantum mechanics we need a description that’s different to what we see in our lives everyday, different to classical physics, a new set of equations. And in this new formalism the equations work just as well whether they are written forwards or backwards in time. But there are cases where the reversibility is broken and the order is important. This suggests that time both has and does not have an arrow when it comes to quantum mechanics. 

But an equation working without specifying an order of events doesn’t necessarily mean that it violates causality. It was always believed that cause preceding effect remained even without having a definitive arrow of time. But maybe causality is actually a victim to quantum weirdness. 

Philip Walther, a physicst at the university of vienna, explores the idea of ‘superposition of time’, extending quantum superposition beyond particles to the order of events. Walther’s work demonstrates that in quantum systems, events can happen in a ‘superposition of different orders’— cause can happen before effect and after effect at the same time. This phenomenon is known as ‘quantum superposition of causal orders’. Another aspect of Walther's research involves the ‘superposition of time intervals’. This means a particle can experience multiple durations of time simultaneously, pushing the boundaries of how we understand time on a quantum level.

But let’s take this further.

The Schrödinger Equation describes the wavefunction of a quantum object evolves over time. Vlatko Vedral at the University of Oxford proposes that the wavefunction can be written in a way that fully integrates space and time, describing the behaviour of quantum objects over all space-time. And if time is taken into account in this way then time becomes dependent on the observer, time becomes relative on a quantum scale, potentially leading to a better understanding of quantum mechanics and its relationship with gravity

Closed Timelike Curves

To get to quantum time travel we first have to know a bit about closed timelike curves. 

Kurt Gödel was a mathematician, a philosopher and a logician. He’s actually thought to be one of the most significant logicians in history along with Aristotle. In 1939 he left Germany and moved to Princeton where he became close friends with Albert Einstein. They used to take long walks around the grounds together. Einstein once commented that he had no reason to go to the office anymore but he went anyway, just so he could walk with Gödel. 

In the late 1940s Gödel developed a solution to Einsteins field equations for closed timelike curves which described ‘rotating universes’ that would allow for time travel. He gave the solution to Einstein for this 70th Birthday which then caused Einstein to have a crisis of faith in his own theory. 

Closed timelike curves (CTCs) are created when space-time curves so much that it closes in on itself returning to the same point in space and time. They are causal loops creating a route to the past.

This leads, of course, to inconsistencies and time travel paradoxes. Over time some scientists have tried to find a solution to this. My favourite is Novikovs’ self-consistency principle that says that if you time travel to the past nothing you do will affect the future because the events will be self consistent, they will always happen in a way that leads to the same future.

Other scientists have tried to disprove the existence of CTCs such as Hawking with his chronology protection conjecture which says that the mathematical solution doesn’t override the laws of physics. So that while you can say it’s a solution to the field equations it would still violate causality and so the laws of physics would stop it from ever physically happening. 

But what if we apply superposition and entanglemnet to time?  

Let’s think for a moment about the twin paradox in special relativity; it’s a thought experiment that helps us understand how time is relative at fast enough speeds. 

One twin stays on Earth while the other travels for some time in a spaceship close to the speed of light and then returns to Earth. When twin two returns, they find that time passed differently from their perspective and they are now much younger than their twin on Earth. 

Now imagine the twins are entangled particles. One stays here while the other travels along a closed timelike curve, we can call it a loop. Well now the particle on the loop will have different versions of itself, younger and older versions. But the entangled particle outside the loop can’t be entangled with the younger and the older version, not according to our current understanding of quantum mechanics. 

However, if the particles on the loop are entangled in time rather than space, well then the entanglement with the one outside the loop isn’t violated. 

So to have a particle travel a closed timelike curve they would need to be able to be entangled in time and you would need a theory of quantum space-time to describe the behaviour. This type of quantum theory could make time relative to the observer on a quantum level making quantum-time travel entirely possible. 

It’s important to point out that these are all just mathematical ideas that require a lot of conditions to be true, conditions we don’t yet know are true or false. So for now we can only look at what the ideas are and continue to investigate and learn more. But this idea is one of my favourites. 

My next post will be in two weeks time and I’ll be looking at how Avengers Endgame used these ideas to create a story around quantum time travel. We’ll talk more about the Planck Scale and exactly what the ‘Deutsch Proposition’ is supposed to mean. 

You can find a video version of this on my YouTube, and if you’re interested my Patreon is free where all videos, text, recommended articles everything relating to this months topic will be available there. 

Thanks for reading, stay nerdy.

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References/Recommended Reading

1. Experimental aspects of indefinite causal order in quantum mechanics. / Rozema, Lee A.; Strömberg, Teodor; Cao, Huan et al.

   In:Nature Reviews Physics, Vol. 6, No. 8, 08.2024, p. 483–499.

2. Why rethinking time in quantum mechanics could help us unite physics. / Vlatko Vedral

3. Quantum correlations which imply causation. /

   Fitzsimons, J., Jones, J. & Vedral, V.

   In: Sci Rep 5, 18281 (2016). https://doi.org/10.1038/srep18281

4. The New Scientist Essential Guide, No19: Time

5. An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation. /

   Kurt Gödel.

   In: Rev. Mod. Phys. 21, 447 – Published 1 July 1949

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