# The unrecognizable fragments of causality in light of quantum gravity

Updated: Apr 1

In today’s blog we talk to Dr. Magdalena Zych, PhD from the University of Vienna, Australia Research Council DECRA fellow at the University of Queensland, on counterintuitive notions about reality from quantum gravity.

**David**: What is the largest system that has been shown to exhibit quantum effects? In other words, how close are we towards realizing Schrodinger’s cat in the laboratory?

**Magdalena**: The largest objects, in terms of their mass, that were experimentally witnessed to exhibit quantum interference are molecules at about 10^-23kg, while the largest achieved superposition, in terms of the distance between the superposed amplitudes, was about 30 centimetres, with Rubidium atoms.

Some more background on this: The above mentioned molecules are complex oligo-tetraphenylporphyrins molecules with some extra chains added (here is the paper: Fein, Y.Y., Geyer,, Zwick, P. *et al.* Quantum superposition of molecules beyond 25 kDa. *Nat. Phys.* 15, 1242–1245 (2019). https://doi.org/10.1038/s41567-019-0663-9).The technique in that one and similar experiments is to put molecules through three gratings — which serve to prepare a coherent beam of molecules, diffract it, and image — and observe interference patterns at the end. The slits of these gratings are very close together for our everyday life scale, some 500 nm (and they have to be so, as the deBroglie wavelengths of such massive molecules are themselves of order of 10^-5 nm). And so while the experiments unambiguously shows quantum coherence of objects as big as 10^-23kg, the involved length scales aren’t macroscopic — as we would perhaps anticipate from a genuine Schrodinger cat — and therefore one can be interested also in what’s the largest distance over which an object was superposed, which is about 30cm. Click on the following link for reference: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.183602. As this was realised with individual Rubidium atoms, the mass here is about 10^-25 kg. And so while the 30cm size of the superposition is truly macroscopic, we only have a single-atom cat, perhaps a bit too small… (I note there’s a claim of a 54 cm superposition form the same group in this paper http://www.nature.com/articles/nature16155, but I side with critics that the technique used there did not allow for an unambiguous attribution of the result to quantum superposition).

So where are we on the way to a genuine Schrodinger’s cat? This is not so easy to answer as we have to compare different types of experiments: large molecules superposed over 100s of nanometers or single atoms over 10s of centimetres. Which is more macroscopic? There is at least one approach to addressing this, a so-called measure of macroscopicity, developed here: Stefan Nimmrichter and Klaus Hornberger. "Macroscopicity of Mechanical Quantum Superposition States." *Physical Review Letters*. DOI: 10.1103/PhysRevLett.110.160403 . According to this indicator, the molecules score ~14, atoms score ~12.5, while a 4 kg cat in superposition of locations separated by 10cm for 1sec scores 57. It’s a log-scale: a given superposition is assigned the same macroscopicity x as that of an electron held in a superposition for 10^x seconds. And so how close we are to at least an equivalent of a cat? According to this measure we are some 33 orders of magnitude away -- still a lot of ground to cover despite progress!

**David**: If I understand correctly, you are studying the possibility of producing a superposition of two systems that are, or can be viewed as being, in different regions of the gravitational potential so time runs at different rates. What are the challenges?

**Magdalena**: This is correct! The challenge comes from the fact that gravitational time dilation that makes clocks run at different rates is small compared to how precise clocks we can put in a quantum superposition. The most precise clock we can use for such experiments would be a single atom, eg Sr whose internal energy levels can give us a clock able to resolve time to a precision of T=10^-15sec. Gravitational time difference between clocks at heights differing by h after time t is Tau=ght/c^2 where g is gravitational acceleration, approximately 10m/s^2 on earth, and c is the speed of light. We would thus need to put a clock in a superposition of heights h and for a time t such that T=Tau, ie gh=Tc^2/g approximately 10m*s — which is still some 2 orders of magnitude away from what atom interferometry can achieve, plus we need to prepare the internal states in a superposition too in order that the atom serves as a clock and can give the desired signature of time dilation on top of the standard interference pattern. So in fact the challenge is both: the size of the superposition that’s required and the extra difficulty of preparing and manipulating also the internal states such that they remain in superposition.

**David**: When we look at physics more fundamentally, it seems like cause and effect are emergent and from a certain perspective, can be reversed. Your research seems to mix cause and effect in ways that are even more counterintuitive, such that a physical system can be both in a state in which A causes B and in which B causes A, simultaneously. Can you explain this idea, including its implications for the concept of reality?

**Magdalena**: Indeed, in my research I am investigating scenarios where the order of events can be superposed or even be entangled with the order of other events! The idea is to coherently control time order of some operations performed on a quantum system by another quantum system. Such a scenario is called a quantum SWITCH and was first proposed/discovered by Giulio Chiribella and colleagues, from the University of Pavia, in the context of quantum computing. You can realise the SWITCH naturally in quantum optical circuits by letting a photon pass in superposition through a sequence of gates/wave plates: first A then B or first B and then A. When you recombine the superposition (creating a regular interferometer) you end up with a photon that was subject to operations A then B and B then A in superposition. In my work we show that gravity can allow us to create such a superposition or even entangle the causal order. Recall gravitational time dilation: the closer to a mass the slower the time/ticking of any clock. Take a pair of agents each having a clock, and able to apply some operation, say, on the electromagnetic field in their vicinity. The clocks are initially synchronised and the agents perform their operations at some pre-agreed time, e.g. the experiment starts at noon and they have to perform their operations at 3pm. By putting a mass closer to agent A than to B, we slow down the clock of A relative to the clock of B. Crucially, one can arrange this such that the event when A’s clock strikes 3pm can end up in the causal future of the event when B’s clock strikes 3pm — in which case there is time for the electromagnetic field (which can contain e.g. a photon) to propagate from B to A and the operations are performed in the order B then A. If the mass is placed closer to B, then the order of events and operations on the field is A then B. An interesting thing to remember is that while we often picture the required mass as a planet, it does not need to be massive —it “just” needs to be dense. By putting the mass in superposition and then interfering back the superposed amplitudes we achieve the scenario where A causally proceeds B and B precedes A in superposition. This is how gravity and quantum mechanics can give quantum causal order, and crucially this prediction does not require any new physics.

What does it say about reality? I'd say this shows that the possible relations of cause/effect are broader in nature than in our classical experience. In my view this is analogous to superpositions of positions of objects — in classical world being in location x precludes being in a different location y — they are mutually exclusive states of affairs. A quantum superposition of being at x and at y shows (this is how I think about it) that there are more possible ways of being located. Similarly with superpositions of cause/effect this would show us that there are more possible “states” of the cause--effect relationship than either A before B or B before A. In fact we further show that if quantum theory and GR hold with no modifications if we simply superpose two classical scenarios, then it is not possible to describe causal structure of spacetime in terms of any local hidden variables — in analogy to how properties of particles cannot be described by local hidden variables as shown by violations of Bell’s inequalities. So in the same manner that properties like spin, energy, position cannot have local reality, also causal relations cannot!

**David**: Does your work fit more within the efforts geared towards achieving quantum computation, more towards those focused on solving quantum gravity, or somewhere in between?

**Magdalena**: I am definitely driven by the issue of quantum gravity — what can we say about quantum gravity phenomenology without resorting to any particular framework but by exploring to which extent the various concepts of quantum theory and gravity can be pushed together? Some researchers would have said that it is not even possible to make calculations describing our quantum gravitational causal order without a full quantum gravity theory, or that it is even not possible at all (as there is no common time for the different superposed amplitudes). Yet, we have shown how the mathematical tools already present in classical GR and in quantum theory allow us to unambiguously derive all the predictions! I definitely keep an eye on the developments in quantum computing that use the conceptual framework behind the quantum SWITCH, as this is simply very interesting in its own right, and of course can be a trigger for further developments for my own research.

**David**: Thank you Professor!