This started when I was reading The Order of Time (2018) by the rather poetic physicist Carlo Rovelli, and read that he said that causality is not certain, and two events can have a superposition of causality: a superposition of two possibilities: A causes B, and B causes A.
Quantum corelations with no causal order
The paper that started this seems to be a highly cited (over 200 currently) Quantum correlations with no causal order (2012), Ognyan Oreshkov, Fabio Costa, Časlav Brukner.The abstract starts with a question: is causality fundamental?
The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature?
Here, we address these questions from the standpoint of quantum mechanics in a new framework for multipartite correlations that does not assume a pre-defined global causal structure but only the validity of quantum mechanics locally.This is the theoretical approach used in the paper, which the authors later compared to General Relativity's take on spacetime: locally, spacetime is flat, but globally, not. This allows weird things like a time loop happen globally. Similarly, the authors here only use local quantum mechanics which can give global weird things.
All known situations that respect causal order, including space-like and time-like separated experiments, are captured by this framework in a unified way. Surprisingly, we find correlations that cannot be understood in terms of definite causal order. These correlations violate a 'causal inequality' that is satisfied by all space-like and time-like correlations.Here's the cool thing: the familiar kinds of causality can be explained in this theory, but now new and bizarre kinds can also appear. There are correlations that are not causality.
We further show that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition.Here, it's suggesting that maybe causality is not fundamental, but an approximation, just like how classical world is an approximation of quantum world.
In a thought experiment, there are two observers Alice and Bob, in two labs A and B. The labs are small enough so that locally, quantum mechanics and causality works as usual.
It's possible that A and B would have related observations, for example, if A sends a signal to B after A's observations but before B's observations. The strange thing is that it's possible for A and B to have related observations in a way that cannot be causal.
Correlation without causality!
We find that, surprisingly, more general correlations are possible, which are not included in the standard quantum formalism. These correlations are incompatible with any underlying causal structure: they allow performing a task—the violation of a 'causal inequality'—that is impossible if events take place in a causal sequence.It's like non-localism. Now it's non-causalism.
This is directly analogous to the famous violation of local realism: quantum systems allow performing a task—the violation of Bell's inequality—that is impossible if the measured quantities have pre-defined local values...
The thought experiment is thus:
What happens in Alice's lab:
- A coin (technically, a quantum bit) appears in front of Alice.
- Alice measures it, and writes down the measurement result as a bit $a$ (can be $0$ or $1$).
- Alice puts the coin in a teleporter that sends the coin away.
- Alice writes down an "answer" bit $x$.
What happens in Bob's lab:
- Bob throws a fair coin (given by God, probably) and writes down the result as $b'$.
- A coin appears in front of Bob.
- Bob measures it, and writes down the measurement result as $b$.
- Bob puts the coin in a teleporter that sends the coin away.
- Bob writes down an "answer" bit $y$.
Alice and Bob are playing a game with God. The rules of God says that
- If $b'=0$, then Alice and Bob both live if $x = b$. Else they both die.
- If $b'=1$, then Alice and Bob both live if $y = a$. Else they both die.
Before the thought experiment starts, Alice and Bob can arrange the causality of the world to increase their survival chance.
For example, they can arrange so that the coin is moved to Alice after Bob measures it (or the other way around), so that Alice always measures the same as Bob, so $a = b$. Alice can then always guess $x = a = b$. Bob is helpless and can only guess randomly.
If $b' = 0$, they both survive. If$b' = 1$, then they survive with $1/2$ chance.
In this way, the chance of survival is $3/4$ in total.
They can also try to improve their chances of survival by arranging some kind of entanglement between the two coins they receive. The point, though, is that no matter how they try, the chance of survival is $\le 3/4$ in total.
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| (a): Global causality is preserved. (b): No global causality, survival rate increased to $(2+\sqrt{2})/4$. |
Alice and Bob survived, but global causality is sacrificed.
At the end of the previous paper, the authors noted possible experiments for this kind of causality-breaking: "superposition of wires".
... quantum circuits by using superpositions of the 'wires' connecting different gates... As the instant when a system enters a device depends on how the device is wired with the rest of the computer's architecture, superpositions of wires may allow creating situations in which events are not localized in time (similarly to the way in which a quantum particle may not be localized in space).Imagine a quantum computer, with quantum gates wired together in a quantum circuit, operating on quantum bits that are in superposition. Then imagine the computer itself in a superposition. That's so meta. This has no fixed global causality structure, and can be used to experimentally verify predictions of this paper.
In detail, imagine two gates A and B in a superposition of two wiring diagrams: |A's output goes into B>, and |B's input goes into A>. To achieve this, imagine a "control bit". If the control bit is $0$, it's A to B, but if $1$, it's B to A. Now prepare the control bit to a superposition $(|0> + |1>)/sqrt(2)$. This is explained in Quantum computations without definite causal structure (2013).
Further, such weird causality-breaking can be used for quantum computing:
... new quantum resources for information processing might be available—beyond entanglement, quantum memories and even 'superpositions of wires'...
Experimental superposition of orders of quantum gates
Experimental superposition of orders of quantum gates (2015) demonstrates this superposition of wiring experimentally, using photon polarization as qubits:Here we experimentally... using a second qubit to control the order in which two gates are applied to a first qubit. We create the required superposition of gate orders... The new resource we exploit can be interpreted as a superposition of causal orders...The practical use is that this allows faster quantum computing of some operations:
... it has been shown that using a qubit to coherently control the gate order allows one to accomplish a task—determining if two gates commute or anti-commute—with fewer gate uses than any known quantum algorithm.However, in an expository paper on that experiment, Witnessing causal nonseparability (2015), it's noted that, while this demonstrates "indefinite causality", the causality-breaking is not quite as radical as in the Quantum corelations with no causal order (2012), since Alice and Bob still cannot use this to improve their survival chance:
We show however that the quantum switch does not violate any causal inequality.Here, the "causal inequality" really means $P(\text{Alice and Bob survives}) \le 3/4$.
Okay why?
The reason is that Alice and Bob are not radical enough. They put the universe into a superposition of two states. In one, Alice sends the coin to Bob. In another, Bob sends the coin to Alice. But in either case, their survival would come out to just $3/4$, so the superposition still gives a survival rate of $3/4$.
Experimental verification of an indefinite causal order
Experimental verification of an indefinite causal order (2017) improves over the previous experiment by being more direct:However, the absence of a causal order was inferred [in the paper Experimental superposition of orders of quantum gates (2015)] from the success of an algorithm rather than being directly measured. Here, we explicitly demonstrate the realization of a causally nonordered process by measuring a so-called “causal witness”.Note that in this experiment, Alice and Bob are still not breaking the causality inequality, since it's the same causality setup, just with more explicit measurement.
Indefinite Causal Order in a Quantum Switch
Indefinite Causal Order in a Quantum Switch (2018), same experiment, but with even better accuracy:We show that our quantum switch has no definite causal order, by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound.18 standard deviations. That's hardcore.
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| Not sure if quantum optics or Rongorongo |
Bell's Theorem for Temporal Order
Bell's Theorem for Temporal Order (2017) shows that in quantum mechanics + general relativity (qunatum gravity), causality must break. Imagine a neutron star, miraculously placed in superposition. Then, the spacetime around that star would be in a superposition as well. If the star is there, the spacetime would be highly distorted. If not, the spacetime is flat.It's possible to push this harder and break the classical ordering of time:
When the distribution of matter requires a quantum description, temporal order is expected to become non-classical... We consider a massive body in a spatial superposition and show how it leads to "entanglement" of temporal orders between time-like events in the resulting space-time. This entanglement enables accomplishing a task, violation of a Bell inequality, that is impossible under classical temporal order. Violation of the inequality means that temporal order becomes non-classical...
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