The universe may not be alone, in the sense that it might be one of many universes in a multiverse. One feature that multiverse concepts entertain is that it may be that there are universes very similar to our own. Arbitrage works by exploiting small differences in value across markets. So could a hypothetical multiverse arbitrageur do something similar?
Arbitrage is a method used in trading to exploit differences in the valuation in different markets. Let's imagine a future world where traders can communicate with other traders across a multiverse of universes. What would multiverse arbitrage be like? This article will consider this question from a scientific perspective (though the physics is itself speculative), but bear in mind that nothing like this exists or is likely to exist for a long time, if ever.
Arbitrage is predicated on the same underlying markets being valued in different contexts. For example, CFD prices are based on the underlying market but can diverge. Arbitrageurs bring prices back into alignment by making a profit on that difference. So a multiverse arbitrage would need two-way communication, firstly to inform traders in different universes that there is a price difference and then to allow them to make trades to bring them back into alignment.
The multiverse
The multiverse is a speculative concept suggesting that the universe as we know it might be one of many universes. Two approaches to a multiverse will be lightly considered in this article. Firstly, the Many-Worlds Interpretation (MWI) suggests that there is a single, universal wavefunction that does not collapse. Rather, every quantum event leads to a branching of reality into different outcomes, each representing a version of that universe where that particular result happens. Secondly, the Brane-World Scenario (BWS) suggests that the universe exists in a higher-dimensional space that contains other universes, potentially in very large numbers.
Conditions for arbitrage
To arbitrage across the multiverse, one would need universes with very similar states. The MWI and the BWS allow this but in different ways. For the MWI, at the moment of branching, the universe will be identical to the current universe but will start to diverge from there. For the BWS, a near-identical universe to a given universe at a moment in time is possible but may be separated by enormous distances.
To be aware of an arbitrage differential, one needs to communicate signals. There is no known way to send a signal across the multiverse, no matter what the framework. However, we have to assume an advanced technology that allows for this. But we don't want to pass over this; we need to think about how this might happen.
For the MWI, universes may be linked by entanglement, but they would not be connected in any way that might allow for signals to be sent, even faster than light. Entanglement allows for instantaneous correlations between states. It does not allow for a signal to be sent faster than light. So we will assume that there is a way to send a signal via entanglement. This would allow for a trader in universe A to arbitrage a market in branched universe B by sending a signal there and receiving it back.
For the BWS multiverse, we could envisage a communication backbone consisting of an advanced faster-than-light communication method, for example, utilizing wormholes and exotic matter, to send signals there and back.
Given the communication issue, one might imagine an advanced machine learning system, utilizing quantum computing perhaps, that tries to predict the arbitrage based on information about the universe in question, or about this universe and how it might change.
This technology could allow for a trade to be simulated that is then confirmed by some communication method. So trades wait in a queue to be confirmed, depending on the speed and reach of the communication system.
One could even imagine derivatives based on speculations about the difference between the prediction and the communicated result, assuming there is one such prediction machine, when in fact there may be many, with different capabilities.
Other possibilities
A multiverse can arise in other speculative ways. String theory proposes that underlying reality includes a complex 6-dimensional shape called a Calabi-Yau manifold. This manifold structures strings, giving rise to reality as we know it. However, the complexity of this manifold allows for many other configurations. These configurations may give rise to entirely different universes. This 'string landscape' problem is not necessarily one that would lend itself to arbitrage, as the universes will tend to be very different from each other.
When you think about it, if the very foundation of reality alters, then everything else will tend to be very different. In the MWN, identical universes initially arise from the same quantum event, so the similarity is taken care of, for a time. In the BWS, physics allows there to be similar universes, but as we have seen, the issue is communicating the differences across unfathomable distances.
Arbitrage works by exploiting small differences. The scope of arbitrage has increased as technology allows faster communication. High-frequency trading is a type of arbitrage on very small differences. So we speculate in this article about a very different scale. The structures that allow for these similar universes to exist may arise in different ways: dimensions may be curled up in complex shapes, or form large-scale structures in which different universes may coexist (BWS), while in the MWI, similar structures may correspond to the seemingly inaccessible outcomes of quantum events. But the scale, both large and very small, of this type of arbitrage requires technology far beyond anything possible today. Would this advanced civilisation be interested in arbitrage? Well, it is something that has fascinated humans and appeared in different forms as technology has advanced, so it may well continue to do so in a possible distant future, but they may also pursue entirely different interests.
