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 arbitrageurs do something similar?
Arbitrage is a method used in trading to exploits 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 considered in this article. Firstly, the Many-Worlds Hypothesis (MWH) suggests that the wavefunction's collapse branches a new universe. Secondly, the Brane-World Hypothesis (BWH) suggests that the universe exists in a higher dimensional space that contains other universes, potentially an infinite number.
Conditions for arbitrage
To arbitrage across the multiverse, one would need universes with very similar states. The MWH and the BWH allow this but in different ways. For the MWH, at the moment of branching, the universe will be identical to the current universe but will start to diverge from there. For the BWH, 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 MWH, 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 BWH 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 is a complex 6-dimensional shape called a Calabi-Yao 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 are 'spawned' from each other, so the similarity is taken care of, for a time. In the BWH, 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 dimensions that allow for these similar structures to exist may be curled up in complex shapes, they may be large-scale structures for different universes to co-exist (BWN) or they may be seemingly inaccessible creations of quantum events (MWH). But the scale both large and very small of this type of arbitrage requires technology far beyond anything possible today.
