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Blockchain and The Pauli Exclusion Principle

The Double Spending Problem

The original Bitcoin whitepaper laid the foundation for Blockchain. In the abstract, Satoshi Nakamoto outlines one of the revolutionary aspects of this new technology.

We propose a solution to the double-spending problem using a peer-to-peer network

I want to begin by giving a brief overview of the significant components of the Blockchain system as outlined in this seminal paper. I then want to look at the curious similarities between this technology, and a fundamental law of nature: the Pauli Exclusion Principle.

Imagine I have a piece of paper containing all the monetary exchanges between a group of friends. I number them in order of occurrence, and require transacting parties to sign their names next to their transactions as verification. A few problems are apparent. Ideally, as the guardian of this list, my job is to check that nobody engages in more transactions than their balances allow, ensuring they don’t double-spend their money. However, being the sole keeper of this document, I can easily add of subtract transactional lines at my discretion.

Blockchain technology removes the central authority (me) by giving every transacting member their own copy of the transaction list. Another problem arises — how do we ensure that everybody has the same copy of this ledger? Furthermore, how do we add transactions to one copy and ensure all the others are updated correctly in real time? Why can’t I just edit my copy and give myself free money?

Given that there is no central authority-the entire network needs to agree on a single transaction history. It does so in the following way: every member of the distributed network receives a list of transaction. A certain number of these are collected into a block and a proof-of-work is computed by the nodes in the network. The ledger that the entire network will believe as the real one is the one with the most computational work put into it.

This idea of work can be thought of as finding a difficult solution to a mathematical puzzle. The computational work is intrinsically linked to every single block of transactions, every block contains some part of the previous block within in (the blocks are chained). This means that if you wanted to go back and forge an old transaction — you would not only have to change the specific transaction, but redo all the work until your blockchain was as long as the original one. Only then would the entire peer-to-peer network believe that your ledger is the real. However, this process is completely infeasible as the amount of work required would be astronomical. Furthermore, while you’re busy hacking away, the real Blockchain is continually growing in size such that yours would never have time to catch up. The whitepaper outlines this concept succinctly:

“The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power.”

The Pauli Exclusion Principle

It’s almost trivial to point out that no two things are ever perfectly identical. Even in a highly optimized manufacturing process, tiny defects are always present for a discerning eye to point out. However, in the realm of the microscopic quantum world, things are different. Electrons are completely identical, in a way that no macroscopic objects are. There is no way to distinguish between them. Modern quantum field theory makes this coherent, by describing that particle electrons are simply excited vibrational modes of an underlying field.

No two fermions can have exactly the same quantum state

This is a statement of the Pauli Exclusion principle found in one of my undergraduate quantum texts. A quantum state is denoted by a specific configuration of quantum numbers. These numbers represent things such as spin, angular momentum and other parameters. Fermions are a certain class of elementary particles to which the electron belongs. The spin parameter for fermions is restricted to half-integer values, wheras the other class of elementary particles, bosons, has integer values for spin.

Simply put, the principle says that for any two electrons, the numbers denoting their quantum state can never all be the same. This is not an ad hoc rule formulated by Wolfgang Pauli — but a consequence that emerges out of the rules of quantum mechanics. In the macroscopic world, we can denote the state of something by specifying its position and momentum (as functions of time). From this state, we can calculate what our object will do in all future moments. In the microscopic world however, the state is represented by a state vector. We cannot specify the exact position or momentum of particles (as dictated by the Heisenberg Uncertainty Principle), so this state doesn’t contain definite, deterministic facts of the matter. It contains all probabilistic information pertaining to the situation. The Pauli Exclusion Principle is a consequence of how we write state vectors for multi-particle systems of electrons. If any of these electrons had all the same quantum numbers — the states would be nonsensical.

Abundance and Lack

Upon enlightenment, many Zen masters come up with singular sayings to encapsulate the totality of their experience. Here is one of Dogen’s many phrases:

Drop off body and mind — leap clear of abundance and lack

Leaping clear of abundance and lack — what a perplexing thought! We exist in a world within this dichotomy, yet Dogen urges us to go beyond. By going beyond — he means embracing the interpenetrating nature of these two opposites. The formulation of blockchain and Pauli’s Principle shed light on what is meant.

We have two global rules: one that governs the universe, and one that governs a system. One is created, the other is discovered.

How do you tackle the double-spending problem?
How do you ensure that no two fermions are in the same quantum state?

The Pauli Exclusion Principle emerges out of quantum mechanics — we don’t need to ensure that particles adhere to it since it is a consequence of our previous science. There are no dishonest electrons — none of them will sneak into the same quantum state as one another. This principle is an inseparable aspect of electrons. It gives us a restriction, a lacking. There cannot be unlimited electrons in the valence shell (outer shell) of an atom for instance. It is precisely because of this lack that we have an abundance of molecules in the world. This fact alone gives rise to the periodic table of elements, and the internal mechanics of stars.

The double spending problem is an intuitive, almost banal example of the balance between abundance and lack. You don’t want someone to spend a coin they’ve already spent — when they lack, you don’t want them to falsely claim abundance. Here is where things get interesting and where blockchain begins to mirror nature. The proof-of-work is inseparable from the block, the system is linked together in a way that a local change (an attempt to malevolently change a transaction) has global effects (you need to redo every previous block). Similarly, changing the quantum state of an electron in a small system (a local change) has the global effect of changing the state vector of the entire system. This kind of inextricable linkage does not only demand adherence to a principle — but necessitates it. I think this is what Dogen meant when he describes leaping clear of abundance and lack. We can never live without the polarity — but embracing their relationality is what gives us true richness.

Observing how nature functions is a good way to find inspiration for our own creations. The trust-less and automatic adherence to rules is a hallmark of nature — and Blockchain has successfully repurposed this technique.



Blockchain Explanation:

Quantum Texts: Intro to QM by Griffiths — Principles of QM by Shankar