A quantum-cryptocurrency analogy
Unlike some other people, I am not a real member of the cryptocurrency cult.
I think that the economics orthodoxy as imagined by the founders as well as champions of the Bitcoin is deeply flawed. Also, I don't find the key "virtue" of the cryptocurrencies – decentralization of the list of transactions – terribly important or practical. By the way, JP Morgan boss Dimon said that the Bitcoin was a fraud (something that most of the financiers may agree with) and the currency instantly lost almost 10% of the value. Not too resilient! BTW I have written exactly the same thing as his 1-minute monologue. When the tax losses etc. become significant, the Bitcoin will simply be banned, will drop to near zero, and this "economy" will be over.
On the other hand, I think that the switch from classical physics to quantum mechanics was the most important event in science of the last 100 years. And I generally dislike vague analogies. For these reasons, you would think that I just can't possibly sell the following analogy. But the analogy looks so self-evident and catchy to me that I simply have to dedicate a blog post to it.
First, think about the blockchain. This concept is a key part of the Bitcoin network. It's a list of records that remember which payers have moved the cryptocoins to which recipients. This list is growing. All the new transactions are added on top of the old ones. The new transactions are added in blocks. The blocks are finalized when some miner solves a mathematical problem. The solution is being verified by others.
The whole obsession of the cryptocoin community is the ability of the blockchain technology – and therefore the payment system based on the Bitcoin etc. – to decentralize the list of records. Normally, when you're making payments through a bank, the bank's computers remember the "official" balance of each account and the list of payments that have taken place.
But the Bitcoin enthusiasts are mostly anti-capitalist whackos who imagine that the main hobby of a banker is to tamper with the list of payments and to steal the electronic money from the clients' accounts. Well, it has never happened to me and I think that there exist mechanisms that make sure that this is almost never happening – which is why I consider the cryptocurrencies to be a mathematical curiosity, not something that is very useful.
However, the cryptocurrencies' users also have their list of record – a copy of the blockchain – but the copy isn't copied from any single centralized place. It is decentralized, it only comes from some collective communication. When you download, install, and run Bitcoin Core, the simplest Bitcoin wallet that your computer may run, it continues by downloading the approximately 150-gigabyte-long blockchain from some place. A big portion of your hard disk is reserved for a copy of all payments that have ever been done by the Bitcoin.
Now, it's funny. No copy of the blockchain is "the truly official one". Nevertheless, virtually everyone agrees about some old enough transactions. How is it possible? And haven't we seen something similar in physics?
Yes, we have. Each copy of the blockchain is analogous to an observer's wave function or the density matrix by which he describes the real world. There is no "single, centralized, objective truth" about the state of the world and the events in the world. And every observer in principle has his own wave function or density matrix because he has done his observer-dependent observations that have made the collapses whose character and timing depends on the observer.
However, despite this subjectivity in principle, almost all the observers agree what big measurements have been made in the past and/or which payments have been made. These two things are really analogous.
Just like the laws of quantum mechanics guarantee some correlations so that the outcome that you directly measure will probably agree with the outcome measured by another observer who tells you about his results, the Bitcoin technology guarantees that the "classical truth" reproduces itself, so in effect, almost everyone uses the same blockchain after some time – with some possible differences that usually affect the newest transactions only – despite the fact that there is no centralized objective source of the truth about the payments.
This picture shows a chain of events. The past is at the bottom, the present is at the top. The boxes may correspond to the projection operators that describe a measurement that has taken place. It's important that in quantum mechanics, the projection operators are chronologically ordered – the order matters because the operators are not commuting. The black boxes correspond to "the rather universally accepted truth", they are part of the longest chain that you can find. On the other hand, you may extend the longest chain by the violet blocks – events that may be temporarily considered as vague, preliminary, quantum truths by an observer (especially a "not quite macroscopic" observer) but that haven't been copied to sufficiently many places, to macroscopic properties of classical objects yet, so they may have been revised and they have been revised, indeed.
Well, I claimed that the interpretation of this picture is all about quantum mechanics. But I picked the picture from the Blockchain page on Wikipedia. It shows the blockchain which is composed of blocks and the black chain is the longest sequence of blocks and generally considered to be "the right list of transactions" at a given moment (really, by a given observer/user of the cryptocurrency in a place of the spacetime). The violet blocks are known as "orphaned blocks". They arise when the mathematical problems that the miners solve are solved by several miners almost at the same moment. One of them will later be accepted as the truth. The orphaned blocks are the losers and they may exist basically due to the vagueness of quantum mechanics.
Again, the main analogy is that each observer has his own list of events and they generally differ from each other. But with hindsight, it's unavoidable that almost all observers will agree about which events – and the events are transactions e.g. payments in the Bitcoin analogy – have taken place. So despite the intrinsically decentralized, and therefore observer-dependent, character of the wave function, density matrix, or the copy of the blockchain, all macroscopic and old enough events ultimately behave almost just like in a classical world where the truth about the history is objective, unique, or stored on a single official hard disk of a bank.
That's how the blockchain manages to replace the single-computer-based record of payments so that the economy may work analogously even though there is no central authority; and how the wave functions and density matrices may replace the objective value of the classical degrees of freedom in the whole spacetime even though the wave functions and density matrices are fundamentally observer-dependent and subjective. The cryptocurrencies effectively work much like the list of records on a single official bank server; and quantum mechanics may be used to describe the events in the world analogously to classical physics even though it's fundamentally different. However, some slightly nontrivial mathematics is needed both in the Bitcoin and in quantum mechanics which guarantees that the macroscopic and old results look very similar to those in a single-bank economy or in classical physics.
The uniqueness and universality of the "truth about events" (e.g. payments) is no longer a precisely valid axiom in quantum mechanics or the Bitcoin. It is no longer a dogma or a trivial truth you can make for granted. In fact, it's not quite true if you're precise enough. To say the least, different observers or Bitcoin users update their wave functions or copies of the block chain at different moments. The agreement between the people (observers or users who run the Bitcoin Core) is an approximate emergent consequence of nontrivial and novel fundamental laws that govern quantum mechanics or cryptocurrencies.