…we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions.
— Satoshi Nakamoto, Bitcoin: A Peer-to-Peer Electronic Cash System

Bitcoin is a peer-to-peer distributed timestamp server that provides proof of the chronological ordering of transactions. This ordering applies to all transactions and we show that it has significance not just between blocks, but also for the transactions within each block.

Someone suspicious of such a claim that transactions are ordered chronologically within blocks, might remark:

“It is false that transactions are chronologically ordered within each Bitcoin block. We know that the many other non-dependent transactions within the block can be arranged in any order the miner of a block chooses and thus cannot possibly be ‘chronologically ordered’.”

We show in a future article that it is possible to gain improved time precision despite only having explicit block timestamps to work with. Furthermore, we show that there is a well-defined meaning of chronological order, despite being “chosen” by a miner in a seemingly ad-hoc fashion.

The consensus requirement that transactions must appear after their parent dependent transactions is the key ingredient for showing that transaction ordering between, and within*,* blocks is fundamentally chronological in nature.

We will show that this chronological ordering of transactions has significance for various classes of applications and use-cases, and even more so when transaction volumes are larger by orders of magnitude.

Let us begin.

What “Chronological Ordering“ means

First we provide definitions and additional motivation for this discussion.

Definition — Chronological: Relating to chronology; containing an account of events in the order of time; according to the order of time; as, chronological
— Webster’s Dictionary 1913

“Chronological” refers to layout out events in a series where events happening at a later time, follow events happening at an earlier time. The benefits of doing this allows us to simplify, visualize, and process data in the order in which events were perceived to have happened.

It is tempting to think there is a ‘universal’ or ‘real time’ in which something happened and that the chronology is an approximation of the ‘true, single time’ — however this is not how time works and is an illusion that was destroyed almost 100 years ago by Einstein.

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance.
— Albert Einstein, Relativity: The Special and General Theory. (3)

Simply put, a timeline or chronology serves a purpose of communication to the agents (observers) in a system. It is more important that there is a consistent clock or chronology rather than whether it is “true”.

“The most valuable property of the bell tower time was not its accuracy, but its fairness. Even if it broadcast the wrong time, it broadcast the same wrong time to everybody.”
“The productive synchronization of human relationships funded the bell towers; the bell towers would provide a ready market for public clocks. Thus did in Europe emerge a“virtuous circle” that would advance both its timekeeping technologies and time-dependent institutions beyond those of the other continents.”
 — Nick Szabo http://www.fon.hum.uva.nl/rob/Courses/InformationInSpeech/CDROM/Literature/LOTwinterschool2006/szabo.best.vwh.net/synch.html

Chronological is related to causality:

… By “chronology,” we mean what happened, in which order.
Chronology is important because the exact order in which events occur helps us understand the cause and the effect of those events, and thereby allow us to step back and view the “big picture” of history — how and why events unfold in the way they do, and how they are related.”
https://qcpages.qc.cuny.edu/writing/history/considerations/chronology.html

Quick Preview of The Idea That Arbitrary Precision of Event Times Are Possible

Block B1:
Tx1 ← Tx2
other unrelated transactions

Block B2:
more unrelated transactions

Where Tx1 and Tx2 are both transactions mined into a block B1, and where Tx2 depends on outputs from Tx1.

Since Tx2 depends on Tx1, we know that Tx1 must have occurred before Tx2.

The relationship is:

Time(Tx1) = Timestamp(B1) + (Plank Time * (Position(Tx1) + 1*))*

Time(Tx1) < Time(Tx2) < Timestamp(B2)

We can see that if transaction Tx2 depends on Tx2, then it necessarily follows that it happened after Tx1 by at least the minimum time increment possible in our universe (Which is the Plank Time of 10^–43 seconds)

However, since all time is really a mutually agreed upon chronology, we can actually break up a 10 minute block into 1-minute increments with:

Tx1 ← Tx2 ← Tx3 ← Tx4 ← Tx5 ← Tx6 ← Tx7 ← Tx8 ← Tx9 ← Tx10

This means that with 10 dependent transactions in causal/chronological order, we have effectively simulated 1-minute event time increments and now have a way to track arbitrary time precision! Any comments about "Well it's just an approximation" and not "Real", I will suggest reading the quotes above and the nature of time and chronology. (Ask this: If a block is orphaned today, did the transactions "really" happen at the block time?)

In the limit, we can fit 6 x 10⁴⁵ dependent transactions within 10 minutes, or 1 transaction every 10^–43 second for 10 minutes to provide a time continuum that is as granular as possible in any universe that described by the equations of General Relativity and Quantum Mechanics.

Today, we will leave it at this for now and then in Part 2 elaborate on this technique and the implications for the participants in Bitcoin and the various classes of applications that are possible taking advantage of this technique.

In Conclusion, Chronological (Causal) Ordering of Transaction was not an accident when Satoshi Nakamoto implemented this in Core 0.1. This allows inter-planetary scale distributed time stamping and maintaining a consistent chronology not just between blocks, but within blocks. Since Bitcoin is fundamentally a timestamp server, we should think very hard about whether this property of block ordering is worth losing for some other optimizations such as Canonical/Lexical Transaction Ordering.

…we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions.
— Satoshi Nakamoto, Bitcoin: A Peer-to-Peer Electronic Cash System
(emphasis mine)