"What is true for you is true for you, and what is true for me is true for me" – Protagoras sneered (1).
“I cannot but agree” – Plato replied, terse and tight-lipped.
They were bitter ideological enemies. Whilst Protagoras sold a world built entirely on human perception, Plato demanded absolute, unchanging facts: forms and realities that existed independently of human viewing (2). For millennia, the discipline of physics sided vehemently with him. The entire enterprise of the physical sciences was a crusade to banish the ‘will’ of anthropomorphic gods and heroes, to uncover the definitive and rational "facts" behind the universe. The pursuit of logos, rather than mythos.
Eight years following Plato’s death, a student of his, Zeno of Citium, established the Stoic school, spreading the belief that the universe operated due to reason (logos), was monistic (i.e. one interconnected physical system governed by consistent laws), and operated on cause and effect (3). This belief in determinism (the idea that events in the future had been determined by a chain of past occurrences) reached its zenith in the Scientific Revolution of the 17/18th centuries.
Fact: repeatable, reversible and reliable
We will start with an easy question: what is a fact?
I would argue that a statement is a fact if it:
(i) stems from a pre-existing state of affairs in the world; and
(ii) is singular, i.e. is restricted to reality, of which there is one.
This is described in perhaps the most incomprehensible quotation of mankind by Aristotle (4).
“To say that that which is, is not, and that which is not, is, is a falsehood; therefore, to say that which is, is, and that which is not, is not, is true” (4).
‘Pre-existing’ requires a past. For something to already be there, waiting for us to see it, it can't have just spawned from the void. Every 'is' requires a 'why'.
This relentless search for the chain of cause and effect reached its extreme in the 18th century with the French polymath, Pierre-Simon Laplace. His proposal of a hypothetical entity, now famously known as Laplace’s Demon, served as the ultimate thought experiment for the deterministic worldview that dominated the Scientific Revolution.
Imagine a massive, omnipresent intellect – a demon. If this intelligence knew the exact location and force of each single atom in the universe right now, it would know everything. Uncertainty would vanish. The past and the future would be simultaneously now (5).
A rock does not "choose" to roll; rather it rolls because gravity acts upon its mass. Similarly, in a deterministic universe, you do not "choose" to act. Your current physical state was caused by the state of the universe one second ago. That state was caused by the state one year ago, which was caused by the state of the universe before you were born, stretching all the way back to the initial conditions of the Big Bang.
We conclude: there only exists one unique solution that maps space to time.
Two different pasts never merge into the exact same future.
Two identical presents never split into different futures.
‘c’ is a constant (crisis):
Classical mechanics, in all its beautiful and symmetrical mathematics, provides us this shocking revelation that reality may be deterministic, and that free will is an illusion, a fiction within the slow march of time (7).
Occam’s razor (that is, that the simplest explanation is usually the correct one) is seemingly disproven through two fundamental flaws within the classical framework.
Firstly, the speed of light (denoted as c) is unique because it stays the same regardless of how fast you are moving. James Clerk Maxwell discovered that electric and magnetic fields are perfectly synced; a ripple in an electric field creates a magnetic one, and that magnetic ripple in turn regenerates the electric field. This continuous loop creates an electromagnetic wave, which we see as light. The speed of this wave is determined by two fundamental properties of empty space: how easily it allows electric and magnetic fields to form and spread. As these properties of the vacuum itself never change, light always travels at the exact same speed, whether you are racing toward the light source or standing perfectly still.
The immediate consequences of forcing light to travel at a constant value are rather disturbing. Consider the unfortunate events of a German salary worker in the early 20th century:
It was another miserable, grey day in Germany. Albert was staring out the window of a Deutsche Bahn train that was currently four hours late, thinking that his day couldn’t get any worse.
CRACK.
Lightning strikes the metal frame of the train car, right at the front. Albert jumps, spilling his lukewarm coffee. But before he can even dry off his trousers, a second lightning bolt strikes the very back of the train. He spills his coffee over his shirt. Albert has to get off the train at the next stop, Bern, to get to his job working at the Swiss Patent office.
As he dries off his clothes on the platform, he observes an express train that runs straight through the station. Lightning, particularly vicious today, strikes both the front and end of the train carriage at the exact same time.
When he was sitting inside the moving carriage, the light from the front strike had reached his eyes first because he was moving toward it. Remember, the speed of light remains constant even in his moving carriage.
But now, standing completely still on the damp Bern platform, the light from both strikes on this new express train reached him exactly simultaneously (9).
The man on the platform and the passengers on the train would fundamentally argue on the chronological order of events in the universe. Yet the frightening fact was neither of them was wrong (10).
(This assumes that the Deutsche-Bahn moves at speeds close to the speed of light, however due to strikes from the train worker union, it would be a challenge for the train to move at a non-zero speed at all.)
Recall our first condition for the definition of fact – the existence of a pre-existing past. Yet, if two observers cannot even agree on "when” an event took place, this condition fails.
Fact, it seems, depends entirely on how fast you go.
Bohr-ing reality is fundamentally uncertain.
The second deviation from naive Laplace was the discovery of the hollow atom. Rutherford used the analogy of planets (the electrons) orbiting a star (the nucleus) seemingly never straying from their tidy, well-defined and circular orbits.
Electromagnetism prevented this model from being taken seriously. Any particle that possesses charge must release energy when accelerated. Now, imagine a satellite that constantly releases energy each orbit around Earth. Naturally, the satellite will fall into the Earth. The same would occur to the electron. It would spiral into the nucleus in less than a fraction of a picosecond. Every atom in the universe would instantly implode.
Two independent theories then arose almost simultaneously following this discovery. In 1925-26, the landmark papers of Heisenberg’s matrix mechanics (which uses matrices to calculate important quantum properties) and Schrödinger’s wave mechanics (an equation that relates a quantum state to its energy) attempted to provide reasons as to why energy did not disappear from the electron’s orbit (11).
Breaking with the tradition of presenting the quantum ‘ghost’ of randomness, quantum mechanics actually provides a more deterministic theory than one may realise.
Akin to Laplace’s demon, Schrödinger’s equation describes the time evolution of a quantum system: given an initial quantum state, we can make a definite and certain prediction of what that quantum state will be at any later time (12).
This is a very intangible concept and would likely be poorly understood, so let me demonstrate this by way of an example of a coin toss.
Imagine a coin spinning rapidly on a table. If you try and guess whether it’s showing heads or tails at that specific microsecond, you probably can’t. It’d be too blurry.
However, the blur itself is not random. The way the coin spins, its momentum, its wobble, the friction against the table is governed by strict, unbreakable rules. If you know exactly how the coin was flicked (the initial quantum state), Schrödinger’s formula can predict with 100% certainty exactly what that "blur" will look like five seconds from now, ten days from now, or one hundred years from now.
The deterministic nature of quantum mechanics is that the blur itself evolves predictably. The infamous and rather misrepresented "quantum randomness" only applies at the very end, when you finally get fed up and slap your hand down on the coin, forcing it to be either heads or tails (the measurement) (13).
The issue, therefore, with this notion of fact under a quantum lens is the lack of a singular outcome. Time evolution is a well-defined function, yet outcome can only be predicted probabilistically. Therefore, we fail yet again the second condition of fact.
Fact is – the friends we made along the way?
An ongoing unresolved issue in quantum theory is how to explain the two conflicting ways in which systems evolve. Unobserved states evolve smoothly, yet exhibit discontinuous jumps into an outcome when measured.
The infamous “Wigner’s Friend” paradox provides an example (14).
Suppose your friend is inside a sealed lab watching a spinning coin. In their perspective, when they stop the coin and read its face, its state collapses into a singular outcome.
In the shivering cold, you curse that you had to be the one to stand outside. According to the rules of quantum mechanics, because you haven’t seen the coin face, the smooth, unbroken evolution is still happening.
You get sick of suffering in the name of science, so you rush into the laboratory and ask your friend what the coin landed on. At that moment, the superposition abruptly collapses for you.
Facts no longer appear grounded in an objective, observer-independent past. Instead, they become relational, contingent upon who is observing the system. Worse still, facts seem capable of multiplying: different observers may legitimately describe different realities.
This forms the basis for Rovelli’s Relational Quantum Mechanics (15).
In RQM, an object (like an electron, a coin, or a cat) does not inherently "possess" properties like position or momentum in isolation. Instead, those properties only exist when two physical systems interact.
Asking "Where is the particle right now?" when nothing is looking at it is a grammatically incorrect question, equivalent to asking “What is the sound of one hand clapping?" The property of "position" only truly comes into meaning if there exists a detector for which the electron interacts with (16).
Any interaction is essentially an exchange of information between two systems. Rovelli formalises this by proposing two foundational postulates. First, there is a finite limit to the relevant information one system can extract from another. Second, it is always possible to extract new information (17).
At first glance, these seem at odds: how can you continually extract new data if the total capacity is capped? The consequence of this tension is what we traditionally call "collapse", but RQM reframes it simply as an update of relative information. If you have maxed out the information capacity of a system — for instance, by pinning down the spinning coin’s exact momentum — then asking a new question about its position forces the system to "forget" old information to make room for the new. This directly yields Heisenberg’s uncertainty principle.
If we wish to keep using the word "fact" in our theory of modern physics, we must redefine it. Facts are no longer global, pre-existing truths built into a singular reality. Instead, they are by nature local, inherently plural, and entirely dependent on the relationship between the watcher and the watched.
Protagoras peers down, then looks up at Plato with a bright-eyed grin.
"As I was saying,”
References
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