In the end, there was no opportunity to ask questions.
But I still took one home from Brian Cox’s talk, even without a microphone:
Why is nature so simple and symmetrical at its foundations when the world that emerges from them is so extraordinarily complex?
Atoms, hydrogen, quarks, stars, galaxies and black holes appeared on stage. Running through it all was the idea of emergence: a few simple rules can produce something that does not look simple at all.
Yet we do not have to look billions of light-years away for the most beautiful example.
Just catch a snowflake in your hand.
It has sixfold symmetry because, as water freezes, its molecules form a crystal structure with a hexagonal arrangement. But as the crystal falls through a cloud, temperature, humidity and growth conditions change. The same molecules and the same basic rules produce thousands of beautiful shapes.
A simple rule. A complex result.
And that is exactly what the universe does on a much larger scale.
A few kinds of elementary particles and a few fundamental interactions have given rise to atoms, stars, carbon, planets, oceans, DNA, brains and, eventually, a civilisation capable of wondering why a snowflake is symmetrical.
This may be one of reality’s strangest features:
The universe looks complicated. Its basic rules, however, seem almost suspiciously economical.
Note: This is a popular-science research essay. Established physics is distinguished from informational interpretations and the open questions of ITHKOR. It does not claim that ITHKOR has already derived spacetime, gravity or the laws of nature.
Why every place does not need its own physics
For a moment, imagine the opposite kind of universe.
An electron would have one charge in Bratislava and a slightly different one in Košice. Gravity would work differently on Monday and Tuesday. Rotating a laboratory through ninety degrees would require a new set of equations.
A physics textbook would not be enough to describe such a world.
We would need an endless catalogue of exceptions.
rule A applies here,
a metre away it is A',
tomorrow it is B,
after rotating the experiment it is C...
Our universe does not behave that way.
An electron has the same properties here and in a distant galaxy. The laws do not change with the direction in which we turn an experiment. Physics tries to describe as many situations as possible with the same rule.
And this is where symmetry enters the picture.
In everyday language, symmetry brings to mind a butterfly or a snowflake. In physics, it means something deeper: we can change the description of a system in a particular way while its physical content stays the same.
Then Emmy Noether showed one of the most beautiful results in modern physics: continuous symmetries are directly connected to conservation laws.
If the laws do not change over time, this is associated with conservation of energy. If they remain the same when an experiment is moved through space, we obtain conservation of momentum. If rotating it makes no difference, conservation of angular momentum appears.
Symmetry is more than aesthetics.
Symmetry tells us which differences in our description nature simply ignores.
From an informational perspective, it has another beautiful feature.
It shortens the description of the world.
without symmetry:
a billion situations → a billion separate rules
with symmetry:
a billion situations → one rule + a transformation
No, this does not mean that the universe runs inside a ZIP archive.
But it does mean that a world with deep symmetries can be described far more economically than a world full of arbitrary exceptions.
And that leads to the question that interests me even more after Cox’s talk:
Is the simplicity of physical laws merely a fortunate feature of our world, or is it somehow necessary for a stable reality?
Nature loves symmetry. Then it gently spoils it
Perfect symmetry might produce a very simple universe.
But perhaps also a very dull one.
Our world is interesting because nature often creates an almost perfect symmetry, then breaks it ever so slightly.
The proton and neutron provide a beautiful example.
At first glance, they are almost identical. A proton has a rest energy of about 938.27 MeV; a neutron, about 939.57 MeV.
The difference is only around 0.14 per cent.
Almost nothing.
Yet that “almost nothing” matters enormously.
A proton contains two up quarks and one down quark (uud). A neutron contains one up quark and two down quarks (udd). The down quark is slightly heavier than the up quark, pushing the neutron towards a higher mass. Electromagnetic contributions partly act in the opposite direction. Adding all the effects leaves a difference of approximately 1.293 MeV.
This difference allows a free neutron to beta-decay into a proton, an electron and an antineutrino.
Suddenly, a beautiful pattern becomes visible:
A broad symmetry creates order. A small breaking of symmetry creates diversity.
The proton and neutron are almost two versions of the same object, yet the tiny difference between them has consequences for nuclei, stars and the chemical composition of the universe.
Perhaps the most interesting question is therefore not just:
Why is nature symmetrical?
But also:
Why are some symmetries broken by so little, and in precisely a way that allows a complex world to emerge?
The quantum world: when simplicity stops being intuitive
Atoms, hydrogen and quarks came up several times during the talk, but Brian Cox touched only briefly on quantum paradoxes. In a show lasting roughly two hours, that is understandable. Quantum mechanics alone could comfortably fill another evening.
Yet it makes the whole story even stranger.
Quantum mechanics is one of the most precise theories we have. It predicts experimental results with extraordinary accuracy.
And the world it describes does not match our everyday intuition at all.
A quantum system can be described as a superposition of possibilities. Heisenberg’s uncertainty principle tells us that certain pairs of physical quantities cannot be prepared simultaneously with arbitrarily high precision. Entangled systems can exhibit correlations that a classical local picture cannot explain.
Yet when we wake up in the morning, the bed is not smeared across three rooms.
An instrument displays a definite reading.
A photograph remains a photograph.
A computer’s memory contains a definite bit.
In the macroscopic world, stable records emerge.
Decoherence helps explain much of this transition: a quantum system becomes entangled with its environment, making interference between certain alternatives practically unobservable to us. This alone, however, does not settle every philosophical debate about the interpretation of quantum mechanics.
For me, one question stands out:
How does a world of quantum possibilities become a world capable of preserving a shared history that can be read repeatedly?
There is a pleasing parallel here.
Symmetry removes arbitrariness from the laws.
A stable record removes arbitrariness from the history we can read together.
This is not yet an explanation of quantum measurement. But it is a very good question for any informational model of reality.
Black holes: when area starts speaking the language of information
Then we come to black holes.
Here, the story suddenly comes together in a way that sounds almost too beautiful.
Bekenstein and Hawking showed that a black hole can be assigned an entropy
SBH = kBA / (4ℓP2)
If equations mean little to you, just notice one letter:
A.
It is the area of the event horizon.
Not the black hole’s volume.
Its area.
That is extraordinarily strange.
For an ordinary object, we would intuitively expect its information content or the number of available microscopic states to have something to do with how much “room inside” it has.
A black hole points instead to its boundary.
And it does so very precisely: the relationship contains a factor of one quarter and the Planck area.
At the boundary of extreme gravity, geometric area appears directly in the equation for entropy.
This is not a metaphor. It is physics.
Results like these helped inspire the holographic principle. In certain theoretical frameworks, an even closer connection later emerged between quantum entanglement and the geometry of spacetime.
Ryu and Takayanagi connected entanglement entropy to geometric area in a holographic description. Ted Jacobson showed a deep connection between horizon thermodynamics and Einstein’s equation. Mark Van Raamsdonk explored how quantum entanglement might relate to the very connectedness of spacetime.
This does not mean that the universe is a computer.
It does not mean that we live in a simulation.
And it certainly does not mean that ITHKOR has been confirmed.
But it is entirely legitimate to ask:
Why do geometry and information meet precisely where physics reaches its deepest boundaries?
A snowflake and a black hole may not be so far apart
A snowflake and a black hole look like two objects with nothing in common.
One melts in your palm.
The other can trap light.
One forms in a cloud a few degrees below freezing.
The other represents an extreme of spacetime curvature.
Yet in both cases we see the same motif:
simple rules → enormous structure.
A snowflake shows how a local growth rule and symmetry can produce immense diversity of form.
The proton and neutron show how a tiny breaking of symmetry can fundamentally change the behaviour of matter.
Quantum mechanics shows that a space of possibilities lies beneath the classical world, yet stable records still emerge from it.
And a black hole shows that, at gravity’s boundary, geometry becomes directly connected to entropy.
Perhaps these are four entirely separate stories.
But perhaps they all ask the same question:
What are the simplest rules capable of creating a world that is stable, consistent and able to preserve information, while remaining rich enough for stars, life and consciousness to emerge?
For me, this is where ITHKOR begins.
With a question.
Not an answer.
ITHKOR: first, make sure the result does not depend on how we calculate it
With grand hypotheses, it is easy to skip several floors at once:
information plays an important role in physics
↓
reality is informational
↓
the universe is a computer
↓
someone started it
But that leap is not physics.
Even if information eventually turns out to be more fundamental than our ordinary picture of matter or space, an external computer, simulator or programmer does not follow.
General ITHKOR therefore asks a more cautious question:
Could space, time, stable objects and physical response emerge from a deeper network of informational relationships and constraints?
Special ITHKOR currently investigates only small, precisely bounded models.
One of its first results was instructive precisely because it did not match the original expectation.
When a result depended on the technical order in which a computer processed events, that was a problem. The same candidate physical model should not produce a different result merely because we performed allowed steps in a different order.
More stable candidates appeared only with canonical structures and checkpoints that retained the same meaning across different allowed schedules.
This is not yet Lorentz invariance.
It is not a derivation of space or time.
But a simple principle behind it resonates strongly with the theme of symmetry:
If something is to be physical, it should not depend on a detail of our description that has no physical meaning.
Perhaps this is one way to gradually break a large philosophical question into small tests.
A beautiful story is not enough
This is where we need to slow down, exactly when the story starts sounding its best.
It is very tempting to say:
symmetry, quantum information, black holes, emergent spacetime — surely all of this must be one thing.
Perhaps it is.
But until we have a mechanism that derives these relationships, it remains an interesting possibility.
If ITHKOR ever wanted to claim that a single principle really underlies it all, it would have to do far more than connect familiar results with an appealing story.
For example, it would have to obtain the area scaling of black-hole entropy and the correct factor of one quarter without inserting them by hand. It would have to reproduce Lorentz invariance, known physical symmetries and, in the appropriate limit, general relativity. Finally, it would have to deliver a new prediction that could fail experimentally.
That is the boundary between metaphor and physics.
And that is precisely why the question is interesting.
Not because we already know the answer.
But because we can refine it until an experiment might one day be able to answer it.
Perhaps simplicity is the greatest mystery
When we look at the universe, its size can easily overwhelm us.
Hundreds of billions of stars in a single galaxy. Galaxies scattered billions of light-years apart. Black holes with billions of solar masses. Quantum fields whose behaviour defies our intuition.
Yet perhaps the opposite is even stranger.
How few rules all of this requires.
A water molecule does not need a blueprint for a snowflake.
A proton does not need to know that it will one day belong to a star.
A carbon atom does not need instructions for a cell.
And the laws of physics do not need a separate chapter for every galaxy.
Simple local rules repeat again and again. Their combinations generate a complexity that nobody looking at the rules alone might have expected.
Perhaps physics is beautiful because the human brain projects beauty onto mathematics.
Perhaps we simply pay more attention to the parts of nature that admit elegant descriptions.
But there is a bolder possibility:
Perhaps simplicity is a condition of stability. A world capable of existing for a long time, changing and yet remaining consistent may have to build enormous diversity on a small number of invariant rules.
Then symmetry would be more than an aesthetic property of equations.
It would be the way one rule works in countless situations.
Small symmetry breakings would be the way diversity grows from a simple foundation.
Quantum records would be the way possibilities become a readable history.
And a black hole would be the place where geometry most openly admits that it has something to do with information.
From a snowflake to an event horizon, we would keep returning to the same kind of question:
How can a few simple rules create a world of such extraordinary complexity, and why do information, symmetry and geometry keep ending up in the same room?
We do not have an answer yet.
But after an evening devoted to emergence, I think it is a pretty good question to take home.
Scientific reference points
- Jacob D. Bekenstein, Black Holes and Entropy, Physical Review D 7, 2333 (1973), DOI: 10.1103/PhysRevD.7.2333.
- Stephen W. Hawking, Particle Creation by Black Holes, Communications in Mathematical Physics 43, 199–220 (1975), DOI: 10.1007/BF02345020.
- Emmy Noether, Invariant Variation Problems (1918; English translation), arXiv:physics/0503066.
- Ted Jacobson, Thermodynamics of Spacetime: The Einstein Equation of State, Physical Review Letters 75, 1260 (1995), DOI: 10.1103/PhysRevLett.75.1260.
- Shinsei Ryu and Tadashi Takayanagi, Holographic Derivation of Entanglement Entropy from AdS/CFT, Physical Review Letters 96, 181602 (2006), DOI: 10.1103/PhysRevLett.96.181602.
- Mark Van Raamsdonk, Building up spacetime with quantum entanglement, General Relativity and Gravitation 42, 2323–2329 (2010), arXiv:1005.3035.
- Particle Data Group, Review of Particle Physics — particle masses and Standard Model parameters.
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