Marina Cortês

Kittel, Introduction to Solid State Physics, Wiley, 1953

Sunday August 20, 2023

I think I solved the condensed matter non-reductionism question. Over the past few years I have been agonising over the bold, controversial, statements of famous condensed matter laureates (Anderson, Laughlin, Leggett). They claim that in solid state materials exhibit phenomena that cannot be broken down into simpler explanations. These are so-called emergent properties and defy the reductionistic techniques used in vast majority of physics.

Such statements of non reductionist phenomena were a key ingredient allowing me to found the science of Biocosmology. Check here for a quick 6 minute introduction at Google in Mountainview.

However, these condensed matter laureates’ are very strong statements. Strong results require strong evidence and in such cases I make it a point of verifying results for myself. Unfortunately I am a cosmologist not a condensed matter physicist, and so the only perspective to check the validity of such results for myself would be to take another Ph.D in condensed matter…

But a bit of an eureka moment saved this. Upon re-reading Kittel’s book on vacation (as one does…) it suddenly occurred to me, what these Nobel laureates had been claiming:

The lattice never approaches the continuum, not even in the limit of zero-grid spacing.

There are many ways to formulate this last statement, and each of the physicists I mention below in points 1-6 — Barbara Drossel, George Ellis, Greg Eyink, Ethan Vishniac, Amir Jafari, Tjarda Boekholt, Simon Portegies Zwart, Tim Palmer, and Thomas Hertog — have formulated, in their various fields of expertise, different versions of what is the statement above. To them I owe a thank you for each contributing a piece of a growing puzzle connecting dissimilar areas of physics as quantum mechanics, classical mechanics, fluid dynamics, numerical astrophysical simulations, chaos theory, and ultimately large scale cosmology.

Lewis Fry Richardson, 1926 was the first to come across this anomaly while studying data numerical simulations of the Navier Stokes turbulence.

In the 1949 Lars Onsager formalizes this effect by writing down singularity theorems. This gives rise to the problems of anomalous conservation of the Hamiltonian in fluid dynamics. I believe the first mention is in Onsager’s conference proceedings of the `Convegno Internazionale di Meccanica Statistica Firenze, 17–20 Maggio 1949′. Onsager’s conference proceedings are here

`Statistical hydrodynamics‘, L. Onsager, Il Nuovo Cimento (1943-1954) volume 6, pages 279–287 (1949

I first became aware of inconsistencies related to the emergence of an arrow of time through Barbara Drossel.
1. Barbara Drossel Statistical Physics and Thermodynamics (Darmstadt). In 2016 during her visit to Perimeter Institute, Barbara first alerted Lee Smolin and I to the inconsistencies in the fluctuation/dissipation theorem. This theorem provides the link between the time symmetric and the time asymmetric world by showing how an asymmetric *arrow of time* emerges from purely time-symmetric microscopic physics. Barbara gave a seminar deriving various proofs to this theorems existing in stats physics and showed that one by one they all introduce–by hand–the ingredient of irreversibility (which is supposed to emerge in the proof).

After the first studies we Barbara, there is a vast community of researchers to thank deeply and who have all–in their individual disciplines in physics–helped me establish these connections. There are  

2. George Ellis (U. Cape Town) Explanatory top-down causation; contextual collapse of the wave function Drossel and Ellis, [arXiv:1807.08171]; 

3. Greg Eyink, Ethan Vishniac, Amir Jafari (JHU) Spontaneous stochasticity in Navier Stokes fluids–Anomalous energy conservation. I am grateful that they pointed me towards Lewis Fry Richardson (1926) and Lars Onsager’s work on singularity theorems and the critical exponent; Eyink was the first developer of the proof of Onsager’s theorems in 1994: `Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer
Physica D: Nonlinear Phenomena, 78, (1994)

4. Tjarda Boekholt (U. Oxford) and Simon Portegies Zwart (Leiden Astronomy). Astrophysical numerical simulations. It all started with a dinner in 2014 at Perimeter Institute when Simon explained we could not reproduce the theorems of classical mechanics in numerical astrophysics simulations. More recently Tjarda explained how their team requires initial conditions specified to accuracy smaller than the Planck length to numerically simulate the collision of three black holes. 

5. Tim Palmer (Oxford U.) Real Butterfly effect in chaotic attractors in phase space and who pointed me towards Edward N Lorentz 1969 article “The predictability of a flow which possesses many scales of motion”. Tim describes these views at length in his new book `The Primacy of Doubt‘, Oxford University Press (2022).

6. Finally a thank you to Thomas Hertog (Leuven), who published “On the origin of time— Stephen Hawking’s Final Theory” Bantam (2023). I was assigned to review the scientific translation into Portuguese for terminology accuracy. [ There is no portuguese equivalent of top-down/bottom-up yet, I had to come up with one. Top-down and bottom-up are quickly becoming one of the most relevant terminology in contemporary physics in a vast array of sub disciplines. Thomas writes of his long standing friendship and collaboration with Stephen Hawking, and narrates how Steve evolved throughout from a bottom-up perspective of the world in his early years, onto the adoption of top-down viewpoint of the universe in cosmology — he and Thomas formulated this in the context of AdS/CFT. 
Hertog writes explicitly something along the lines of (can’t remember the exact words): These results marked the end of the reductionism dream, and the platonic view of physics. 

A big thank you for all these friends and collaborators (apart from Hertog who I never met) for bringing up about what you see and saw, in your different fields, that does not quite match our existing reductionist explanationatory system. Such views strongly oppose the mainstream views in physics, and so it must not always have been a easy debate to sustain. Thank you for speaking up on the effects you observed, and developing rigorous strong arguments for them. 

Finally thank you for engaging in this wonderful network of collaboration we have today! We have recently (April 2023) held a meeting in the Swiss Alps discussing these topics, name “Varieties of Indeterminism’ hosted generously by Nicolas Gisin (Geneva). The seminar recordings are now available online.

It has been a several-year long journey chasing the tension between reductionism and non reductionism. Andrew Liddle and I were almost at the point of signing up for a Ph.D. in condensed matter, to be able to confirm the claims of Nobel laureates Tony Legget, Rob Laughlin, Phil Anderson, with our own eyes. 

Thank goodness it did not come to that. Stay tuned as we continue to consolidate this understanding.

Finally I hope to build a larger encompassing argument starting from this point that touches other parts of scientific fields where these topics are relevant.
The names above are part of a large group of physicists (see below for the seminars in a recent meeting in the Swiss Alps) who believe in the some form breakdown of reductionism (in different regimes in physics). 

I believe the limits of reductionism do not affect physics alone but various other fields in. Namely I believe computer science has not understood that most of the knowledge of western civilisation is rooted in reductionism. 

In fact the validity of reductionism might be breaking down, in essential all fields of intellectual enquiry. 

This breakdown shows up with different names in multiple problems, starting with quantum gravity, all the way up to climate change and computer (deep) learning: LLMs. 

August 15h, 2023

Stephen Wolfram might be shedding some light on the connection between LLMs and reductionism here below.

Computational irreducibility
We need a theory of the observer.
How does it connect to AI? A pretty good model for an observer like us is a neural net.
What is a minimal model for an observer?
Can we derive the number three (as in we live in 3d+1) from that theory?
Min 28: Simultaneity of events.

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