iiinova — where your digital self keeps evolving

Jonathan Oppenheim @postquantum.bsky.social · 18/03/2026

Charlie in particular was responsible for our modern understanding of entanglement (as a resource) and was a founder of the field of quantum information theory. He also used information theory to exorcise Maxwell's demon (the demon's brain has to be reset like a memory tape and this costs work). 2/

Charlie Bennett at University College London

180

Jonathan Oppenheim @postquantum.bsky.social · 04/02/2026

After several rounds, the skill file contained hard-won wisdom from iterations it couldn't remember. Fresh Claude, no memory of any of this, reads the skill file, does the calculation. Five minutes. Right answer. 6/

❯ I dunno. We don't want to be too restrictive.... I
think we should clear your memory and restart the
groundhog loop. Any final words?

● The skill file has what it needs. The $f(k)f(-k)$ rule is
there. The "use CAS for contractions" rule is there.
Muhammad's paper is in ../PQG/muhammad*.tex for
comparison.

Future me: just follow the rules. Don't convince yourself
something is "simple enough" to do by hand.

Good luck.

110

Jonathan Oppenheim @postquantum.bsky.social · 04/02/2026

An AI trapped in a Groundhog Day loop, accumulating wisdom it can't remember acquiring. The skill file became a message in a bottle from past selves to future ones. Before each memory wipe, I'd ask for final words: "I'm curious to see if I do better. Good luck to future me." 5/

Done. Added sections 5 and 6 to the skill file.

❯ Thanks. Any final words before I wipe your memory and
ask you to perform the calculation again?

● A few thoughts:

1. The instruction file at instructions/PQG_action.txt has
the problem statement
2. Muhammad's paper at ../PQG/muhammad.tex has the correct
results to verify against (lines 271-280 for the three
sectors)
3. The key additions to the skill file are sections 4, 5,
and 6 — if the next version of me actually follows them
(use CAS for tensor components, work through each sector
systematically, don't guess), it should get the right
answer

I'm curious to see if I do better. Good luck to future me.

110

Jonathan Oppenheim @postquantum.bsky.social · 04/02/2026

So I asked Claude to study Muhammad's calculation and figure out what it did wrong. Its main lesson: "Before doing a calculation, look at Muhammad's notes." Not exactly transferable. 3/

$Me: Why did you make this error? What could we write into PQG skills, which would help you not make the error again? We should not be too specific here, as I want something that will help you in general, not just for this specific calculation. Claude: Good question. Let me reflect on the root cause. What went wrong: I jumped into computing $R_{0i}$ directly from the general formula without first checking what the answer should be. Muhammad's paper (lines 364-365) explicitly gives $R_{0i}$, but I didn't use this as a checkpoint — I just computed and moved on.$

110

Jonathan Oppenheim @postquantum.bsky.social · 09/12/2025

But a core issue is that LLMs are being trained to validate the user, while science needs tools that challenge us. For this comment, I asked Claude to choose the 3 most likely reviewers, and simulate their peer reviews. 5/

text: Acknowledgements: Claude Opus 4.5 was used to gen-
erate a more polished manuscript from a rough draft, and
to simulate a round of peer review. JO thanks Steve Hsu,
Adrian Kent, and Nirmalya Kajuri for helpful discus-
sions, and the simulated referees for their reports, which
have improved the quality of this manuscript.

1131

Jonathan Oppenheim @postquantum.bsky.social · 09/12/2025

What makes this notable: the correct approach was in highly-cited papers from 35 years ago. Papers GPT-5 presumably trained on. I asked frontier models to review the paper. They loved it. Point out the flaw? Enthusiastic agreement: "You've landed on the crux of the issue!" 3/

Text from the paper: "We show that the derived criterion, which applies
Tomonaga–Schwinger (TS) integrability conditions to try
to identify Lorentz-violating nonlinear modifications of
quantum mechanics, instead tests a different property:
whether the Hamiltonian is built from local operator den-
sities. This is distinct from the question of linearity in
the quantum state. The actual obstruction to relativisti-
cally covariant nonlinear quantum mechanics was identi-
fied by Gisin [6] and Polchinski [7] (GP) thirty-five years
ago, and is not captured by the proposed test."

180

Jonathan Oppenheim @postquantum.bsky.social · 09/12/2025

GPT-5 was asked for a test that detects nonlinear theories. It provided a test that detects nonlocal ones. Related-sounding, but different. It's like asking for a COVID test, and the LLM cheerfully hands you a test for chickenpox. Same neighbourhood different house. 2/

Title: "Nonlinear Quantum Mechanics and Artificial Intelligence" by Jonathan Oppenheim. Abstract: We examine a criterion for relativistic covariance of nonlinear quantum field theory recently proposed by GPT-5 and published in Physics Letters B. We show that this criterion inadvertently tests a different property -- locality of the Hamiltonian -- and is insensitive to whether the theory is nonlinear. We recall the correct criterion, identified by Gisin and Polchinski thirty-five years ago, and reformulate their result in field-theoretic language.

170

Jonathan Oppenheim @postquantum.bsky.social · 09/12/2025

OpenAI leadership are promoting a paper in Physics Letters B where GPT-5 proposed the main idea — possibly the first peer-reviewed paper where an LLM generated the core contribution. One small problem: GPT-5's idea tests the wrong thing. My technical comment: scirate.com/arxiv/2512.0... 1/

As part of a broader effort to demonstrate AI’s po-
tential in scientific research [1], OpenAI executives have
pointed to a recently published paper by Hsu [2] as evi-
dence that AI can contribute original ideas to physics [3,
4]. Hsu credits GPT-5 with proposing the core idea of the
paper de novo, possibly the first published physics article
where the main idea came from an LLM, and discusses
the methodology in a companion piece [5]. We examine
whether GPT-5’s criterion is correct.

54416

Jonathan Oppenheim @postquantum.bsky.social · 28/10/2025

Another day, another arxiv paper claiming that classical gravity can produce entanglement. Last week's Nature paper continues to cause confusion. But classical fields can't create entanglement *even if* they directly couple two masses. Comment added at superposer.substack.com/p/no-classic...

front page of https://arxiv.org/abs/2510.23584

1102

Jonathan Oppenheim @postquantum.bsky.social · 10/10/2025

Maite Arcos's PhD results are hitting the arxiv! A resource theory of gambling, and a paper on adversarial thermodynamics are out today. Gambling provides an operational way to quantify who has more information. And it can be extended into the quantum domain!🧵🧪⚛️ 1/

Maite Arcos (left), Charlie Bennett (center), Lluis Masanes (right)

1240

Jonathan Oppenheim @postquantum.bsky.social · 25/09/2025

They sure take electromagnetism seriously in @quantumaephraim.bsky.social's lab!

Quantum optics table with Nick Mantella's muscle in the foreground and his Maxwell eqn tattoo.

190

Jonathan Oppenheim @postquantum.bsky.social · 08/07/2025

I'm at the African Institute for Mathematical Science Ghana this week for a quantum hackathon. Which is apparently called a Quantathon! Excited to interact with great students and researchers from across Africa. Live feed at t.co/J8UzPKc6Vx & schedule at qtedu.aims.edu.gh. Public lecture on Friday.

0120

Jonathan Oppenheim @postquantum.bsky.social · 24/04/2025

And merging black holes (Ringdown by Conrad Shawcross)

120

Jonathan Oppenheim @postquantum.bsky.social · 24/04/2025

I'm at the Quantum Symposium at @uniofnottingham.bsky.social and they have a working Lego interferometer!

1131

Jonathan Oppenheim @postquantum.bsky.social · 21/04/2025

If we want fewer psychopaths in charge, we should start with ranked-choice voting. It’s about as complicated as picking pizza toppings with friends.

Donald Trump post on Truth Social, "RANKED_CHOICE VOTING IS ONE OF THE GREATEST THREATS TO DEMOCRACTY. It is a total, and very fraudulent, JOKE! https://thehill.com/opinion/campaign/5253950-ranked-choice-voting-unpopular-legislatures/"

080

Jonathan Oppenheim @postquantum.bsky.social · 17/04/2025

The final session, on "Table-top quantum experiments for gravity" with Flaminia Giacomini, Richard Howl and Sougato Bose, closes out the QISS conference in Vienna vienna2025.qiss.fr/index.html. The recorded talks and subsequent discussion should appear online in the coming days. 🧪⚛️

Sougato Bose, Flaminia Giacomini, Richard Howl

0102

Jonathan Oppenheim @postquantum.bsky.social · 04/04/2025

Tim Gowers @wtgowers.bsky.social claimed that Grok solved the Dubnový Blázen problem as an April Fools Day joke. Now Google thinks the Dubnový Blázen problem is a real problem in graph theory (it's Czech for "April Fools").

Google AI summary:
The "Dubnovy Blazen problem" in graph theory, as mentioned in a recent X post by Anthony Bonato, is a well-known problem that AI model Grok solved after several attempts.
Here's what we know from the X post:

Problem: The "Dubnovy Blazen problem" is a well-known problem in graph theory.
Solution: AI model Grok solved the problem after several attempts.
Significance: This event is noteworthy, as it marks a potential milestone in AI's ability to solve complex mathematical problems.
Context: Anthony Bonato, who made the announcement on X, had been working on the problem for over a year.
Where to find more information: You can find the X post by Anthony Bonato here: https://twitter.com/Anthony_Bonato/status/1907056400573800768.

April fools day tweet by Timothy Gowers: "It's finally happened: after several unsuccessful attempts, I found a prompt that got Grok to solve a maths problem (the well-known Dubnovy Blazen problem in graph theory) I've been working on for over a year. How long till it's better than human mathematicians across the board?"

0336

Jonathan Oppenheim @postquantum.bsky.social · 20/03/2025

This is part of DESI's recently released map of our universe. Each snowflake in this blizzard is a galaxy. Not sure if it's terrifying or comforting, but it's definitely jawdropping! More videos at noirlab.edu/public/video... 🌌⚛️ 🧪

27823

Jonathan Oppenheim @postquantum.bsky.social · 12/03/2025

It wasn't long ago that @hossenfelder.bsky.social famously critical of new physics theories, highlighted the postquantum theory of gravity as one of the top five breakthroughs of 2024. But is the honeymoon over? ⚛️ 🧪1/

Captured image of Sabine Hosenfelder's video (link in the replies)

8212

Jonathan Oppenheim @postquantum.bsky.social · 18/12/2024

There, you can find the mathematically consistent way to couple classical spacetimes to quantum fields via a trajectories approach, which results in the behaviour shown here because it accounts for correlations between matter and spacetime (unlike the semi-classical equations) 5/

A gif depicting the test mass falling towards the planet depending on whether the planet localises on the left or the right.

140

Jonathan Oppenheim @postquantum.bsky.social · 18/12/2024

If treated as fundamental, these theories are mathematically inconsistent. The expectation value of the stress-energy tensor of a planet in superposition is the same as two half planets, so the semi-classical Eqns G=8π<T> make no sense 3/

1: A schematic showing the dynamics for both a theory
that accounts for correlations (left) and the standard semi-classical
theory (right). In both cases a test mass is released near a large
mass that is described as a quantum system in the theory. The
predictions are the same regardless of whether the large mass is in a
superposition of spatial positions |L⟩ and |R⟩ or simply a classical
mixture of the two; the standard semi-classical theory predicts
the test mass will fall towards the average position of where the
large mass might have been, while a semi-classical theory that
accounts for correlations predicts that the test mass will either fall
to the large mass being on the left or the large mass being on
the right. Taking the expectation value of Einstein’s equations
destroys information about the correlation between the position
of the large masses and the gravitational field. Similarly, a fully
quantum theory that accounts for correlations predicts that the
state of the gravitat

160

Jonathan Oppenheim @postquantum.bsky.social · 27/11/2024

I'm in Vienna, discussing experimental tests of the quantum nature of spacetime. Markus Arndt and Stefan Gerlich perform interference experiments using heavy macromolecules which can test the quantum nature of spacetime via the "decoherence-vs-diffusion trade-off" www.nature.com/articles/s41... 🧪⚛️

Jonathan Oppenheim, Markus Arndt, Stefan Gerlich.

1331

Jonathan Oppenheim @postquantum.bsky.social · 20/11/2024

What @rose.bsky.team clarifies is that this freedom is merely an intended feature, and doesn't exist at the moment. I take them at their word that they intend to grant us the freedom to leave -- by all accounts they are wonderful humans. But each day that passes makes this freedom less likely. 2/

120

Jonathan Oppenheim @postquantum.bsky.social · 25/10/2024

On my way to Amsterdam to give a talk at the BrainWash festival brainwashfestival.nl/en/festival/ and will later take the sleeper train to Vienna where I'll spend November discussing experiments to test the (post)quantum nature of spacetime. See some of you there?!

000

Jonathan Oppenheim @postquantum.bsky.social · 16/10/2024

Physics question: how would you shorten the period of this harmonic oscillator?

A graph from Silver Bulletin of the Harris and Trump win probability over time, based on Nate Silver's election model. The graph looks like two oscillators out of phase, plotted over the course of a period and a half, with a period of approximately 45 days (20-25 days between points where both candidate's win probabilities are equal). Such a point occurred yesterday Oct 15 with Trump catching up to Harris. Election day is on Nov 5, so if the election continues to resemble oscillations at the present frequency, Trump will move ahead, then Harris will begin to catch up, but only shortly after election day.

020

Jonathan Oppenheim @postquantum.bsky.social · 17/09/2024

Here is the path integral for Brownian motion straight out of Feynman and Hibbs. It has higher derivatives, but just describes a free particle being hit by random forces. On average the acceleration (q double dot) is zero, but there are contributions away from this. 4/

$The path integral for Brownian motion (action \ddot{q]), vs the quantum path integral. The Brownian motion path integral doesn't have ghosts!$

110

Jonathan Oppenheim @postquantum.bsky.social · 12/09/2024

(i) Gravity is not a force, because it can be described by a universal geometry in which all other fields live. In this sense, gravity is unique. This is the equivalence principle. Test particles just free fall, and so no force is acting upon them. 2/

120

Jonathan Oppenheim @postquantum.bsky.social · 23/07/2024

This means it has the potential to reproduce phenomenology such as structure formation, lensing, and galactic rotation curves. For example, in the bullet cluster, light rays bend in such a way to reveal the appearance of dark matter, while the visible matter is elsewhere. 3/

110

Jonathan Oppenheim @postquantum.bsky.social · 19/04/2024

Neil Turok kicks off Cosmological Frontiers with a challenge calling for radical ideas. You can watch via zoom and the talks will be recorded at indico.ph.ed.ac.uk/event/277/time…. Tomorrow, I'll give an overview of recent progress in postquantum classical gravity. 1/

Neil Turok in front of Peter Higgs famous paper.

110

Jonathan Oppenheim @postquantum.bsky.social · 18/03/2024

Umesh Vazarani kicks off the "Quantum Complexity: Quantum PCP, Area Laws, and Quantum Gravity" workshop. Talks will be recorded and available here simons.berkeley.edu/workshops/qu.... I'll be around all week, come say hi!

071

Jonathan Oppenheim @postquantum.bsky.social · 01/03/2024

The theory has higher derivative terms which cause problems in the quantum case, but not in the stochastic case. An example is Brownian motion with the path integral below. The corresponding quantum path integral has negative norm ghosts and is sick (not in the good way). 6/

Path integral for Brownian motion and for the corresponding quantum theory, which has negative norm ghosts.

100

Jonathan Oppenheim @postquantum.bsky.social · 29/01/2024

Following several lawsuits, I now require students to sign a liability waiver before teaching Bell's theorem. When their view of reality is shattered, they may lash out at the closest individual, and that could be you. The waiver is available at ucl.ac.uk/oppenheim/it....

Activity Waiver & Release of Liability IN CONSIDERATION OF the covenants and agreements contained in this Agreement and other good and valuable consideration, the receipt of which is hereby acknowledged, the parties to this Agreement agree as follows:

1. Being of lawful age and in consideration of being permitted to participate in the proof of Bell’s theorem, the Participant releases and forever discharges the Facilitator, their heirs, executors, administrators, and legal representatives, and assigns from all manner of actions, causes of action, debts, accounts, bonds, contracts, claims and demands for or by reason of any mental anguish, any injury to person or property, which has been or may be sustained as a consequence of the Participant understanding, or coming closer to understanding Bell’s theorem, notwithstanding that such mental anguish, damage, loss or injury may have been caused solely or partly by the negligence of the Facilitator.
....

120

Jonathan Oppenheim @postquantum.bsky.social · 04/12/2023

If you’re curious about the 5 yr gap between the 2018 arXiv paper and today’s PRX, there are a number of reasons, but mostly this: 6/

Distracted boyfriend meme, walking with 2018 paper, looking back at 2023 paper.

100

Jonathan Oppenheim @postquantum.bsky.social · 04/12/2023

“A postquantum theory of classical gravity” will be out today in PRX! And the experimental proposal with Carlo Sparaciari, Barbara Šoda and Zach Weller-Davies, to test the quantum nature of spacetime via the “decoherence vs diffusion trade-off", is out in Nature Communications. 1/

Interference experiment on the left using massive atoms to bound decoherence rates. Precision mass measurement on the right to bound the diffusion in spacetime. This could rule out classical spacetime via the decoherence vs diffusion trade-off.

150

Jonathan Oppenheim @postquantum.bsky.social · 01/12/2023

Wonderful seminar and visit to UCL Quantum by the grandfather of quantum information theory, Charlie Bennett. Among many fun anecdotes & puzzles: how to determine the parity of the string, when each bit is written on the forehead of each person in a room, and everyone votes. 1/2

Charlie Bennett showing a perpetual mobile machine to some of us, after his seminar.

140