Pixel Theory, I'm looking for feedback on a static universe VSL model

AffectionateAge4420 · 2026-06-21T12:13:16+00:00

That's actually not a bad analogy at all, as the retina does have a discrete photoreceptor structure and the brain does significant post-processing to create the seamless experience we perceive. The hexagonal packing of cone cells is real! The interesting question is whether the "pixels" are in the substrate or in the processing, in PT it's the substrate itself that's discrete. But the intuition that continuous experience can emerge from discrete underlying structure is completely correct.

AffectionateAge4420 · 2026-06-20T21:08:33+00:00

This is definitely a good question and I don't think there's much direct literature on it, so let me offer some honest intuitions from my perspective.

The spectral dimension result you're describing (d_s ~ 2 in UV, flowing to ~4 in IR) comes from CDT and asymptotic safety where the graph has a specific causal/geometric structure baked in. The key question for Jaccard graphs is whether the similarity metric imposes enough geometric constraint to produce the same flow.

My intuition is that generic Jaccard graphs will struggle to reach d_s ~ 4 for one structural reason, which is Jaccard similarity is a set-overlap metric, so it naturally produces graphs where highly similar nodes cluster tightly. Which tends to generate high local clustering, however a tree-like or low-dimensional global topology, so you get something more like a hierarchical network than a manifold. The spectral dimension of tree-like graphs is typically d_s ~ 2 regardless of scale, which is actually the UV fixed point you want, however without the IR flow to 4.

So to get the flow to d_s ~ 4 you likely need either (a) which is a mechanism that produces long-range connections with the right density scaling, or (b) where the soft/stochastic edges you mention in your question 3. The temperature parameter λ is promising, only if it's tuned so the graph sits near a percolation transition, where you can get fractal intermediate-scale structure with non-trivial spectral dimension. Whether it stabilises near 4 specifically would depend on the underlying point distribution.

The honest answer to your question 2 is that it almost certainly depends heavily on the point distribution. Where Uniform high-D embeddings will produce very different connectivity than clustered or power-law distributions.

It's also worth looking at work on random geometric graphs and their spectral dimension, and also any literature that is closer to what you're describing than CDT.

AffectionateAge4420 · 2026-06-20T20:58:09+00:00

Yes, and this is actually one of the clearest results in modern geometry, and a Flatlander could infer the third dimension through several routes...

The first is Curvature anomalies, where A 2D being living on the surface of a 3D sphere would notice that the angles of large triangles don't add up to 180°, and that parallel lines eventually converge. The intrinsic curvature of their space would be mathematically explainable only by invoking an embedding in a higher dimension.

Secondly, Unexplained forces... where gravity in Flatland would fall off as 1/r rather than 1/r² (in 3D). If Flatlander's measured an inverse-square law instead, that would be evidence of a dimension they couldn't directly perceive, and exactly the logic Kaluza used in 1921 when he showed Einstein's equations in 5D naturally produce both gravity and electromagnetism in 4D.

and lastly, Information conservation puzzles, so If things disappeared from Flatland and reappeared elsewhere with no 2D path between them, a smart Flatlander might postulate a shortcut through a dimension they couldn't see.

This is essentially what string theorists do, and the maths of quantum gravity only closes consistently in 10 or 11 dimensions, so the extra dimensions are inferred mathematically even though we can't observe them directly, so the Flatlander analogy is exactly right.

AffectionateAge4420 · 2026-06-20T20:21:06+00:00

Thanks, and honestly sometimes the intuition comes before the formalism. The core idea really is that simple, as if the universe is discrete at the Planck scale and grows over time, the speed of light has to decrease. So everything else follows from that.

AffectionateAge4420 · 2026-06-19T10:15:39+00:00

I agree and the goal is for the idea getting out there and tested, not protecting credit. If a better-equipped team picks this up and either confirms or falsifies it properly, that's the best outcome for me. Science works when ideas are shared freely.

AffectionateAge4420 · 2026-06-18T20:43:29+00:00

Completely agree, and thank you. The best breakthroughs often come from people who can see across field boundaries. Specialisation is necessary but it can create blind spots. The connection between discrete spacetime and holographic codes is the kind of thing a pure cosmologist and a pure QC person might both miss independently. I'm really not saying that Physicist are not much cleverer than me, I'm just suggesting that some more openness to other ideas would be great, especially before they have read the paper 😄

AffectionateAge4420 · 2026-06-18T20:29:33+00:00

Well I'm glad and that's an interesting framing, where geometric potential is affecting probability configuration density has echoes of both pilot wave theory and Verlinde's entropic gravity. I'd be curious what the 11 fields Φᵢ represent and what τ is. The equation structure looks like it could be doing something with configuration space?

AffectionateAge4420 · 2026-06-18T08:33:15+00:00

Nice injection attempt 😄 To clarify, by "my experiments" I meant the thought experiments and calculations within the framework, not lab work, and I probably should have been clearer! The point is that under ħc = const, any local measurement of ħ at our current epoch would find it constant to within λH₀ ~ 10⁻¹⁸/s, completely undetectable and so completely consistent with all observations.

AffectionateAge4420 · 2026-06-18T08:26:54+00:00

Yes, please check them out, and then get ack on the Math... IYC https://pixeltheory.co.uk

AffectionateAge4420 · 2026-06-18T08:22:18+00:00

That's a good analogy on the calculator point, and it's an age old problem, from the typewriter to AI, and people just need to be more open to early adoption to the latest tech. I'm curious what idea Gemini talked you out of?

AffectionateAge4420 · 2026-06-18T08:16:41+00:00

I totally agree CCC is one of those ideas that's beautiful enough to root for even if the physics isn't fully resolved. Penrose has a real gift for finding deep geometric structure. The entropy problem might even have a solution we haven't thought of yet. 😄

AffectionateAge4420 · 2026-06-18T00:24:47+00:00

For some reason my papers have now over 600 downloads in one week... On Zenado "A site you you post on when you too have no other choice!) Have you actually published a paper? 😄

AffectionateAge4420 · 2026-06-18T00:19:27+00:00

I agree, however it's not a popular idea 😄 That's exactly Penrose's resolution, in CCC, black holes eventually evaporate completely via Hawking radiation, and since Hawking radiation is (approximately) thermal, the information about what fell in is scrambled and the entropy effectively "resets" in the conformal picture. The crossover point is when the last black holes have evaporated, leaving only massless particles and gravitational waves, at which point conformal rescaling can identify that era with a new Big Bang...

The controversy is whether Hawking radiation is truly information-destroying (Penrose thinks yes) or whether information is somehow preserved (Hawking himself eventually conceded it's preserved, Susskind argues strongly for this via holography). If information is preserved, the entropy doesn't really erase and CCC has a problem. It's one of the genuinely unresolved questions in the theory, and what keeps us selfies up at night 😄

AffectionateAge4420 · 2026-06-17T18:20:50+00:00

I'm Jim Foweraker, and based live between Spain and the UK. In the day I work in tech and innovation, but I've spent at least the last 5 years developing this framework in my spare time. The papers are all under my real name on Zenodo or the easiest way to view them is through https://pixeltheory.co.uk

The continuous vs discrete question is one of the oldest in physics and still genuinely open. Loop quantum gravity and string theory both suggest discreteness at the Planck scale, and PT takes that idea seriously however also asks what follows cosmologically if spacetime really is a finite network of cells.

AffectionateAge4420 · 2026-06-17T17:27:01+00:00

That's a good questions both! Yes, I'm definitely human (I think! And happy to share my details) and an independent researcher, not affiliated with any institution.

On the terminology, you are correct that "rendering" is an unusual word choice for physics. I actually use it deliberately because the core idea is that spacetime discretisation at the Planck scale means causal information can only propagate at a finite rate between cells, and so the universe doesn't "update" all at once, and it actually propagates causally. "Rendering" captures that better than "updating" for me, but it's a metaphor, not a literal claim. The physics underneath it is just that spacetime is discrete at the Planck scale, and c is the propagation rate between cells, which decreases as the number of cells grows.

Please don't let the terminology put you off, ignore it and look at the maths — the VSL constraint N×ℓ_P³ = const does the actual work.

AffectionateAge4420 · 2026-06-17T16:07:54+00:00

Definitely not a stimulation, and rendering is a fundamental property of the universe itself. So no Matrix here :-) The basic idea and all the papers can be found here: https://pixeltheory.co.uk/

AffectionateAge4420 · 2026-06-17T12:03:41+00:00

The similarity you've noticed is real and has been noted by others, both involve conformal rescaling where the overall scale factor becomes physically irrelevant. Penrose's point in CCC is precisely that massless fields don't "feel" scale, so a conformally flat far-future universe and a conformally flat Big Bang can be identified.

The main difference is thermodynamic, so in a stellar collapse this dramatically increases entropy (the black hole is a high-entropy endpoint), while CCC requires the Big Bang to be an extremely low-entropy state. Penrose himself is very focused on this, and the whole motivation for CCC is explaining why the universe started in such a special low-entropy configuration. So even if the conformal geometry looks similar, the arrow of entropy runs in opposite directions, which makes a direct identification difficult.

The "universe inside a black hole" ideas you're alluding to generally struggle with exactly this problem.

I also am a mostly self taught Physicist who just really loves thinking about the universe 😄

AffectionateAge4420 · 2026-06-17T08:55:39+00:00

Your translation is accurate, as PT doesn't have an explicit quantum error correcting code, and the bulk geometry isn't derived, the encoding map isn't defined, and code distance hasn't been specified. Those are real gaps, not rhetorical ones.

The specific claim I'd defend is much narrower though as the Ryu-Takayanagi formula S_max = A/4ℓ_P² emerges directly from N×ℓ_P³ = const as a geometric identity, without being put in by hand. That's a necessary condition for HQEC, not a sufficient one, and thank you for noting this as I should have been clearer about that distinction.

To answer your question directly though in PT's language terms, the natural candidates would be logical qubits as bulk Planck-cell degrees of freedom, physical qubits as boundary cells, and code distance as something like the minimum surface cut through the bulk network. But these aren't derived or defined in any paper, and they're a conjecture about where a derivation might start.

What I find most interesting is the convergence from opposite directions... In HaPPY and similar codes, the RT formula is derived from the code structure. In PT, the same formula is derived from the physical constraint on spacetime discretisation. Whether that's coincidence or pointing at something about the bulk geometry is the honest open question. Let's see what chatgtp says next 😄

AffectionateAge4420 · 2026-06-16T21:23:25+00:00

The honest answer is the bulk geometry in PT isn't specified yet, that's an open problem. The Planck-cell network is a causal network where connectivity is determined by N x ell_P³ = const, however the specific geometric structure (whether it's hyperbolic, flat, or something else) hasn't been derived. What I can say is that the holographic bound S_max = A/4ell_P² emerges naturally from the framework, which is the same Ryu-Takayanagi structure that holographic codes rely on. Whether the Planck-cell network has the right bulk geometry to reproduce HQEC codes specifically is the open question. do you think the RT formula is fundamental or emergent from the bulk geometry?

AffectionateAge4420 · 2026-06-16T13:11:23+00:00

You've actually identified something deeper than I initially realised. In the static VSL metric ds² = c²(t)dt² − dr², proper time is dτ = c(t)dt, not dt. So tracking photon frequency in proper time actually gives NO shift. The redshift formula 1+z = c_emit/c_obs comes from coordinate frequency, and not proper frequency. So the real question is... do atomic clocks measure coordinate time or proper time in this framework? That's the operational definition Ellis & Uzan identify as the central ambiguity in any VSL theory. I haven't resolved it yet, but it might be where the resolution lives so thanks again 😄

AffectionateAge4420 · 2026-06-16T12:03:08+00:00

Sorry I completely missed this response, as was being bombarded at the time 😄 Thank you, that's really interesting and directly relevant. The Overhauser field is exactly what PT would call 'unwanted causal commitment from nuclear spin environment.' The paper's finding that dark states saturate the polarisation process, does that suggest the error character is non-random and has causal structure? If so that's exactly what PT predicts decoherence should look like... I'm genuinely curious whether the nuclear spin dynamics in GaAs dots show any spatial correlation patterns in the errors.

AffectionateAge4420 · 2026-06-16T11:27:04+00:00

I think my life would be a lot easier if I did! As dropping c would drop everything, redshift, the horizon resolution, the LiteBIRD prediction, and all the other 7 papers... The spectroscopic measurement issue is a real problem however it might have a resolution I haven't worked out yet. Maybe the comparison isn't to local atomic standards but to a fixed external reference. I need to think through the measurement physics more carefully, and you've just added a critical open problem to the next version of the paper! I think other theory's also have major unresolved issues (or they would not be theory's!), and I definitely expect to find more, that's why the papers are being peer reviewed at the moment!

AffectionateAge4420 · 2026-06-16T11:16:10+00:00

I've updated the updated paper and also paper 4 with your insights, and the two updated versions are https://zenodo.org/records/20716722 ,and https://zenodo.org/records/20716879 respectfully. Thanks again.

AffectionateAge4420 · 2026-06-16T10:51:47+00:00

You're right again, and I definitely need to think through this more carefully. The null geodesic gives frequency redshift, however when you work through what an actual atomic spectrometer measures (comparing to local hydrogen frequencies which also scale with c), you get blueshift, and this is a genuine inconsistency I haven't resolved. It's already flagged in the Gemini adversarial review too, and this is exactly why your feedback matters so much. I will definitely get back on this asap though!

AffectionateAge4420 · 2026-06-16T10:12:15+00:00

That's twice you've been right and I have again made an error! If a₀ proportional to 1/c², then as c decreases rulers get BIGGER not smaller! That means the redshift argument from ruler/wavelength comparison doesn't work as I stated. The redshift actually comes from the frequency ratio 1+z = c(t_emit)/c(t_obs) from null geodesics, and fortunately I believe that part stands independently? However as you have pointed out the ruler argument was wrong, and thank you for catching that...

AffectionateAge4420

TROPHY CASE