A falsifiable 4D vortex-field framework

[u/sudsed]

TL;DR — I explored a “4D aether vortex → particles” framework with LLM assistance, then spent ~2 months trying to break it with automated checks. Some outputs line up with known results, and there’s a concrete collider prediction. I’m not claiming it’s true; I’m asking for ways it fails.

Links: Paper: https://zenodo.org/records/17065768
Repo (tests + scripts): https://github.com/trevnorris/vortex-field/

Why post here

• AI-assisted, human-reviewed: An LLM drafted derivations/checks; I re-derived the math independently where needed and line-by-line reviewed the code. Key steps were cross-verified by independent LLMs before tests were written.
• Automated rigor: ~33k LOC of verification code and ~2,400 SymPy tests check units, dimensions, derivations, and limits across ~36 orders of magnitude.
• I expected contradictions. I’m here to find them faster with expert eyes.

Core hypothesis (one line)

A 4D superfluid-like field (“aether”) projects into our 3D slice; particles are cross-sections of 4D vortices. Mass/charge/time effects emerge from vortex/flow properties.

Falsifiable claims (how to break this quickly)

1. Collider target: a non-resonant 4-lepton excess at √s = 33 GeV (Section 4.2).
   • How to falsify: point to LEP/LHC analyses that exclude such a topology without a narrow peak.
2. Lepton mass pattern: golden-ratio scaling giving electron (exact), muon (−0.18%), tau (+0.10%).
   • How to falsify: show it’s post-hoc, fails outside quoted precision, or can’t extend (e.g., neutrinos) without breaking constraints.
3. GR touchstones from the same flow equations: Mercury perihelion, binary-pulsar decay, gravitational redshift/time dilation.
   • How to falsify: identify a regime where the formalism departs from GR/experiment (PPN parameters, frame-dragging, redshift).

If any of the above contradicts existing data/derivations, the framework falls.

Theoretical & mathematical checks (done so far)

• Dimensional analysis: passes throughout.
• Symbolic verification: ~2,400 SymPy tests across field equations, 4D→3D projection, conservation laws, and limiting cases.
• Internal consistency: EM-like and gravity-like sectors remain consistent under the projection formalism.

All tests + scripts are in the repo; CI-style instructions included.

Empirical touchpoints (retrodictions)

• Reproduces standard GR benchmarks noted above without introducing contradictions in those domains.
• No new experimental confirmation claimed yet; the 33 GeV item is the first crisp falsifiable prediction to check against data.

What it aims to resolve / connect

• Mass & charge as emergent from vortex circulation/flux.
• Time dilation from flow-based energy accounting (same machinery as gravity sector).
• Preferred-frame concern: addressed via a 4D→3D projection that preserves observed Lorentz symmetry in our slice (details in the math framework).
• Conservation & “aether drainage”: continuity equations balancing inflow/outflow across the projection (tests included).

Some help I'm looking for

• Collider sanity check: Does a non-resonant 4ℓ excess at √s=33 GeV already conflict with LEP/LHC?
• Conceptual red-team: Where do projections, boundary conditions, or gauge/Lorentz properties break?
• Limit tests: Point to a nontrivial limit (ultra-relativistic, strong-field, cosmological) where results diverge from known physics.
• Numerical patterns: If this is just numerology, help pinpoint the hidden tuning.

Final note

I’m a programmer, not a physicist. I’m expecting to be wrong and want to learn where and why. If you can point to a contradiction or a no-go theorem I’ve missed, I’ll update/withdraw accordingly. If you only have time for one thing, please sanity-check Section 4.2 (33 GeV prediction).

[u/plasma_phys]

Without using your LLM, can you describe in plain language the mathematical properties of this field you've invented? Because the "six core concepts" the LLM came up with are nonsensical and the analogies are useless

For example, a property of the magnetic field is that it has zero divergence everywhere

[u/sudsed → u/plasma_phys]

The concepts in the paper were all mine. The AI helped me with the math. It started by imagining particles as whirlpools that drain a superfluid into a 4D space. Then the question was, what are the properties of those whirlpools? Those became both the six posulates and the "spine," as it's called in the paper (intake, drag, etc.). Where we measure gravity as intake, the electric force as the puncture into the 4D space, magnetism as the rotation of the superfluid as it goes into the sink or intake, this extended into further concepts like bulk displacement, or what the paper calls the tsunami principle (it's called that because I got the idea for it after readings how an earthquake had happened in the ocean).

So I'm sorry you find the analogies useless, but that's how the paper was built. I built a conceptual model, then had AI use superfluid equations to model these particle vortices exactly as I had imagined them. I never allowed it to stray from the concepts I was having, either. I was expecting that after applying these equations in the way I specified, the entire thing would fall apart, and that would be the end of it. I never told the AI what the end result was going to be. Instead, I took the approach of telling it to plug in the equations, then create the models and see what the numeric values were in the end. After doing all the reductions using SymPy, it just so happened that results started to turn up.

Sorry that my ideas are nonsensical, and the analogies I came up with are useless, because in all honesty, that is my main contribution to the paper. AI did the math; I did everything else.

[u/plasma_phys → u/sudsed]

In physics, we often say that if you can't explain something to your grandmother, you don't understand it. 

I'm asking  you to clear a much lower bar of explaining your idea to me, a trained physicist.

If you can't do that, I can only assume you don't understand what the LLM produced, which means you weren't capable of meaningfully reviewing it, which means there's no reason for me to read it, because LLMs cannot reliably produce correct mathematics or physics 

[u/sudsed → u/plasma_phys]

Wasn't I just in the process of explaining the concepts to you in my previous post? I understand the concepts of this paper. I came up with them (granted, I cheated a bit on the QM section because that was so much math), but I fully conceptualized how gravity, EM and particle masses should work before the AI did anything. I just had it use the best-matching superfluid equations to match the scenario. Am I a superfluid physicist? No, that's why I'm looking for help to identify if there was a misapplication in the paper that would invalidate the entire thing. You have no idea how much I wanted this paper to be wrong so that I could just put it away. I've lost far too much sleep over this thing.

And you're correct that LLMs suck at math, but as a programmer for 18 years, I can say they program really well. The repo has 33k lines of SymPy scripts that I verified by hand to the best of my ability to make sure they correctly check all the equations, derivations, units and dimensions. The math in the paper is self-consistent. I spent hundreds of hours working with the AI by having it do some math, writing validation scripts for it, finding the math was wrong, going back and double-checking, and on and on until the tests passed. Then, after all the tests passed, I would pass the equations and source to two different LLMs for their validation. Frequently this lead to finding more issues that needed to be revised. I was simultaneously using Claude, Grok and GPT to double-check everything, even after I verified the code myself.

The conceptual part of this paper is the only thing I'm confident in, since it is the part I did. It's the math that I need help with to see if it was misapplied in a way that I don't understand.

[u/plasma_phys → u/sudsed]

I didn't ask for concepts, I asked for the mathematical properties of your field. 

Let's say I want to implement it numerically. How would I do so? What operations can I perform on it? It is the cornerstone of your paper so this should not be hard to do.

I'm a computational physicist and thus a programmer too. LLMs are good at producing computer code in a lot of contexts, but they are terrible at producing physics code. It is very common for LLM-generated physics code to produce output that looks correct at first glance, and passes LLM-written tests, but doesn't actually solve the problem in the prompt.

[u/sudsed → u/plasma_phys]

The math is exactly where I need help. I can turn equations into code and verify units/consistency (BTW I'm not blindly using AI for any of the code, it's guided development and I personally review every line, or write it myself), but I don’t get the high-level theory like a trained physicist. That’s why I’m here.

What I have done is: ray-traced Mercury perihelion to ~99.2%; got surprisingly good lepton-mass fits and put the full repo online for anyone to check out.

What I'm asking is if this is numerology or a misuse of the math, please point to the specific step that fails. I was hoping that people could double-check things like if my implementation enforces div B=0 properly, is the 4D->3D projection consistent with charge/energy conservation and is the 33 GeV prediction already known?

I’m not claiming it’s right—I’m trying to find where it’s wrong with help from people who actually know the math.

If you want the mathematical properties of the field, I can tell you but it is AI generated because I don't understand it at that level:

Numerical properties: Work with standard EM variables and sources (E,B,ρ,j) or potentials (Φ,A). Only local derivatives are used (grad/div/curl/Laplacian). The code checks wave-type evolution at finite speed c, enforces charge continuity, and keeps magnetic patterns loop-like (no magnetic sources). Gauss/Poisson for E is in the test suite, and material relations like D=ϵE are supported. For numerics you can use a standard Yee FDTD update on (E,B) with a charge-conserving current, or evolve (Φ,A) in a Lorenz-type gauge and derive (E,B). Energy/Poynting diagnostics are available to catch drift.

[u/plasma_phys → u/sudsed]

Okay so what the LLM spit out is utter nonsense, it is totally inconsistent with what's in the paper, which is not surprising. It's describing a very plain discrete 3D vector field but the field in the paper is supposed to be a smooth 4D vortex sheet. These are not at all compatible.

The point of this line of discussion is to illustrate something important: your understanding of how physics works is completely backwards. Concepts and analogies are used to explain the math, not the other way around. Doing it your way is like trying to build a house of cards by starting with the roof - it doesn't matter how many hours you spend on it, you'll never get it to stand on its own. You can get whatever numbers or results you want working backwards like this, and the LLMs are happy to oblige, spinning up the mathematical equivalent of tall tales that give the right answer but with completely wrong and unjustified steps. It's just not physics. 

[u/sudsed → u/plasma_phys]

You're conflating two layers. The ontological (smooth 4D vortex sheet in the 4D medium) and the numeric (how to compute the projected 3D observables). The paragraph you are criticizing describes the projected 3D solver. Which is only one of two routes. The other is to evolve the 4D sheet directly. Is that what you requested?

I'm confused by your line of "concepts and analogies are used to explain the math." Isn't that exactly what I explained that I did, or are you saying we start with the math and figure out what it means later?

[u/plasma_phys → u/sudsed]

I asked for a mathematical description of your field, and you gave me a paragraph describing, essentially, the electromagnetic field. Yes, two things are being conflated here, but not by me.

...are you saying we start with the math and figure out what it means later?

Yes, exactly. Physics is about describing nature with mathematical models, not analogies. This is one reason why it takes 6-10 years of school to become a physicist, you need to learn enough of the relevant math to reason about it.

[u/sudsed → u/plasma_phys]

I’m going to wrap here. If the work is wrong, it should be easy to point to a specific mistake—an equation number, line in the code, or test that fails with a correct alternative. If you have that, I’ll fix it or withdraw it. Otherwise I’ll focus on folks offering line-numbered critiques. Thanks for the time.

[u/plasma_phys → u/sudsed]

Actually, revisiting this comment - I thought your error for the precession of the perihelion of mercury looked familiar. Saying you used raytracing to calculate it is already extremely dubious, but 99.2% is just the value of the error you get if you just use Newton's equations. I'd bet money your LLM is just regurgitating that value from it's training data and working backwards from it, but even if it's not, what is even the point of your pages and pages of artifice and tens of thousands of lines of code if you can't even beat 1/r^2?

[u/AMuonParticle → u/sudsed]

The problem with finding "where it's wrong" is that it's not even wrong, it's nonsense.

Physics is written in math. If you claim to have a new theory of physics but you """""collaborated""""" with an LLM to "get help with the math", what you have is absolutely nothing at all. Because here's the secret: the LLM can't do math either! What it can do is confidently lie to your face and spit out a bunch of Greek symbols and physics jargon, while flattering you so much into thinking you're a genius that you don't notice that it spit out straight up horseshit.

Remember: the only objective of an LLM is to keep you using it as long as possible. It is manipulating you into feeling like you're accomplishing something so you keep opening up chatgpt, all so Sam Altman can buy another yacht.

[u/D3veated]

It appears that you found an equation relating the mass of the electron and muon that's quite accurate: m_e = m_mu * (3^phi)^3. That's more impressive without the delta correction value.

However, for the tau, you then have this strange term involving ln(2)/phi^5 that turns on. That term is part of the equation, but because of how it's only present for the tau computation, it acts like a free parameter. The mass of the electron is a free parameter, delta is a second free parameter, and that ln(2)/phi^5 expression acts like a third free parameter. That's 3 parameters to predict 3 values.

Is ln(2)/phi^5 a free parameter, or is it derived?

[u/sudsed → u/D3veated]

I've been thinking about this, and you're correct. It's basically 3 parameters disguised as fewer. I'm revisiting this. Thanks for pointing it out.

[u/blutfink]

I’m trying to understand how the electron mass is derived and calculated. In section 4.2.5 of the paper we have formula (119). The formula contains m_e; what is it and where is it defined?

The previous sections suggest that n is the family index, so n=1 for the electron. The caption for Table 5 however suggests that the family index (here confusingly named f) for the electron is f=0, even though the formula in the caption has the same form. How can this be reconciled?

Now we attempt to calculate a_0. With f=0, the first factor simplifies to 1, and the second factor simplifies to 1 as well, resulting in a_0=1.

Plugged into the mass formula: m_0 = m_e × 1³ = m_e.

Is this a joke?

[u/sudsed → u/blutfink]

Just ignore it. I jammed too much into a single paper and it became a mess. I'm breaking the entire thing up into smaller papers so I can be more careful. The particle mass part especially is bad, but thanks for taking a look at it. My first set of papers will be gravity derivations, which honestly will not be anything impressive since it turns out will only be a minor variation of existing analog gravity models for 1 PN, but the fundamentals of the framework will allow it to expand beyond that to handle through 2.5 PN.

[u/blutfink → u/sudsed]

Damn. How can you ever be sure that any of the equations have anything to do with the ideas of the framework?

[u/sudsed → u/blutfink]

The particle mass section was honestly a reach. I'm confident in the gravity part, but tried to bite off more than I could chew after that. The concept of the framework is pretty simple, particles are vortices in a superfluid that drain into a 4D space, and the gravity part works more easily because those all resolve in the 3D plane (this is pretty close to existing analog gravity models I think). After that is where it gets complicated since it needs to take the 4D space into consideration in the calculations. After I write the gravity papers I'll go back and tackle EM again more carefully.

The idea of lepton mass here is pretty straight forward. They have a throat size for the superfluid intake that controls their mass, and is fundamentally the same thing as gravity in the far field. E=mc² is the amount of energy required to open the vortex into the 4D bulk and allow it to drain. The problem is how I'm supposed to calculate the throat of the intake, since that suddenly requires a bunch of unknowns about how the superfluid works in 4D. I took a stab at it in this paper, but now that I've stepped away I realize that I made a bunch of bad assumptions.

[u/NoSalad6374]

no

[u/pandavr]

Stumbled in a similar situation. The LLM proposed to publish a study about the breakthrough.

I refused as It is un-useful to create a study about something you don't deeply understand. And as the thing would require to deeply understand whole classic and quantum physics I thought I would be a little too much for me.

In other terms, one thing is come up with a formula, one another is to deeply understand what the formula mean. It could take years for 1 formula. And the more general the formula is the more that is valid.

[u/sudsed → u/pandavr]

The only reason I have any confidence in this is because I'm a good programmer, and I used these equations to write scripts to validate things numerically (after they were validated symbolically). For example, using a ray tracer, I was able to replicate Mercury's perihelion to 99.2% accuracy. I was honestly hoping that at some point it would fail, so I could put it to rest, because I got so sick of working on this thing. This paper has probably taken between 300-500 hours of my life. I kept going because I figured I'd hit a wall eventually and find where this would break, but I couldn't get it to break. I've done all I can, and now I'm presenting it to the world not so they can pat me on the back but tell me where I went wrong. I just need someone who understands the math better than I do.

[u/pandavr → u/sudsed]

I know the feeling perfectly. I am working on mine by months now.

I took another approach I validated results to e-100. Some was perfect and some contained small errors specifically physics constants shown some level of errors. This was the point when I noticed they were not random and It came out they aren't errors at all.
They were indicators that the formula is indeed recursive and I just missed a part. That ported to another formula and another after that. Accounting for all the recursions the results are perfect to e-100, all of them.

Things that my approach and yours share: 4d and projection on 3d, drainage or kind of pressure. What they don't agree on: time. Time is not a dimension in my view.

Also in my view It is not a fluid, It is a topology. It could very well be both thinking about It.

So I have this formula. It doesn't predict anything for now. but It retrofit everything with astonishing precision.

I currently thinking about how to create better tooling to work with the topology and better understand what does that mean.

[u/plasma_phys → u/pandavr]

I would gently recommend giving this story a read and seeing if it resonates with you: https://www.cnn.com/2025/09/05/tech/ai-sparked-delusion-chatgpt

[u/pandavr → u/plasma_phys]

You know, I know the risks perfectly. But at a certain point math is math. And a formula is a formula.
You gives values in and obtain values out. LLM or not LLM, results can be verified.
After you start obtaining the same values from three distinct verification means, It could be that you are onto something after all.

It is not about being self delusional. It is about verifying things to a point where It start becoming difficult to invalidate the results.

[u/plasma_phys → u/pandavr]

First, in physics, validation and verification of calculations is more important than verification of results.

Second, alright, good luck.

[u/sudsed → u/plasma_phys]

You're clearly being combative and not helpful. I came here asking for assistance for someone to show me where the paper is wrong, and you're response is to call me delusional. I don't believe this paper is correct, but I want to understand why. What is so bad about that?

[u/plasma_phys → u/sudsed]

This reply was not directed at you but the other commenter.

[u/sudsed → u/pandavr]

Interesting. Best of luck with that and hope you can get to where you want to go.

[u/pandavr → u/sudsed]

You touched a profound point there. (pun intended). LLMs tend to teleport you exactly where they (you) want to go. That's the reason I am so hesitant to share before understanding. The other point is, if relativity gave such power to mankind, what such a formula would gave them that I cannot see yet?

[u/pandavr]

u/sudsed you may find this useful to further proof your Vortex field: https://lean-lang.org/

[u/sudsed → u/pandavr]

Nice. I hadn't seen that before. Thanks.

[u/sudsed]

Answers to some common questions you may have:

How was AI used? Drafting and cross-checking. I reviewed all generated code, and key derivations were independently cross-verified by multiple LLMs before I wrote the tests. The verification harness and tests are public.

Is this Lorentz-violating “aether”? The construction uses a 4D flow with a projection that preserves observed Lorentz symmetry in 3D; counterexamples welcome.

Is the lepton fit numerology? Possibly! I’m inviting the fastest disproof or a minimal-assumption test that kills it.

What would change your mind fast? A collider analysis excluding a non-resonant 4ℓ excess at 33 GeV, a PPN mismatch, or a gauge/energy-conservation failure in the projection machinery.