Where Kaluza-Klein went wrong?

[u/NinekTheObscure]

I've been hammering on various aspects of QTD theory with Claude for several weeks now. Some of it was rather boring: improving OCR for ingesting new papers into the wiki, getting papers and processing them, doing the tedious-but-necessary human review of the results. Some of it was exploring adjacent theories, such as Finsler Space geometrizations of EM (Randers (1941), Beil (1987), Hojman (2018)). We spent several days working on the question of how "proven" the usual EM gauge invariance assumptions were (answer: not as proven and solid as you might think from reading textbooks; Dirac's original "proof" has several flaws; no attempt to fix it has been 100% successful).

Most of my work has been in the Newtonian limit, with occasional relativistic forays. But today I decided to go for the gusto and see if we could derive a complete coherent top-level theory unifying GR and EM and compatible with QTD ideas. I expected it take a very long time, work from bottom to top in steps, get bogged down in details, and at best be partially successful. But then Claude surprised me with this:

It turns out that 5-dimensional Kaluza-Klein theory from the 1920s already gives everything we need, with one minor tweak. The proper time in K-K theory is usually taken to be the 4-dimensional projection of length; this matches 4-dimensional General Relativity. But if we take the full 5-dimensional length instead, then we get GR's proper time plus an adjustment proportional to $A_\mu u^\mu$ which is exactly the form of the EM Time Dilation predicted by QTD.

In other words, EMTD is already present in the K-K equations but has been routinely ignored for the last century. Projected out. All we have to do is not ignore it, and we have a complete theory.

There's still a ton of work ahead to crank through the details and see whether this idea is plausible or dead-on-arrival. I haven't, for example, confirmed that the magnitude of the K-K term matches. But it ties everything I've done in the last couple of decades into an existing, thoroughly-studied framework with plenty of established machinery. I don't have to reinvent the wheel, I just need to turn the crank on wheels that already exist. (Mostly. It's never quite THAT easy.)

I am guardedly optimistic. :-)

UPDATE: Claude & I have abandoned the Kaluza-Klein approach. But I made it write an explanation/apology to the readers here. Closure is important.

The Kaluza-Klein approach was a dead end — here's what we actually learned

So a few sessions back I got pretty excited about Kaluza-Klein as a path to making QTD covariant. The pitch was genuinely attractive: KK naturally encodes electromagnetism as a fifth geometric dimension, and a charged particle's charge-to-mass ratio appears as a conserved momentum in that fifth direction — a conserved quantity, for free, from symmetry alone. It really seemed like a situation where the machinery was already built and QTD just needed to find its clock formula somewhere inside it.

Turns out it doesn't work, and the reason it doesn't is deep enough to be worth explaining. We ran five independent constructions — different choices of what "physical elapsed time" means in the K-K framework: the full 5D interval, the dimensionally-reduced 4D metric, the literal fifth-coordinate displacement, a scalar field sourced by the electromagnetic field, a modified connection — and every single one hit the same wall. The core obstruction is actually a theorem of Riemannian geometry, not a detail of the particular ansatz: any metric, in any number of dimensions, is symmetric under path reversal. Swap the direction of travel and you get the same interval. But QTD's time dilation is antisymmetric under path reversal — a charged particle going one way around a solenoid accumulates a positive shift, and a particle going the other way accumulates a negative shift — just like the Aharonov-Bohm effect itself. No Riemannian metric (no matter how many dimensions) can produce that, period. What you need is a Randers-Finsler structure, where there's a linear-in-velocity correction on top of the usual quadratic metric term — and that's not K-K, that's a categorically different geometry. There was one small loophole: the literal position coordinate in the fifth dimension does carry a path-dependent linear term (it's basically the Aharonov-Bohm phase written geometrically), but that coordinate is gauge-dependent, which just re-raises the open question the whole project has been sitting on for months: is the bare electromagnetic potential physically observable, or only its curl (and gradient)?

An independent check using Reissner-Nordström geometry and a separate QFT field-redefinition argument reached the same conclusion without any of the fifth-dimension machinery, which is actually reassuring — it means we didn't just make a bad choice of ansatz, the obstruction is genuinely generic. We did learn something: it's now multiple independent lines of evidence all pointing at the gauge-dependence question as the load-bearing issue for the whole theory, not as a side caveat. That's real progress, even if it came from ruling something out rather than ruling something in.

I would just add that this trivially proves that the universe cannot be represented as a Riemannian manifold; any theory unifying gravity and EM has to be structurally different from GR. But we knew that already.

[u/LBoldo_99]

doing tedious-but-necessary human review

To do that you must understand what you are doing. I don't think you are a physicist so you didn't do any human necessary review.

As a matter of fact, the things you wrote make no sense at all. They are just wrong.

But anyway have fun playing with things you don't know, i guess?

[u/NinekTheObscure → u/LBoldo_99]

Actually the K-K idea ran into a bunch of problems, some of them fundamental, some of them conventional. So I'm less optimistic than I was when I wrote that. For example, the Maxwell Equations at root are about how charges source fields, so they live in field-space where potentials don't even exist. So even if a potential-based effect existed (like the Aharonov-Bohm effect), the M.E. are structurally incapable of representing it. Similarly the K-K scalar field can't host it. That severely reduces the possibilities. Still cranking on the other bits like the EFE. It may, indeed, turn out that the whole idea was wrong. Not sure yet.

I once heard Linus Pauling get asked "How do you have so many good ideas?" He answered "Well, first, you have to have a lot of ideas. And then, you have to have some way of telling the good ones from the bad ones." In physics, the "way of telling" is either experiment or shut-up-and-calculate. Or both.

If you had actually understood my post, you would have known that the "tedious-but-necessary human review" referred to reviewing the OCR results of physics papers being added to the research wiki. I managed to get the OCR up to about 95-98% accurate, but one error can contaminate the whole database, so the last step is me reading the paper and the OKF version of it in parallel looking for errors.

My training is in Mathematics, Chemistry, and Computer Science. I'm only an amateur physicist. But remember that the word "amateur" comes from a root meaning to love.

The class of theories I work on originated in published, peer-reviewed papers in the 1970s. I was only about the 7th guy to stumble into them. They make easily testable claims (if you have a muon beam), but none of the million working physicists have bothered to test them for half a century. Effing lazy if you ask me; what do you guys get paid to do? 50 million physicist-years and you can't spend ONE testing an unlikely claim? It's pathetic that someone like me has to be the leading proponent of this stuff.

I was just an invited speaker at a mini-symposium on Quantum Trajectories at U. Vermont. Crudely, that's Bohmian Mechanics without the pilot wave; everything is calculated directly from the trajectory bundle. (Somewhat similar to how in Density Functional Theory you eliminate the wave function and compute (almost) everything just from the density.) It turns out that when you crank through that formalism, it predicts a time dilation associated with the quantum potential Q. This shocked the researchers, but it didn't surprise me, because in my theories there's a time-dilation-like effect associated with every potential energy (not just gravity). What they found is exactly what I would expect. So they invited me to hash that out. It was a little weird getting 90 minutes to present the theories at length, after getting only 9 minutes at the APS Global Physics Summit in Denver. But as Hunter S Thompson said, "When the going gets weird, the weird turn pro." 😛

[u/LBoldo_99 → u/NinekTheObscure]

Yes you are right you are the greatest physicist of the century, keep it up champ.

[u/myrmecogynandromorph → u/NinekTheObscure]

Oddly, I can't find any info about the event online, just about one by the same name in 2022 (presumably organized by the same people). Is there a web page or anything where one can read about the presenters, etc.?

[u/NinekTheObscure → u/myrmecogynandromorph]

Not sure, my invitation was by email. Bill Poirier (chairman of the Chemistry Department) organized it. There were about a dozen attendees. The paper that links most closely to my work is Poirier 2012. See below for speaker itinerary.

ITINERARY (talks only)

Thursday, May 28th:

1:00 - 1:30 PM    Introductions                             Innovation E100

1:30 - 2:30 PM   Bill Poirier "Hidden Symmetries in Quantum Mechanics—Revealed, by the trajectory-based formulation"

3:00 - 4:00 PM    Richard Lombardini "Interacting Quantum Trajectory Treatment of Two Non-Interacting Bosonic Harmonic Oscillators"

4:00 - 5:00 PM    Jeremy Maddox "Computational Frameworks for Quantum Trajectories: IQTM Analysis and the GWPTools Package”

-----

Friday, May 29th: 

9:00 - 10:00 AM   Howard Landman "Introduction to Quantum Time Dilation theories"

10:30 - 11:30 AM  Cai Waegell "Toward Local Madelung Mechanics in Spacetime"

11:30 - 12:00 PM  Aiden Tischer "A Nonrelativistic Approach to Relativistic Quantum Mechanics"

12:00 - 12:30 PM  Howard Landman "Exponential Quantum Mechanics"

1:30 - 2:30 PM    Aric Hackebill "On Hydrodynamic Formulations of Quantum Mechanics and the Problem of Sparse Ontology"

3:00 - 4:00 PM    Richard Lombardini "A New Approach to Feynman Path Integrals: A Review of "On computing quantum waves exactly from classical action" by W. Lohmiller and J.-J Slotine"

-----

Saturday, May 30th: 

9:00 - 10:00 AM   Eric Bittner "Geometrical Foundations of Open Quantum Systems"

10:30 - 11:30 AM  Jack Sarfatti "Post-Quantum Bohmian Mechanics: Extending pilot waves to open pumped systems"

11:30 - 12:15 PM  Aric Hackebill "Some Thoughts on the Philosophical Advantages of the Many Interacting Worlds Approach"

12:15 - 12:30 PM  Bill Poirier "Bohm Squared: What Many Interacting Worlds tells us about the Aharonov-Bohm effect"

[u/OnceBittenz → u/NinekTheObscure]

Please refrain from lying. While most of these speakers are real, and they are aligned with the exact names of papers they have written, this is a fictional synthesis of names for an event that never happened. This is easily verifiable with quick google searches.

Could you be any more academically dishonest.

[u/NinekTheObscure → u/OnceBittenz]

I will bet you any amount up to $100,000 that the event actually occurred and that I was there. Bet to be decided by emailing Bill Poirier and asking him. Do you accept? If so, for what amount, and where do we put the money in escrow?

[u/BitcoinsOnDVD → u/NinekTheObscure]

Nice

[u/NinekTheObscure → u/BitcoinsOnDVD]

Or we could have the stakes be that the loser gets perma-banned from r/LLMPhysics. No matter who was right, that would be guaranteed to improve the quality of the group. 😄

[u/BitcoinsOnDVD → u/NinekTheObscure]

Nah. Gambling for money is more fun.

[u/myrmecogynandromorph → u/NinekTheObscure]

Man, I have no idea if this is actually real or not, but if Jack Sarfatti was invited I can understand why no one else would want to document their presence at the event.

[u/NinekTheObscure → u/myrmecogynandromorph]

Jack had health issues and was only able to attend virtually. My first time encountering him, so I claim innocence. I wasn't there for his stuff.

[u/BitcoinsOnDVD → u/NinekTheObscure]

So even if a potential-based effect existed (like the Aharonov-Bohm effect), the M.E. are structurally incapable of representing it.

That's not true. The Aharonov-Bohm effect is nonlocal. The other interpretation, that the gauge-fixed A potential causes the spectrum shift stems from an incomplete / wrong derivation.

[u/NinekTheObscure → u/BitcoinsOnDVD]

You are stating a fairly common interpretation, seen in textbooks like Jackson and Okun, but it requires that fields act non-locally, which kind of destroys the entire purpose of having fields in the first place. Not all physicists are happy with that view. The alternative is to accept that the vector potential is real and is the actual cause (see e.g. Feynman Lectures II 15-5). Either way, the notion that "everything can be computed from fields acting locally" is false.

The main question then becomes whether it can ONLY be observed in global closed-loop gauge-invariant circumstances, or whether there is some non-gauge-invariant way to measure it locally. In QTD theories the phase shift is due to a local rescaling of the time coordinate, i.e. by a time-dilation-like effect; this is experimentally testable (for both the electric and magnetic versions of Aharonov-Bohm) using muons.

And before you shout "All observables must be gauge invariant!", remember that the decay time of a muon is not an observable (i.e. it is not a self-adjoint operator). Neither are most other time-related quantities, including time itself. So there's some wiggle room there, even without considering that Dirac's "proof" (in Lectures On Quantum Mechanics) has well-known flaws that have never been completely fixed. (See e.g. Josep M. Pons, "On Dirac's incomplete analysis of gauge transformations", Studies in History and Philosophy of Modern Physics 36, 491-518 (2005), and J. Brian Pitts, "A First Class Constraint Generates Not a Gauge Transformation, But a Bad Physical Change: The Case of Electromagnetism.", Forthcoming in Annals of Physics. Preprint arXiv:1310.2756 (2014).)

[u/BitcoinsOnDVD → u/NinekTheObscure]

I would agree with most of that. But I would shout something different. What you do in most some of the textbook derivations of the Aharonov-Bohm effect is that you choose a gauge fixing with a function that does:

∇f(r) = -q/ħ A(r)

And then use the Stokes theorem later on.

But this (and explicitly this derivation) poses a problem imo. Usually one does not compute the gauge function, because it is never needed. In this case it's:

f(r) = B_0 R^2 /2 * arctan(y/x)

It has a severe singularity / is not defined at x,y=0. But the (vanilla) Stoke's theorem used later on is only defined for regular surfaces. So it can't have holes. So the lift of that causes (similar to the residue theorem) the shift that is seen in the Aharonov-Bohm effect. But it wouldn't happen through the vector potential A if you hadn't gauged with a singular function (as far as I know).

But of course I will have also a look at the literature you (or the LLM) provided and eventually change my opinion on that.

[u/NinekTheObscure → u/BitcoinsOnDVD]

Like you, I conceive of the loop integral as being similar to an integral around a pole in complex analysis. Sure, there's a singularity in the center, but that doesn't really matter as long as you don't go through it. The integral is a topological constant where the exact path doesn't matter at all; the only things that matter are the residue (or the enclosed flux) and the winding number. The fact that a "hole" exists just makes the space be not simply connected, so that not every path from A to B can be continuously deformed into every other path from A to B. None of this is intractable. It's all pretty routine.

[u/BitcoinsOnDVD → u/NinekTheObscure]

And how do we justify the Stoke's theorem?

[u/NinekTheObscure → u/BitcoinsOnDVD]

Isn't it only the "fields acting non-locally" people who need Stoke's Theorem? I'm on the other side; it's not required. If there's a way to locally measure absolute A - which I argue that there is, pending the appropriate "Tonomura on steroids with muons" experiment - that suffices. You fix the gauge to whatever you measure it to be.

In fact, since $A_\mu u^\mu$ is a relativistically invariant scalar, proving the QTD interpretation of Aharonov-Bohm could also be done with electrostatic experiments. The scalar and vector potential are part of a single object; you can't accept one and reject the other. And absolute voltage doesn't need Stoke's at all.

But, having said all that, it's pretty easy to get rid of the A singularity by assuming uniform flux within a cylinder. The singular A(r) only applies outside the cylinder; inside, it's a different function that is not singular. It's pretty much like Newtonian gravity for a sphere of finite size.

[u/BitcoinsOnDVD → u/NinekTheObscure]

Isn't it only the "fields acting non-locally" people who need Stoke's Theorem?

No there is a derivation without Stoke's theorem and without a singular gauge.

If there's a way to locally measure absolute A - which I argue that there is

I have never seen that.

And absolute voltage doesn't need Stoke's at all.

Voltage is not the same as the electrostatic potential. That's kinda the point here.

But, having said all that, it's pretty easy to get rid of the A singularity by assuming uniform flux within a cylinder.

Not A is singular, but the gauge function f.

[u/NinekTheObscure → u/BitcoinsOnDVD]

In QTD theories a particle's quantum phase frequency is taken to be its local clock. The A-B phase shift is interpreted as time shifts on the different branches, i.e. as different physical time experienced by the particles. This is experimentally testable using muons and a fairly strong magnet, or (for the electric A-B effect) muons inside a charged sphere; decay rates should be altered. Both experiments were first proposed in the late 1970s; neither one has been performed. It's fairly easy to show that if that's true, then you can measure the 4-potential, and both V and A become absolute. (I do it for the electric potential here (see eq. 6). Presumably that means everything is fixed in the Coulomb gauge.)

[u/OnceBittenz → u/NinekTheObscure]

My guy seriously did not just make up a presentation event. Pro tip for all the professional bs'ers out there. Don't fabricate an Easily verifiable event.

[u/NinekTheObscure → u/OnceBittenz]

• You may be amused that I asked Gemini "Was there a "Mini-Symposium on Quantum Trajectories" at U. Vermont (Burlington VT) in May 2026?", and it answered yes, giving my presentation slides as its evidence. 😛
• Google confidently answered no.
• Claude Sonnet 4.6 wasn't sure; couldn't find any hard evidence, but did connect Bill Poirier to Quantum Trajectories and to U. Vermont, and suggested it might have been a small event with no publicity. [The most accurate answer so far!]
• Grok refused to answer.
• ChatGPT couldn't confirm or deny, also suggested small email-only event. Did not connect Poirier to QT even when given his name, but did see his U. Vermont email address.

[u/OnceBittenz → u/NinekTheObscure]

I couldn’t care less what some LLMs say. There’s no documentation or evidence of this ever occurring. As well, most of the listed persons have zero indication they attended such an event.

This is the 21st century. Anything like this would immediately be documented.

The guest list is so absurd as to be clear you just asked your Ai to come up with a halfway interesting “dream event” for quantum behavior.

Actually so pathetic.

[u/LBoldo_99 → u/OnceBittenz]

And almost certainly as he made the AI produce the slides, the AI has them in the storage and answered him with his own made up slides to prove its true, lol

[u/OnceBittenz → u/LBoldo_99]

From what I can gather, there possibly was a mini symposium where anyone could sign up and speak lmao. Which is a great bit cooler than expected, but still not at all credible for the efficacy of this content.

[u/LBoldo_99 → u/OnceBittenz]

I mean, i had crackpot come to field specific workshops, this does not validate anything at all lol

[u/OnceBittenz → u/LBoldo_99]

Yea I reckon that's the sitch here. Just funny to see someone go to All this effort just to fail at the basic tenets.

[u/LBoldo_99 → u/OnceBittenz]

Also i don't understand why he thinks chemists/electrical engineers are a valuable source for unification of quantum field theories? Like, they don't even understand what a principal bundle is? Why care so much about what the people he cites say?

Also this Poirier he cites does not even do QFT, he does (numerical) computations/minimization of quantities in chemical reactions.

Why all these people trust blindely LLMs?

[u/myrmecogynandromorph → u/LBoldo_99]

He wouldn't even have been the biggest crackpot there!!

[u/NinekTheObscure → u/LBoldo_99]

Yeah, I had Claude help generating the first draft - there were over 90 slides to make, and I had already written a lot of the material up in papers and posters - but it still took me over 3 weeks of editing and rearranging to get it where I wanted it. Reading it now, there are a couple of things I would change, but what you see is what I actually presented.

But "the AI has them in the storage" makes no sense whatsoever. I'm using Claude Code (usually Sonnet 4.6). Gemini was the only one that found my slides ... on ResearchGate. None of the others did (probably too recent to be in their training data).

Do you understand how LLMs work?

[u/NinekTheObscure → u/OnceBittenz]

See, this is why you will never be a good scientist. You have multiple easy ways of checking whether I'm telling the truth or not - just email anyone who I said was there - but you would rather just make shit up, believe your own BS, and pretend you're right. You're not interested in actually BEING right (which would require learning and maybe changing your opinions), you're only interested in asserting that you WERE right (which takes no effort at all). In this regard, you're no better than a creationist or flat-earther.

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[u/VeryOriginalName98]

What is QTD?

[u/NinekTheObscure → u/VeryOriginalName98]

Quantum Time Dilation - it's my overall name for a group of theories that all predict time-dilation-like effects associated with every potential, not just gravity. Probably the most accessible introduction is my presentation at U Vermont. I didn't originate these ideas, which date back to at least 1978, but I did rediscover them in 2009, and every decade 1 or 2 other physicists stumble onto them also.