I was just curious if you were programming that completely yourself or also with the help of Chat GPT?

Well done, sir!

Oh, wow. This thread is still going. Might as well get in here.

I may need to ask ChatGPT what's going on here…

I'll be curious to see what it has to say

 

I asked Copilot to try to address some of the concerns it pointed out, and it was able to derive from "first principles". I do not understand the results, of course, but the fact it can do that is encouraging for your S Theory.

Quote:

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Prompt Attempt a derivation from quantum information,... | Try in Copilot Chat
Attempt a derivation from quantum information, then from statistical mechanics, and then from tensor network theory.

Response
Excellent! Let's proceed step by step to attempt a derivation of the S Theory growth law and constraint-based dynamics from three foundational perspectives:

1. From Quantum Information Theory
Goal:
Derive the entanglement growth law: $ \frac{dS{ij}}{d\tau} = \eta{ij}(S{\text{max}} - S{ij}) $ as a coarse-grained description of entanglement dynamics between two subsystems ( i ) and ( j ).
Assumptions:

• Each "spatom" is a quantum subsystem (qubit or qudit).
• The system evolves under local unitary dynamics or open system decoherence.
• Entanglement entropy ( S{ij} ) increases due to interaction or decoherence, approaching a maximum value ( S{\text{max}} ) (e.g., the Page limit).

Derivation Sketch:
[ol]

Entanglement Entropy Growth: In open quantum systems, the von Neumann entropy of a subsystem increases due to interaction with an environment: $ \frac{dS}{dt} \geq 0 $ and saturates at thermal equilibrium or maximal entanglement.

Lindblad Dynamics: For a density matrix ( \rho ), the Lindblad equation governs non-unitary evolution: $ \frac{d\rho}{dt} = -i[H, \rho] + \sumk \left( Lk \rho Lk^\dagger - \frac{1}{2} {Lk^\dagger L_k, \rho} \right) $ This leads to entropy production and decoherence.

Phenomenological Model: Assume the entanglement entropy between ( i ) and ( j ) grows toward a saturation value ( S{\text{max}} ), with a rate proportional to the remaining "headroom": $ \frac{dS{ij}}{d\tau} \propto S{\text{max}} - S{ij} $ This is a first-order relaxation process, common in thermodynamics and information theory.

Interpretation of ( \eta{ij} ): The coefficient ( \eta{ij} ) encodes the interaction strength or entangling power between the two subsystems.

[/ol] Conclusion: The growth law is a coarse-grained, thermodynamic approximation of entanglement dynamics under decoherence or local interaction, consistent with quantum information theory.

2. From Statistical Mechanics
Goal:
Derive the same growth law from entropy maximization and relaxation dynamics.
Assumptions:

• The entanglement network is a statistical ensemble of configurations.
• Each link ( S_{ij} ) represents a microstate variable.
• The system evolves toward maximum entropy under constraints.

Derivation Sketch:
[ol]

Entropy Functional: Define a global entropy functional: $ \mathcal{S} = -\sum{ij} p{ij} \log p{ij} $ where ( p{ij} ) is the probability of a given entanglement configuration.

Relaxation Dynamics: Use Onsager's reciprocal relations or FokkerPlanck dynamics: $ \frac{dS{ij}}{d\tau} = -\frac{\partial \mathcal{F}}{\partial S{ij}} $ where ( \mathcal{F} ) is a free energy-like functional: $ \mathcal{F} = \mathcal{E} - T \mathcal{S} $

Assume Quadratic Energy Penalty: Let: $ \mathcal{E} = \sum{ij} \frac{1}{2} \eta{ij} (S{\text{max}} - S{ij})^2 $ Then: $ \frac{dS{ij}}{d\tau} = \eta{ij}(S{\text{max}} - S{ij}) $

[/ol] Conclusion: The growth law emerges as a gradient descent on a free energy landscape, where entanglement increases to maximize entropy and minimize informational tension.

3. From Tensor Network Theory
Goal:
Interpret the growth law and constraint terms as arising from tensor network optimization.
Assumptions:

• The entanglement network is a tensor network (e.g., MERA, PEPS).
• Each link ( S_{ij} ) corresponds to a bond dimension or entanglement weight.
• The network evolves to minimize a cost function under topological constraints.

Derivation Sketch:
[ol]

Tensor Network Cost Function: Define a cost function for optimizing the network: $ \mathcal{C} = \sum{ij} \left[ \eta{ij}(S{\text{max}} - S{ij})^2 + \lambda \cdot \text{Constraint}(S_{ij}) \right] $

Gradient Descent Dynamics: The evolution of ( S{ij} ) follows: $ \frac{dS{ij}}{d\tau} = -\frac{\partial \mathcal{C}}{\partial S{ij}} = \eta{ij}(S{\text{max}} - S{ij}) - \lambda \frac{\partial \text{Constraint}}{\partial S_{ij}} $

Constraint Terms:

• Frustration: penalizes irregular entanglement flow.
• Asymmetry: encodes directional bias (e.g., spin).
• Loop closure: rewards topological consistency (e.g., particle stability).

[/ol] Conclusion: The growth law and constraint dynamics can be derived from variational optimization of a tensor network, where entanglement structure evolves to minimize a global cost under geometric and topological constraints.

Would you like me to formalize these derivations into a document or visual summary?

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I want to see how this ends

I've asked AI to derive the terms from first principles as well but because most of the S-theory terms are related to each other, the derivations just walk from one term to the next and back to the first term. It's not actually deriving anything except proving that S-theory is internally consistent which I suppose has its own value.

lb3 said:

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I've asked AI to derive the terms from first principles as well but because most of the S-theory terms are related to each other, the derivations just walk from one term to the next and back to the first term. It's not actually deriving anything except proving that S-theory is internally consistent which I suppose has its own value.

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I'm too dumb to know any difference.

I haven used co pilot that much, but a concern I always have is that it's just regurgitating what it's reading instead of actually putting thought into it.

I'll be updating the white paper this weekend to touch up some wording and show that I can get a 0.0kg spin 1 SEM to propagate at exactly 1 link per tick.

I did an audiobook on the basics of quantum mechanics a few years ago…and it was apparently completely worthless because I am completely lost

Philip J Fry said:

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I haven used co pilot that much, but a concern I always have is that it's just regurgitating what it's reading instead of actually putting thought into it.

I'll be updating the white paper this weekend to touch up some wording and show that I can get a 0.0kg spin 1 SEM to propagate at exactly 1 link per tick.

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Are you a physicist or just a really smart guy? Or both?

I'm not "getting at" anything, what I asked is just what I wanted to know. I wanted to know if Chat GPT was writing the simulations or if you were, and yes, primarily because of the reasons you lay out in that post.

Philip J Fry said:

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I've definitely felt more at ease talking in entropic time than local time from a conceptual standpoint. Not sure if I'm making that term up, but it seems natural to have a master clock.

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You might find this interesting:

I didnt watch that video, but I know exactly what Star Talk conversation its going to be discussing, and I'm not sure that what Oluseyi said was on the up-and-up or properly explained. My understanding is that both observers "see" the same photons, but they will disagree on a calculation of the present time. Because of their relative motions, each persons personal clock is not the same, and neither is the same as Andromeda local clock either, so if both had some kind of physics breaking instant communication device that linked their "present" together with Andromeda, it would be a paradox, because each of our observers would be "communicating" with an Andromeda that is 4 days off from the Andromeda the other person communicates with, and then one would know "the future" (on Andromeda) compared to other and it would be a paradox, but as far as we know, information cant propagate like that anyway.

Anyway, I think both are receiving the same photons emitted from the same place and the same time, but they will disagreee by 4 days if each tries to calculate to the exact day when those photons were emitted, but for someone at Andromeda, those photons will have been emitted a specific present time too, and not days apart. Or maybe I'm in some kind of reality denial mode.

The video explains that they misunderstand the paradox and then goes on to talk about time a bit.

PeekingDuck said:

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The video explains that they misunderstand the paradox and then goes on to talk about time a bit.

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Cool I might check it out later.

Philip J Fry said:

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JJxvi said:

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I was just curious if you were programming that completely yourself or also with the help of Chat GPT?

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I guess I'll direct this. What exactly are you getting at? Whatever you think the short comings are about LLM, you're going to have to let that go. That I used an openly available tool that anyone can use to develop a math model? Guilty as charged. Do I take whatever code it gives me without checking it and putting it through the ringer? No, I do not do that. ChatGPT gets a lot of stuff right, but it can hallucinate and sometimes straight up lie to you. I've lost count of the number of times it would show me data and say "There it is, the creation of the universe!" only to show a straight line. Don't you think that didn't weigh on me heavily throughout this whole process? I fought through that nonsense daily.

I'm no Einstein and I don't pretend to be. I didn't get a phd in astrophysics and quantum mechanics and slave like a lot of really smart people on this stuff. They are the ones who should be taking this work and running with it. Not me.

If this theory holds, which I actually think it will, there's going to be an explosion of entanglement based studies out there very soon.

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This is a great example of what you can do with AI. You don't have to take it at its word. You can correct it and lead it in the right direction. Right now, anyway, it isn't perfect, but it's a fantastic tool when used properly, which you are clearly doing. Amazing work!

You need to work on red shifts for entanglements traveling from high to low density regions. Then do Doppler shifts.

I was going to start pulling James Webb data. I asked for a small grant from FQXI, but I think it matters to me more that I get it done than waiting on some committee to make a decision.

Any suggestions on a high power computing resource I could use? I'm afraid some of this stuff is going to start requiring more than my macbook can handle.

Nothing that would be free. Someone like Rescale might be able to help, but I have no experience with them. Most of the ones I've interacted with are primarily engineering oriented, using established software like ANSYS or Matlab. I'm guessing that you're using something very different.

No, my code is all in MATLab as well. ChatGPT works in python, so I end up porting it over.

Thanks for sharing all this here. I find it fascinating what people can come up with out of sheer curiosity. My math skills aren't anywhere near capable of understanding the details, but at a conceptual level this is so interesting. It would make sense that time, at least how we understand it from inside the universe, didn't exist before the Big Bang. Someone eventually has to push us to a deeper understanding of reality, exciting but not at all surprising it could be an Aggie.

He's Alex McColgan and you are watching Astrum.

If I understand that model it doesn't appear to be showing a red shift, just that it takes 1 tic to reach each subsequent node.

A red shift would show the SEM repetition rate would be different for different observers. A gravitational red shift should be possible with your theory by looking at the local time clocks for fixed observers. The more general case for Doppler and cosmological red shifts will be harder because your model is still in a special relativity stage and doesn't seem to account for moving frames yet.

Yeah. Doppler effect is my next phase, but I think before I do that, I need to get my photon to behave. Right now, if I add a proximity constraint, I get exactly 1 link per tick. I'm trying to decide if that's cheating though because it feels like it is.

I was also struggling a little conceptually with the scale. You think it's safe to say I need cosmological scales? Basically shoot a photon from one large moving mass to the other? Or can it just be an idealized pulse. Easy to get lost in the weeds

Philip J Fry said:

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Yeah. Doppler effect is my next phase, but I think before I do that, I need to get my photon to behave. Right now, if I add a proximity constraint, I get exactly 1 link per tick. I'm trying to decide if that's cheating though because it feels like it is.

I was also struggling a little conceptually with the scale. You think it's safe to say I need cosmological scales? Basically shoot a photon from one large moving mass to the other?

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You don't need cosmological scales, at least not right now.

I would try to get the gravitational red shift working first. You should be able to use the proper vs local time at different locations to show that the cyclical entanglement (photon frequency) slows as the photon climbs out of a gravity well (moving from an area of high density entanglements to low density).

The observer in the regions with slow entanglement growth (high gravity regions) will see the proper time slowed down so to the observer with a faster proper time will observe the photon with a red shift.

The cosmological case involves photons emerging at the perimeter of the universe where the expanding network of entanglements lengthens space and thus the wavelength of the photon so I think your model can show this.

Moving reference frames are more complicated and I'm not sure how your theory would show photon frequency changes in General Relativity cases.

I am a true idiot. I was so focused on getting my lensing to work. Let's try again.

Z=tlocal/temit-1.

This assumes the observer is on the green node looking in at an emitting signal at node 1.

This is a fun follow but I'll admit that Idon't think you're deriving anything new and are just creating a new framework or narrative with which to attach existing relativity and quantum equations. I have particular trouble with you using c to define c.

But back to your simulations, the cosmological red shift should be possible at the edge of your universe. I would switch to a 1d simulation of an expanding universe where your nodes are moving outward with the left most and right nodes moving away from the center at a velocity of c, then emitting a photon from the next innermost node towards the center. This should show increased wavelengths to observers at other nodes because space is being stretched at the edges.

This should work because the math says as much but until I can see a derivation of c that doesn't include c I'm not sure you have anything more than just relativity repackaged.

Page Tres!

Seriously interesting and entertaining (in the best kind of way), looking forward to seeing how this evolves and to this thread being in the Smithsonian. Just need to get that dang ole c defined independently. Light work!