Important Note-My exams are starting from tomorrow.I will be very less active.
I will appereciate if i get critiques while i am busy,so i can develop my theory after it.
The ones pointed related to spacetime,photons,massless object etc are resolved.

1 minute ago, swansont said:

You said this energy density creates chortons from photons, so you must already have photons

Yes,this is what i have to change now,as photons are supposed to exist before spacetime.

45 minutes ago, Dhillon1724X said:

The ones pointed related to spacetime,photons,massless object etc are resolved.

Don't forget that you still haven't answered my question yet.

19 minutes ago, KJW said:

Don't forget that you still haven't answered my question yet.

For a massless particle (such as a photon or graviton), which experiences no proper time, the trajectory is instead governed by the null geodesic equation:

\[\frac{d^2 x^\mu}{d\lambda^2} + \Gamma^\mu_{\nu\sigma} \frac{dx^\nu}{d\lambda} \frac{dx^\sigma}{d\lambda} = 0,\]

where \( \lambda \) is an affine parameter along the particle’s worldline.

I added it after your question.

Edited July 21Jul 21 by Dhillon1724X

6 hours ago, Dhillon1724X said:

I now realize that declaring a curvature-energy density commutator without a well-defined conjugate field structure isn't correct. I've rewritten Axiom 6 based on canonical quantization of the Chorton field χμν(x)\chi_{\mu\nu}(x)χμν(x), with proper conjugate momentum πμν(x)\pi^{\mu\nu}(x)πμν(x)

That's not the point. Conjugate pairs of the field variables must comply with the principle of microcausality. Field values at space-like separated points must commute (or anti-commute if they are fermionic) and be canonically conjugate only at points time-like separated or null.

7 hours ago, Dhillon1724X said:

You're right that I describe spacetime as emergent — not fundamental. So when I refer to photons "concentrating in a region," I don't mean a classical volume in existing space. Instead, I use a pre-geometric substrate — a discrete quantum graph or network

No, you're not describing spacetime as emergent; you're saying you're describing it. Saying you're doing something is not the same as doing something.

You wouldn't even have photons, very much in the spirit of what @Markus Hanke told you. In order to have quanta of a field the way we understand them, you need to establish commutation rules according to local values. Otherwise you don't even have quanta (and therefore photons). You wouldn't have spin, you wouldn't have on-shell/off-shell separation, or mass, or energy, momentum, Fourier transform of the fields. Nothing makes sense in your theory as far as I can tell.

You haven't bothered to define such concepts as pre-geometric substrate. Using new words as shields against legitimate criticism doesn't do the trick. I'm sorry.

4 minutes ago, joigus said:

No, you're not describing spacetime as emergent; you're saying you're describing it. Saying you're doing something is not the same as doing something.

You wouldn't even have photons, very much in the spirit of what @Markus Hanke told you. In order to have quanta of a field the way we understand them, you need to establish commutation rules according to local values. Otherwise you don't even have quanta (and therefore photons). You wouldn't have spin, you wouldn't have on-shell/off-shell separation, or mass, or energy, momentum, Fourier transform of the fields. Nothing makes sense in your theory as far as I can tell.

You haven't bothered to define such concepts as pre-geometric substrate. Using new words as shields against legitimate criticism doesn't do the trick. I'm sorry.

I understand that sir,
I will no longer force photons to collapse into chortons.I check if my work can stand without it.
I welcome any further critiques

2 hours ago, Dhillon1724X said:

For a massless particle (such as a photon or graviton), which experiences no proper time, the trajectory is instead governed by the null geodesic equation:

[math]\dfrac{d^2 x^\mu}{dλ^2} + \Gamma^\mu_{\nu\sigma} \dfrac{dx^\nu}{dλ} \dfrac{dx^\sigma}{dλ} = 0[/math],

where λ is an affine parameter along the particle’s worldline.

Perhaps you can elaborate on what an affine parameter is, particularly with regards to null geodesics, which cannot be parametrised with proper time or arc length.

I have uploaded the updated version,
Should i send DOI or maybe you can access from first version.

Thanks to @Markus Hanke for catching that very critical and very foolish mistake.

In this new version i dont use photons.
The theory stands still and stronger now.

1 hour ago, Dhillon1724X said:

The theory stands still and stronger now.

Moderator Note

This is an unsupported assertion. If you state something like this, we expect you to elaborate. NOBODY here is going to simply take your word that you make a major change to your idea that makes it stronger. Please explain your new position without making up new terms, and perhaps go back to answer unanswered questions from other members.

46 minutes ago, Phi for All said:

Please explain your new position without making up new terms

Due to shortage of time i had to use those words.
I will keep in my mind to do it from next time.

This version represents a major refinement and formal advancement of the Quantum Chorton Framework (QCF). The key changes and additions are as follows:
1. Removal of Photon-Based Assumptions

• The original version included speculative assumptions about high-energy photons as the origin of curvature quanta.In this revised version, photon dependence has been fully removed.Chortons are now modeled as fundamental excitations triggered by local energy density thresholds, making the theory fully background-independent and self-contained.
  2. Reorganized and Extended Mathematical Foundation

  • A Master Lagrangian has been constructed to unify all formulations of the Chorton field.

  • A new section introduces Feynman rules for the Chorton interaction field, compatible with perturbative expansions.
    
    There are some more minor refinements.
    

1 hour ago, Dhillon1724X said:

Chortons are now modeled as fundamental excitations triggered by local energy density thresholds,

You’ve not answered where these conditions exist. Under what circumstances do we have 10^115 J/m^3?

8 hours ago, swansont said:

You’ve not answered where these conditions exist. Under what circumstances do we have 10^115 J/m^3?

Looks like due to some error my answer didn’t get posted.

These conditions are very high and impossible to reach in presence of spacetime as Planck scales emerge with gravity or spacetime.But spacetime emerges from chortons and before them there was none,so there was no limit.The Big Bang era had huge numbers of energy,temperature etc

58 minutes ago, Dhillon1724X said:

Looks like due to some error my answer didn’t get posted.

These conditions are very high and impossible to reach in presence of spacetime as Planck scales emerge with gravity or spacetime.But spacetime emerges from chortons and before them there was none,so there was no limit.The Big Bang era had huge numbers of energy,temperature etc

Presumably one could correlate the energy density with a temperature and see when this could have happened. But if you’re forming chortons with this energy, shouldn’t the temperature rapidly drop, since that energy is no longer available to whatever field is creating the chortons?

If they were created right after the Big Bang, there are a finite number of them. How does gravity get rearranged under that scenario? The gravity in some region of space will change as galaxies coalesced and stars formed

2 hours ago, Dhillon1724X said:

.But spacetime emerges from chortons and before them there was none

Before ???
There was no before, as there was no space-time.

One could assume that there was also enough energy density to spontaneously create green leprechauns driving pink cadillacs ...
Where is the evidence, or the need, for this 'flight of fancy' ?

5 hours ago, swansont said:

If they were created right after the Big Bang, there are a finite number of them. How does gravity get rearranged under that scenario? The gravity in some region of space will change as galaxies coalesced and stars formed

yes,there are finite numbers of them,the total number formed after or during the Big Bang is large, gravity is not frozen.Chortons do not propagate, but their field values (χμν) can evolve. As structure forms (like galaxies), the Chorton field aligns and redistributes curvature across the network via the graph Laplacian dynamics. This allows gravity to adapt to new mass distributions without needing new Chortons.

5 hours ago, swansont said:

But if you’re forming chortons with this energy, shouldn’t the temperature rapidly drop, since that energy is no longer available to whatever field is creating the chortons?

Sorry sir,
I am unable to understand,
Do you mean temperature during Big Bang?

Update!
I tested this using Planck 2018 cosmological parameters. Starting with standard ΛCDM energy components (dark energy, matter, and radiation) and adding the redshifted Chorton field (approximately 5.5% of the radiation sector), the total energy density becomes:

\[

\rho_{\text{total}} = \rho_{\Lambda} + \rho_{\text{matter}} + \rho_{\text{radiation}} + \rho_{\text{chorton}} = 7.6429 \times 10^{-10} \, \text{J/m}^3

\]

This closely matches the critical density derived from the Friedmann equation with:

\[

H_0 = 67.4 \, \text{km/s/Mpc}

\]

\[

\rho_c = \frac{3H_0^2}{8\pi G} = 7.643 \times 10^{-10} \, \text{J/m}^3

\]

The difference is only:

\[

\Delta \rho = 1 \times 10^{-13} \, \text{J/m}^3 \quad \text{or} \quad 0.0013\%

\]

This minor offset arises due to rounding in component densities (especially dark energy and matter), and the addition of a redshifted geometric background (Chorton field). The result stays within observational tolerance and confirms that the QCF addition is consistent with ΛCDM energy structure.

Edited July 23Jul 23 by Dhillon1724X

5 hours ago, MigL said:

Before ???
There was no before, as there was no space-time.

I am using before to explain in normal language.
But yes,
You're absolutely right that in conventional GR, there's no "before" spacetime — since time itself is part of the manifold. What I'm suggesting is not a temporal "before" in the usual sense, but rather a pre-geometric phase, where energy fields existed without classical spacetime geometry.

5 hours ago, MigL said:

Where is the evidence, or the need, for this 'flight of fancy' ?

The "flight of fancy" you're referring to is actually a theoretical response to a serious gap in our understanding
There is precedent — many quantum gravity approaches, including Loop Quantum Gravity, Spin Foam models, and even aspects of String Theory, suggest spacetime is not fundamental, but emergent. My proposal simply specifies how that emergence could occur: through quantized curvature nodes (Chortons) triggered by Planck-scale energy density. It’s no less motivated than any other pre-geometric framework being seriously discussed in theoretical physics today.

As for evidence — the model isn’t just metaphysical. It recovers the observed total energy density of the universe (Planck 2018) within 0.0013% accuracy when evolved with redshift and standard ΛCDM parameters. That’s not fantasy — it’s predictive consistency.

If there's a better explanation for where spacetime comes from that also fits observational data this tightly, I’m open to seeing it. Until then, I'd argue Chortons are at least more plausible than leprechauns with luxury vehicles.

I agree that it may have flaws but its being developed by a 15 year old(almost) and solo.

Edited July 23Jul 23 by Dhillon1724X

3 hours ago, Dhillon1724X said:

yes,there are finite numbers of them,the total number formed after or during the Big Bang is large, gravity is not frozen.Chortons do not propagate, but their field values (χμν) can evolve.

How?

3 hours ago, Dhillon1724X said:

As structure forms (like galaxies), the Chorton field aligns and redistributes curvature across the network via the graph Laplacian dynamics. This allows gravity to adapt to new mass distributions without needing new Chortons.

Where does the angular momentum come from for these spin-2 particles?

3 hours ago, Dhillon1724X said:

Sorry sir,
I am unable to understand,
Do you mean temperature during Big Bang?

Yes. You’re forming these chortons which have energy, so for each one there must be a discrete drop in available energy in the field, so the temperature must decrease.

8 minutes ago, swansont said:

How?

Chortons are non-propagating, localized curvature excitations, but their field values [math]\chi_{\mu\nu}(x, t)[/math] evolve due to changes in energy and matter across the universe. This includes both quantum-scale energy fluctuations and classical mass-energy — such as that from galaxies, stars, planets, and particles.

In QCF, the field evolves through:

Hamiltonian field dynamics:

[math]
H_\chi = \frac{1}{2} \left( \pi_{\mu\nu}^2 + \nabla_\lambda \chi_{\mu\nu} \nabla^\lambda \chi_{\mu\nu} + V(\chi) \right)
[/math]

with time evolution:

[math]
\frac{d}{dt} \chi_{\mu\nu}(x, t) = \frac{\delta H}{\delta \pi_{\mu\nu}(x, t)}
[/math]

Graph-based dynamics (discrete spacetime nodes):

[math]
f(\rho_\Omega) \cdot \Delta_G \chi_{\mu\nu}(v) = \beta \cdot T^{\text{eff}}_{\mu\nu}(\Omega)
[/math]

where [math]T^{\text{eff}}_{\mu\nu}(\Omega)[/math] reflects local energy fluctuations, which include contributions from bulk matter like galaxies and planets after geometry emerges.

Additionally, QCF allows matter fields [math]\phi(x)[/math], [math]\psi(x)[/math] to couple to the emergent metric [math]g_{\mu\nu}(x) = \eta_{\mu\nu} + \alpha \chi_{\mu\nu}(x)[/math], such that:

[math]
S_\phi = \int d^4x \sqrt{-g_\chi} \left( \frac{1}{2} g^{\mu\nu}\chi , \partial\mu \phi , \partial_\nu \phi - V(\phi) \right)
[/math]

Thus, as matter moves or clusters (e.g., during galaxy formation or planetary dynamics), it modifies the local stress-energy, which updates the Chorton field configuration — even though Chortons themselves remain fixed in position.

This is similar to spin lattices or quantum magnetism: field configurations evolve due to neighboring energy changes, not due to moving particles. In QCF, curvature is dynamic even if the underlying excitations are fixed.

Edited July 23Jul 23 by Dhillon1724X

2 minutes ago, Dhillon1724X said:

Chortons are non-propagating, localized curvature excitations, but their field values χμν(x,t) evolve due to changes in energy and matter across the universe. This includes both quantum-scale energy fluctuations and classical mass-energy — such as that from galaxies, stars, planets, and particles.

How does the energy and matter interact with the chorton field?

2 minutes ago, Dhillon1724X said:

In QCF, the field evolves through:

\textbf{Hamiltonian field dynamics}:

Your math isn’t rendering, so it’s not really helpful.

1 minute ago, swansont said:

Your math isn’t rendering, so it’s not really helpful.

Sir can you guide me to fix this.I tried many times but i dont know where i am messing up.

43 minutes ago, Dhillon1724X said:

Sir can you guide me to fix this.I tried many times but i dont know where i am messing up.

I use the sandbox section in this forum to test mathematical formulas and latex. Usually it involves some trial and error before finding out what is wrong,

Edited July 23Jul 23 by Ghideon

46 minutes ago, Dhillon1724X said:

Sir can you guide me to fix this.I tried many times but i dont know where i am messing up.

All of the mathematical expression, including the opening and closing tags, needs to be on the one line. It can wrap to multiple lines, but no new line characters. The rendered LaTex can have multiple lines using "\\", but everything needs to be on the one line in the edit box.

Edited July 23Jul 23 by KJW

34 minutes ago, Ghideon said:

I use the sandbox section in this forum to test mathematical formulas and latex. Usually it involves some trial and error before finding out what is wrong,

29 minutes ago, KJW said:

All of the mathematical expression, including the opening and closing tags, needs to be on the one line. It can wrap to multiple lines, but no new line characters. The rendered LaTex can have multiple lines using "\\", but everything needs to be on the one line in the edit box.

Thanks for helping.

1 hour ago, swansont said:

Where does the angular momentum come from for these spin-2 particles?

You're right — each Chorton carries energy, so its formation does reduce the available energy in the quantum vacuum. In the Quantum Chorton Framework, this process is fully accounted for.

Chortons form when the local energy density on the quantum graph exceeds a Planck-scale threshold:

[math]\rho(x) \geq \rho_{\text{crit}} \sim \rho_{\text{Planck}} \Rightarrow \chi_{\mu\nu}(x) \neq 0[/math]

At that point, the curvature field χμν\chi_{\mu\nu}χμν is activated, and its evolution is governed by the Hamiltonian:

[math]
H_\chi = \frac{1}{2} \left( \pi_{\mu\nu}^2 + \nabla^\lambda \chi_{\mu\nu} \nabla_\lambda \chi_{\mu\nu} + V(\chi) \right)
[/math]

So yes — energy is transferred from unstructured vacuum energy into structured curvature excitations. But QCF does not begin with classical thermal equilibrium. The universe at that stage is a graph of quantum energy nodes — not a photon gas or thermal bath.

The temperature drop occurs, but it’s not a sudden collapse. As Chortons form across the graph, they gradually convert quantum energy into curvature, and the redshifting process begins. In fact, this is how QCF explains the smooth emergence of the CMB. The model predicts that the residual background energy density after Chorton activation matches observed CMB values — showing thermodynamic consistency.

So the temperature does decrease, but as a structured, geometric evolution, not as simple heat loss.

---

Edited July 23Jul 23 by Dhillon1724X

49 minutes ago, Dhillon1724X said:

Chortons in the Quantum Chorton Framework (QCF) are non-propagating, localized curvature excitations

If these 'Chortons' ( from which space-time emerges ) don't propagate, how do they manage to establish causal connectivity throughout the universe and the resulting homogeneity and isotropy ?

13 minutes ago, MigL said:

If these 'Chortons' ( from which space-time emerges ) don't propagate, how do they manage to establish causal connectivity throughout the universe and the resulting homogeneity and isotropy ?

In the QCF, causal connectivity and large-scale smoothness emerge before spacetime exists, through quantum graph dynamics — not classical field propagation. Here's how:

1. Pre-Spacetime Graph Activation

• Chortons activate at nodes where local energy density exceeds Planck scale:
  [math]\rho(x) \geq \rho_{\text{Planck}} \Rightarrow \chi_{\mu\nu}(x) \neq 0[/math]

• Since the early universe’s energy density was nearly uniform, this threshold was crossed near-simultaneously across the graph.

2. No Lightcone Limitation

• Before geometry forms, there's no light speed, no spacetime, no causal horizon.

• So the field can activate globally — not via signal exchange, but quantum threshold conditions.

3. Graph Laplacian Smoothing

• Chorton field values align via discrete Laplacian dynamics:
  [math]f(\rho_\Omega) \cdot \Delta_G \chi_{\mu\nu}(v) = \beta \cdot T^{\text{eff}}_{\mu\nu}(\Omega)[/math]

• This acts like curvature diffusion, smoothing the field and producing homogeneous and isotropic geometry over the entire graph.

4. Emergent Geometry

• The metric forms as:
  [math]g_{\mu\nu}(x) = \eta_{\mu\nu} + \alpha \chi_{\mu\nu}(x)[/math]

• Lightcones and causal structure emerge only after the field has already aligned.

Conclusion:

QCF doesn’t need inflation or field propagation to solve the horizon or isotropy problems. It provides an entirely pre-geometric mechanism that ensures the early universe is smooth and causally connected, consistent with CMB observations.

I welcome any further critiques or questions on my model. If there are no major issues left from your perspective, I’d appreciate knowing that — so I can consider the current version of the framework stable and ready to move forward. Your insights have already helped me improve it significantly

As i have written in my signature “I am supposed to fall, but I dive.”
I was supposed to fall when the photon birth idea collapsed,but i dived and let it collapse.
As a result i got this new version.
Maybe that light was just to guide me to here.