Discussion

It makes sense to treat gravity differently from the other interactions.

In canonically or perturbatively quantised gravity, the entanglement between matter and its gravitational field can be best understood by what is called a ‘dressing’ in the context of quantum field theory. This is the formal acknowledgement that a particle which carries a charge—say, an electron that carries electric charge—never occurs in nature without the field created by that charge.

5 The assumption that particles and geometry are ultimately the same does not per se require the existence of gravitons. However, I find it hard to see how one could have geometry with quantum features and not also have propagating modes, i.e. gravitons.

A bare electron appears only in the mathematics. Real electrons always come with soft (low energy) photon clouds: This is the dressing.

If one has an electron that is in a superposition of two branches, then each branch has its own dressing. They are independent from each other and can have a relative phase. Consequently, the electron is entangled with the soft photon dressing. The entanglement in quantum gravity comes about in the same way: it describes a dressing by soft gravitons that can then be interpreted as the field caused by the particle, or the geometric deformation respectively.

In the approach that I started from, however, soft photons are very different from soft gravitons. The photons are particles and independent of the electrons. The soft gravitons, however, are not because, by assumption, the particle and its geometry are ultimately the same. They are the same, that is, up to freely propagating modes that are hard gravitons. The reason this makes sense at least to me is that if we treat the graviton dressing like the photon dressing, then the mathematical description of a particle in a superposition of multiple locations carries no information about it in fact being one particle. There is formally no way we could know that, say, half an electron with its own dressing is actually not itself a fundamental particle other than by normalisation. But the normalisation just tells us that we cannot measure only one branch in isolation, which is exactly the fact that needs explanation. But half an electron does not exist any more than an electron without an electric field. To put this differently: Two branches of one particle are not physically independent because they cannot exist separately.

The product state requirement can thus be seen as a way to make sure that it is always entire particles that create a geometry, and this in turn explains why we can only measure entire particles. In other words, the Hamiltonian constraint should act per particle sector (of Fock space), and not pointwise. This is why, intuitively, the state of a particle in two branches has mixed terms that essentially describe part of a particle in one place with a gravitational field sourced from another place. This happens exactly because the rest of the particle must be somewhere. I know that I did not, in fact, put forward the mathematics for these statements. That is because it would just add assumptions that are unnecessary to arrive at the phenomenological consequences which were the focus of this paper. However, I wanted to provide this explanation as motivation. It is also worth mentioning that the estimate presented here does not rest on the product state assumption. By order of magnitude one would expect most deviations from canonically quantised gravity to give a similar result.

I interpret this model as a way to reconcile the present formalism of quantum mechanics with a possibly underlying theory. The teleology of this model is likely a mathematical artifact that originates in the way that we have developed quantum mechanics. This is because the teleology of the model presented here ultimately comes from the way that we describe the initial (prepared) state of the system. But how do we even know what this state is? We have simply inferred these states (and their Hamiltonian operators) from the results of countless experiments. We have no evidence that the initial state in standard quantum mechanics is an ontological state, rather, it is a reconstruction for the purpose of fitting our measurement results.

Is it any surprise, then, that if we ask for the local time evolution of such a reconstructed state, we get a model in which the choice of measurement variable must fit with what happened before the measurement? I think that this odd feature will make sense once we understand the underlying physics, just like the electron’s magnetic moment made sense once we understood what a spin 1/2 particle is.

Finally, I want to stress that nowhere have I assumed that the geometry is classical. Indeed, in general it is not classical: The geometry can have superpositions and it can also be internally entangled. It is just that states of the geometry with significant quantum features will not survive for long because of the residual build-up.

6. SUMMARY

I have shown here how the assumption that matter and geometry have the same fundamental origin requires the time evolution of a quantum state to differ from the Schrodinger ¨ equation. This has the consequence that the ideal time evolutions which minimise the action are those with end states that are to good approximation classical. We can then identify these end states with the eigenstates of the measurement device. This new model therefore explains why quantum states seem to ‘collapse’ into eigenstates of the measurement observable, and how this can happen while preserving locality. Since the collapse process is governed by quantum gravitational contributions whose strength is known, the resulting model is parameter free.

Collapse happens in this model whenever the accumulated phase difference between dislocated branches, τm|Φ12|, exceeds ∼ 1. The model’s phenomenology—notably the collapse itself—can be tested in roughly the same parameter range as other tests of the weak field limit of quantum gravity.

Acknowledgements

I acknowledge help from ChatGPT 5 for literature research as well as checking this manuscript. I swear I actually wrote it myself.