No. The construction of the space of states of a quantum system is mathematically well-defined and can be experimentally probed and these are the only things that matter.

The confusion is due to the mistaken assumption that a quantum system has the same space of states as its classical limit. That it doesn't doesn't imply any inconsistency, however.

Stam Nicolis, thank you very much for your comment and for taking the time to read my proposal. I understand the difference between the quantum state space and its classical limit, although I would like to further explore the relationship between them. My approach seeks to investigate whether certain phenomena, such as entanglement or Bell inequality violations, can be understood from a relational systems perspective without relying on purely mathematical superpositions. I truly appreciate your observations and remain open to any further suggestions or critiques that could help me refine the idea.

Ricard Desola Mediavilla There's no such thing as ``purely mathematical superpositions''. The space of states of a classical system is, usually, defined within the Hamiltonian formalism; the space of states of a quantum system, also. However the two spaces are different.

For example, the space of states of a classical harmonic oscillator is the plane R2, a two-dimensional space, whose coordinates are the position and momentum of the harmonic oscillator; the space of states of the quantum harmonic oscillator is infinite-dimensional; it's the space of all linear combinations of the functions Hn(x)e-x^2/2, with n=0,1,2,3,... integer, where Hn(x) are the so-called Hermite polynomials. It is a standard exercise to show that the average values obey the classical equations of motion.

What Bell's inequalities try to control is the fact that a quantum system describes a physical system in equilibrium with a bath of fluctuations. So one can ask the question-up to now unanswered-what are the degrees of freedom that can resolve the quantum fluctuations, just like atoms and molecules caan resolve the thermal fluctuations in classical thermodynamics. Bell's inequalities place constraints that any ``local" degrees of freedom that can resolve quantum fluctuations must satisfy. What they imply is that the degrees of freedom that can resolve them can't be local degrees of freedom. Their usefulness is that they lead to predictions that can be checked by experiment; it took seventeen years for this to be done by A. Aspect and collaborators and that earned Aspect the Nobel Prize a few years ago.

What Peter Freund found-the same year Aspect did his experiment, in fact-was a way for the degrees of freedom that can resolve quantum fluctuations to evade the assumptions of Bell's inequalities. He noticed that Bell's inequalities are established under the assumption that the degrees of freedom that resolve the quantum flucutuations are described by commuting variables and that if the variables are anticommuting, then Bell's inequalities can be satisfied.

This paper was published here: https://inspirehep.net/literature/165169 Unfortunately it hasn't been the subject of study that could lead to designing experiments, yet.

Let me just mention, however, that the ``Current interpretative problems'' mentioned, are not, in fact, problems at all.

``Apparent non-locality'' isn't a problem, because phase space-the space of states of a physical system-does not carry any notion of locality.

``Collapse'' (with or without decoherence), also, isn't a problem. What quantum mechanics does differently from classical mechanics is how it computes the probability of any event; not how it manipulates probabilities. Bayes' theorem remains as valid in quantum mechanics as it does in classical mechanics.

Entanglement isn't an issue at all, it's an inevitable consequence of the fact that the Schrödinger equation is a linear equation for the wavefunction, that the wavefunction is not an observable quantity, that the observable quantity is the probability density, that's defined by the square of the modulus of the wavefunction. All of which are consistent with the property that there exist solutions of the Schrödinger equation that lead to probability distributions of multiparticle systems are linear combinations of products over the individual probability densities not a single product.

Ricard Desola Mediavilla

Thank you for opening this stimulating discussion. Your systemic perspective is both refreshing and intellectually sincere.

I’d like to offer a complementary point of view: the Pure Time Theory (PTT), which provides a unified framework to interpret quantum entanglement and the violation of Bell inequalities, without invoking any ad hoc or supernatural assumptions.

PTT in a nutshell PTT proposes a paradigm shift: time is not just a coordinate, but a physical, evolving field denoted by T_relax(x^μ). In this view:

• The geometry of spacetime emerges from this time field through the relation: g_μν = κ (∂_μ T_relax)(∂_ν T_relax) (κ being a constant tied to Planck scale units).
• The arrow of time is irreversible by construction: ∂_μ T_relax ≠ 0, everywhere in the universe.

Implications for Quantum Entanglement

• Relational coherence: Two entangled particles share a common temporal origin. Their spatial separation is secondary, their quantum coherence persists because of a shared causal history in T_relax.
• Measurement = temporal desynchronization: When a detector (with its own local T_relax_det) interacts with a particle, it induces a local shift in temporal structure (∇T_relax), breaking coherence naturally, without invoking wavefunction collapse.
• Violation of Bell inequalities: PTT explains these correlations without invoking non-local forces. Instead, the particles remain synchronized through their common past in T_relax. The detector does not measure a hidden variable, it perturbs the local temporal flow.

Advantages over standard interpretations

• No "spooky action at a distance" . correlations emerge from a shared temporal field, not instant influence.
• No superdeterminism, the irreversibility of T_relax prohibits backward causality.
• Natural bridge to gravity, the same field (T_relax) underlies both quantum coherence and spacetime curvature.

Concrete proposal If your relational model were to integrate a fundamental time field such as T_relax, it might:

• Formalize the idea of "stable relational systems" as temporal synchronization zones.
• Derive Bell-type correlations from gradients in T_relax, rather than postulating them externally.

I’d be happy to share resources or collaborate on a more formal framework, PTT is not just an interpretation; it’s a predictive and testable model, already applied in areas like black hole horizons and galactic dynamics.

With sincere appreciation for your open-minded approach!

Stam Nicolis, once again, thank you for your kindness and your explanations. I truly appreciate the time and clarity with which you’ve shared them.

Essam Allou, thank you very much for your interest and for your encouraging comment. I'm glad to know that you found my proposal thought-provoking. I would indeed be interested in establishing some form of collaboration or dialogue with you to compare ideas. My approach is based on a logic of systems that I try to apply not only to particle physics, but to all kinds of systems — although I find the study of particles particularly useful, as they are (in principle) very simple or even fundamental systems. In order to move forward with this dialogue, I will read with interest the articles you've shared on this site and try to learn as much as I can about your proposal of the Pure Time Theory (PTT), to get a clear sense of its perspective. If you can also point me to any other place where I might find more information, I would really appreciate it. I remain open to exchange and thank you once again for your interest.

Ricard Desola Mediavilla

Thank you very much, Ricard, I'm honored by your openness. All core elements of the Pure Time Theory are already published here on ResearchGate.

To get started, I recommend beginning with these three papers:

• The Illusion of Accelerated Expansion
• Universal Time Relaxation: Multi-Scale Validations
• Creation of Matter and Atoms in PTT

They give a solid overview of the theory’s foundations, predictions, and quantum implications. I’ll be happy to exchange more once you've had a look!

Dear Ricard-Mediavilla:

Since you are a philosopher teacher, let me add a novel idea that seems logical and intuitive to me. But first, please add a third axiom to your previous two principles; that is crucial to this quantum phenomenon because it deals with the behavior in one split system:

The answer can be found in extra dimensions; a projection of 4D over 3D. For example, in a 3D dice that contains six different values in each two-dimensional face. This extra third dimension agrees with Aristotle's Law of non-contradiction by understanding the possibility of having "A" in one 2D face and "not-A" in another 2D face, making their simultaneous existence acceptable in 3D. With this simple analogy, you can understand how the existence of many antagonist solutions can coexist (superposition of states) and how these 4D multiple solutions are 3D-observed as one state (collapse or projection of 4D multiple states over 3D single state). And more importantly, the inclusion of the 4th dimension solves the problem of this phenomenon by making it local at 4D even when the split system contains partial spatial zones quite far from each other in 3D.

The next step needed in this novel concept is to understand the 4th D. Einstein and especially Minkowski presented the 4th D as C*t where "t" is the time evolution of events. This C*t is Ok for the event analysis promoted by Minkowski, but the value of it depends on the initial value selected for "t" and especially on its historical passage over energetic sources because of Lorentz´s time dilation. The solution for this is "Delta t" or the management of intervals C*Delta t. But that isn´t sufficient! From quantum mechanics (Planck and Einstein), we are aware that energy has a 3D presence in chunks and depends only on its periodic time "tau". So, C*tau is the "quantum interval" which expresses the best 4th D of both core theories (relativity and quantum). Now, C*tau is the wavelength of energy or Lambda, and this 4D gives a greater sense of how the 4th D interacts with the observable 3D. A greater energetic presence implies smaller tau and smaller C*tau, which goes other with the Lorentz´s space contraction (Poincare´s invariance).

There is a whole new way presented in this novel, an oscillatory existence between the 3D and this energetic 4th D, and much more. Attached are two of the papers that develop this proposal.

I hope this will inspire your research and make the quantum world reasonable and understandable with this intuitive 4D model. Regards

Yes, I see problems with this approach. However, I have also heard similar proposals from others along these same lines. I can see why your ideas sound promising because entanglement doesn't make sense, but it is well-known that interactions are symmetric for all exchanges of energy and momentum. So, perhaps this is the real reason we see what looks like properties of entanglement.

However, this does not solve the biggest problems that forced physicists to propose the idea of entanglement in the first place. Actually, the underlying principles of entanglement were first discovered and proposed after studying the implication of aspects of quantum formalism, which are mathematical principles that physicists have developed over decades to determine how to use quantum mechanics.

Let's get to your question, what are the problems with your proposal. First, symmetric interactions do not achieve the most confounding aspects of entanglement.

For example, when two photons are entangled, if you measure those photons independently using an electric field that is at right angles to the field they were created in, then you have no way of know whether photon A or photon B will turn up as spin-up or spin-down. But if you measure the photons using the same exact electric field polarity as the two photons were first entangled in, then if photon A was originally spin-up, it will be spin-up when you measure it again, and if photon B was spin-down at first, it will remain spin-down when you measure it again.

In other words, when you measure the photons using a electric field polarity that is at right angles to the original polarity of the photons, it is a 50-50 change either photon will be spin up or spin down. Now here is the problem: If the photons are truly entangled, they will always measure opposite spins if they had opposite spins to begin with. However, if the only thing happened is that the two photons started out with opposite spins, but they are not entangled, then you will not see them always having opposite spins if you measure them at right angles to their original electric field polarity.

This creates a completely different result of the two photons simply happen to have opposite spins, or if they have opposite spins and are truly entangled.

The same thing happens if you are using polarization angles instead of electric field polarities. If you create two entangled photons by emitting two photons from one atom at the same time, and you run them through a polarizer so that you know the angle of polarization they are in, then if you later measure them after they have traveled long distances away from each other, and you use a polarization angle that is 90 degrees off from the original polarity, then, just as above, you have no idea which photons will be up and which will be down, but if they are truly entangled as opposing, then they will still remain opposing. This is what it means when we say the photons are entangled.

But if you are using two photons that are not entangled, even if they start out opposing in their polarized state, after they go through a polarizer that is at right angles to their original polarized state, then then two photons will not always be opposing. They will only oppose each other 50% of the time. That shows they were not entangled.

The other thing you should be aware of, and maybe you are, but it is worth mentioning, is that when you say the two photons interact, you should know that there are different kinds of interactions. Some interactions and create entangled states, some interactions will not.

This is why running photons through a polarizer does not create a change in their entangled state. You can't entangle photons or unentangle them, even though the polarizer is interacting with the photons. And photons don't bump into each other if they cross the same paths, so you can't create those kinds of interactions with photons.

If one electron bumps into another electron, this creates an interaction where there is an actual exchange of energy between the two of them. A photon carries the energy from one photon to another, and this can create an entangled state. This is what happens when electrons repel each other. However, electrons only actually repel each other rarely at the quantum level. In those cases, the electrons do have an influence on each other, but no photon carries energy from one to the other. These sorts of interactions will not create entangled states.

The results of classical interactions between particles tells us that the momentum and energy they exchange is always symmetric. And, yes, this does seem to create a sort of entanglement because this carries on as they fly away from each other. But this is not what is meant by entanglement. The mind-boggling part of entanglement comes after you have run them through an electric field or a polarizer at right angles to their original orientation. That is when you see the stark difference between particles that are entangled and those that are not.

Hopefully this helps.

José Oreste, thank you very much for reading and for your kind comment. I will reflect on the ideas you shared and will read with interest the texts you’ve linked.

Thank you very much, Doug, for your detailed comment. I greatly appreciate it, as it focuses on one of the most robust experimental benchmarks that any interpretive proposal must take seriously: the correlation pattern between measurements at different angles, as observed in Bell-type experiments.

I’ve been reflecting on this, and I believe there might be a way to integrate this phenomenon within the relational framework I’m exploring. I start from the idea that entanglement is a particular case of a composite system that maintains an internal relational equilibrium, established through an initially perfectly symmetric interaction. I analyze this within a systems logic framework based on the principle that every interaction produces effects on all the systems involved.

Every measurement is an interaction, and from the perspective of this systems logic, every interaction modifies both systems involved, even if the change is not sufficient to destroy the system or fully break its symmetry. In this sense, there are no truly "neutral" interactions, but rather interactions that may alter only certain aspects or properties of the system without affecting others.

In the case of entanglement, I propose that if both particles are measured at the same angle, the perturbation they undergo is symmetric and does not disrupt the relational equilibrium of the system, which continues to exhibit perfect correlations. On the other hand, if the particles are measured at different angles, the perturbation becomes asymmetric, and the angular difference determines the degree of imbalance. The pattern observed in the experiments (such as the cosine squared of the angle) could thus be understood as an expression of the degree of internal relational deformation within the composite system.

This dynamic symmetry does not imply preexisting values, nor communication between particles, but rather a global response of the system to how it is being interrogated. I’m not sure yet whether this interpretation can be sustained at all levels, but I would truly value your opinion on this.

Thank you again for your clarity and thoughtful explanations!