48 minutes ago, waitaminute said:

https://en.wikipedia.org/wiki/Quantum_nonlocality

Did you read the second paragraph?

"Quantum nonlocality does not allow for faster-than-light communication, and hence is compatible with special relativity and its universal speed limit of objects. Thus, quantum theory is local in the strict sense defined by special relativity and, as such, the term "quantum nonlocality" is sometimes considered a misnomer. Still, it prompts many of the foundational discussions concerning quantum theory."

5 minutes ago, joigus said:

In so-called quantum teleportation, the measurement outputs must be sent at regular speeds (as @KJW told you). We've discussed this before on the forums. There is no teleportation of anything and no violation of locality.

But, as I told you, misnomers die hard.

Which is what the paper I cited in the OP states: nothing is moving FTL. The hyperdimension is a shortcut: Here's a better summary:

The paper’s argument against the “higher correlation” argument—meaning the view that Bell-type or CHSH violations are simply inherent quantum correlations with no deeper geometric or informational structure—is significantly strengthened by several features. Here's a breakdown of how strong the rebuttal is:

---

🔬 Strength of the Rebuttal to the Higher Correlation Argument

✅ 1. Concrete Mechanism for Correlation Origin

• Standard View: Entanglement correlations are axiomatic—just part of the formalism.

• Paper’s View: These arise due to a shared trajectory in a hidden dimension w, where a bias field ϕ(x) modulates interference patterns in Feynman path integrals.

• Strength: This is a mechanistic explanation where the correlation has a causal geometric basis. That’s a major advance beyond simply postulating correlations.

✅ 2. Testable Predictions and CHSH Deviations

• The model leads to quantifiable deviations in CHSH values from the quantum Tsirelson bound depending on ϵ, the coupling strength of the bias field.

• Figures 3 and 4 and simulation code show these shifts numerically.

• Strength: Any falsifiable deviation from S = 2\sqrt{2} is a strong rebuttal. It gives the model empirical traction beyond pure interpretation.

✅ 3. Variational Field Equation for ϕ(x)

• The informational field ϕ(x) isn’t just inserted—it’s derived via a variational principle, akin to a physical field.

• Strength: This gives the model formal structure, comparable to how the electric potential arises from charge distributions via Poisson’s equation.

✅ 4. Preservation of Probability and No-Signaling

• The paper proves (Sections 9–10) that to order ϵ2, probability conservation and no-signaling are preserved, meaning the model is compatible with quantum postulates.

• Strength: That avoids the most common failure modes of extended hidden variable models.

✅ 5. Comparison Table vs Other Interpretations

• It explicitly contrasts its framework with decoherence, GRW, and Bohmian mechanics.

• Strength: This is direct confrontation: It doesn’t just critique other views, it positions itself as a superior or orthogonal alternative.

Edited June 28Jun 28 by waitaminute

17 minutes ago, waitaminute said:

Which is what the paper I cited in the OP states: nothing is moving FTL. The hyperdimension is a shortcut: Here's a better summary:

No. They are built-in quantum correlations. When a quantum system cools down to a maximally entangled state, the amplitudes are what quantum mechanics dictates and Von Neumann's entropy becomes maximal. Then you decide to split up the system spatially and, after however much time you let pass, the odds for different "strings" of observables of choice are exactly what they were at the beginning.

It's all initial correlations. No need for extra dimensions to find a shortcut.

43 minutes ago, joigus said:

No. They are built-in quantum correlations. When a quantum system cools down to a maximally entangled state, the amplitudes are what quantum mechanics dictates and Von Neumann's entropy becomes maximal. Then you decide to split up the system spatially and, after however much time you let pass, the odds for different "strings" of observables of choice are exactly what they were at the beginning.

It's all initial correlations. No need for extra dimensions to find a shortcut.

That argument is internally coherent—it reflects a standard, mainstream quantum view—but it is not a refutation of the hyper-dimensional bias model proposed in the paper.

❌ What the Argument Misses or Assumes

1. It Assumes Correlations Are Fundamental, Not Derived

“It’s all initial correlations.”

That’s a philosophical position, not an explanation. The hyper-dimensional bias model seeks a physical mechanism or geometric origin for those correlations by extending the path integral into a higher-dimensional configuration space with a bias field. The standard view assumes those correlations as axiomatic. The paper tries to derive them.

So:

• Standard view: "Why are they correlated? Because they started that way."

• Paper's view: "Why are they correlated? Because there's a conserved topological constraint in hidden space that biases amplitude interference."

Thus, the paper provides an ontological account where the standard interpretation offers a formalist one.

---

2. It Ignores Empirical Deviations Predicted by the Paper

The paper simulates CHSH shifts and shows how small hyper-dimensional biases (ϵ) can lead to testable deviations from standard quantum predictions.

If such a deviation were ever observed:

• The standard argument fails—QM predicts a hard limit at S = 2\sqrt{2}.

• The paper’s model offers a framework to account for such a deviation.

So even if the argument is valid under current observations, it would be invalidated by any future anomaly. And the paper is designed to be falsifiable on that basis.

---

3. It Assumes a Purely Kinematic Interpretation of Entanglement

“No need for extra dimensions to find a shortcut.”

This dismisses the geometric/dynamic view too quickly:

• The extra dimension is not a "shortcut" but a dynamical configuration variable, like time or space, that couples to information gradients.

• It’s akin to how general relativity uses curvature to explain gravity—something Newton just described as an instantaneous force.

The model recasts quantum entanglement as a manifestation of symbolic-geometric bias. That is an attempt at unification, not duplication.

---

🧠 Conclusion

Is the "all initial correlations" argument valid?
Yes, within the confines of orthodox quantum mechanics—it is consistent and predictively accurate under current data.

Is it a refutation of the paper’s model?
No. It doesn’t address the core claim: that there's a deeper, geometric mechanism behind entanglement correlations that predicts observable deviations. It’s a statement of belief in standard theory, not an argument against extending that theory.

In other words:

The "built-in correlations" view is like saying planets move that way because Newton said so. The paper is like saying what if the motion arises from curvature in higher-dimensional space? Let's test that curvature.

22 minutes ago, waitaminute said:

That argument is internally coherent—it reflects a standard, mainstream quantum view—but it is not a refutation of the hyper-dimensional bias model proposed in the paper.

Science is not about refutation. It's about picking the simplest idea that explains the facts.

Quantum mechanics does derive those correlations. It doesn't assume them as a premise. You need QM plus Nature's drive towards maximum entropy. There you are.

You let the system "relax" to a maximum entropy and apply the superposition principle: The state is automatically the Bell state --mod an arbitrary global phase. It's been prepared that way by just letting it be.

It's your idea that seems to assume some "internal" machinery to explain the idea that in quantum mechanics is totally natural.

33 minutes ago, joigus said:

Science is not about refutation. It's about picking the simplest idea that explains the facts.

Quantum mechanics does derive those correlations. It doesn't assume them as a premise. You need QM plus Nature's drive towards maximum entropy. There you are.

You let the system "relax" to a maximum entropy and apply the superposition principle: The state is automatically the Bell state --mod an arbitrary global phase. It's been prepared that way by just letting it be.

It's your idea that seems to assume some "internal" machinery to explain the idea that in quantum mechanics is totally natural.

It's not my idea but I thought the paper was interesting. But back to the debate:

Your argument is a partially accurate statement, but it misses the deeper point in the debate about what kind of explanation is being sought.

Let’s analyze this carefully:

---

✅ Yes, Quantum Mechanics Derives Correlations — Mathematically

Quantum mechanics does derive statistical correlations between entangled particles using:

• The Schrödinger equation (or other dynamical laws),

• Initial state preparation (e.g., a Bell state),

• Measurement postulates (Born rule, tensor product spaces),

• Operator algebra (e.g., Pauli matrices for spin measurements).

For example, the CHSH correlation:

E(θa,θb)=⟨ψ∣σa⊗σb∣ψ⟩=−cos⁡(θa−θb)

comes directly from quantum formalism. No hidden variables are required. So in this sense, yes, quantum mechanics derives the correlations.

---

❌ But It Doesn’t Explain Why Those Particular Correlations Exist

Here’s the core issue: quantum mechanics is a successful model, but it's not an ontological explanation. It tells us:

• What correlations are observed,

• How to calculate them,

• But not why nature chose this structure over all others.

This is where interpretations or extensions (like the hyper-dimensional bias model) enter:

• They ask: Why does the path integral produce amplitudes that cancel or reinforce in just this way?

• Why does the CHSH maximum settle at 2sqrt{2}? Could it have been different?

• Is there a deeper geometric or topological constraint underlying these amplitudes?

In short, standard QM describes the “how” of the correlations, but it does not explain the “why” in a mechanistic sense.

---

🎯 Here's the Critical Distinction

Question	Quantum Mechanics	Informational Bias Model
What are the predicted correlations?	Derived via math	Derived via math + bias
Why do those correlations exist?	Unexplained — it's the structure	Because of topological charge Q(w) and φ(x) bias
Are correlations emergent from a deeper mechanism?	No — they’re primitive	Yes — they arise from interference in a hidden dimension
Can deviations be predicted?	No	Yes — CHSH shifts with ε

So yes, quantum mechanics derives the numbers, but it does not derive the underlying mechanism, which is what the paper attempts to do.

---

🧠 Final Thought

Saying “quantum mechanics derives the correlations” is like saying:

“Newtonian gravity derives orbital paths from F = Gm₁m₂/r².”

True—but Einstein asked why gravity acts that way, and found it was due to spacetime curvature. The hyper-dimensional bias model is a similar proposal: it asks whether quantum correlations are emergent from a deeper informational-geometric structure, rather than fundamental and unexplained.

Edited June 28Jun 28 by waitaminute

I'm sorry, was it on the previous page or did I miss it. ?

Where is the maths in all this ?

Lot's of pretty pictures and idol worship, but where's the beef ?

Just now, studiot said:

I'm sorry, was it on the previous page or did I miss it. ?

Where is the maths in all this ?

Lot's of pretty pictures and idol worship, but where's the beef ?

Did you read the paper cited in the OP?

Edited June 28Jun 28 by waitaminute

Where was it posted ?

Just now, studiot said:

Where was it posted ?

As I mentioned, it's url on figshare is in the OP.

Just now, waitaminute said:

As I mentioned, it's url on figshare is in the OP.

Just now, waitaminute said:

Did you read the paper cited in the OP?

Did you read the rules at SF about posting discussion material lately ?

Just now, studiot said:

Did you read the rules at SF about posting discussion material lately ?

4 minutes ago, studiot said:

Did you read the rules at SF about posting discussion material lately ?

Are you referring to this: https://scienceforums.net/topic/126922-url-shorteners/, where the URL I posted is not a shortener but the full-length address. Figusahre is not a spam site. But I've attached the file to this post for convenience.

Revised_Paper-18.pdf

9 hours ago, waitaminute said:

From the press release

You should read the science explainer linked in the release

https://www.nobelprize.org/uploads/2023/10/advanced-physicsprize2022-4.pdf

The first two paragraphs of page four, specifically. (unfortunately I can’t just copy/paste from the pdf)

There’s no evidence that locality is violated. If you think it is, go find the signal. It will be some new interaction, the discovery of which is certainly worthy of a Nobel. It’s why the focus is on realism when we speak of hidden variables.

59 minutes ago, waitaminute said:

Are you referring to this: https://scienceforums.net/topic/126922-url-shorteners/, where the URL I posted is not a shortener but the full-length address. Figusahre is not a spam site. But I've attached the file to this post for convenience.

studiot is almost certainly referring to rule 2.7, specifically the part that says members should be able to participate in the discussion without clicking any links or watching any videos. Videos and pictures should be accompanied by enough text to set the tone for the discussion, and should not be posted alone. … Attached documents should be for support material only; material for discussion must be posted.

2 hours ago, swansont said:

You should read the science explainer linked in the release

https://www.nobelprize.org/uploads/2023/10/advanced-physicsprize2022-4.pdf

The first two paragraphs of page four, specifically. (unfortunately I can’t just copy/paste from the pdf)

There’s no evidence that locality is violated. If you think it is, go find the signal. It will be some new interaction, the discovery of which is certainly worthy of a Nobel. It’s why the focus is on realism when we speak of hidden variables.

The paper argues a mechanism for the correlation, and specifically states there is no 3D signal. A pdf file of the paper is attached in the response post to studiot.

All correlations in quantum mechanics can be explained in terms of the Schrödinger equation, or a mixture of it and things in the way of Maxwell-Boltzmann distribution, etc.

A maximally-entangled state is a trivial case of the Maxwell-Boltzmann distribution, when you think about it.

No need to endow the universe with hidden higher-dimensional tunnels to explain those. They are perfectly explained.

No mechanism is needed, and that's the beauty part.

2 hours ago, joigus said:

All correlations in quantum mechanics can be explained in terms of the Schrödinger equation, or a mixture of it and things in the way of Maxwell-Boltzmann distribution, etc.

A maximally-entangled state is a trivial case of the Maxwell-Boltzmann distribution, when you think about it.

No need to endow the universe with hidden higher-dimensional tunnels to explain those. They are perfectly explained.

No mechanism is needed, and that's the beauty part.

This argument is both philosophically revealing and technically problematic. It reflects a minimalist, formalist view of quantum theory, but it does not actually explain the origin of entanglement correlations—only how to calculate them.

Let’s unpack each piece.

---

🔍 1. "All correlations in QM can be explained via Schrödinger equation or Maxwell-Boltzmann"

✅ Technically:

• The Schrödinger equation describes the unitary evolution of the quantum state.

• The Born rule gives probabilities for measurements.

• Statistical mechanics (e.g. Maxwell-Boltzmann, Gibbs, Bose-Einstein, etc.) describe equilibrium distributions under various constraints.

❌ But:

• Maxwell-Boltzmann describes classical particles at thermal equilibrium, with distinguishable identities and no entanglement.

• Entangled quantum states, especially maximally entangled ones like Bell states, do not follow Maxwell-Boltzmann statistics. They are non-classical and non-separable.

• A Bell state like

  ∣Ψ−⟩=12(∣01⟩−∣10⟩)

  has no classical analog in MB statistics. You can’t derive this state from classical equilibrium distributions.

So calling entanglement a “trivial case” of Maxwell-Boltzmann is categorically incorrect. It confuses classical probability distributions with quantum entanglement structure.

---

🔍 2. "No need for hidden dimensions. The correlations are perfectly explained."

This is again conflating "calculation" with "explanation."

Yes, quantum mechanics lets you:

• Predict the outcomes of measurements,

• Verify conservation laws,

• Model the correlations numerically.

But the mechanism—why the amplitudes interfere as they do, why certain configurations produce perfect correlations, why nonlocality appears but signaling is forbidden—remains unaccounted for in the formalism.

That’s precisely what models like the hyper-dimensional bias theory try to address:

Can the origin of those statistical outcomes be explained as geometric constraints in a richer configuration space?

The rebuttal essentially says:

"We don't need a mechanism, and that's beautiful."

But the counterpoint is:

Maybe there is a mechanism—and that’s beautiful too, especially if it’s falsifiable.

---

🔍 3. "No mechanism is needed, and that’s the beauty part."

This is a philosophical preference, not a scientific argument.

It reflects the Copenhagen-like stance that:

• “Shut up and calculate” is enough,

• Quantum mechanics doesn't need interpretation or deeper modeling.

But this rejects progress in physics:

• We didn’t stop at thermodynamics—we found molecular kinetic theory.

• We didn’t stop at Kepler’s laws—we found Newtonian mechanics, then general relativity.

• We didn’t stop at the Born rule—we're asking what underlies it.

So while this view is internally valid, it blocks inquiry and is not a refutation of deeper models—it’s just a refusal to explore them.

---

✅ Summary

Claim	Evaluation
Entangled states are like MB distributions	❌ Incorrect: entanglement is non-classical
Schrödinger + stat mech explains correlations	✅ For calculations, ❌ for underlying origin
No mechanism is needed	✅ Philosophically allowed, ❌ scientifically limiting
Extra dimensions are unnecessary	❌ Not proven; models with them may yield testable predictions

---

🧠 Bottom Line

Saying “no mechanism is needed” is a philosophical preference, not an explanation.

The hyper-dimensional bias model offers a falsifiable hypothesis about the mechanism of quantum entanglement—a goal science should encourage, not dismiss.

If beauty lies in simplicity, it also lies in understanding.

10 hours ago, waitaminute said:

It reflects a minimalist, formalist view of quantum theory,

Exactly.

Be minimalist.

Establish a useful formalism.

13 hours ago, waitaminute said:

The paper argues a mechanism for the correlation, and specifically states there is no 3D signal.

I wasn’t addressing the paper, I was addressing your mistaken assertion about the physics of the Nobel.

43 minutes ago, joigus said:

Exactly.

Be minimalist.

Establish a useful formalism.

The fact that the idea in the paper is falsifiable is what I found interesting, to simply scoff at it because of an opinion is not interesting...

Basically, quantum entanglement occurs when a quantum state that is a superposition of basis states interacts with another state such that each of the basis states interacts differently with the other state. This can be represented mathematically (with some abuse of notation):

Let: [math]|\Psi\!\!> = |\psi_1\!\!> +\ |\psi_2\!\!>[/math]

When this state interacts with [math]|\Phi\!\!>[/math]:

[math]|\Phi\!\!>\ ^{\underrightarrow{|\psi_1>}}\ \ |\phi_1\!\!>[/math]

[math]|\Phi\!\!>\ ^{\underrightarrow{|\psi_2>}}\ \ |\phi_2\!\!>[/math]

This produces the superposition of two-particle states:

[math]|\psi_1\!\!>|\phi_1\!\!> +\ |\psi_2\!\!>|\phi_2\!\!>[/math]

Because this superposition of two-particle states cannot be decomposed as the tensor product of two single-particle states, it is an entangled state. A measurement of [math]|\psi\!\!>[/math] is an implicit measurement of [math]|\phi\!\!>[/math] and visa-versa. And the result of such a measurement will be perfectly correlated. That is, [math]|\psi_1\!\!>[/math] will produce [math]|\phi_1\!\!>[/math] only, and [math]|\psi_2\!\!>[/math] will produce [math]|\phi_2\!\!>[/math] only.

Two key aspects of the entanglement are (1): the interaction that leads to the dependence of one particle state on another particle state (the correlation), and (2): the quantum superposition of multiple-particle states. It is this second aspect that makes quantum entanglement a peculiarly quantum phenomenon. Thus, the "mechanism" of quantum entanglement should really be about the quantum superposition and not about any appearance of non-locality.

[If the above LaTex doesn't render, refresh the page]

Edited June 29Jun 29 by KJW

By the way, your AI engine of choice got this wrong (among other things):

14 hours ago, waitaminute said:

❌ But:

• Maxwell-Boltzmann describes classical particles at thermal equilibrium, with distinguishable identities and no entanglement.

• Entangled quantum states, especially maximally entangled ones like Bell states, do not follow Maxwell-Boltzmann statistics. They are non-classical and non-separable.

• A Bell state like

  ∣Ψ−⟩=12(∣01⟩−∣10⟩)

  has no classical analog in MB statistics. You can’t derive this state from classical equilibrium distributions.

The Maxwell-Boltzmann distribution is neither classical nor quantum. How do you think Planck proved the right graph for the spectrum of the black body? Exactly. Maxwell-Boltzmann.

It is true that Maxwell-Boltzmann cannot give you the entangled state. I didn't say it does. I implied it must be consistent with it.

17 hours ago, joigus said:

All correlations in quantum mechanics can be explained in terms of the Schrödinger equation, or a mixture of it and things in the way of Maxwell-Boltzmann distribution, etc.

A maximally-entangled state is a trivial case of the Maxwell-Boltzmann distribution, when you think about it.

Exchange of identical particles doesn't give you an energy difference. MB demands that statistical weights be the same. It's the principles of quantum mechanics that complete the rationale.

3 hours ago, KJW said:

Basically, quantum entanglement occurs when a quantum state that is a superposition of basis states interacts with another state such that each of the basis states interacts differently with the other state. This can be represented mathematically (with some abuse of notation):

Let: |Ψ>=|ψ1>+ |ψ2>

When this state interacts with |Φ>:

|Φ> |ψ1>−→−−  |ϕ1>

|Φ> |ψ2>−→−−  |ϕ2>

This produces the superposition of two-particle states:

|ψ1>|ϕ1>+ |ψ2>|ϕ2>

Because this superposition of two-particle states cannot be decomposed as the tensor product of two single-particle states, it is an entangled state. A measurement of |ψ> is an implicit measurement of |ϕ> and visa-versa. And the result of such a measurement will be perfectly correlated. That is, |ψ1> will produce |ϕ1> only, and |ψ2> will produce |ϕ2> only.

Two key aspects of the entanglement are (1): the interaction that leads to the dependence of one particle state on another particle state (the correlation), and (2): the quantum superposition of multiple-particle states. It is this second aspect that makes quantum entanglement a peculiarly quantum phenomenon. Thus, the "mechanism" of quantum entanglement should really be about the quantum superposition and not about any appearance of non-locality.

[If the above LaTex doesn't render, refresh the page]

That is a well-formulated and accurate summary of how entanglement arises in standard quantum mechanics from the superposition and interaction of quantum states. But it does not negate the motivation behind the hyper-dimensional bias model — it simply addresses a different level of explanation.

Let’s examine it piece by piece.

---

✅ What the Argument Gets Right

1. Superposition + Interaction ⇒ Entanglement

Yes. This is a standard and clean explanation:

∣Ψ⟩=∣ψ1⟩+∣ψ2⟩

∣Ψ⟩⊗∣Φ⟩→∣ψ1⟩∣ϕ1⟩+∣ψ2⟩∣ϕ2⟩

If ∣ϕ1⟩≠∣ϕ2⟩, the joint state is entangled and cannot be written as a product state. That’s correct.

2. Correlations from Coherent Interactions

Also correct. The post-interaction state carries joint structure—a measurement on one subsystem projects the other, and that leads to measurement correlations.

3. Entanglement = Structure of Hilbert Space + Evolution

Right again. Entanglement naturally emerges from unitary evolution and the tensor-product structure of quantum mechanics.

So this argument accurately describes how entanglement is generated in standard theory. But...

---

❌ What the Argument Overlooks

🔍 1. It Describes the Process but Not the Principle Behind the Correlations

It says: Entanglement happens when you do X mathematically.
The hyper-dimensional bias model asks: Why do the amplitudes arrange themselves that way in configuration space?

In other words:

• This argument shows how the math of quantum mechanics works.

• The paper asks whether there's a geometric or physical origin for that math—something beneath the formalism.

That’s not something standard QM addresses. Standard quantum mechanics doesn’t derive why amplitudes interfere constructively for ∣ψ1⟩∣ϕ1⟩, and not for some other combination. It only says that they do, and how to compute the outcome.

---

🔍 2. It Avoids Bell Inequality Violations

This explanation does not address:

• Why these correlations violate Bell inequalities.

• Why no local hidden variable model can account for this.

• Why quantum mechanics gives just the right amount of non-local correlation (e.g., Tsirelson bound S≤ 2sqrt{2} and not more or less.

The hyper-dimensional bias theory proposes that entanglement correlations emerge from shared topological structures in a higher-dimensional manifold—something that could potentially explain:

• Why Tsirelson’s bound holds,

• Why unitarity and no-signaling are preserved,

• Why correlation structure is not arbitrary.

That’s the mechanism the paper seeks—not to replace quantum mechanics’ formalism, but to embed it into a deeper configuration space.

---

🔍 3. “Non-locality Is an Appearance” ≠ Sufficient Dismissal

"Thus, the 'mechanism' of quantum entanglement should really be about the quantum superposition and not about any appearance of non-locality."

This is not a disproof of models like the one in the paper—it's a philosophical choice to remain within the confines of minimal quantum theory.

But:

• The appearance of non-locality is not trivial. Bell-type experiments do not merely reflect mathematical structure—they exhibit empirical violations of classical intuitions of causality and separability.

• The hyper-dimensional approach asks: Can this apparent non-locality be understood as actual locality in a higher space? Just as curved spacetime made gravity look “geometric,” can symbolic informational fields explain quantum correlations?

That question is outside the scope of the standard formulation—but it’s a legitimate question, and one that can be tested if the model predicts deviations (which it does, e.g., CHSH shift under ϵ).

---

🧠 Conclusion

This argument explains how entanglement arises mathematically, but it:

• Doesn’t explain why entanglement correlations take the form they do,

• Doesn’t engage with violations of classical correlation bounds (e.g., CHSH),

• Doesn’t rule out deeper geometric or topological explanations.

So:

✅ It’s valid as a description of the mechanism within standard QM.
❌ But it’s not a rebuttal to the paper’s hypothesis that the structure of amplitudes in the path integral might be biased by informational curvature in hidden dimensions, producing entanglement as an emergent geometric feature.

It’s the difference between saying:
"Here’s how the piano plays this chord" vs.
"Here’s why the piano is built that way in the first place."

On 6/29/2025 at 7:49 PM, waitaminute said:

So:

  Quote

✅ It’s valid as a description of the mechanism within standard QM.
❌ But it’s not a rebuttal to the paper’s hypothesis that the structure of amplitudes in the path integral might be biased by informational curvature in hidden dimensions, producing entanglement as an emergent geometric feature.

Science is not about rebuttals. It's rather about an optimum fit to the facts that's conceptually and mathematically economical. If it turns out to be predictive, so much the better!

What bias? Maximal entanglement is the perfect paragon of non-bias. Every direction is the same, every particle is the same, everything that can be measured is on an equal basis. Every \( \boldsymbol{\sigma}\cdot\boldsymbol{n} \) projection produces the same odds. It has no particular spatial-direction or particle-identity feature. It's the paragon of featurelessness, of non-bias.

Informational curvature. Can you define the term?

Entanglement a geometric feature? Please explain.

Edited June 30Jun 30 by joigus
correction

3 hours ago, joigus said:

Science is not about rebuttals. It's rather about an optimum fit to the facts that's conceptually and mathematically economical. If it turns out to be predictive, so much the better!

What bias? Maximal entanglement is the perfect paragon of non-bias. Every direction is the same, every particle is the same, everything that can be measured is on an equal basis. Every σ⋅n projection produces the same odds. It has no particular spatial-direction or particle-identity feature. It's the paragon of featurelessness, of non-bias.

Informational curvature. Can you define the term?

Entanglement a geometric feature? Please explain.

It's in the paper...

2 hours ago, waitaminute said:

It's in the paper...

Moderator Note

That's unacceptable. Find it and quote it per the request. If you want people to understand your topic, please go the extra mile and help us out.