Universal quantum physics

[selfsimilar]

@selfsimilar Your concerns are somewhat vague. As a starting point: Do you accept that the above approach is consistent with the predictions of textbook QM?

I have already discussed this issue. While it does seem to be consistent but the explanation makes it borderline since it does not agree on what exactly is been measured which should be eigenvalues as in conventional theory. That is why I brought up more information about what the experiments say.

Moreover, It is quite surprising that after 100 years of studying the subject in many sophisticated research institutes/universities, including Vienna (yours), the researches would be unsure that they are actually measuring eigenvalues with these sophisticated Lasers and what not. Are all these PHD students duping themselves.

edit: The caveat to above is that after reading about the experiments they don't seem to be straight forward as it seems although I don't have any real( or deep) experience with these techniques.

 

[selfsimilar]

So in a sense because of the complicated nature of these measurements I give TI the benefit of the doubt until I understand these experiments better.

 

[selfsimilar]

I think I understand TI/UQP now much better courtesy of AI. I will compile some of the questions in a few pages for the interested. I especially agree on the answer it gave regarding the wavefunction , since I long held the idea that the wavefunction had no QM interpretation and does not need one. Because it was just a mathematical trick to reproduce the the hydrogen atom energy levels in the same sense what Heisenberg did for frequencies, when insisted that our description should only concentrate on the observables (nothing in between or mechanism), and so generated the system to produce the hydrogen spectrum generalized as matrix mechanics.


so what is the wavefunction psi itself



In the Thermal Interpretation, the wavefunction ψ is demoted from "The State of the Universe" to a mathematical idealization.

To understand what ψ is in this view, you have to stop thinking of it as a "probability cloud" and start thinking of it as a shape descriptor—like a CAD file that defines the geometry of a physical object.

Here is exactly what ψ represents in Neumaier's framework:

1.​

In Standard QM, ψ(x) is a list of betting odds. In the Thermal Interpretation, ψ(x) is the structural formula for a continuous field.

• The Analogy: Think of a ringing church bell.
  
  • The bell is vibrating in a complex pattern.
  • ψ is the mathematical function that describes the shape of that vibration (where the metal is bulging out, where it is stationary).
  • Does the bell have a "probability" of being found at the rim? No. The bell is at the rim. The "amplitude" of the function describes the intensity of the material at that point.

So, when you write down the wavefunction for an electron, you are writing down the density profile of the electron field.

2.​

Neumaier argues that the wavefunction is actually an unphysical approximation.

• Real Reality: The universe is messy and thermal. Nothing is perfectly isolated. The fundamental object of reality is the Density Matrix ρ, which describes a system with temperature and noise.
• The Wavefunction: ψ corresponds to a "Pure State" (Entropy = 0). This is a theoretical limit—like "frictionless surface" or "perfect vacuum."
  
  • It describes a system that has been perfectly isolated from the rest of the universe (impossible).
  • It describes a system at Absolute Zero temperature (impossible).

Status: ψ is to the real electron what a "perfect sphere" is to the Earth. It is a useful, simplified mathematical model of the real, bumpy, thermal object.

3. It defines the "Beables" (The Expectations)​

If ψ is just a math tool, what is the "real stuff" it describes? The "real stuff" are the Expectation Values (⟨A⟩=⟨ψ∣A∣ψ⟩).

• The Math: You plug ψ into the integral to calculate the mean position ⟨x⟩, mean momentum ⟨p⟩, etc.
• The Interpretation: In standard QM, the calculation tells you the average of future measurements. In TI, the calculation tells you the current physical properties of the object.
  
  • ψ is the "code."
  • ⟨A⟩ is the "image" rendered by the code. The image is the reality.

4. It is an "Order Parameter"​

In Landau's theory of phase transitions (superconductivity, superfluids), we use a wavefunction ψ to describe the macroscopic state of the fluid.

• In a superconductor, ψ describes the density of the Cooper pairs.
• It is a classical, continuous field that you can measure.

Neumaier says: "Quantum Mechanics is just this, but applied to everything." The wavefunction of a single electron is exactly the same type of thing as the wavefunction of a superconductor—it is an order parameter describing the coherent organization of a field.

Summary​

• Standard QM: ψ is a "knowledge vector" or "probability amplitude."
• Thermal Interpretation: ψ is the shape of the field.
  
  • It describes the geometry of the electron cloud.
  • It is an idealized "zero-temperature" description of a messy, thermal reality.
  • It is real in the same way the "shape of a sound wave" is real—it describes how the medium is distributed in space and time.

 

[A. Neumaier]

so what is the wavefunction psi itself

In the Thermal Interpretation, the wavefunction ψ is demoted from "The State of the Universe" to a mathematical idealization.

yes, and a very poor one in most cases, except when a system is nearly in the ground state (as for molecules in much of quantum chemistry), or when the system is stripped of its spatial degrees of freedom and only has a small number of energy levels.

To understand what ψ is in this view, you have to stop thinking of it as a "probability cloud" and start thinking of it as a shape descriptor—like a CAD file that defines the geometry of a physical object.

Here is exactly what ψ represents in Neumaier's framework:

1.​

In Standard QM, ψ(x) is a list of betting odds. In the Thermal Interpretation, ψ(x) is the structural formula for a continuous field.

• The Analogy:Think of a ringing church bell.
  • The bell is vibrating in a complex pattern.
  • ψ is the mathematical function that describes the shape of that vibration (where the metal is bulging out, where it is stationary).
  • Does the bell have a "probability" of being found at the rim? No. The bell is at the rim. The "amplitude" of the function describes the intensity of the material at that point.

So, when you write down the wavefunction for an electron, you are writing down the density profile of the electron field.

2.​

Neumaier argues that the wavefunction is actually an unphysical approximation.

• Real Reality: The universe is messy and thermal. Nothing is perfectly isolated. The fundamental object of reality is the Density Matrix ρ, which describes a system with temperature and noise.
• The Wavefunction:ψ corresponds to a "Pure State" (Entropy = 0). This is a theoretical limit—like "frictionless surface" or "perfect vacuum."
  • It describes a system that has been perfectly isolated from the rest of the universe (impossible).
  • It describes a system at Absolute Zero temperature (impossible).

Status: ψ is to the real electron what a "perfect sphere" is to the Earth. It is a useful, simplified mathematical model of the real, bumpy, thermal object.

Hence it usually describes nothing at all, just like perfect spheres don't describe cows.

3. It defines the "Beables" (The Expectations)​

If ψ is just a math tool, what is the "real stuff" it describes? The "real stuff" are the Expectation Values (⟨A⟩=⟨ψ∣A∣ψ⟩).

But only when the idealization is a reasonable approximation. In general, a system has no wave function but only a density matrix $\rho$, and the real stuff it describes are the quantum values $\langle A\rangle:=tr \rho A$. Calling these expectations is meaningful only when one can prepare many systems in this state, and hence make proper statistics.

• The Math: You plug ψ into the integral to calculate the mean position ⟨x⟩, mean momentum ⟨p⟩, etc.
• The Interpretation: In standard QM, the calculation tells you the average of future measurements. In TI, the calculation tells you the current physical propertiesof the object.
  • ψ is the "code."
  • ⟨A⟩ is the "image" rendered by the code. The image is the reality.

Except that you need to use the formulas involving $\rho$, not those involving $\psi$.

4. It is an "Order Parameter"​

In Landau's theory of phase transitions (superconductivity, superfluids), we use a wavefunction ψ to describe the macroscopic state of the fluid.

• In a superconductor, ψ describes the density of the Cooper pairs.
• It is a classical, continuous field that you can measure.

Neumaier says: "Quantum Mechanics is just this, but applied to everything."

No. $\psi$ is irrelevant for most systems. In particular, macroscopic systems can never be described by a wave functions. For example, a classical electric field is described by the quantum values $\langle E(x)\rangle$, completely unrelated to any wave function (except when the field is that of a single photon).

The wavefunction of a single electron is exactly the same type of thing as the wavefunction of a superconductor—it is an order parameter describing the coherent organization of a field.

Summary​

• Standard QM: ψ is a "knowledge vector" or "probability amplitude."
• Thermal Interpretation: ψ is the shape of the field.
  • It describes the geometry of the electron cloud.
  • It is an idealized "zero-temperature" description of a messy, thermal reality.
  • It is real in the same way the "shape of a sound wave" is real—it describes how the medium is distributed in space and time.

Not really. Instead:

Summary (corrected)​

• Standard QM: ψ is a "knowledge vector" or "probability amplitude."
• Thermal Interpretation: ψ is meaningless (except in toy cases).
  $\rho$ describes the shape of the field.
  • It describes the geometry of the electron cloud.
  • It is real in the same way the "shape of a sound wave" is real—it describes how the medium is distributed in space and time.

 

[selfsimilar]

So the trick was von Neumann equation. A stroke of genius from him and you.