From Newsgroup: sci.physics.research
Recently, I posted a couple of replies on Stack Exchange pertaining to
the following questions:
Does the electron "know" it is in a superposition before measurement,
or is superposition purely an epistemic description?
https://physics.stackexchange.com/questions/853605/does-the-electron-know-i= t-is-in-a-superposition-before-measurement-or-is-supe/853817#853817
and
Are standard QFT and general relativity contradictory?
https://physics.stackexchange.com/questions/543814/are-standard-qft-and-gen= eral-relativity-contradictory/795065#795065
In turn, the second of these is an addendum to the GitHub archive that
I have put up on the matter of Classical / Quantum hybridization.
Classico-Quantum
https://github.com/LydiaMarieWilliamson/ClassicoQuantum
Following up on these is a recap of some ideas that I have fleshed out
here with the aid of Chat GPT.
https://chatgpt.com/share/6850acf9-f3d0-8007-9481-9491f3d7e303
[[Mod. note --
It's very dangerous to rely on chatbots to try to understand physics
(or any other science). As the saying goes, chatbots are always confident,
but often wrong. See
https://statmodeling.stat.columbia.edu/2025/08/24/chatbot-still-cant-handle-tic-tac-toe/#comment-2402766
https://mindmatters.ai/2025/08/chatgpt-5-tries-out-rotated-tic-tac-toe-you-be-the-judge/
for a funny example of a chatbot being presented with the game of
"tic-tac-toe rotated 90 or 180 degrees". The chatbot ("ChatGPT 5") produced
a lengthly discussion of how humans do & don't perceive rotated shapes,
but completely missed that fact that the game of tic-tac-toe is *completely* *unaffected* by the rotation.
-- jt]]
Instead of reproducing the dialogue here in full (which would be up to
1000 lines) I will provide a recap of the full discussion, followed by
the relevant parts of the queries comprising my end of the conversation
that were fleshed out by ChatGPT. Those who are interested in seeing
the details, including the several tables of comparison produced
showing what deficiencies have been addressed and resolved, can (for
now) look back to the linked chat: for instance, the comparison of the
Lindblad Picture and the Deutsch-Wallace formulation. I might add a reconstruction of the dialogue or expanded summary later, in TeX,
on=C2=A0the Classico-Quantum page.
This is the link, mentioned in the queries, that was shared on the
earlier Chat GPT dialogue "from a year ago"
https://chatgpt.com/share/670df97d-40b4-8001-b5da-19404f53c4e8
that also went very deep into the interpretative issues related to the
Lindblad Picture, particularly its ability to solve the riddle of time
on the matter of "Block Time" versus "Moving Time", with their fusion
into the below-mentioned "Growing Block Universe". Their discussion
also delved into the matter of what the nature of the AIs themselves
were. In particular, do they see time as a flow (no) or are they more
like the "wormhole aliens" of Deep Space Nine (yes). Chat GPT says it
has no self-awareness. When pressed on the root of its self-described deficiency it served reminder that it has no "self" that flows in time,
and no perception of time as a flow, at all.
The questions behind what the AI's are or are becoming, of course, are
the kinds of issues that Sabine Hossenfelder has covered, but never
anywhere in that level of depth, and never getting to the root of the
matter. Apart from noting it here, and with the link above, I won't be
saying anything more on that matter.
RECAP:
This is a summary of a discussion of the proposed *Lindblad Picture*:
an alternative picture of quantum dynamics inspired by the well-known Schroedinger and Heisenberg pictures. The Lindblad Picture is
especially suited for systems governed by open quantum dynamics
described by the Lindblad equation, and in particular, attempts to
repair the operator algebra inconsistencies that arise in the
Heisenberg Picture when applied to such systems.
Though independent of it, but motivated by it, the discussion also
builds upon the work of Oppenheim's group, especially the 2023 "Post-
Quantum Gravity" paper,
[[Mod. note -- I think this is a reference to
Jonathan Oppenheim
"A Postquantum Theory of Classical Gravity?"
Physical Review X 13, 041040 [open access]
https://doi.org/10.1103/PhysRevX.13.041040
-- jt]]
and suggests a deeper connection between the
Lindblad Picture, the interpretation of time, and the quantum-classical interface in hybrid Markovian-Lindbladian dynamics.
Though not specifically mentioned in the dialogue, Oppenheim's
framework gives us "stochasticism" as a self-consistency condition
for classico / quantum hybridization, which can be used as a starting
point for the ensuing discussions relating to stochastic dynamics.
1. The Lindblad Equation and Pictures of Dynamics
The Lindblad equation for the evolution of a density matrix rho(t) is
given by:
d rho / dt =3D -i[H, rho] + L_D[rho],
where H is the system Hamiltonian (generating unitary evolution) and
L_D is the dissipative Lindbladian superoperator encoding decoherence
and dissipation.
1.1. The Lindblad Picture: Definitions
We define the Lindblad Picture by separating the evolution as follows:
* The *state* evolves under the dissipative (non-unitary) part:
rho(t) =3D e^{(t - t0)L_D} rho(t0)
* The *observable* evolves under the unitary part:
A(t) =3D e^{i H (t - t0)} A(t0) e^{-i H (t - t0)}
This construction is formally analogous to the _Interaction_Picture_ in
quantum field theory, with a different physical motivation: decoupling
the non-unitary effects of decoherence from coherent unitary evolution.
2. Algebraic Consistency and the Heisenberg Anomaly
The Heisenberg Picture becomes ill-defined for open systems governed by
the Lindblad equation. Specifically, it fails to preserve operator
products and commutators:
HP{AB} !=3D HP{A} HP{B}
HP{[A, B]} !=3D [HP{A}, HP{B}]
This anomaly undermines the algebraic structure central to quantum
theory.
By contrast, in the Lindblad Picture, observables evolve purely under
the unitary part. Hence, the operator algebra is preserved:
LP{AB} =3D LP{A} LP{B}
LP{[A, B]} =3D [LP{A}, LP{B}]
This restores mathematical coherence and enables a robust extension of measurement theory.
3. Philosophical Implications of the Lindblad Picture
3.1. Time and Tangency
The explicit presence of t0 in both evolution equations defines a _point_of_tangency_ between the Schroedinger and Lindblad Pictures:
rho(t) =3D e^{(t - t0)L_D} rho(t0),
A(t) =3D e^{i H (t - t0)} A(t0) e^{-i H (t - t0)}
This implies a "rolling tangent" to Schroedinger Picture dynamics--a continuously shifting present, or "now", where the transformed
observables and states match.
3.2. Growing Block Universe and Everett Without Everett
The Lindblad Picture realizes a version of the _Growing_Block_Universe_
view of time. Unlike the traditional view where the future simply
doesn't exist, here the future exists as a set of possibilities
accessible through non-unitary, stochastic evolution.
This effectively implements a structure akin to Everettian branching--
without invoking global wavefunction splitting. One might call it
"Everett without Everett", where branching arises from the stochastic
structure encoded in the dissipative dynamics.
4. Hybrid Markovian-Lindbladian Dynamics
In Oppenheim's formalism, the total state space is modeled as a bundle
of Hilbert spaces over a classical phase space. Dynamics consist of
both quantum and classical components:
* Quantum part:
- Lindbladian (non-unitary) evolution: acts on the state
- Commutator evolution: acts on observables via [H, A]
* Classical part:
- Markovian stochastic evolution: acts on the state
- Poisson bracket: acts on observables via {H_C, A}_{PB}
Thus, the Lindblad Picture can be generalized:
* States evolve under both the Lindbladian and Markovian dynamics.
* Observables evolve under both the quantum commutator and classical
Poisson bracket terms.
5. Measurement Theory and Projection in the Lindblad Picture
Traditional measurement theory is framed in the Schroedinger Picture
and often assumes the projection postulate, Born rule, and Lueders
rule. But there is a notable absence of this framework in the
Heisenberg Picture.
This may be because projection, in realistic (non-idealized) scenarios,
is dynamically implemented via Lindbladian evolution, which is not Heisenberg-compatible. Thus, the Heisenberg Picture lacks a robust
formulation of measurement.
5.1. Deutsch's Attempt
David Deutsch proposed an operator-centric approach to measurement in
the Heisenberg Picture by treating information flow between subsystems
and using a unitary interaction model. While elegant, this approach
still assumes ideal measurements and doesn't fully capture decoherence
or collapse.
5.2. Lindblad Picture as Measurement Framework
The Lindblad Picture offers a pathway to resolving this: measurement
theory in realistic settings is actually better represented in the
Lindblad Picture. This gives a formal, algebraically consistent way to
describe generalized measurement (e.g., POVMs) and environment-induced decoherence, while restoring operator evolution under unitary rules.
6. Open Questions
* Can the Lindblad Picture be formalized as a replacement or
alternative to the Interaction Picture in quantum field theory?
* Can the rolling-tangent structure of t0 be developed into a new
formal notion of time in quantum mechanics?
* What insights can this picture offer in cosmological settings where irreversible processes (entropy production, measurement, etc.)
dominate?
7. Conclusion
The Lindblad Picture provides a novel and potentially foundational lens
through which to view open quantum dynamics, measurement theory, and
even time itself. It resolves mathematical inconsistencies in the
Heisenberg Picture, offers philosophical clarity on temporal flow, and
opens new directions in hybrid classical-quantum modeling.
QUERIES:
Query 1:
I've closely read many of the papers from Oppenheim's group and have
seen how much they are using the dynamics of the Lindblad equation, as
well as Markovian dynamics in their framework. A curious note was added
in the appendix to the 2023 landmark "Post-Quantum Gravity" paper by
Oppenheim, noting that neither Lindbladian dynamics, nor the hybrid Lindbladian-Markov dynamics posed by Oppenheim, were particularly well-
suited for the Heisenberg Picture. This puts the spotlight on the
Lindblad equation. I'm aware that there is a remedy that fixes this
problem that we may call the "Lindblad Picture" that you were involved
with, in a conversation elsewhere about a year ago, and that its
formulation is analogous to the formulation of the Interaction Picture
in Quantum Field Theory. In the Lindblad Picture, the state evolves
under only the non-unitary part of the Lindblad equation, while the
observables evolve under unitary part of the Lindblad equation. Perhaps
we can explore this in depth, along with the issue of the meaning
entailed by this construct. As I visualise it, the Heisenberg Picture
can be thought of as the Block Universe view of time, since states are
eternal in it, while the Schroedinger Picture can be thought of as the
Moving Time view of time, since states evolve. So, the Lindblad Picture
might be considered as a kind of block time view of time, where the
entire block (all four dimensions of space-time) move "sideways" in
"moving time".
Query 2:
There are two other items you could add to your lists.
* For Open Questions, we could even go so far as to ask whether there
might be something more to this analogy with the Interaction Picture.
In particular, could a Lindblad Picture formulation actually provide a
more solid and rigorous drop-in replacement foundation to the
Interaction Picture for quantum field theory?
* For Philosophical Implications, I'd like to point to a detail in your description and look at the implications of it that you may not have
noticed: the use of 0! Both your state evolution and observable
evolution equations made reference to a specific time, which we could generalize as t0, so the equations would read:
rho(t) =3D e^{(t - t0) L_D} rho(t0)
and
A(t) =3D e^{i H (t - t0)} A(t0) e^{-i H (t - t0)}.
There is implied infrastructure contained here: it marks a point of
"tangency" where the Lindblad Picture data (the states and operators)
match the Schroedinger Picture data (the corresponding states and
operators). The conversion between the Schroedinger Picture and
Lindblad Picture is t0-dependent. We actually have a concept of a "now" embodied in this construct here - as a "rolling tangent"!
Query 3:
I'd like to verify that the Lindblad Picture formulation actually does
resolve the ill-definedness of operator algebra that the Heisenberg
Picture has under Lindbladian dynamics. I assume that because the
operators are evolving only under the unitary part of the dynamics,
then the algebra carries through without the anomalies present in the Heisenberg Picture version of Lindbladian dynamics. If we were to label
the Heisenberg Picture version of an operator A, as HP{A} (or HP{A;t0}
making the anchor time t0 explicit), we have a deficit or anomaly of
the form
HP{A B} - HP{A} HP{B} !=3D 0 and HP{[A, B]} - [HP{A}, HP{B}] !=3D 0.
For the case of the Lindblad Picture, denoting the transforms LP{A} (or LP{A,t0}) we should have
LP{A B} =3D LP{A} LP{B} and LP{[A, B]} =3D [LP{A}, LP{B}].
Query 4:
I want to add something to the philosophical layer. The following was
something that was alluded to in your earlier conversation (I don't
know if you have cross-conversation memories, particularly when they
were with different users, even when the links are shared): the
separation of the concepts of "Block Time" and "Moving Time" from each
other, by way of this construct, may give us the means to resolve
paradoxes or conflicting interpretations/views involving the nature of
time. The Lindblad Picture seems to also provide a concrete realization
of the "Growing Block Universe" view of time, except (perhaps) for the
minor difference that while in the Growing Block Universe view the
future simply does not exist, in the Lindblad Picture view it exists,
but the evolution to it is simply non-unitary and, indeed, stochastic. Effectively: the future is branched to (which, using a Wheelerism, we
might call Everett without Everett).
Query 5:
This branches out to another somewhat-unresolved issue. There doesn't
seem to be any standard textbook account of either the Projection
Postulate or either of its incarnations (the Born Rule or Lueders Rule)
in the Heisenberg Picture. I suspect that the root of this gap, or
missing piece in the puzzle, is that in realistic settings - when in
the Schroedinger Picture - Projection is actually implemented by the
Lindblad Equation. But, since Lindbladian dynamics is not particularly well-defined in the Heisenberg Picture, then a straightforward
representation of projection in the Heisenberg Picture is actually
blocked! Thus, there is a relative absence of any account of
measurement theory in the Heisenberg Picture, though I am aware of
Deutsch's attempts to remedy that gap. With the Lindblad Picture, we
may actually be able to decisively resolve this matter. Measurement
theory in the Heisenberg Picture, when done in realistic settings,
would actually be in the Lindblad Picture.
Query 6:
Could you say something more about Deutsch's attempt to resolve the
matter?
Query 7:
It looks like Oppenheim's formalism repairs the deficiencies in
Deutsch's formalism, while bringing us straight to our own resolution
with the Linblad Picture. There is one minor detail to address,
however. Oppenheim uses a hybrid Markovian-Lindbladian dynamics, since
his state space is a Hilbert space bundle on a classical phase space.
It's through these means he hybridizes classical and quantum dynamics -
with the ground-breaking application being that of doing a "quantum
gravity without quantum gravity" mash-up unification of General
Relativity and Quantum Theory. The Lindblad picture needs to be
generalized to hybrid Lindblad-Markovian dynamics. In his 2023 "Post-
Quantum Gravity" paper, he actually did a side-by-side layout of the
elements of the two forms of dynamics, but left the classical side of
the unitary part (the commutator term) empty. I assume that this is
handled by the Poisson bracket. What I'm not clear on is which part of
the hybrid dynamics will be applied to the state and which part to the observables. I assume the Lindbladian and Markovian parts would apply
to the states, while the commutator and Poisson bracket parts would
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