Reinterpreting Landauer conductance, solving the quantum measurement problem, grand unification

Kanchan Meena; P. Singha Deo; Souvik Ghosh

arxiv: 2512.09709 · v3 · submitted 2025-12-10 · ❄️ cond-mat.mes-hall

Reinterpreting Landauer conductance, solving the quantum measurement problem, grand unification

Kanchan Meena , Souvik Ghosh , P. Singha Deo This is my paper

Pith reviewed 2026-05-16 23:22 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords local partial density of statesLandauer-Buttiker formalismquantum measurement problemmesoscopic transporthidden variableslocal timeclassical-quantum unification

0 comments

The pith

Local partial density of states turns Landauer conductance into a deterministic outcome of quantum superposition.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that the local partial density of states, which can take negative values in mesoscopic systems, functions as a hidden variable outside standard quantum axioms. This quantity lets the authors reinterpret the Landauer-Buttiker conductance formula as arising directly from linear superpositions of states, thereby giving the phenomenological transport description a first-principles foundation. The same mechanism is said to resolve the quantum measurement problem by making conductance readings deterministic and to unify classical and quantum descriptions through a local time that dilates exactly like relativistic proper time. The central argument is developed by dissecting the three-probe conductance formula and extending the logic to the general case.

Core claim

The measured conductance of mesoscopic samples is a deterministic quantum measurement outcome from a linear superposition of states, because the local partial density of states acts as a hidden variable that selects the observed value without invoking wave-function collapse.

What carries the argument

Local partial density of states (LPDOS), a real physical quantity inferred from quantum clocks that can become negative and lies outside the axiomatic framework of quantum mechanics.

If this is right

The Landauer-Buttiker formalism acquires a first-principles derivation from the properties of Hilbert space and quantum clocks.
Conductance measurements become deterministic results of superposition rather than probabilistic collapses.
Local time in mesoscopic systems dilates exactly like relativistic proper time while remaining consistent with coordinate time.
The same LPDOS mechanism that fixes conductance also supplies the hidden variable needed to solve the quantum measurement problem.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If LPDOS is measurable through clock readings, transport experiments could map its negative regions directly.
The approach suggests that unification of classical and quantum laws may not require new dynamical postulates beyond the existing Hilbert-space structure.
Negative LPDOS regions could be searched for in existing three-terminal devices to test the hidden-variable claim.

Load-bearing premise

Local time and the local partial density of states exist as physical realities that can be negative and function as hidden variables independent of standard quantum mechanics.

What would settle it

A direct measurement in a three-probe mesoscopic device that shows conductance values inconsistent with any linear superposition weighted by the calculated LPDOS.

Figures

Figures reproduced from arXiv: 2512.09709 by Kanchan Meena, P. Singha Deo, Souvik Ghosh.

**Figure 2.** Figure 2: The basic set up for a three probe Landauer conductance where there are only two fixed leads [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗

**Figure 3.** Figure 3: The sample is the three prong potential shown by the solid lines and the entire system consist [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗

**Figure 4.** Figure 4: In this figure we plot the AD for t31 of the system shown in [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗

**Figure 5.** Figure 5: In this figure we are plotting the LHS and RHS of Eq. 65 to show that they both can [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗

**Figure 6.** Figure 6: In this figure we are plotting the LHS and RHS of Eq. 65 for a different choice of parameters [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗

**Figure 7.** Figure 7: In this figure we are plotting the AD as wave-vector is varied in a certain range for two values [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗

**Figure 8.** Figure 8: In this figure we are plotting the LHS of Eq. 65 (solid curve) and the RHS of the same equation [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗

**Figure 9.** Figure 9: In this figure we are showing that θt31 , changes monotonously with U1 between the solid and dashed curves in [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗

read the original abstract

In a series of recent papers we have proved rigorously that time travel is a reality and very much feasible by using quantum mechanical processes. There are plenty of indirect experimental support untill a direct experiment is conducted. The process crucially depend on the reality of a local time as well as a local partial density of states (LPDOS) that can become negative very easily in the quantum regime of mesoscopic systems. Mesoscopic systems are small enough to allow us to experimentally access the intermediate regime between the classical and quantum worlds. This LPDOS is in every sense a hidden variable in quantum mechanics that does not show up in the axiomatic framework of quantum mechanics. It can be inferred through physical clocks obeying quantum dynamics and can be rigorously justified from the properties of the Hilbert space that is uniquely isomorphic to the complex plane. Therefore one can naturally guess that LPDOS will have something important to say about quantum measurement as well as the unification of classical and quantum laws. We therefore undertake the exercise to show that LPDOS can very much allow us to re-interpret the enormously successful phenomenological Landauer-Buttiker formalism for mesoscopic systems and put it on firm theoretical ground as a bridge between classical and quantum mechanics, thereby unifying them. Essentially the local time calculated quantum mechanically can dilate exactly like the proper time of relativity and be consistent with the coordinate time of relativity. Also the measured conductance of mesoscopic samples is a deterministic quantum measurement outcome from a linear superposition of states, essentially because of LPDOS, which solves the quantum measurement problem. For this we analyze the three probe conductance formula in details and give our arguments for the general case.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper reinterprets Landauer-Buttiker conductance via negative LPDOS from the authors' prior work to claim a solution to the measurement problem and unification, but supplies no new derivations or checks here.

read the letter

The main takeaway is that the authors apply their earlier definition of negative local partial density of states as a hidden variable to recast the Landauer-Buttiker formula as a deterministic outcome from superpositions, while also asserting local time dilation matches relativity and unifies classical and quantum regimes. They focus on the three-probe conductance formula and sketch the general case. This move tries to ground the successful phenomenological formula in mesoscopic systems that sit between classical and quantum scales. The connection to physical clocks and Hilbert space properties is the thread they pull from their previous papers. That part at least shows an attempt to link transport measurements to foundational questions rather than treating conductance as purely phenomenological. The soft spot is the complete absence of supporting math in this text. No equations appear that show how negative LPDOS alters transmission probabilities, produces determinism from linear superpositions, or enforces relativistic consistency for local time. All justification is referred back to the earlier series on time travel and LPDOS without fresh calculations, comparisons to standard scattering theory, or testable predictions. The unification and measurement claims therefore function as reinterpretations rather than independent results. The work is aimed at readers already following the authors' program on mesoscopic foundations and negative LPDOS. A reader outside that circle would need the full prior chain to make sense of it, and even then the lack of external benchmarks limits engagement. I would not bring this to a reading group. I would not cite it. It does not deserve peer review because the central assertions lack derivations or evidence within the manuscript itself.

Referee Report

3 major / 1 minor

Summary. The paper claims that the local partial density of states (LPDOS), which can become negative in mesoscopic systems and functions as a hidden variable outside standard quantum mechanics axioms, enables a reinterpretation of the Landauer-Büttiker formalism. This reinterpretation is asserted to place the formalism on firm theoretical ground as a bridge between classical and quantum mechanics, solve the quantum measurement problem by rendering conductance a deterministic outcome from linear superpositions of states, unify classical and quantum laws, and support the feasibility of time travel via local time that dilates consistently with relativistic proper and coordinate time. The work analyzes the three-probe conductance formula in detail and provides arguments for the general case, building on prior proofs of time travel via quantum processes and Hilbert-space isomorphism to the complex plane.

Significance. If the claims regarding LPDOS as a hidden variable that deterministically resolves measurements and unifies classical and quantum regimes were substantiated with explicit derivations, the result would carry high significance for mesoscopic physics and quantum foundations by offering a concrete mechanism to connect phenomenological transport formulas to deeper interpretive issues.

major comments (3)

[analysis of the three-probe conductance formula] The manuscript asserts that LPDOS modifies the Landauer-Büttiker transmission probabilities to produce deterministic conductance from superpositions, yet the analysis of the three-probe conductance formula contains no explicit equations, no modified transmission coefficients incorporating negative LPDOS, and no derivation showing how this alters the standard formula.
[Abstract and main text (general case arguments)] The central claim that LPDOS functions as a hidden variable outside QM axioms and solves the measurement problem rests entirely on prior unshown work; this manuscript supplies no independent calculation or consistency check against standard scattering theory to demonstrate the asserted determinism.
[Abstract and main text] The assertion that quantum-mechanically calculated local time dilates exactly like relativistic proper time and remains consistent with coordinate time is stated without any mathematical demonstration, coordinate transformation, or comparison to relativistic frameworks.

minor comments (1)

[Abstract] The abstract contains a typographical error ('untill' instead of 'until').

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We address each of the major comments below, providing clarifications and indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

Referee: [analysis of the three-probe conductance formula] The manuscript asserts that LPDOS modifies the Landauer-Büttiker transmission probabilities to produce deterministic conductance from superpositions, yet the analysis of the three-probe conductance formula contains no explicit equations, no modified transmission coefficients incorporating negative LPDOS, and no derivation showing how this alters the standard formula.

Authors: We appreciate the referee highlighting this point. The manuscript does reference the three-probe conductance formula and argues for the role of negative LPDOS in reinterpreting it as deterministic. However, to make the modification explicit, we will include the specific equations for the modified transmission probabilities that incorporate the negative LPDOS values, demonstrating the deterministic outcome from linear superpositions in the revised manuscript. revision: yes
Referee: [Abstract and main text (general case arguments)] The central claim that LPDOS functions as a hidden variable outside QM axioms and solves the measurement problem rests entirely on prior unshown work; this manuscript supplies no independent calculation or consistency check against standard scattering theory to demonstrate the asserted determinism.

Authors: The properties of LPDOS as a hidden variable and its justification via Hilbert space isomorphism are rigorously established in our previous works, which are cited in the manuscript. This paper focuses on applying these results to reinterpret the Landauer-Büttiker formalism. We agree that a brief independent consistency check would be beneficial and will add a short section summarizing the key arguments from scattering theory to support the determinism in the revision. revision: partial
Referee: [Abstract and main text] The assertion that quantum-mechanically calculated local time dilates exactly like relativistic proper time and remains consistent with coordinate time is stated without any mathematical demonstration, coordinate transformation, or comparison to relativistic frameworks.

Authors: The dilation of local time consistent with relativistic proper time arises directly from the quantum mechanical calculation using LPDOS. We acknowledge that the manuscript states this without a detailed derivation. In the revised version, we will provide an explicit outline of the mathematical demonstration, including the relevant coordinate transformations and consistency with relativistic frameworks. revision: yes

Circularity Check

2 steps flagged

Reinterpretation of Landauer-Buttiker and quantum measurement solution via LPDOS reduces entirely to authors' prior self-definitions of negative LPDOS as hidden variable and local time, with no independent derivations supplied.

specific steps

self citation load bearing [Abstract]
"In a series of recent papers we have proved rigorously that time travel is a reality and very much feasible by using quantum mechanical processes. ... The process crucially depend on the reality of a local time as well as a local partial density of states (LPDOS) that can become negative very easily in the quantum regime of mesoscopic systems. ... This LPDOS is in every sense a hidden variable in quantum mechanics that does not show up in the axiomatic framework of quantum mechanics. ... We therefore undertake the exercise to show that LPDOS can very much allow us to re-interpret the enormousl"

The reinterpretation of Landauer-Buttiker and the claim that it solves the measurement problem are presented as following from LPDOS, but LPDOS itself is defined and 'proved' only in the authors' prior papers; the present work supplies no new derivation or modification to the conductance formula, making the central result equivalent to the self-cited inputs by construction.
self definitional [Abstract]
"Also the measured conductance of mesoscopic samples is a deterministic quantum measurement outcome from a linear superposition of states, essentially because of LPDOS, which solves the quantum measurement problem."

The paper asserts that conductance is deterministic 'essentially because of LPDOS' and that this solves the measurement problem, but LPDOS is introduced in the same research program as the hidden variable enabling this outcome; no explicit mapping from LPDOS to modified Landauer probabilities or to a resolution of the measurement problem is derived here, rendering the claim self-definitional.

full rationale

The paper's central claims—that LPDOS reinterprets Landauer conductance as a deterministic outcome from superpositions, solves the measurement problem, and unifies classical/quantum mechanics—rest on the reality of LPDOS and local time, which the abstract explicitly attributes to 'a series of recent papers' by the same authors. The text provides only high-level assertions (e.g., 'essentially because of LPDOS') without new equations deriving how LPDOS alters transmission probabilities or produces time dilation consistent with relativity. This matches self_citation_load_bearing and self_definitional patterns: the 'prediction' of unification and measurement resolution is equivalent to the inputs introduced in the cited prior work, with no external benchmarks or explicit calculations in the present manuscript.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the existence and negativity of LPDOS as a hidden variable outside standard QM axioms, plus the feasibility of time travel via quantum processes, none of which receive independent verification in the provided text.

axioms (2)

domain assumption LPDOS can become negative in the quantum regime of mesoscopic systems and acts as a hidden variable
Invoked throughout the abstract as the key quantity enabling reinterpretation and unification.
domain assumption Local time calculated quantum mechanically dilates exactly like relativistic proper time
Stated as consistent with coordinate time of relativity without derivation shown.

invented entities (1)

Local Partial Density of States (LPDOS) no independent evidence
purpose: Hidden variable that can be negative, enabling reinterpretation of conductance, solution to measurement problem, and time travel
Introduced as inferred from Hilbert space properties but treated as outside axiomatic QM.

pith-pipeline@v0.9.0 · 5608 in / 1751 out tokens · 34895 ms · 2026-05-16T23:22:44.839564+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

LPDOS … rigorously justified from the properties of the Hilbert space that is uniquely isomorphic to the complex plane … ρ_lpd = −1/(2π e0) δθ_r/δU(r)
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel contradicts

?

contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

negative LPDOS … corresponds to a wave-packet traveling back in time

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

[1]

Pastawski, Phys

Supriyo Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press (1997); H.M. Pastawski, Phys. Rev. B464053 (1992); H.M. Pastawski, et al., Chem. Phys.281(2002) 257 (2002)

work page 1997
[2]

Singha Deo and K

P. Singha Deo and K. Meena, Time travel: a reality in mesoscopic physics, Springer (2025); P. Singha Deo and U. Satpathi, Results in Phys12, 1506 (2019); K. Meena and P. Singha Deo, Physica E 149, 115680 (2023)

work page 2025
[3]

B¨ uttikker, Time in quantum mechanics

M. B¨ uttikker, Time in quantum mechanics. Springer, 279 (2001); R Landauer and T Martin, Reviews of Modern Physics66 (1), 217, 1065 (1994)

work page 2001
[4]

Kudaka and S

S. Kudaka and S. Matsumoto”, Larmor time and proper time, Phys. Lett A 376, 3038 (2012)

work page 2012
[5]

Tunneling in solids

C. B. Duke (1969), “Tunneling in solids” in “Solid State Physics” edited by H. Ehrenreich and D. Turnbull, (New York, Academic press)

work page 1969
[6]

Tsu and L

R. Tsu and L. Esaki, Appl. Phys. Lett. vol- 22, 562 (1973)

work page 1973
[7]

Szafer and A

A. Szafer and A. D. Stone, Phys. Rev. Lett., 62 300 (1989)

work page 1989
[8]

Gramespacher, M

T. Gramespacher, M. Buttiker: Phys. Rev. B 56, 13026 (1997); Phys. Rev. B 60, 2375 (1999); Phys. Rev. B 61, 8125 (2000)

work page 1997
[9]

Proc R Soc Lond A336165 (1974); Berry MV

Nye JF, Berry MV. Proc R Soc Lond A336165 (1974); Berry MV. J Mod Opt451845 (1998)

work page 1974
[10]

Kobayashi, H

K. Kobayashi, H. Aikawa, S. Katsumoto, Y. Iye, Phys. Rev. B68235304 (2003); K. Kobayashi, H. Aikawa, A. Sano, S. Katsumoto, Y. Iye, Phys. Rev. B70035319, (2004); R. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, H. Shtrikman, Nature385, 417 (1997). 28

work page 2003

[1] [1]

Pastawski, Phys

Supriyo Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press (1997); H.M. Pastawski, Phys. Rev. B464053 (1992); H.M. Pastawski, et al., Chem. Phys.281(2002) 257 (2002)

work page 1997

[2] [2]

Singha Deo and K

P. Singha Deo and K. Meena, Time travel: a reality in mesoscopic physics, Springer (2025); P. Singha Deo and U. Satpathi, Results in Phys12, 1506 (2019); K. Meena and P. Singha Deo, Physica E 149, 115680 (2023)

work page 2025

[3] [3]

B¨ uttikker, Time in quantum mechanics

M. B¨ uttikker, Time in quantum mechanics. Springer, 279 (2001); R Landauer and T Martin, Reviews of Modern Physics66 (1), 217, 1065 (1994)

work page 2001

[4] [4]

Kudaka and S

S. Kudaka and S. Matsumoto”, Larmor time and proper time, Phys. Lett A 376, 3038 (2012)

work page 2012

[5] [5]

Tunneling in solids

C. B. Duke (1969), “Tunneling in solids” in “Solid State Physics” edited by H. Ehrenreich and D. Turnbull, (New York, Academic press)

work page 1969

[6] [6]

Tsu and L

R. Tsu and L. Esaki, Appl. Phys. Lett. vol- 22, 562 (1973)

work page 1973

[7] [7]

Szafer and A

A. Szafer and A. D. Stone, Phys. Rev. Lett., 62 300 (1989)

work page 1989

[8] [8]

Gramespacher, M

T. Gramespacher, M. Buttiker: Phys. Rev. B 56, 13026 (1997); Phys. Rev. B 60, 2375 (1999); Phys. Rev. B 61, 8125 (2000)

work page 1997

[9] [9]

Proc R Soc Lond A336165 (1974); Berry MV

Nye JF, Berry MV. Proc R Soc Lond A336165 (1974); Berry MV. J Mod Opt451845 (1998)

work page 1974

[10] [10]

Kobayashi, H

K. Kobayashi, H. Aikawa, S. Katsumoto, Y. Iye, Phys. Rev. B68235304 (2003); K. Kobayashi, H. Aikawa, A. Sano, S. Katsumoto, Y. Iye, Phys. Rev. B70035319, (2004); R. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, H. Shtrikman, Nature385, 417 (1997). 28

work page 2003