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

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.

💡 Research Summary

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The manuscript attempts to build a grand unifying framework that links three seemingly disparate topics: the Landauer‑Büttiker conductance formalism for mesoscopic systems, the quantum measurement problem, and even speculative notions of time‑travel. The authors introduce two new constructs – a “local partial density of states” (LPDOS) and a “local time” – and claim that these hidden‑variable‑like quantities can be inferred from physical clocks (e.g., electron spin precession) and that they provide a deterministic underpinning for quantum conductance and measurement outcomes.

The paper begins with a broad motivation: mesoscopic devices sit at the interface between classical and quantum physics, allowing experimental access to the “intermediate regime.” The authors argue that the traditional Landauer picture, which treats conductance as the product of a transmission probability |t(E)|² and a density of states (DOS) taken to be 1/hv, is conceptually incomplete. They contend that the DOS is not a fundamental property of the system but rather a convenient normalization constant that can be freely chosen as long as current conservation holds. By re‑interpreting this constant as the LPDOS, they claim to have removed the need for any phenomenological DOS and to have placed the conductance formula on a firmer theoretical footing.

To justify the existence of LPDOS, the authors invoke a “physical clock” model originally suggested by Landauer and Büttiker, wherein the electron’s spin acts as a classical magnetic dipole precessing in an external magnetic field. The precession angle, divided by the Larmor frequency, defines a “Larmor precession time” (LPT). They argue that the LPT, when averaged over all spatial coordinates and outgoing channels, reproduces the known quantity called “injectance.” However, the non‑averaged LPT is claimed to give a local time and, consequently, a local partial density of states ρ_lpd. The authors assert that this object is a natural consequence of treating the mesoscopic device as an open quantum system coupled to classical reservoirs, and that it cannot be defined within the closed‑system axioms of standard quantum mechanics.

A striking claim is that ρ_lpd can become negative in the quantum regime, and that such negativity corresponds to a wave‑packet traveling backward in time. The authors extrapolate from this to suggest that time‑travel is physically realizable via quantum processes, and that the negative LPDOS provides a mechanism for sending information into the past. No concrete experimental protocol, nor any analysis of causality violations, is presented; the statement remains speculative and unsupported by any known theory or data.

The manuscript then tackles the quantum measurement problem. By positing that the conductance measured in a mesoscopic sample is a deterministic outcome of a linear superposition of states, the authors claim that the LPDOS (through its associated local time) collapses the wavefunction without invoking stochastic collapse postulates. In other words, the measurement result is pre‑determined by the hidden LPDOS variables. Again, no explicit model of how a detector couples to the LPDOS, nor any statistical analysis showing agreement with Born’s rule, is provided.

Throughout the text, the authors repeatedly refer to the “isomorphism between the Hilbert space and the complex plane” as a deep mathematical justification for the existence of LPDOS. While it is true that any separable Hilbert space over ℂ can be represented by complex vectors, this observation does not endow any physical meaning to a new density of states beyond the standard spectral density derived from the Hamiltonian’s resolvent. The paper also contains numerous typographical errors, inconsistent notation, and a lack of clear derivations; many equations are quoted without derivation, and key steps are omitted.

In summary, the paper puts forward an imaginative but highly speculative framework. Its central objects—LPDOS, local time, and negative density—are introduced without rigorous definition, without clear operational meaning, and without experimental evidence. The claim that these concepts resolve the Landauer conductance formula, the measurement problem, and even enable time‑travel stretches far beyond what is justified by the presented analysis. For the work to be taken seriously, the authors would need to:

1. Provide a mathematically precise definition of LPDOS as an operator on the Hilbert space, prove its positivity (or controlled negativity) and demonstrate how it can be measured.
2. Show, via explicit scattering calculations, how the traditional Landauer formula emerges from their formalism and under what conditions it deviates.
3. Offer a concrete experimental proposal that could detect negative LPDOS or backward‑in‑time wave‑packets, including a discussion of causality and relativistic constraints.
4. Develop a detailed model of measurement that reproduces the Born probabilities while explicitly involving LPDOS, thereby addressing the long‑standing objections to hidden‑variable approaches.

Absent these elements, the manuscript remains an intriguing but unsubstantiated collection of ideas that does not meet the standards of rigorous theoretical physics.