. Yakir Aharonov s time-symmetric formulation of quantum mechanics • Physics Forums
Yakir Aharonov s time-symmetric formulation of quantum mechanics • Physics Forums
Yakir Aharonov s time-symmetric formulation of quantum mechanics • Physics Forums

Yakir Aharonov's time-symmetric formulation of quantum mechanics

The discussion centers on Yakir Aharonov's time-symmetric formulation of quantum mechanics, exploring its implications, historical context, and connections to other quantum theories. Participants examine the two-state vector formalism, weak measurements, and the relationship between initial and final states in quantum systems, with references to various academic papers and videos.

Discussion Character
  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Historical
Main Points Raised
  • Some participants note that Aharonov's recent presentations contain ideas previously published in various papers, including a 2010 article co-authored with Popescu and Tollaksen.
  • There is a discussion about the practicality of the perfect initial preparation and final measurement in laboratory settings, with suggestions to consider density matrices instead.
  • One participant questions whether Aharonov's approach to density matrices is a time-symmetric version of the decoherent histories (CH) formalism or a distinct methodology.
  • Another participant references a Wikipedia article that describes how Reznik and Aharonov's work encompasses both probabilistic and nonprobabilistic observables, indicating a potential divergence from traditional CH approaches.
  • Some participants express uncertainty about the correlation between initial and final states in Aharonov's framework, suggesting that mixed states may arise from partial knowledge of these conditions.
  • Historical context is provided regarding the development of weak measurements and the contributions of Aharonov and his collaborators over the years.
Areas of Agreement / Disagreement

Participants express a range of views on the implications and interpretations of Aharonov's formulation, with no clear consensus reached on whether it aligns with or diverges from existing theories like decoherent histories.

Contextual Notes

Participants reference various academic papers and videos, indicating a complex interplay of ideas that may not be fully resolved. There are mentions of specific equations and concepts that require further exploration to understand their implications in the context of Aharonov's work.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, particularly in relation to time-symmetric formulations, weak measurements, and the historical development of these concepts within the field.

Science Advisor Gold Member Messages 1,205 Reaction score 896

I recently watched "A New Approach to Quantum Mechanics" by Dr. Yakir Aharonov Part 1 (12.12.2023 | Institute for Quantum Studies) on YouTube (and also Part 2 and 3). I was naive enough to believe it was really new. Only when I searched for a valid reference in order to be allowed to ask about it here on PF, I learned that most of the content was already present in:

Aharonov, Yakir, Sandu Popescu, and Jeff Tollaksen. "A Time-symmetric Formulation of Quantum Mechanics." Physics Today 63.11 (2010). doi: 10.1063/1.3518209 (https://typeset.io/pdf/time-symmetric-formulation-of-quantum-mechanics-2gvmqarts5.pdf)​

and all the content already got mentioned in another YouTube video J. Tollaksen: The Time-Symmetric Formulation of Quantum Mechanics, Weak Values and the Classical Limit of Quantum Mechanics (EmQM13) which also mentions much earlier publications like Weak measurement: The Aharonov-Albert-Vaidman effect:

Phys. Rev. Lett. 60, 1351 (1988) (https://doi.org/10.1103/PhysRevLett.60.1351)​ Y. Aharonov, P. G. Bergmann, J. L. Lebowitz, Phys. Rev. 134, 1410 (1964)​

One of my first thoughts triggered by this two-state vector perspective was that it offers a nice way to look at the “n qubits in (quantum) context” can contain up to 2n classical bits riddle. A completely different thought was that I found the prefect initial preparation and perfect final (postselection) measurement used for the explanation of that perspective unrealistic regarding what you can actually do in a laboratory. So I wondered what would change when you described the initial preparation and the final (postselection) measurement by density matrices instead. Turns out somebody asked exactly this question in another video at 58:30, but I was unable to find the reference where it was done, which Aharonov mentioned in his answer. Then I remembered that I once used the time-symmetric formulation of CH to get "at least some intuition why there is that unexpected product in the bound":

gentzen said: For thinking about the sharp bound itself, the time-symmetric formulation of CH with two hermitian positive semidefinite matrices ##\rho_i## and ##\rho_f## satisfying ##\operatorname(\rho_i \rho_f)=1## seems well suited to me. The decoherence functional then reads ##D(\alpha,\beta)=\operatorname(C_\alpha\rho_i C_\beta^\dagger\rho_f)## and the bound on the number ##m## of histories ##\alpha## with non-zero probability becomes ##\operatorname(\rho_i)\operatorname(\rho_f)\geq m##. Interpreting ##\rho_i## as corresponding to pre-selection ("preparation") and ##\rho_f## as post-selection ("measurement") gives at least some intuition why there is that unexpected product in the bound.

I didn't notice before that this bound is actually a nicely rigorous occurrence of that unexpected “n qubits in context

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