تفسير_المعاملات
النقاشات
حُلّت هذه المشكلة في ورقة بحث كرامر عام 1986 والتي قدم من خلالها العديد من الأمثلة عن تطبيق تفسير المعاملات على أنظمة الكم متعددة الجسيمات. وإذا كان السؤال حول وجود توابع للموجات متعددة الجزيئات في الفضاء ثلاثي الأبعاد العادي فإن كتاب كرامر لعام 2015 وضّح بعض التفاصيل الخاصة بوظائف الموجات متعددة الجزيئات في الفضاء ثلاثي الأبعاد. طُرح نقد لدراسة كرامر عام 2015 يخص التعامل مع أنظمة الكم متعددة الجسيمات ضمن دراسة كاستير لعام 2016، «نظرة عامة على تفسير المعاملات وتطورها في القرن الحادي والعشرين». تعتبر دراسة كارمر في عام 2015 غير واقعية فيما يخص حالات الجزيئات المتعددة: إذا كانت الجزيئات فقط جزء مما يسمى الخريطة فهي ليست حقيقية، ويصبح بذلك تفسير المعاملات تفسيرًا فعالًا.The Quantum Handshake by John G. Cramer, p. 184. Cramer's earlier publications "provided many examples of the application of the TI to systems involving more than one particle. These include the Freedman-Clauser experiment, which describes a 2-photon transaction with three vertices, and the Hanbury-Brown-Twiss effect, which describes a 2-photon transaction with four vertices. [Other publications contain] many examples of more complicated multi-particle systems, including systems with both atoms and photons. But perhaps the question posed above is based on the belief that quantum mechanical wave functions for systems of more than one particle cannot exist in normal three-dimensional space and must be characterized instead as existing only in an abstract Hilbert space of many dimensions. Indeed, Kastner’s "Possibilist Transactional Interpretation" takes this point of view and describes transaction formation as ultimately appearing in 3D space but forming from the Hilbert-space wave functions. ... The "standard" Transactional Interpretation presented here, with its insights into the mechanism behind wave function collapse through transaction formation, provides a new view of the situation that makes the retreat to Hilbert space unnecessary. The offer wave for each particle can be considered as the wave function of a free (i.e., uncorrelated) particle and can be viewed as existing in normal three-dimensional space. The application of conservation laws and the influence of the variables of the other particles of the system on the particle of interest come not in the offer wave stage of the process but in the formation of the transactions. The transactions "knit together" the various otherwise independent particle wave functions that span a wide range of possible parameter values into a consistent ensemble, and only those wave function sub-components that are correlated to satisfy the conservation law boundary conditions at the transaction vertices are permitted to participate in this transaction formation. The "allowed zones" of Hilbert space arise from the action of transaction formation, not from constraints on the initial offer waves, i.e., particle wave functions. Thus, the assertion that the quantum wave functions of individual particles in a multi-particle quantum system cannot exist in ordinary three-dimensional space is a misinterpretation of the role of Hilbert space, the application of conservation laws, and the origins of entanglement. It confuses the "map" with the "territory". Offer waves are somewhat ephemeral three-dimensional space objects, but only those components of the offer wave that satisfy conservation laws and entanglement criteria are permitted to be projected into the final transaction, which also exists in three-dimensional space."