Quantum Cheshire cats do not exist in the TGD Universe

The article Quantum Cheshire Cats of Aharonov, Popescu, Rohrlich, and Skrzypczyk published in New Journal of Physics (see this) claims that the particle can be separated from its properties relies on the notion of weak measurement (see this). The mathematical model of weak measurements is not taken seriously by the mainstream and there are good reasons for the skepticism.

The claimed apparent separation of the particle from its properties (the grin of Cheshire cat from the Cheshire cat) could be an illusion and have a more mundane interpretation. This strange separation actually occurs in the sensory perception: the object and its properties, say the state of motion, are represented separately and one can ask whether something like this could occur at quantum level. The hypothesis raises many questions.

1. For instance, what does one mean with the particle? Usually the particle is identified as a collection of its properties like spin, energy and momentum. Now one adds the notion of particle path and this is in conflict with the standard QM. Only if one accepts path as observable, one can speak of states |A⟩ and |B⟩.
2. The detection of the particle is taken to mean its absorption: not a measurement of any usual property. The measurement would mean a localization to path |A⟩ or |B⟩ in the space of paths but in standard QM only the localization to a point of 3-space makes sense.
3. The conclusion is that the particle and its spin, parallel to the plane defined by the paths A and B, travel through different paths. This claim follows from the observation that the addition of a very weak magnetic field, orthogonal to the quantization axis of spin, has effect only at the second path, call it B, whereas the addition of a very thin absorbing screen has effect on the different path, call it A. Therefore one concludes that the spin moves along B and the particle along A.

   In reality, the experimental arrangement guarantees that the spin directions are opposite on path A and B so that the claim about Chesire cat property is misinterpretation if taken literally.

4. How the spin directions at paths A and B are fixed.i.e. what determines the quantization axis of the spin. Could there be a magnetic field B_q, parallel to the plane defined by paths A and B, determining the quantization axis. When one adds a weak magnetic field ΔB orthogonal to the plane of A and B and therefore to B_q, it produces a torque trying to change the spin direction.

   If the direction of the spin at path B is opposite to that of B_q, it corresponds to the maximum of the dipole energy E=-μ ċB_q which is unstable against the torque caused by the addition of ΔB. Think of a particle at the top of a hill. At path A the dipole energy is negative and minimum: this gives rise to stability and the addition of B. The torque has a negligible effect. One has quantum criticality at path and stability at path A.

5. Is the addition of a very thin screen ΔS analogous to the addition of the weak magnetic field ΔB. Is path B stable and not affected by ΔS and is path A critical and affected by ΔS This would explain the experimental findings.
6. There is however still a question to be answered. Why are the criticalities with respect to ΔB and ΔS orrelated? Why the criticality with respect to addition of ΔB implies stability with respect to the addition of ΔS and vice versa.

   Could one understand the findings in the TGD framework?

   1. There are the notions of preselection and postselection. Preselection is defined as a formation of a state (|A⟩ + |B⟩)|0⟩ and post selection as use of filter at path B to create state |A⟩|0⟩ + |B⟩|1⟩. As noticed, there is no notion of particle path in wave mechanics. The notion of spin state makes sense.
   2. In TGD, point-like particles are replaced by 3-surfaces. Holography = holomorphy principle (see this and this) implies that 3-surfaces are replaced by 4-surfaces as analogs of Bohr orbits of 3-surfaces. This eliminates path integral and the associated infinities. This also forces zero energy ontology (see as new quantum ontology (see this and this) solving the basic paradox of quantum measurement theory.

      In TGD the introduction of states |A⟩ and |B⟩ makes sense in TGD. Fermions are located at Bohr orbits and define the spin states |0⟩ and |1⟩.

   3. In TGD the classical description in terms of paths as Bohr orbits of 3-surfaces is an exact part of quantum description. At this level one can speak of classical energy and the notions of stability and criticality as unstability make sense.
   4. Suppose that Bohr orbit A is obtained from stable Bohr orbit B by a deformation which increases its classical energy. This would make A unstable against the addition of ΔS. The state in which the Bohr orbit A ends by absorption at the screen is the stable state. Bohr orbit |B⟩ is unstable against the addition of ΔS because it is not a minimum of classical energy.

      If the preselected spin state |0⟩ is minimum of the magnetic energy then the |1⟩ associated with |B⟩ has a higher energy and is unstable against the addition of ΔB.

   5. These assumptions imply the correlation between the two kinds of criticalities and would explain the claimed findings without the Cheshire cat hypothesis.

   See the article Some comments related to Zero Energy Ontology or the chapter Zero Energy Ontology.

   For a summary of earlier postings see Latest progress in TGD.

   For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.