Memory materials and zero energy ontology

Memory materials (or smart materials) provide a challenge for the view of condensed matter based on the standard quantum theory since standard quantum theory does not allow a mechanism for the coding of information about the past of the quantum past of the system involving possibly quantum jumps to its recent state. In TGD, zero energy ontology (ZEO) combined with holography = holomorphy vision provides this kind of mechanism discussed in article and blog article (see this and this). In what follows, the general mechanism of conscious memory is discussed first and then it is applied to memory materials.

1. ZEO and holography make possible memories by coding the quantum jump as a conscious event to the final state of the quantum jump

We have memories about the conscious experiences of the past. How are these memories formed? Zero energy ontology (ZEO) (see this) and this) suggests a rather concrete model for the representations of the memories in terms of the geometry of the space-time surface.

Consider first a brief summary of ZEO.

1. The basic notions of ZEO are causal diamond (CD), zero energy state, and state function reduction (SFR). There are two kinds of SFRs: "small" SFRs (SSFRs) and "big" SFRs (BSFRs).
2. A sequence of SSFRs is the TGD counterpart for a sequence of repeated measurements of the same observables: in wave mechanics they leave the state unaffected (Zeno effect). Already in quantum optics, one must loosen this assumption and one speaks of weak measurements. In the TGD framework, SSFRs give rise to a flow of consciousness, self.
3. BSFR is the counterpart of the ordinary SFR. In the BSFR the arrow of the geometric time changes and BSFR means the death of self and to a reincarnation with an opposite arrow of geometric time. Death and birth as reincarnation with an opposite arrow of time are universal notions in the TGD Universe.

Consider now this view in more detail.

1. Causal diamond CD=cd× CP₂ (see this) is the intersection of future and past directed light-cones of M⁴. In the simplest picture, cero energy states are pairs of 3-D many-fermion states at the opposite light-like boundaries of the CD.
2. Zero energy states are superpositions of space-time surfaces connecting the boundaries of CD. These space-time surfaces obey holography, which is almost deterministic. Holography = holomorphy principle allows their explicit construction as minimal surfaces and they are analogous to Bohr orbits when one interprets 3-surface as a generalization of a point-like particle. Already 2-D minimal surfaces fail to be completely deterministic (a given frame can span several minimal surfaces). This non-determinism forces ZEO: in absence of it one could have ordinary ontology with 3-D objects as basic geometric entities.

   The failure of complete determinism makes 4-dimensional Bohr orbits dynamical objects by giving them additional discrete degrees of freedom. They are absolutely essential for the understanding of memory and one can speak of a 4-dimensional brain.

3. The 3-D many-fermion states and the restriction of the wave function in WCW to a wave function to the space-of 3-surfaces as the ends of Bohr orbits at the passive boundary of CD are unaffected by the sequence of SSFRs. This is the counterpart for the Zeno effect. This requires that a given SSFR must correspond to a measurement of observables commuting with the observables which define the state basis at the passive boundary.

   The states at the opposite, active, boundary of CD are however affected in SSFRs and this gives rise to self and flow of consciousness. Also the size of CD increases in a statistical sense. The sequence of SSFRs gives rise to subjective time correlating with the increase of geometric time identifiable as the temporal distance between the tips of the CD. The arrow of time depends on which boundary of CD is passive and the time increases in the direction of the active boundary.

4. Ordinary SFRs correspond in TGD to BSFRs. Both BSFRs and SSFRs are possible in arbitrarily long scales since the h_eff hierarchy makes possible quantum coherence in arbitrary long scales.

   The new element is that the arrow of geometric time changes in BSFR since the roles of the active and passive boundaries of CD change. BSFR occurs when the set of observables measured at the active boundary no longer commutes with the set of observables associated with the passive boundary.

   The density matrix of the 3-D system characterizing the interaction of the 3-surface at the active boundary with its complement is a fundamental observable and if it ceases to commute with the observables at the active boundary, BSFR must take place.

Consider now what memory and memory recall could mean in this framework.

1. The view has been that active memory recall requires what might be regarded as communications with the geometric past. This requires sending a signal to the geometric past propagating in the non-standard time direction and absorbed by a system representing the memory (part of the brain or of its magnetic/field body). In the ZEO this is possible since BSFRs change the arrow of the geometric time.
2. The signal must be received by a system of geometric past representing the memory. This requires that 4-D space-time surfaces are not completely deterministic: Bohr orbits as 4-D minimal surfaces must have analogs of frames spanning the 2-D soap film, at which determinism fails. The seats of memories correspond to the seats of non-determinism as singularities of the space-time surface as a minimal surface.

3. How are the memories coded geometrically? This can be understood by asking what happens in SSFR. What happens is that from a set of 3-D final states at the active boundary some state is selected. This means a localization in the "world of classical worlds" (WCW) as the space of Bohr orbits. The zero energy state is localized to the outcome of quantum measurement. In ZEO the outcome therefore also represents the quantum transition to the final state! This is not possible in the standard ontology.

   The findings of Minev et al (see this and this) that in quantum optics quantum jumps correspond too smooth classical time evolutions leading from the initial state to the final state provide a direct support for this picture.

   ZEO therefore gives a geometric representation of a subjective experience associated with the SSFR. One obtains conscious information of this representation either by passive or active memory recall by waking up the locus of non-determinism assignable to the original conscious event. The slight failure of determinism for BSFRS is necessary for this. The sequence of SSFRs is coded to a sequence of geometric representations of memories about conscious events.

   This is how the Universe gradually develops representations of its earlier quantum jumps to its own state. Since the algebraic complexity of the Universe can only increase in a statistical sense the quantum hopping of the Universe in the quantum Platonic defined by the spinor fields of WCW implies evolution.

2. ZEO and memory materials

Basic facts about memory materials and shape-memory alloys can be found from Wikipedia (see this) The following summary is essentially the summary of the Wikipedia article

1. Basic examples of shape-memory alloys are copper-aluminium-nickel and nickel-titanium (NiTi), but SMAs can also be created by alloying zinc, copper, gold and iron. NiTi, NiTi-based SMAs are preferable for most applications due to their stability and practicability as well as their superior thermo-mechanical performance. NiTi SMAs can exist in two different phases, with three different crystal structures (i.e. twinned martensite, detwinned martensite, and austenite) and six possible transformations. The thermo-mechanical behavior of the SMAs is governed by a phase transformation between the austenite (A) and the martensite (M).

   Twinning of M means that it decomposes to crystals behaving like separate units. If quantum coherence is involved this could mean a reduction of quantum coherence length.

2. The thermal behavior of NiTi alloys is described by a hysteresis curve (see this) in which the percent or M varies between 100 and 0 corresponding to pure M and pure A.

   NiTi alloys change from A to M upon cooling starting from a temperature below M_s at which the heating has completely transformed A to M ; M_f is the temperature at which the transition by cooling from A to M is completed. During heating A_s and A_f are the temperatures at which the transition from M to A starts and is complete.

3. Applying a mechanical load to twinned M leads to a re-orientation of the crystals, referred to as de-twinning , which results in a deformation which is not recovered (remembered) after releasing the load. De-twinning starts at a certain stress σ_s and ends at f above which M continues to exhibit only elastic behavior (as long as the load is below the yield stress). One can interpret the de-twinning as loading of elastic energy to the twinned M so that detwinned M would have a lower energy.
4. The phase transformation from A to M can also be induced at a constant temperature by applying a mechanical load above a certain level. The transformation is reversed when the load is released. The reversibility suggests that the system's time evolution is analogous to a unitary evolution: in ZEO a sequence of SSFRs separated by analogs of unitary evolutions would characterize it.

5. The memorized deformation from detwinning of M is recovered after the heating to A. The transition from M to A depends only on temperature and stress. The transition does not depend on time, as most phase changes do. The reason would be that there is no diffusion involved.

   While the rapid cooling of carbon-steel is analogous to the cooling of A, it is not reversible and involves diffusion. Steel does not have shape-memory properties.

   ZEO suggests that in the case of A-M system a quantum phase transition describable as a sequence of SSFRs defining a generalization of unitary evolution making possible memory is in question. In the case of steel the description in terms of a sequence of SSFRs is not possible and memory would be lost.

The heating and also de-twinning process by applied pressure involves a feed of energy.

1. The hierarchy of effective Planck constants defines a hierarchy of phases of the ordinary matter behaving like dark matter. The increase of h_eff requires energy and the heating would provide it: one could speak of forced quantum coherence. I have proposed that this makes possible also high Tc superconductivity as a forced superconductivity. Metabolic energy feed would make this possible in living matter.
2. The heating would increase the h_eff of the detwinned M to that of A. The difference between A-M system and steel could be that h_eff is larger for A than steel. The larger the value of h_eff, the larger the time span of the (conscious) memory. The memory span of steel would be shorter.
3. One expects that energy is liberated in the A to M transition. However, the stress used to de-twin the twinned M produced by the cooling of A pumps energy to the twinned M. How can one understand this?

   The twinned configuration consists of copies of the same configuration and de-twinning would fuse them together and energy would be liberated in the fusion. Mechanical loading would feed energy to the system but minimization of free energy would induce de-twinning and would liberate energy. The applied stress could kick the system over a potential wall to a state with a lower energy.

   The process would be analogous to that proposed to occur in the biocatalysis (see this). The shortening of the monopole flux tubes connecting the reactants, induced by the reduction of h_eff, would bring reactants together and liberate energy making it possible to overcome the potential wall preventing the reaction. In the recent case the compression decreasing h_eff would shorten the distance between the basic units of twins and induce fusion.

See the article TGD and condensed matter or the chapter with the same title.

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.