I found that I could not understand anything about the popular article. I however found the article "Quantum asymmetry between space and time" by Joan Vaccaro. I tried to get grasp about the formula jungle of the article but became only confused. I expected clear logical arguments but I found none.

My comments are based mostly on the abstract of the article.

** Asymmetry between time and space**

[JV] An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time, whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental, is represented by equations of motion and conservation laws that operate differently over time and space.

My comments:

- One might argue like JV does if one does not keep in mind that Lorentz invariance allows to distinguish between timelike and space-like directions and base the notion of causality on their properties.
In Euclidian geometry there would be no such special choice of time coordinate. But also now field equations would define slicing of space-time to 3-D slices since initial values at them would fix the time solution. Now however the slices could be chosen in very manner manners - for instance 3-spheres rather than hyperplanes as in Minkowski space.

- JV argues that there is an asymmetry in the quantum description of space and time in conventional quantum theory. The spatial coordinates of particle are treated as operators but time is not represented as an operator.
The first mis-understanding is that the position of operator of particle is

**not**space-time coordinate but specifies position of point-like particle in space time.The second mis-understanding is to think that the configuration space of the particle would be 4-D space-time. The configuration space of particle in non-relativistic wave mechanics is 3-space and time is the evolution parameter for unitary time evolution, not space-time coordinate. In the relativistic picture it could correspond to proper time along a world line.

In quantum field theory (QFT) the spatial and temporal coordinates are in completely symmetric position. Wave mechanics is an approximation in which one considers only singlenon-relativistic particle. One should start from QFT or some more advanced to see whether the idea makes sense.

- JV identifies subjective and geometric time as practically all colleagues do. In geometric time time evolution is determined by field equations and conservation laws. In TGD zero energy ontology (ZEO) does not identify these times and resolves the problems caused by identification of these two times. The counterpart of time evolution with respect to subjective time is sequence of small state function reductions.
- The asymmetry between the two time directions appears in two manners.
- There is the thermo-dynamical arrow of time usually assumed to be the same always. In TGD both arrows are possible and the arrow changes in "big" (ordinary) state function reduction (BSFR). Subjective time correlates with geometric time but is not identical with it is closely related to the thermo-dynamical breaking of time reversal.
- The field equations (geometric time) have slightly broken time reflection symmetry T. This breaking is quite different from the generation of the thermo-dynamical arrow of time.

** Could we give up the conservation laws and unitary time evolution and could the
breaking of time reversal symmetry bring them back?**

[JV] If, however, the asymmetry was found to be due to deeper causes, this conventional view of time evolution would need reworking. Here we show, using a sum-over-paths formalism, that a violation of time reversal (T) symmetry might be such a cause. If T symmetry is obeyed, then the formalism treats time and space symmetrically such that states of matter are localized both in space and in time.

In this case, equations of motion and conservation laws are undefined or inapplicable. However, if T symmetry is violated, then the same sum over paths formalism yields states that are localized in space and distributed without bound over time, creating an asymmetry between time and space. Moreover, the states satisfy an equation of motion (the Schrdinger equation) and conservation laws apply. This suggests that the timespace asymmetry is not elemental as currently presumed, and that T violation may have a deep connection with time evolution.

My comments:

- JV is ready to give up symmetries and conservation laws altogether in the new definition of path integral but of course brings them implicitly in by choice of Hamiltonian and by using the basic concepts like momentum and energy which are lost if one does not have Poincare symmetry.
What remains is an attempt to repair the horrible damage done. The hope is that the tiny breaking of T invariance would be capable of this feat.

- Author uses a lot of formulas to show that T breaking can save the world. There are however ad hoc assumptions such as coarse graining and assumptions about the difference between Hamiltonian and time reversed Hamiltonian argued to lead to the basic formulas of standard quantum theory.
The proposed formulas are based on single particle wave mechanics and do not generalize to the level of QFT. If one is really ready to throw away the basic conservation laws and therefore corresponding symmetries also the basic starting point formulas become non-sensible.

Holistic mathematical thinking would help enormously the recent day theoretical physicists but it is given the label "philosophical" having the same emotional effect as "homeopathic" to the average colleague. What my colleague called formula disease has been the basic problem of theoretical physics for more than half century.

- This modification of path integral formula looks rather implausible to me.
- Giving up the arrow of time in the sum over paths formalism breaks the interpretation as a representation for Hamiltonian time evolution (path integral is mathematically actually not well-defined and is meant to represent just Schroedinger equation).
If there were no asymmetry between time and space, quantum states would be wave packets in 4-D sense rather in 3-D sense. This is of course complete nonsense and in conflict with conservation laws: an entire galaxy could appear from nothing and disappear. Author notices this but does not seem to worry about consequences. By the way, in TGD inspired theory of consciousnessthe mental image of the galaxy can do this but this does not mean the disappearance of the galaxy!

The use of the wave mechanics which is not Lorentz invariant, hides the loss of Lorentz invariance implied by the formalism whereas ordinary Schrödinger equation as non-relativistic approximation of Dirac equation does not break Lorentz invariance in non-relativistic approximation.

- It is optimistically assumed that the tiny breaking of T symmetry could change the situation completely so that the predictions of the standard quantum theory would emerge. Somehow the extremely small breaking of T would bring back arrow of time and save conservation laws and unitary time evolution and we could be confident that our galaxy exists also to-morrow.
Why the contributions to modified path integral for which time arrow is not fixed would magically interfere to zero by a tiny breaking of T invariance?

The proposal seems to be in conflict with elementary particle physics. The view is that neutral kaon is a superposition of a state and its T mirror image and this means tiny T breaking. Neutrinos also break T symmetry slightly. In this framework all other particles would represent complete T breaking. Usually the interpretation is just the opposite. This does not make sense to me.

- The test for proposal would be based on the idea that neutrino from nuclear reaction defined flux diminishing as 1/r
^{2}, r the distance from the reactor. This should somehow cause an effect on clocks proportional to 1/r^{2}due to the incomplete destructive interference of the contributions breaking the ordinary picture. I do not understand the details for how this was thought to take place.The small T violation of neutrinos would affect the maximal T violation in environment and somehow affect the local physics and be visible as a modification of clock time - maybe by modification of the Hamiltonian modelling the clock. This is really confusing since just the small T violation is assumed to induce the selection of the arrow of time meaning maximal T violation!

- Giving up the arrow of time in the sum over paths formalism breaks the interpretation as a representation for Hamiltonian time evolution (path integral is mathematically actually not well-defined and is meant to represent just Schroedinger equation).

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

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