You never step in the same river twice. The name of the river remains the same but the river is constantly changing. This does not mean we can't know anything about it nor any less real.
If A=A fails, then nothing is knowable and there is no fixed reality. In such a case there would be no possibility of reason, and our whatever we take for existence would not be real.
Hello Sir and good evening. I hope you are yours are well. It is my intention to always remain on friendly and cordial relational grounds with those I interact with on message boards.
Thank you for the river metaphor. I've always enjoyed those times I had to spend near moving waters. The sound of a babbling brook is soothing. Nevertheless and in spite of the failure of the Theory of Elemental Waves, the orthodox Copenhagen interpretation of Quantum physics is being challenged. Although, I suspect you and the regular denizens already are aware of Eric Denis' article at Quantum Mechanics and Dissidents
on the Objective Science site. Denis explained with the following.
In fact, a politically disinclined group of dissidents--including Einstein, Schrodinger, David Bohm, and John Bell--maintained their commitment to realism against the idealist and positivist tendencies of the physics establishment .
There is a misconception, of some currency, that Bell's results close the door on all realist versions of quantum mechanics. This is ironic because these very results were motivated by Bell's surprise and profound appreciation upon discovering such a version already in the literature. This was David Bohm's completion of an idea that started with Louis de Broglie. It has emerged as a powerful and precise alternative to the fuzziness of standard theory.
The de Broglie-Bohm (dBB) theory is the most straightforward way of including real particles, with continuous trajectories and well-defined velocities, into the mathematical framework of quantum mechanics. Bohm showed, with real particles, how measurement processes may be put on the same footing as all other physical processes, reproducing quantum predictions while obviating any notion of observer-created reality, indeterminism, probability-as-fundamental, or "wavefunction collapse.''
Denis goes on to convey in footnote 11 that:
"Any serious consideration of a physical theory must take into account the distinction between the objective reality, which is independent of any theory, and the physical concepts with which the theory operates. These concepts are intended to correspond with the objective reality, and by means of these concepts we picture this reality to ourselves." from Einstein, Podolsky, Rosen, Phys. Rev., vol. 47, pp. 777 (1935).
"For example, would it be possible for us to choose the natural laws... in accordance with our tastes...? The fact that we cannot actually do this shows that these laws have an objective content, in the sense that they represent some kind of necessity that is independent of our wills and of the way in which we think about things." D. Bohm, Causality and Chance in Modern Physics, pp. 165, Harper (1961).
Bell advocates a "programme for restoring objectivity" to physical theory, which "will not be intrinsically ambiguous and approximate.... Rather it should again become possible to say of a system not that such and such may be observed to be so but that such and such be so." in "Subject and Object," Speakable and Unspeakable in Quantum Mechanics.
Denis describes how de Broglie-Bohm (dBB) theory explains quantum phenomena without resort to indeterminism. Thus dBB entails that the effort to replace Axioms with mysticism, reason with appearances, morality with altruism, and capitalism with collectivism is unjustified.
The following newer work supports Denis' assertions. Time in relativistic and nonrelativistic quantum mechanics by H. Nikolic
Nikolic's abstract reads as:
The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The spacetime-position operator acts in the Hilbert space of functions of space and time. Dynamics, however, makes eigenstates of the time operator unphysical. This poses a problem for the standard interpretation of QM and reinforces the role of alternative interpretations such as the Bohmian one. The Bohmian interpretation, despite of being nonlocal in accordance with the Bell theorem, is shown to be relativistic covariant.
I do not pretend to understand what this means save for the last two sentences. Despite my deep and profound ignorance, it seems clear that Copenhagen is not the slam dunk you and your fellow mystics are making it out to be.
Best Wishes and Regards for Continued Success