Yuri I. Ozhigov is Professor, Chair of Quantum Informatics, Faculty VMK, Moscow State University and author of Constructive Physics. This conversation was first published on European Scientist, in January 2020.
Grégoire Canlorbe: Your theoretical insights in quantum physics emerged both in the light of the constructive branch of mathematics and in the one of what you call “the method of collective behavior.” How do you sum up your vision—and what it owes to those two influences?
Yuri I. Ozhigov: Analysis of infinitesimals is the “sacred cow” of natural science. And it works fine, but only when the particles are identical in one sense or another. This is the basis for modern instrumentation. But in a living thing all particles are different. You can’t rearrange nucleotide bases in a DNA molecule. Living is not amenable to mathematical analysis, here we need a quantum computer. But even in creating this unprecedented device, traditional analytical methods of physics failed. Constructive mathematics is an actual alternative to analysis. In it, fixing the resolution grain has a special meaning, and algorithms come to the fore.
This point of view is not shared by the majority, but it is much more consistent with reality than the traditional analytical approach. The behavior of the air in the room where you sit, strictly speaking, does not obey the Navier-Stokes equation, because you can not direct the spatial step to zero: if it becomes less than a nanometer, it will be impossible to determine the air density or air impulse at a point, because such a cube will either get one molecule, or nothing at all. Here we need a method that I conventionally called collective behavior. In a normal situation with air in a room, you can ignore this, but if it was not about air, but about a bacterium, it is impossible to ignore the discreteness of the world.