Quantum Topology

Roman Zapatrin, Quantum topologist
Roman Zapatrin | Starlab 

Roman R. Zapatrin is working on the "Quantum Topology" project. He has recently developed mathematical methods which take away the last pieces of ground under our feet: Einstein took away the predefined metric from spacetime, and Roman Zapatrin – with his physicist colleagues – is taking away spacetime itself.

Another possible application of quantum topological jumps, for which he has provided the theory, is to store information for quantum computers. He graduated from St. Petersburg State University as a pure mathematician. He does not respect any kind of scientific supervision, nor any academic degree; indeed his university diploma was written by himself.

He is an accomplished composer and musician; he plays the balalaika, the domra, the mandola and the mandolon-cello. He enjoys unconventional and ‘uncivilized’ travelling - crossing snow passes in the Alps with a small folding bike, or skiing in the Russian backwoods. He claims just to be providing tools which to wrestle with Nature's challenges.

For several years he worked on quantum logic, and managed to build the theory of automata simulating quantum system; after that he began grappling with the quantization of spacetime. Still, for him, his main achievement is that he is happy with what he is doing. Roman Zapatrin believes that—theoretically at least—we shall be able to change spacetime, so that by a click we may change both the future and the past.

Quantum Topology 

Physical phenomena are supposed to require an arena in which they may occur. That stadium is spacetime. But in the quantum realm is there such an arena—that is to say, does the stadium exist before the game begins? Or does it emerge as we observe it? Can we change spacetime? May we alter the past without time travel?

It is by now generally accepted that, in the quantum realm entities—minuscule particles—somehow come into existence at the instant that they are observed. In the study of quantum topology there may be different scales at which explorations may be conducted, ranging from the very small to the entire universe.

According to the laws of quantum mechanics a basic assumption is made: an assumption of a pre-existing structure. At the very small scale all attempts to observe that assumed structure inevitably change the topology itself; the large amount of energy which has to be applied distorts the arena's very structure.

The topic of quantum topology spawned two projects at Starlab:

Project Aphrodite: Spacetime Foam

The beauteous Aphrodite, she of the wondrous form, took shape and emerged, fully made in her perfection, out of the foam. The notion of spacetime as foam dates from ideas put forward by John Wheeler of Princeton's Institute for Advanced Study during the 1960's. The Aphrodite project aims to dive deep into the broth of geometrical fluctuations and give perfect shape to that which was formless.

This project explores the structure of spacetime at the Planckian scale. The Planck length is the smallest naturally occurring measurement used by scientists: about a billionth of a billionth of a billionth of a millionth of a centimetre. It is at this scale those quantum phenomena and the arena—or the topology in which they occur—emerge as they are observed.

The task here is to provide a mathematical solution to this physical problem. There is no desire to give up Einsteinian relativity; it presents a very good working model, in its domain of application. But at the sub-Planckian scale, Einstein's theory cannot even be tested. Because it is not testable, the notion of pre-existing spacetime is swept away and may be replaced by an appropriate quantum observable–an entity whose values at the moment it is measured.

Then care is taken to make this work compatible with existing working theories such as relativity, so that the beautiful Aphrodite may be safe wherever she roams.

Project Undo: Topology Leaps

Undo follows from the claims of quantum topology. `Undo' involves the changing of spacetime.
Say for instance that an explosion has occurred; in principle it is possible that by observation itself the arena that is spacetime may be so altered that the explosion did not occur. In this sense it has been undone.

This is a quasi undoing or altering, which occurs as a result of appropriate measurement. This would not be possible without quantum effects, and the goal of this project is to find appropriate measurements of spacetime, which involve those effects. Quantum measurements are those which unavoidably effect that which is being measured. The point about this process is that it is the act of measurement itself, which creates the stadium, and further measurements may create altered or different stadia. This is not the same as travelling back in time; what takes place is an alteration so that a previous setting is undone, in the sense that it did not exist.

Einstein claimed that the past and the future are in a given, predefined or frozen spacetime. The Undo project melts it.

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