Quantum Attention Function Theory of Amit Ray and the Immortal Quasiparticles
Dr. Amit Ray of Compassionate AI Lab introduced the Theory of Quantum Attention Function in his recent book, I am fascinated by that. He used the concept of quasiparticles to explain the mystery of the Schrödinger’s Cat Box. In this article I highlighted the developments of different quantum interpretations.
Rebirth of the Particles
Quasiparticles can decay, however some new and identical particle entities emerge from the debris. If this decay proceeds very quickly, an inverse reaction will occur after a certain time and the debris will converge again. This process can recur endlessly and a sustained oscillation between decay and rebirth emerges. Despite the peculiar nature of these immortal quasiparticles, they do not violate any known law of physics, especially not the second law of thermodynamics. The entropy of the quasiparticles stays the same and that’s why they don’t truly decay.
“ Inside the Schrödinger’s cat box, the quasi quantum particles are dancing on the net of quantum attention function, vanishing and arising. — Amit Ray
Quantum mechanics, perhaps one of the most successful scientific theories in the history of mankind, is in some respects counterintuitive, challenges our imagination, seems to violate fundamental principles of classical physics, and raises many questions that have preoccupied the minds of physicists and philosophers since the early 1930s. Classical physics is deterministic; we know how a system will evolve in time if we determine the initial state of the physical system by observing its properties at the time we choose to be the initial moment, as well as all external forces acting on the system.
Copenhagen Interpretation
The Copenhagen interpretation of quantum mechanics is the name given to a set of principles formulated by Niels Bohr, Werner Heisenberg, Max Born, and several other physicists who spent time at the Institute for Theoretical Physics of the University of Copenhagen, Denmark Between the years 1925 and 1927.
Birth of Quantum Matrix Mechanics
Niels Bohr with his great prestige and authority in the world of quantum physics commenced a program in Copenhagen to extend quantum analysis. He brought younger physicists Werner Heisenberg from Germany to help in his program. Heisenberg developed a new system of quantum analysis, called matrix mechanics, based upon square matrices of infinite order.
Uncertainty Principle
In 1927 Heisenberg published his article on what came to be known as the Uncertainty Principle. Niels Bohr was not in agreement with Heisenberg on this matter and did not want Heisenberg to publish that article, but Heisenberg did so anyway. Because, according to this principle, the location and momentum for a particle cannot both be known to arbitrary precision. Heisenberg concluded that subatomic particles cannot have material existence and trajectories. This conclusion is also unjustified. For simple physical systems for which explicit mathematical solutions are known the time-spent probability density functions easily satisfy the Uncertainty Principle.
But just after Heisenberg’s great success in the development of matrix mechanics seemingly out of nowhere came a superior formulation by an Austrian physicist, Erwin Schrödinger, based upon partial differential equations. Schrödinger was in his late 30’s and had never before done anything in quantum theory. His specialty was optics. He was inspired to investigate quantum theory by the work of Louie de Broglie. De Broglie argued that just as radiation waves have a particle aspect particles have a wave aspect. De Broglie duality principle says; photons, electrons, and other atomic or subatomic objects sometimes exhibit wave-like behavior, and at other times, particle-like behavior.
Birth of Wave function Mechanics
Schrödinger’s equation involved a variable the nature of which he did not specify. He thought it was analogous to a variable involved in the equations of optics. It was labled the wave function. The terminology of interpretation originally referred to the interpretation of the wave function. Max Born in Göttigen, Germany concluded that the squared magnitude of wave function was the probability density. He communicated this interpretation to Bohr and Heisensenberg in Copenhagen Bohr responded that they never considered it to be anything else. Thus was born the Copenhagen Interpretation of quantum theory.
In 1935, the Austrian physicist Erwin Schrödinger offered a thought experiment aimed at highlighting the flaws in the interpretation of Copenhagen. More particularly, Schrödinger wishes to show the paradox posed by the principle of superposition. In quantum mechanics, an object is described entirely by its quantum state; this is contained in its wave function , itself calculated using the Schrödinger equation . This equation has the property of being linear , that is to say that the combination of two solutions of the equation also forms a solution (this is called a “ linear combination “).
Principle of Superposition
If there are two possible states for a particle, then the combination of these two states is also an admissible result in quantum physics. Combining these two states gives a third state for the particle. This different states of the particle are then found “ superimposed “ (they exist simultaneously) and the latter is thus in a “state of superposition”: this is the principle of superposition . However, when the particle is measured, i.e. when it interacts with the measuring device, then the system is disturbed and only one state is chosen.
Collapse of the wave function
This determination of a single state by measurement is called “ reduction of the wave packet “ or “ collapse of the wave function “, because the superimposed state is reduced to only one; the wave function collapses and there is only one state left.
The determined state corresponds to the probabilities contained in the wave function. Thus, even if the result of the measurement is fundamentally indeterministic, it is the wave function which gives the probabilities of finding the particle in an X or Y state. Although for the Copenhagen School the collapse of the function is necessarily linked to the measurement, the latter never appears concretely in the mathematical formalism of quantum mechanics.
Schrödinger’s Cat Box
It is this apparent contradiction that Schrödinger wants to point the finger at with his thought experience. The latter consists of enclosing a cat in an airtight container containing a vial of hydrocyanic acid. A device must break the vial and release the acid (thus killing the cat) when it detects the decay of an atom of a radioactive compound using a Geiger counter. Now consider that, by calculating the wave function of the atom, it has a 50% probability of disintegrating after two minutes. One might therefore expect that if the probability is realized, the cat dies at the end of the two minutes, regardless of whether or not it is checked whether this is indeed the case.
However, according to the principle of superposition, as long as the box is not open, that is to say until an observer has not measured (with his eyes) the situation, the atom is in a state superimposed : it is simultaneously intact and disintegrated. But since the fate of the cat is directly linked to the state of the atom, if it is superimposed, then the cat is too; he is simultaneously dead and alive . It is only by opening the lid and looking inside the box that the wave function collapses and that a single state is determined: the atom is intact and the cat alive , or the atom is disintegrated and the cat is dead. Before the observation, it is therefore impossible to know the situation of the cat.
Of course, this experiment was never really carried out for obvious reasons related to the fact that it is, by definition, impossible to directly observe a state of superposition, because it would then collapse immediately. It was simply for Schrödinger to demonstrate that if quantum mechanics theoretically allows a cat to be both dead and alive, then it is necessarily incomplete or requires reinterpretation.
Einstein and the Schrödinger’s Cat
Einstein will also offer a thought experiment involving a cat and a barrel of powder with the same objective as Schrödinger’s. For the father of relativity, the situation of the cat is perfectly defined before the observation, it is not she who determines its state. Indeed, the latter refused any notion of indeterminism and affirmed that if the cat was dead or alive when the box was opened, it was because he was either dead or alive already before being placed in it. He thus responded to his detractors by saying “ the positivist mystic will retort that one cannot speculate on the state of the cat as long as one does not look, on the pretext that it would not be scientific “.
Other solutions to the measurement problem
For many physicists, the experience of Schrödinger’s cat does not demonstrate the inconsistency of quantum mechanics but only the impossibility of wanting to translate a quantum phenomenon in classical terms. However, beyond the positivist approach to the interpretation of Copenhagen (of which Stephen Hawking was a fervent defender), several other solutions have been proposed in order to solve the problem of measurement.
Theory of Decoherence
Thus, physicists like Murray Gell-Mann proposed the theory of decoherence, which proposes that the collapse of the wave function is not caused by direct observation but by the different interactions of the particle with its environment . The more these interactions, the faster the collapse. The rupture of the superimposed state does not require any measurement or observer, it is simply a function of physical environmental interactions. With decoherence, the state of the cat is therefore already fixed before even opening the box.
The resulting decoherence is thought to be responsible for the emergence of the classical realm of our Universe out of the quantum substrate.
Multiple worlds theory
Another solution was brought by the physicist Hugh Everett in 1957 and proposes, contrary to the positivist approach, that quantum mechanics fully describes reality. When a measurement is made and the wave function collapses, the non-chosen states do not disappear but are realized in the underlying universes. All realities therefore occur, but in different universes, starting from measurement. This theory, called “ Everett’s multiple worlds theory “, attracted a certain number of physicists.
Quantum Field Theory
Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom.
The quantum waves are, in fact, the particles of field theory. In other words, when we say that there is a particle in the field, we mean that there is a wave of oscillations propagating across it. These particles (the oscillations of the field) have a number of properties that are probably familiar from the days when you just thought of particles as little points whizzing through empty space.
Final Thoughts
The notion of a completely objective reality is the bedrock principle of science, which is the main reason Einstein was so uncomfortable with Bohr’s “nothing exists without observation” take on quantum theory.
The human knowledge of nature were limited by our five senses over thousands of years. Science has gradually expanded the view upward in the field of astronomy and downward to unseen molecules and at levels much much smaller. It is at such level of tiny size that our intuitive point of view break down.
It turns out that the quantum theory can provide a platform to match theory with experimental data faultlessly. However the mathematic formulas do not have a correspondence of a world confined by our five senses. Since then people had tried to make sense of this newly discovered world according to our limited experience often leading to paradox.
With the introduction machine learning in the field of quantum mechanics, it is now easier to demystify the quantum mechanics paradoxes.
