Empirical analysis of quantum mechanics and harmonic applications

. A brief review of the main ideas (interpretations) of quantum mechanics is given. Each of the considered interpretations contains a number of disputable provisions, the discussion of which allows us to develop our own understanding of the mechanism of paradoxical quantum phenomena. The article is addressed to all students who study the concepts of modern natural science, and to all readers interested in the questions what is the reality beyond the quantum mechanical experiment or if our perception really shapes the physical world in some way. The author believes that the development of quantum information technologies is impossible without answering these fundamental questions.


Introduction
The reality of the surrounding world is not denied, but the fundamental limitation of the analysis of the interaction between the micro-object and the device («phenomenological reality») is pointed out.The explanation of a quantum mechanical phenomenon does not consist in revealing its «mechanism», but in the construction of a consistent theory.In the Copenhagen interpretation, two fundamentally important provisions can be noted:  there is no reality outside of observation. reality is «created» by the observer.The Copenhagen interpretation assumes the presence of classical objects (device, observer) to explain quantum phenomena and considers the reduction of the wave function as a result of the interaction of a quantum system with a classical one.And since any classical object is quantum at the microscopic level, a vicious circle arises.If we admit that all objects are quantum, then the concept of measurement loses its usual meaning and is replaced by the concept of quantum correlation.
Interpretation of Heisenberg-Fock.The next interpretation, which we will consider, was proposed by Heisenberg and developed by the Soviet academician V. A. Fok [4,5].As already noted, the Copenhagen interpretation, shared in principle by most physicists of that time, states that there is no need to look for a deeper description and understanding of the reality given to us in the experiment.Only the phenomena are real, and beyond them there is no deeper reality.Heisenberg was one of the few physicists trying to understand and describe «quantum reality».According to Heisenberg, there really is no reality behind the quantum phenomenon, but in a completely different sense than Bohr put into this statement.Behind the quantum phenomenon, Heisenberg believes, there is only a «semi-reality», not a world of factual existence, but only a potentiality, a «tendency» towards implementation [1].
Heisenberg argued that quantum mechanics brings us back to the idea of a plurality of being, the Aristotelian notions of «being in possibility» and «being in reality».Heisenberg did not develop this treatment consistently enough, and in fact it was done by Fock.Fock introduces the concept of «potential possibilities» and «realized» as a result of measurement, almost completely agreeing with Heisenberg in this.
The point of view of Heisenberg and Fock is shared by a large number of physicists and philosophers, in particular, K. Popper, who put forward the concept of predisposition («propensity») to the realization of a singular event.According to Popper, the wave function describes not the properties of micro-objects known from classical physics, but the potency (predisposition) of objects to exhibit certain properties.Quantum reality is the reality of the potentialities of the behavior of micro-objects.Probabilities are physically real.The concept of «disposition», according to Popper, refers us to «unobservable dispositional properties of the physical world, ... only some of the most external manifestations of this reality are available for observation» (quoted from [1]).Predispositions, according to Popper, are physical realities like forces in mechanics.Indeterminism and the interpretation of probability as a predisposition mean a transition to a new physical picture of the world, in which the probabilistic laws have a higher status than the dynamic laws of classical mechanics [3].
Wheeler's interpretation.The development of the Copenhagen interpretation of quantum mechanics is the interpretation proposed by Bohr's student J. Wheeler [1,2].This interpretation focuses on the second position of the Copenhagen interpretation.The existence of the Universe, according to Wheeler, is the result of the «act of participation of the observer» in the process of self-realization of the Universe, «plunging itself into being through acts of participation».The term «observer» can be replaced, according to Wheeler, by the term «participant».The reduction of the wave function occurs at a certain moment of the measurement process, and one of the possibilities for the behavior of a microobject is realized.The device and the «observer» register this fact of reduction and thereby bring the physical process to fullness, to manifestation.Without reduction at the final stage of the experiment, it makes no sense to talk about the existence of physical phenomena.The «kind» of reality is constituted by the very act of establishing the fact of the reduction of the wave function to the actually obtained result.The act of reduction is registered by the observer.In Wheeler's words, «the observer is as essential to the manifestation of the universe as the universe is to the manifestation of the observer» [2].
Interpretation of von Neumann.In an interpretation closely related to the theory of measurement by J. von Neumann, it is argued that the very consciousness of the observer, associated with the measuring equipment, creates reality [1,7].«We must always divide the world into two parts -the observed system and the observer.The fact that such a boundary can be placed arbitrarily far inside the body of a real observer is the content of the principle of psychophysical parallelism,» wrote von Neumann.E. Wigner, R. Penrose, and in Russiaprof.M. B. Mensky.The latter generally puts an equal sign between the concepts of «alternative choice» and «awareness».Consciousness is seen as a bridge between natural science and humanitarian knowledge, between materialism and idealism.Von Neumann is also the founder of the quantum treatment of quantum mechanics (see Section 7 below) [25].
Prigogine's interpretation.Another name is the Brussels interpretation.As the next interpretation of quantum mechanics, consider the interpretation of I. R. Prigogine, who calls for abandoning the classical concept of a «Galilean object» [1,8].Prigogine proposes to exclude from quantum mechanics «the subjective element associated with the observer».The paradox, according to Prigogine, is that the reversible Schrödinger equation can only be verified using irreversible measurements, which this equation, by definition, cannot describe.From this he concludes that quantum mechanics cannot be a closed theory.According to Prigogine, a fundamental role in modern physics (and not only in quantum mechanics) is played by the concept of the «arrow of time» and, consequently, by irreversible processes.They «have an advantage» over reversible processes, and the latter are just a special case, that is, a «classical exception» to the general rule.In quantum mechanics, the act of measurement is just an irreversible process, an element of irreversibility that interferes with the system.We read about the same in Landau and Lifshitz: «... the measurement process in quantum mechanics has a two-faced character -its roles in relation to the past and the future do not coincide.With respect to the past, it verifies the probabilities of the various possible outcomes predicted from the state created by the previous measurement.In relation to the future, it creates a new state.In the very nature of the process, therefore, lies a profound irreversibility.This irreversibility is of fundamental importance [15].
The basic equations of quantum mechanics are themselves symmetric with respect to the reversal of the sign of time; in this respect quantum mechanics does not differ from classical mechanics.The irreversibility of the measurement process introduces into quantum phenomena the physical non-equivalence of both directions of time, i.e., leads to the appearance of a difference between the future and the past» [9].Discussing Prigogine's interpretation, the following can be noted.The processes occurring in the real world are indeed irreversible in time, while the laws of classical mechanics and the basic equation of quantum mechanics, the Schrödinger equation, are reversible.But the Schrödinger equation is not an equation of motion.The reversibility of motions does not directly follow from its reversibility.Multi-world interpretation.Proposed by Hugh Everett (USA, 1957) [6,10].Prof. M. B. Mensky calls this interpretation «the most interesting and most radical».Let us assume that the measurement of the coordinate of a particle in the state of superposition is made.As a result, one of the possible values of this quantity is obtained with some probability.According to the Copenhagen interpretation, the wave function collapses, i.e., instantly vanishes everywhere except at the point where the particle is found.According to Everett, it is stated that the collapse of the wave function never occurs at all.Any quantum mechanical measurement «splits» the Universe into really existing macroscopic copies.Each of them implements certain possibilities contained in the original superposition.Each component of the quantum superposition is a separate and equal physical reality.
The universe splits into a number of branch universes, each of which corresponds to its own possible outcome of the event.What we perceived as collapse means that our consciousness has chosen a certain path through these branches, and therefore there is one set of results instead of another, out of billions of possibilities.Other copies of our consciousness may observe other possible outcomes in other branch universes.In practical terms, this concept coincides with the Copenhagen one.
When considering Everett's idea, one must keep in mind that the word «existence» can be used in two senses.An object can exist in time and space.For example, we say: there is an Earth or there is an electromagnetic field, etc.But existence is possible in a purely logical sense.This is assumed when talking about the existence of, for example, integers, electromagnetic theory, space and time itself, or Everett's worlds [20] (Figure 1).
Subatomic particles are to some extent similar to small glass beads, but the degree of this similarity is extremely small.The electrons do move around the nucleus, but the movement is not in an elliptical path, as if they were small satellites orbiting around the planet.The true nature of the electrons in the atom is much more unusual and interesting.And images can hardly convey the essence of quantum particles.With the help of music theory, this is much easier to do.
The problem with pictures in tutorials like the one above is that they make you think of particles as "things".And they are not things.They appear and disappear like quick flashesit's more like our idea of energy.What we call "particles" are actually clumps of energy fields.Protons and electrons are attracted to each other like a magnet is attracted to a refrigerator.If electrons were really like small satellites moving around the planet, they could orbit at any distance from the nucleus and could easily fall into the nucleus and collide with protons.But that doesn't happen.Electrons always self-organize into highly specific spatial structures around the nucleus.This fact seemed to be a mystery until scientists began to consider electrons as probabilistic waves in an energy field.
A good analogue of how particles actually behave is television white noise, which consists of a huge number of electrons flashing randomly on the screen.Try to imagine this "static" around the nucleus of an atom, and you will get a much better picture of what is happening than images with satellites orbiting planets give.
When electrons are in orbit around an atom or molecule, their movement pattern is not random, unlike white noise on a TV screen.As electrons orbit atoms, their energy fields are organized into a pattern similar to rolling ripples.You can explore this pattern with Paul Falstead's interactive subatomic visualization -search at the end of the Quantum Mechanics section for a hydrogen atom simulator.
But what does all this have to do with music theory?The vibrations of the electron field around the atom act as harmonic vibrations.Electrons have harmonics, just like guitar strings.Electron harmonics have three dimensions, unlike the one-dimensional string harmonics, but they are based on the same principle.These harmonics determine the structure and interactions of the electronic wave, just as the harmonics of a string form the basis of chords and scales.The harmonics of the electronic field are called orbitals (Figure 2).
The entire physical world consists of harmonics of electrons.This screenshot of the Falstead Quantum Harmonic Oscillation applet shows the first harmonic of the electron field around an H2 molecule, two hydrogen atoms, each consisting of one proton and one electron.This is the "electronic" equivalent of a guitar string harmonica at the 12th fret.The blue drop shows the position of one electron, the red drop shows the position of another electron.At higher energy levels, the orbitals take on more complex shapes.This is a direct analogy to the more complex musical intervals that can be obtained from the higher harmonics of a guitar string.
Orbitals can be thought of as a system of small cells, each of which can be occupied by only one electron.These cells are divided in pairs, and the electrons "prefer" to live in neighboring cells.The structure of all objects and chemical elements is determined by how the outer orbitals of atoms interact.If the outermost cells are unoccupied, electrons from other atoms can fill them, linking the atoms into molecules.All liquid and solid materials retain their structure through the exchange of electrons between orbitals.
Below is the molecular structure of ice created by Masakatsu Matsumoto.The red balls are oxygen atoms.Blue -hydrogen atoms.The yellow rods are bonds -they are created by electrons exchanged between the most distant orbitals of oxygen and hydrogen atoms.
This hexagonal structure of ice comes from the way the orbitals of oxygen and hydrogen line up.You can see how this hexagonal structure is repeated at the macro level in the form of snowflakes and frost.
If you heat ice to its melting temperature, you are essentially bombarding the surface of the ice with photons, knocking electrons out of their orbitals so that they can move more freely from atom to atom.The atoms continue to be bound, but not as rigidly, and their bond structure becomes less "strict".
If you continue the process of photon "bombardment", you will completely break the bonds between the molecules, which will begin to move freely and independently in a state that we call vapor.If you shoot photons at the vapor, you will tear apart the molecules, thereby separating the electrons from the nucleus in the form of plasma.An even greater energy impulse will break the nucleus into protons and neutrons, and the protons and neutrons themselves will split into components: up and down quarks.Quarks, protons, neutrons, atomic nuclei and molecules are vibrating energy fields, each with its own distinct waveform and harmonic.
Classical alternatives are perceived by consciousness separately from each other.M. B. Mensky proposed an extended multi-world concept, according to which the separation of alternatives is identified with the phenomenon of consciousness.This explains the classical nature of alternatives and the unusual manifestations of consciousness that occur «at the edge of consciousness» (that is, in sleep or trance mode) when it becomes possible for her to access another alternative to classical reality.Quantum evolution in this concept is reversible, so all moments of time in the quantum world are equivalent.The impression of the passage of time arises only in the mind.
At present, the many-worlds interpretation is being actively discussed in connection with cosmological problems.«The many-worlds interpretation is a natural choice for quantum cosmology, which describes the state vector for the universe as a whole.There is nothing more macroscopic than the universe.It may a priori not have classical subsystems.It may not have an «external» observer» (V.Zurek).There are many well-known scientists among its supporters.J. Wheeler, R. Feynman, E. Wigner, D. Deutsch, S. Hawking, M. Tegmark, A. Shimoni allow multi-world, in Russia -prof.M. B. Mensky and many others [5].

Methods and results
Developed for the analysis of molecular dynamics and nuclear magnetic resonance data, the method of diagonalization with a filter made it possible to advance in understanding the musical technique called vibrato.This technique consists in the fact that when playing an instrument or while singing, the pitch of the sounds produced fluctuates.It is used to give a piece of music more emotional expressiveness.The work was published in the Journal of Mathematics and Music.
Quantum mechanics sets the limits of sensitivity in the measurements of displacement, velocity and acceleration [18].
A recent experiment at the Niels Bohr Institute aimed to explore these limitations.The scientists analyzed how quantum fluctuations during the measurement set the sensory membrane in motion.The membrane is a blueprint for future ultra-precise quantum sensors, whose intricate, complex nature may help overcome fundamental quantum limitations.
The results of the experiment are published in Proceedings of the National Academy of Sciences.
Many musical instruments are based on vibrating strings and membranes.Plucking a string causes it to vibrate at a frequency determined by the length of the string and its tension.In addition to the fundamental frequency, which corresponds to the musical note, the string also vibrates at higher frequencies.These overtones affect our perception of the sound of the instrument and allow us to distinguish the guitar from the violin.
Likewise, beating a drum stimulates vibrations at several frequencies at the same time.
Reducing the membranes in size will not change the essence of the process.However, scientists led by Professor Albert Schliesser have shown that the vibrations of the membrane, including all overtones, follow the amazing laws of quantum mechanics [4].
Quantum laws imply that even the very attempt to accurately measure the vibration of the membrane sets it in motion [18].
Vibrato is a pitch fluctuation with a frequency of 4-8 Hz and different amplitudes.«We are one step closer to understanding the mechanics of musical communication, the nuances that performers use and the logic behind them,» says research project lead Professor Elaine Chew from the Center for Digital Music at Queen Mary University of London.The technique used allows scientists to extract characteristics based on a small amount of information.In the case of vibrato, this turned out to be a decisive moment, since, due to the short duration of reception, other methods of signal analysis are ineffective.Thus, the characteristics of vibrato were obtained: frequency and duration.«The filtered diagonalization algorithm was originally developed to effectively study complex quantum dynamical resonances of atoms and molecules» explains co-author Khalid Rajab.«Despite the great differences between musical and quantum signals, from a mathematical point of view they have many similarities, including the characteristics of their resonances.In fact, due to the fluctuations in time, musical signals are more difficult to analyze compared to their quantum counterparts».
The basis for the project was a study of the differences in playing the violin and the erhu, a two-stringed Chinese instrument.«When the music of folk instruments such as the erhu is played on the violin, it loses the stylistic and expressive qualities of the original» Chew concludes.-One of the important sources of these differences is the way the notes are played (along with vibrato) and the techniques used by musicians to move between notes (portamento).We wanted to develop a computational framework to identify these differences» [6].
Quantum acoustics is a new term and to some extent conditional.He has not yet received citizenship and belongs to the newly discovered field of acoustics.But before talking about it, it is necessary to clarify the seeming contradiction in the very term «quantum acoustics».
Acoustics is the science of sound, which is elastic waves propagating in gases, liquids and solids.If the oscillation frequency of sound waves lies in the range of 40-15,000 hertz, our ear perceives them as an audible sound.If the frequency exceeds 15,000 vibrations per second, we hear nothing, although the physical process remains the same.Sounds that are not audible to our ears are called ultrasounds.
Acoustics considers the medium in which sound and ultrasound propagate as continuous, continuous.Quantum theory is used to describe the phenomena occurring in the microworld.However, as has been recently shown, there is an interface between the two sciences.As the frequency of elastic ultrasonic vibrations increases, the wavelengths decrease and, finally, become so small that the waves begin to «notice» the discrete structure of solids -the crystalline ionic lattice.This is where quantum acoustics is born -an interesting and promising area in which a number of previously unknown physical phenomena have already been established [11].
When studying the phenomena of quantum acoustics, we first of all encounter difficulties in obtaining short ultrasonic waves.The fact is that usually plates made of piezoelectric materials are used as an emitter and receiver of ultrasound, that is, materials that have the property of "release" electric charges under the action of mechanical stresses.If such a plate is compressed, charges of opposite signs will appear on its surfaces.
If compression is replaced by tension, the signs of the charges are reversed.This effect is reversible.If metal electrodes are applied to the plate and an electric voltage is applied to them, the plate is deformed.If the voltage changes, the plate will oscillate and emit elastic waves.Thus, using a piezoelectric plate, it is possible to emit and receive ultrasonic vibrations [13].
The emission and reception of ultrasound is especially effective when the vibrating plate is tuned to resonance.To do this, it is necessary that its thickness corresponds to half the length of the ultrasonic wave.For frequencies used in conventional ultrasonic flaw detection (several megahertz), the thickness of the radiating plate should be about a millimeter.It is not difficult, however, to realize that in order to obtain frequencies a thousand times greater, one would have to work with plates whose thickness is only a few microns.To make such a plate, to apply on it metal electrodes with a thickness of hundredths of a micron, is a task that the legendary craftsman Lefty would probably not have coped with.Therefore, it is now necessary to use relatively thick non-resonant plates in the study of high-frequency oscillations.
This, of course, greatly reduces the efficiency of receiving and receiving high ultrasonic frequencies.One could try to glue a piezoelectric plate to a steel bar and then grind it down until it is a few microns thick.But the trouble is that the adhesive layer is tens of microns, and all the ultrasound energy will be absorbed by it.The problem can be solved by using semiconductor piezoelectric materials, such as gallium arsenic or cadmium sulfide.If a plate cut from such a material is applied to a metal surface, then a so-called barrier layer is formed at its border with the metal, that is, a layer depleted in electrons.The thickness of this layer is microns, and its resistance is very high.By applying a constant voltage of various magnitudes to the barrier layer of the plate, it is possible to change the thickness of the barrier layer within certain limits [17].
Let us now apply a high-frequency alternating voltage to the ends of a thick semiconductor plate, the same one that we want to convert into an ultrasonic wave.If the plate were homogeneous, then the electric field would be uniformly distributed inside it, and under the action of this field, the plate would begin to oscillate with a certain frequency.Since the thickness of the plate is far from resonant, the amplitude of these oscillations will be negligible.In the presence of a barrier layer, the field inside the plate is distributed unevenly: the main part of the applied voltage falls on a very thin barrier layer.Therefore, the barrier layer begins to oscillate with a large amplitude, playing the role of a resonant ultrasound emitter.
By changing the constant voltage applied to the barrier layer, it is possible, within certain limits, to change the thickness of the barrier layer and, consequently, the resonant frequency of our radiator.This allows you to work in a certain frequency range.
Albert Einstein told reporters that he often «thinks in terms of musical architecture».Einstein was an avid violinist and was at the forefront of quantum mechanics.Perhaps these two facts are related [13].
Did Einstein draw clear parallels between musical and quantum harmonics?We will probably never know about this, but such a connection exists, and future scientists can benefit from it.The concept of electron orbitals is still not fully developed.When I was in high school, my (beautiful) chemistry teacher used to say that we shouldn't even try to visualize the true nature of electrons.She was right in not trying to stoop to primitive explanations or lead us down the wrong path, but she gave up too soon.She did not have the opportunity to use powerful interactive computer visualization, but our school had an excellent music class.If I ever have the opportunity to teach children chemistry, I will first of all try to make sure that they have encountered musical harmonicas in practice.I would show them that it takes more energy to play higher harmonics and how these higher harmonics allow for a richer musical palette.And if later we return to chemistry, then it will become much easier for children to understand it [12].
Physicists at Queen Mary University of London have applied quantum systems analysis to the study of vibrato played on various musical instruments.Scientists have developed an algorithm that automatically determines the amplitude and duration of sound frequency fluctuations, and compared the sound of a violin and a Chinese bowed instrument, the erhu, with its help.The study was published in the Journal of Mathematics and Music and is briefly described in a university press release.
Vibrato is a musical technique that consists in the rapid fluctuation of the tone of a sound made by an instrument or person.It is widely used in the performance of works on strings (for example, on the guitar) and wind instruments to decorate the sound.The main parameters that describe the sound of vibrato are the frequency of sound change (usually 4-8 oscillations per second), duration and amplitude (it can reach up to a semitone).
As the authors of the new work note, the manner of performing vibrato in different cultures and at different times has changed -by examining its characteristics, one can obtain new data on the evolution of music.However, the task of automatically determining vibrato is complicated by its short duration.For example, when using Fourier transforms that decompose the sound into a set of sinusoids, you will need to set the size of the frame inside which the vibrato will be searched.If the frame turns out to be too large or too small, then the characteristic pattern of frequency change will be «smeared» [11].
The scientists proposed to use an algorithm based on the filter diagonalization method (FDM) to determine vibrato.As in the case of the Fourier transform, the task of this method is to represent the signal as a sum of sinusoids.However, this method uses an additional assumption that there is autocorrelation in the signal (relationship between the signal and its shifted copy).This allows us to reduce the decomposition problem to the diagonalization of some matrix.
Traditionally, this algorithm is used to analyze the spectra of nuclear magnetic resonance and the evolution of the quantum state of systems.According to the authors, the new work is the first attempt to apply FDM to sound analysis.«Although musical signals are very different from those of quantum systems, from a mathematical point of view they have a lot in common, including the characteristics of their resonances» says Khalib Rajab, co-author of the work.In addition, unlike the Fourier transform, this method allows the use of a small «reading frame», which allows more efficient detection of vibrato [6].
To test the methodology, the scientists chose the Chinese work «Er Quan Ying Yue» («Moon Reflected from the Waters of the Second Source»), composed in the first half of the 20th century by the blind musician Abin.The authors used four different performances of the work -two on the erhu and two on the violin.«When music written for such a folk instrument as the erhu is played on the violin, it loses some of the style and expressive qualities of the original.One of the main sources of differences in sound is the way the notes are worked out (vibrato) and the transitions between notes (portamento).We were interested in creating a computer method that would allow us to notice this difference, «says one of the authors of the work [12].
Scientists note that the new vibrato search method turned out to be more productive than traditional Fourier transforms and other modern techniques.However, according to the authors, not all data obtained by FDM analysis were used in the work.In particular, using the complex frequency component of sinusoids, one can try to improve the definition of vibrato boundaries.
In 2015, Austrian physicists published another study where quantum mechanics and music also meet.Scientists have described a mathematical model of «quantum music» in which superpositions of notes and other unusual states can exist.And in 2016, American and Dutch physicists demonstrated the behavior of atoms in optical resonators using the Chinese gong.
Physicist Karl Swotzil and musician Volkmar Putz proposed a mathematical model for quantizing music.With its help, one can imagine how such strange properties of the quantum world as superposition, quantum entanglement, and the complementarity principle can be realized in music.
For the purposes of their work, the researchers decided to quantize a specific musical instrument, the piano.To simplify calculations and set a strict framework for the model, the scientists quantized only one octave, represented by eight consecutive white keys (usually denoted c, d, e, f, g, a, b, c').By analogy with quantum information, each tone in the musical nomenclature is assigned such properties as the ability to be in a superposition or be in an entangled state [14].
Given an octave of seven tones, several possible ways of quantization can be applied.The first will be that each tone in an octave can be represented as an independent event that has a certain probability.Different events can be combined into one seven-or eight-dimensional Hilbert space, which will represent the entire octave.In this case, each observation will correspond to a different quantum musical state realized by different versions of the Hilbert space.The quantum musical state in this model will be a linear combination of seven tones with corresponding probabilities, and the quantum melody will be the evolution of such a state in time.
It follows from this that if an audience of seven people listens to such a quantum musical state, then there may be cases when each of them will hear a different musical tone at one point in time, and the sequence of these tones for each listener will always be completely unique.
Two other possible quantization options are to represent the octave as a bosonic or fermionic field.In this case, each tone can have two values 0 (0;1) or 1 (1;0), and each state of such a tone can be represented by a two-dimensional Hilbert space.If we return to our piano, then this will mean the simultaneous pressing of several of the eight keys at any given time.
The scientists also suggested that in quantum music, a state of quantum entanglement can be realized, in which the quantum states of two or more objects turn out to be interdependent, and this interdependence is preserved even if the objects are separated in space beyond any known interactions.Listening to a «tangled tune» in this case will depend on what exactly the neighbor in the audience heard [24].
The scientists see their work primarily as a «mind game» rather than an actual study of music and believe it could inspire new research into quantum mechanics and its applications.

Conclusion
All the interpretations considered above can be divided into two categories: those that recognize and those that do not recognize the wave function as the original concept.In the latter case, the introduction of the wave function is considered as a computational trick.A number of interpretations repeat Bohr's original ideas, only emphasizing some points.«Large-scale» one can single out the Copenhagen, multi-world and Ryazan interpretations.The first of these is of a positivist nature, however denied by Bohr and his students.The second one solves the problem of wave function collapse.And, finally, Ryazanov's interpretation makes it possible to explain quantum phenomena within the framework of classical statistics at the cost of introducing negative probabilities and moving backwards in time.