# From Relativistic to Quantum Universe: Observation of a Spatially-Discontinuous Particle Dynamics beyond Relativity

## Abstract

**:**

## 1. Introduction

#### 1.1. The Current View of the Universe: Why the Minkowski Model of Spacetime

#### 1.2. Bohr’s Quantum Theory: Why “There Is No Quantum World…”

#### 1.3. Paradoxes of “Non-Existent” Quantum World

#### 1.4. Latent Progress of Quantum Realism: From de Broglie’s Seminal Ideas to the Bohm’s Model of Undivided Universe

## 2. Main Part

#### 2.1. An Unexpected Way to Reconcile Quantum Realism with Relativity

#### 2.2. Spatially-Separated Macroscopic Quantum States in the Integer Quantum Hall System

_{N}= ħω

_{c}(N + 1/2), where N is the Landau quantum number, ω

_{c}= eB/m*c is the so-called cyclotron frequency (m*–the electron effective mass). In such system, most electrons are in the flat microscopic orbits with the radius r = (ħc/eB)

^{1/2}. Nominally, the coordinate of the center of such orbit (X

_{0}) is in a correlation with its wave vector along the Y axis: X

_{0}= r

^{2}k

_{y}. But actually this correlation has no physical meaning because of the axial symmetry of the system in the XY plane. Thus, we have a strongly degenerated system (E

_{N}is independent of X

_{0}) where the number of electron states per each Landau level is determined by the dense packing of electron orbits over the system area at a given magnetic field.

#### 2.3. Spatially-Discontinuous Electron Transitions through an Intermediate Orbit-Like Macroscopic State: A Gedanken Experiment

_{p}as well as a much higher probability for the localization in this region. Therefore, if our gedanken experiment is realizable in an IQH-type system, then the inherent nonlocality of spatially-discontinuous dynamics could manifest itself directly in a real experiment.

#### 2.4. Asymmetric IQH System as a System with Atom-Like Pervasive Quantum Ordering

#### 2.4.1. The Structure of Macroscopic Orbit-Like States in an Asymmetric IQH System: A Guess

^{5}V/cm [31]. In the literature, such field is often called “built-in” field (E

_{built-in}) and the structures where this field is high enough are often called asymmetric 2D structures. And this field gives us a chance to provide a high enough crossed electric and magnetic field in the whole IQH system. To this aim, we should only provide an external magnetic field which has not only a quantizing component (B

_{z}) but also an in-plane component (B

_{x}).

_{x}) and their position along the X-axis is again determined by the relation X

_{0}= r

_{x}

^{2}k

_{y}. However, the point is that here this relation has a well-defined physical meaning as the X axis is now precisely the direction of the in-plane magnetic field. Thus, the system is such that each one-electron current has a spatially-separated “counterpart” which flows in strictly opposite direction and is characterized by the same energy as well as by the same absolute value. An asymmetry of the energy spectrum manifests itself through a small mutual shift of the Landau bands. Schematically, such spectrum is shown in Figure 1b. Now, if we shift to a real finite system, then it seems reasonable to assume that each current together with its counterpart is actually the same macro-orbit extended along the Y axis and closed through the sample edges parallel to the X axis. In this case, each Landau band should consist of a great number of almost rectangular macro-orbits where the longer high-energy orbits are closer to the sample edges parallel to the Y axis. Schematically, the spatial distribution of macro-orbits is shown in the inset to Figure 1b.

_{x}× E

_{built-in}. Nominally, it would be the so-called photo-voltaic effect which, as a rule, is detectable in asymmetric semiconductor systems under an intense terahertz laser excitation [34]. However, if we are truly dealing with a system of spatially-separated macro-orbits, then the photo-voltaic effect should differ in principle from that observed in the system of indistinguishable electrons. Indeed, if the energy spectrum is such as in Figure 1b, then the system translational symmetry is broken along the X axis because spontaneous currents depend strongly on the X coordinate in each Landau band and moreover these bands are shifted from each other. This means that even if photo-excitation is strictly homogeneous, light-induced local currents along the Y axis may nevertheless be a strong function of X coordinate and moreover their dependence on the magnetic field may not be the same in different local regions. Most likely, such effect (if any) should manifest itself under the so-called cyclotron resonance (CR) conditions when the energy of light quanta is such that the electrons could transit between the neighboring Landau bands with different electron occupancy. And if a strong difference between local light-induced currents does occur, then it would be a strong argument that we are truly dealing with the macro-orbits distributed over the whole system.

#### 2.4.2. Experimental Evidence for an Atom-Like Spontaneous Quantum Ordering

^{12}cm

^{−2}) as well as a high concentration of charged point-like defects responsible for quasi-elastic scattering. For this reason, the scattering time is as short as about 3 ps and the electron mean free path is as low as about 0.1 µm. To provide an asymmetry of confining potential, the surface-to-well distance is as low as 20 nm so that the surface potential can easily penetrate into the well giving rise to the “built-in” field of about 100 kV/cm [35].

_{2}laser. The laser wavelength is 90.6 µm so that the energy of light quanta is about 13.7 meV. In the selected system, CR conditions are thus expected in quantizing magnetic field of about 4.6 T. Under these conditions, the interband electron relaxation is provided by the so-called optical phonons and its characteristic time is about 30 ps, i.e., one order longer than the characteristic time of intraband relaxation due to the quasi-elastic scattering [36]. To avoid considerable heating, the laser operates in a single-pulse regime with the pulse duration as short as about 50 ns. Light intensity is about 200 W/cm

^{2}. High-speed electric responses are detected in a short-circuit regime with a 50 Ω load resistance per each channel of the detection. Time resolution is about 10 ns.

#### 2.5. Observation of a Spatially-Discontinuous Electron Dynamics

^{8}cm/s. It is really too fast moving even if it would be of a ballistic character without any scattering.

## 3. Fundamental Consequences

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Macroscopic orbit-like quantum states in IQH-type systems. (

**a**) Energy spectrum of conventional (symmetric) IQH system. Landau level degeneracy is lifted near the sample edges (a—the sample length) due to the presence of an electric field pointed toward the sample center. In a combination with the external perpendicular magnetic field, it gives rise to spatially-separated orbit-like quantum states. One of these states is shown schematically in the figure. In this state, electron behaves as a spontaneous current flowing around the macroscopic sample. Dash-dot line denotes the Fermi energy. Inset shows schematically the spatial configuration of macroscopic orbits. (

**b**) Estimated energy spectrum of an infinite IQH system with asymmetric confining potential when external magnetic field has both quantizing and in-plane components. Landau level degeneracy is now lifted throughout the whole system due to a combined effect of both “built-in” electric field and in-plane magnetic field. As a result, electrons are in spatially-separated quantum states in which they behave as spontaneous currents flowing in opposite directions along the Y axis. We show two pairs of such currents and in each pair the currents are a counterpart of each other. Spatial asymmetry manifests itself through a microscopic spatial shift of Landau levels, which increases with increasing of the Landau quantum number. Vertical dashed lines show bands’ minima. Inset shows schematically the expected spatial configuration of macro-orbits in a real finite system.

**Figure 2.**Gedanken experiment to show a potentiality for the spatially-discontinuous transition between two distant local states through an intermediate orbit-like macroscopic state. Here a macroscopic spatial discontinuity of the transition is due to the fundamental indivisibility of the intermediate macroscopic orbit-like state. d–the length of the side of a macroscopic square orbit, τ–electron lifetime at the orbit. Solid cycles shows schematically charged local scatterers.

**Figure 3.**Evidence for a spontaneous quantum ordering throughout the whole system. (

**a**) Sketch of the experiment. All sample area is exposed to the spatially-homogeneous laser radiation. Light-induced electric responses are detected through four contact pairs shifted from each other along the X-axis. (

**b**) The outcome of the experiment. Solid lines are a guide for the eyes. Curves are numbered in accordance with the numbering of contact pairs.

**Figure 4.**Evidence for an indivisible behavior of (H) the system under study. (

**a**) Local responses at B = 5 T; (

**b**) Local responses after reversing the magnetic field; (

**c**) Local responses after splitting the sample.

**Figure 5.**Observation of light-induced electron dynamics with a macroscopic spatial discontinuity. (

**Left-hand panel**) Sketch of the test. Conditions are the same as in Figure 3a but now there are only two contact pairs and the sample is covered by a non-transparent plate with two windows: in the region A (formerly pair No. 1) as well as in the region B (formerly pair No. 4). Responses are measured in both regions. In the figure, only the window A is open. (

**Right-hand panel**) Typical tracks when only the window A is open (B = 5 T): upper track–response from the illuminated region A; lower track–response from the distant (from the laser spot) region B. Both responses are equally pre-amplified. Timescale is 100 ns/div.

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**MDPI and ACS Style**

Emelyanov, S.A.
From Relativistic to Quantum Universe: Observation of a Spatially-Discontinuous Particle Dynamics beyond Relativity. *Universe* **2018**, *4*, 75.
https://doi.org/10.3390/universe4070075

**AMA Style**

Emelyanov SA.
From Relativistic to Quantum Universe: Observation of a Spatially-Discontinuous Particle Dynamics beyond Relativity. *Universe*. 2018; 4(7):75.
https://doi.org/10.3390/universe4070075

**Chicago/Turabian Style**

Emelyanov, Sergey A.
2018. "From Relativistic to Quantum Universe: Observation of a Spatially-Discontinuous Particle Dynamics beyond Relativity" *Universe* 4, no. 7: 75.
https://doi.org/10.3390/universe4070075