# On Ontological Alternatives to Bohmian Mechanics

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## Abstract

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## 1. Introduction

## 2. Bohmian Mechanics and the Microrelational Interpretation in a Nutshell

## 3. Relational Entities

#### 3.1. Mathematical Relations

- One node has four neighbors.
- One node has two neighbors.
- One node has only one neighbor, which has three neighbors.
- One node has only one neighbor, which has four neighbors.
- One node has three neighbors of which one has one neighbor.
- One node has three neighbors of which one has two neighbors.

#### 3.2. Relational Space

#### 3.3. “To Be” in a Relational Space

#### 3.4. Complex Valued Relations

- In a neural network, the directed link between two nodes (which in this case are referred to as neurons) has a weight (the synaptic weight) which determines the transmission intensity of a signal. Negative weights indicate inhibitory influences. As the network is directed, the connection between two nodes is specified by two real-valued weights that can be combined into a complex number. These weights change over time as a result of learning.
- In so-called spiking neural networks, the signal consists of a firing rate (the number of spikes per unit of time) that is transmitted from one neuron to another. The time scales on which these firing rates change are much shorter than the time scales for changes in the synaptic weights, so that the synaptic weights can roughly be considered as constant. The connections (the synapses) between neurons are directed, but it often happens that connections exist in both directions. In addition, firing can occur in a synchronized way between clusters of neurons or asynchronous. Thus, the relative phases in spiking neurons can be important.
- On large scales (averaging over several hundreds of neurons), the activity in neural networks is sometimes described by a complex field (see, e.g., [27,28]). Together with David Bohm(!), the famous neuroscientist Karl Pribram developed a quantum field theoretic approach to consciousness [29], which was related to Bohm’s ideas of an implicate and explicate order [30].

## 4. One-Particle Quantum Mechanics

#### 4.1. The Generalized Relational Structure of “Location”

#### 4.2. The Dynamics of Relations

#### 4.3. The Double-Slit Experiment and “Sum over Histories”

#### 4.4. Measurements

#### 4.5. An “Every-Day” Example for Measurements and the Collapse

## 5. Many-Particle Systems and Entanglement

#### 5.1. General Remarks

#### 5.2. Relations for Two-Particle Systems

- Relations between spatial entities: these are considered to be non-directed and give rise, on a large scale, to the geometry of space.
- Relations between “particles” and spatial entities: these relations maybe directed and give rise, on a large scale, to the wave function.
- Relations between “particles”: These relations are present if the particles are entangled. They allow for a direct information transfer between particles and characterize the form of entanglement.

#### 5.3. Local or Non-Local, That Is the Question

## 6. Relational Space-Time—Relational Events

## 7. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A set with six points and undirected relations. In this case, the relations allow a unique identification of the elements.

**Figure 2.**The location of an object p in a relational structure is defined by the spatial points to which it is related. Equivalently, one can specify this relation by the characteristic function of this set of spatial points. If the relations of the object to ‘space’ are directed, we can specify it by two characteristic functions.

**Figure 3.**In a relational framework, a particle can be at two locations simultaneously. In the given example, the object p “is” at the points x and y simultaneously.

**Figure 4.**Propagation of relations: only via the intermediate step (

**b**) can the additional relation in (

**c**) be created from the relational space (

**a**).

**Figure 5.**In the double-slit experiment, the total amplitude can be obtained by assuming that aparticle propagates along path 1 AND path 2. In the micro-relational interpretation, the relations of a particle propagate along path 1 and path 2.

**Figure 6.**A server connected to a periphery of counters with printers is a model for a measurement in a relational system. A boarding pass exists only virtually as a program instruction in the server. Only when an e-ticket number is presented at a counter—this is the measurement—does the boarding pass become reality at the printer of this counter.

**Figure 7.**(

**left**) two objects in a relational structure. Each object has its own set of relations to the spatial points. The relations factorize; (

**right**) there can also be a direct relation between the two objects. This may lead to entanglement.

**Figure 8.**When there are several objects (in this case two), we have three different types of relations: (1) relations among spatial points, (2) relations between “particles” and spatial points, and (3) relations between the “particles”.

**Figure 9.**(

**left**) the events making up the canvas of “space-time” are endowed with a causal structure; (

**right**) a physical, object-related event can be related to the events of “space-time” in three different ways: It can be causally influenced by events in its past, it can influence events in its future and there may be “space-like” relations to events that are in the causal complement. The distinction between “space-like” events and time-like or light-like events depend on the real and imaginary parts of causal Green’s functions.

**Figure 10.**The lowest order approximation of a Coulomb scattering of two electrons by an exchange of a (virtual) photon. The points ${x}_{i}$ are kept fixed while one has to integrate over all possible positions of the intermediate events at ${y}_{1}$ and ${y}_{2}$.

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Filk, T. On Ontological Alternatives to Bohmian Mechanics. *Entropy* **2018**, *20*, 474.
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Filk T. On Ontological Alternatives to Bohmian Mechanics. *Entropy*. 2018; 20(6):474.
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Filk, Thomas. 2018. "On Ontological Alternatives to Bohmian Mechanics" *Entropy* 20, no. 6: 474.
https://doi.org/10.3390/e20060474