Аннотация: Instead of a differential equation, a program is proposed that becomes a physical justification for the neural picture of the world. If the simplest physical object is a fragment of a neural network, then the entire Universe is also a neural network. Just a little more than simplest object.
Schrödinger's equation in the neural picture of the world
A. V. KARASEV
Instead of a differential equation, a program is proposed that becomes a physical justification for the neural picture of the world.
The Schrödinger equation in neural terminology is written in [1]. However, there I tried to write it for a spin 1/2 particle in three-dimensional space. This in itself is not bad, but it would also be nice to write the Schrödinger equation in the simplest case - for a quantum object with 2 basic states. For example, this is a beam of light separated by a translucent mirror. Or an electron beam split in two by a magnetic field along the spin projection.
This discussion will help to understand the very essence of neural terminology in quantum mechanics, without being distracted by trifles - spin and space.
So. In the neural picture of the world, a separate particle, by itself, IS NOT CONSIDERED AT ALL. Only the object of research is considered as a whole, in conjunction with a source of particles and a device that measures their states. For a particle in two states, this device consists of two counters that count the particles. In neural terminology, such counters are represented by such fragments of a neural network, in which the minimum input signal is branched and multiplied into a sufficiently powerful output signal, which is observed at the macroscopic level in the form of, for example, the click of a counter or the movement of an arrow on a measuring scale.
The source of particles for this device will be represented as an input neural connection. Ideally, this connection should be the only one - after all, in physics we want to study a certain object by itself, in isolation from the rest of the world. That is, a fragment of a neural network representing a quantum object under study must have a single input thread from the rest of the neural network of the Universe.
Wave function of an object
Ф (t) = a Ф1 (t) + b Ф2 (t)
Schrödinger equation
Ф (t + dt) = S (t) Ф (t)
where S (t) = 1-i / h H (t) - (Hamiltonian)
Let's write out this equation in detail, for subsequent comparison with neural terminology.
Ф1 (t + dt) = <1│s│1> Ф1 (t) + <1│s│2> Ф2 (t)
Ф2 (t + dt) = <2│s│1> Ф1 (t) + <2│s│2> Ф2 (t)
In neural terminology, the state of an object is specified by a vector of neural signals - an analogue of the amplitude of the wave function. It is convenient to represent this vector in the form of an SQL table.
AMP - Table Name (Probability Amplitude)
names of columns:
Rel - identifier (address) of the neuron. (1 or 2)
S = + or - 1 - neuron signal
Im = 1 or i is the imaginary unit
For example, if the AMP table for Rel = 1 contains P1 rows with Im = 1 and Q1 rows with Im = i, this means that the excitation amplitude of counter 1 is
F1 = P1 + iQ1
S-matrix corresponds to the matrix of connections between neurons of the network:
SHK - Table name (matrix of connections between neurons)
Columnes names:
Rel1 - is the identifier of the first neuron.
Rel2 - is the identifier of the second neuron.
S + or - 1 - connection of neurons
Im - 1 or i is the imaginary unit
Here we mean that the signal comes from the first neuron (Rel1) to the second (Rel2). As a result, the connection between these two states is expressed by the number of identical rows in this table - a complex number equal to <2│s│1>.
For a neural network, a new state is expressed not by a differential equation, but by a command - to compose a new table Amp for one step of a virtual neural network, the columns of which are filled in as follows:
Select
Shk.rel2 - the rel graph is filled with the address of the second neuron from the Shk table
, Shk.S * Amp.S - the graph S is filled with the product of the graph S from the tables Shk and Amp
, Shk.Im * Amp.Im - the graph Im is filled with the product of the graph Im from the tables Shk and Amp
from Shk, Amp - for all combinations of records from these tables
where Shk.rel1 = Amp.rel - for which the address of the first neuron of the Shk.rel1 table is equal to the address of the neuron of the original table Amp.
So, after this step of the virtual neural network, we got a new table Amp. But with it, you need to perform one more operation, equivalent to summing the amplitude - from the new table Amp, lines with the same addresses, but different values of the signal sign - the graphs S are deleted in pairs (and there, in fact, only the sign is - S = + or - 1). As a result, only rows remain in this table for which there are no more pairs with the opposite sign. The number of these remaining lines determines the sum of the signal (positive, negative or zero) at the input of the neuron.
As a result, we get a completely identical expression
Ф1(t+dt) = <1│s│1> Ф1(t)+ <1│s│2> Ф2(t)
Ф2(t+dt) = <2│s│1> Ф1(t)+ <2│s│2> Ф2(t)
The probability of an event should be determined by the square of the modulus of the amplitude. In neural terminology, for this you need to take the same Amp table 2 times and create a new table that will be the event probability spectrum:
Select
From Amp A, Amp B
- Select all combinations of records from two identical copies (A and B) of the Amp table,
Where A.rel = B.rel - which have the same neuron identifiers
and A.Im = B.Im and imaginary unit graph
As a result, if the Amp table contains N records with some value of the identifier Rel, for which Im = 1 and M records for which Im = i, then in the final table of the probability spectrum, for the excitation of this neuron there will be N² + M² records, which corresponds the square of the modulus of a complex number - ׀ Ф (t) ׀².
One row is equally likely selected from the spectrum table, which determines which of the neurons will be fired.
If a neuron (for example, the first one) is excited, this means that a command like reduction will pass through the entire neural network
Update Amp Set rel = 1
That is, the state of the object changes abruptly - in the Amp table there will be only records with the address of the first neuron. This is a reduction.
Of course, it makes no sense to solve applied problems in such a program. Writing the Schrödinger equation in neural terminology is not intended for solving problems, but for the physical foundation of extrapolation of the neural worldview from a physical laboratory to a new understanding of the Universe and the place of personality in it [2-3].
That is, the state of the object changes abruptly - in the Amp table there will be only records with the address of the first neuron. This is a reduction.
Of course, it makes no sense to solve applied problems in such a program. Writing the Schrödinger equation in neural terminology is not intended for solving problems, but for the physical foundation of extrapolation of the neural worldview from a physical laboratory to a new understanding of the Universe and the place of personality in it [2-3].
Literature
1. Karasev A.V. Three-dimensional space and electron spin in neural terminology. Quantum Magic, 2011, volume 8, issue. 2.http: //quantmagic.narod.ru/volumes/VOL822011/p2168.pdf
2. Karasev A.V. How the neural picture of the world differs from speculation on the topic - we live in a computer. http://samlib.ru/k/karasew_a_w/otl_nkm.shtml
3. Karasev A. V. Neural picture of the world. Bulletin of new medical technologies. 2002.vol. 9.N 2.http: //samlib.ru/k/karasew_a_w/nkmfs.shtml