• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
Quantum superposition is a fundamental principle of quantum mechanics.
That means that it should clearly define what it is and how it should be measured.
It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states.
This by itself means nothing. First you should define what it is .
Anyway in physics, general speaking, it is difficult to study the state of an object.
Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution.
That also may be true but what have the solutions of the schrödinger equation to do with this?
An example of a physically observable manifestation of the wave nature of quantum systems is the interference peaks from an electron beam in a double-slit experiment.
This is a 'poor' example. Better would be something in the order of:
An example of a physically observable manifestation of the wave nature of a quantum system are positions detected (behind the double slit) from a beam of individual photons in a double-slit experiment.

### 2.1 Examples

For example, consider an electron with two possible configurations: up and down.
My understanding is that an electron has a certain axis of rotation, which is assumed to be stable, but can have any direction in space.
This describes the physical system of a qubit
c1|^> + c2|V>
is the most general state.
That means the chance of measuring up and down, each, is 50%.
This raises the question to what extend we can be sure that the electron keeps this capability.
The probability for a specified configuration is given by the square of the absolute value of the coefficient. The probabilities must add to 1, since the electron must be in one of those two states. ust be in one of those two states.
p up =|c1|^2
p down = |c2|^2
p up or P down = P up + P down = 1
Okay
Continuing with this example, if a particle can be in state up and down, it can also be in a state where it is an amount 3i/5 up and an amount 4/5 down.
|Psi> = 3/5i|^> + 4/5|V>.
This raises the question to what extend you can be sure that the particle can be in a state which is a combination of two state which one has a propability of 3/5 and the other one a probability of 4/5.
Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states" |0> and |1>.
The underlying physical implementation has to be explained. What makes a qubit a qubit.

### 2.2 Analogy with probability

For example, if we have a probability distribution for where a particle is, it is described by the "state"
? x ? ( x ) | x >
Where ? is the probability density function, a positive number that measures the probability that the particle will be found at a certain location.
The major problem is how is this probability density function calculated. See also

### 2.3 Hamiltonian evolution

The numbers that describe the amplitudes for different possibilities define the kinematics, the space of different states. The dynamics describes how these numbers change with time.
Okay
For a particle that can be in any one of infinitely many discrete positions, a particle on a lattice, the superposition principle tells you how to make a state:
Sum over all n, function (psi n|n>
Okay
So that the infinite list of amplitudes ( … , psi - 2 , psi - 1 , psi 0 , psi 1 , psi 2 , … ) completely describes the quantum state of the particle.
That may be true. The question is how are these individual parameters psi n (for n going from - infinity to + infinity) measured and calculated? 'I' have no glue.
This list is called the state vector, and formally it is an element of a Hilbert space, an infinite-dimensional complex vector space.
Here I also have the same question: how are the elements of Hilbert space matrix measured and calculated.
It is usual to represent the state so that the sum of the absolute squares of the amplitudes is one:
Sum over all n, function (psi*n times psi n) = 1
This sentence, by itself, does not give any insight.

### 5 Physical interpretation

It is natural to ask why ordinary everyday objects and events do not seem to display quantum mechanical features such as superposition.
The correct question is: How is superposition established unequivocal.
Indeed, this is sometimes regarded as "mysterious", for instance by Richard Feynman.
He is a clever man.
In 1935, Erwin Schrödinger devised a well-known thought experiment, now known as Schrödinger's cat, which highlighted this dissonance between quantum mechanics and classical physics.
In physics you should never perform a thought experiment.
The result of the Schrödinger's cat depends about the half life time of the radioactive element used. This half life time has first to be established by experiments. To observe which elements have a half-life time approximate 1 second see here: https://en.wikipedia.org/wiki/List_of_radioactive_nuclides_by_half-life#100_seconds
If you perform the Schrödinger's cat experiment in real and you use radium-207 the cat will be dead for sure after 5 seconds. As such it physical does not make sense to call the cat both alive and dead.
One modern view is that this mystery is explained by quantum decoherence.
When you try to do that, you try to explain something that is not clear i.e. superposition, by something that is also not clear.
A macroscopic system (such as a cat) may evolve over time into a superposition of classically distinct quantum states (such as "alive" and "dead").
The same problem: you try to explain something that is not clear i.e. etc, by something that is also not clear.
The mechanism that achieves this is a subject of significant research, one mechanism suggests that the state of the cat is entangled with the state of its environment, when averaged over the possible quantum states of the environment the resulting mixed quantum state for the cat is very close to a classical probabilistic state where the cat has some definite probability to be dead or alive, just as a classical observer would expect in this situation.
Sentence not clear
Another proposed class of theories is that the fundamental time evolution equation is incomplete, and requires the addition of some type of fundamental Lindbladian, the reason for this addition and the form of the additional term varies from theory to theory.
Sorry! Carbage.
A popular theory is Continuous spontaneous localization, where the lindblad term is proportional to the spatial separation of the states, this too results in a quasi-classical probabilistic state.
Sorry! Carbage.

### Reflection 1 - electron in superposition - Physical consideration

What does it mean that an electron is in superposition?
Superposition implies that an object is in two states simultaneous.The cat is both alive and dead.
In 2.1 Examples an electron can have two configurations: UP or DOWN. Which also describes a Qubit.
The concepts Up and Down are related to the spin axis of one electron. The physical situation is that each electron is considered physical identical i.e. that all spin, but that the direction can be any. That means when an atom has 10 electrons they all spin in different directions (My understanding).
Considering

### Reflection 2 - Imaginary numbers

Imaginary numbers are used in mathematics, for example to calculate MandelBrot figures. There are many physical forms in nature which can be described as resembling a Mandelbrot figure, but the explanation of these forms has nothing to do with the mathematics underlying the algorithm to calculate the figure.

### Reflection 3 - double slit experiment.

• The double slit experiment is first performed as a single slit experiment.
In that case we have a source which emits a beam of photons.
A wall which has a an opening or slit.
A screen which consists of an linear array of photon counters or ccd's
The experiment goes as follow:
1. First all the counters are reset.
2. The light source is activated, the photons go through the hole and are counted behind the hole at the ccd's.
3. The light source is stopped.
The results show a sequence of numbers like this: 0 2 5 10 15 20 24 20 15 10 5 2 0
The highest number 24 is behind the single slit.
• The double slit experiment resembles the single slit experiment, but as the name implies in the wall there is not one slit but there are two.
The results show a sequence of numbers like this: 0 5 1 15 9 25 15 25 9 15 1 5 0

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Created: 1 January 2022

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