As has been pointed out in this thread there are various interpretations of quantum mechanics including deterministic ones such as the Many Worlds Interpretation which states we are stuck with only one possibility as all other alternatives exist in other universes which are unobservable in our own.
The mathematics of quantum mechanics is based on linear algebra and Hilbert Spaces.
With a central electrostatic Coulomb potential applied to the hydrogen atom, the resulting model gives accurate energy level predictions supported by experimental evidence.
While the mathematics gives us an appreciation of quantum mechanics, understanding the reality of quantum mechanics is extremely difficult if not impossible to grasp leading to the various interpretations.
Quantum mechanics is a mathematical model for reality, it explains ‘how’ the model works not ‘why’ it works which is consistent with science which is about addressing the ‘how’ and not the ‘why’.
In the mathematics you have observable quantities like energy and momentum which are represented by linear operators acting on the Hilbert space, then there are the eigenvalues and eigenvectors which represent the measured value and the state respectively.
The operator A acts on the eigenvector |Ψ> which gives the eigenvalue λ according to the general equation.
A|Ψ> = λ|Ψ>
|Ψ>= Σ λₙ|Ψₙ> which defines the Hilbert space.
In the mathematics there is no observer doing the measuring, in the resulting physics the observer doesn’t have to be a person, it can be a device.
Erwin Schrödinger believed quantum mechanics was deterministic and his cat thought experiment was a dig against it being probabilistic as advocated by Heisenberg and others by illustrating the absurdity of applying quantum mechanics to objects on a macroscopic scale.
The probabilistic interpretations of quantum mechanics could lead to nonsensical situations when scaled up from subatomic particles to macroscopic systems.
The mathematics of quantum mechanics is based on linear algebra and Hilbert Spaces.
With a central electrostatic Coulomb potential applied to the hydrogen atom, the resulting model gives accurate energy level predictions supported by experimental evidence.
While the mathematics gives us an appreciation of quantum mechanics, understanding the reality of quantum mechanics is extremely difficult if not impossible to grasp leading to the various interpretations.
Quantum mechanics is a mathematical model for reality, it explains ‘how’ the model works not ‘why’ it works which is consistent with science which is about addressing the ‘how’ and not the ‘why’.
In the mathematics you have observable quantities like energy and momentum which are represented by linear operators acting on the Hilbert space, then there are the eigenvalues and eigenvectors which represent the measured value and the state respectively.
The operator A acts on the eigenvector |Ψ> which gives the eigenvalue λ according to the general equation.
A|Ψ> = λ|Ψ>
|Ψ>= Σ λₙ|Ψₙ> which defines the Hilbert space.
In the mathematics there is no observer doing the measuring, in the resulting physics the observer doesn’t have to be a person, it can be a device.
Erwin Schrödinger believed quantum mechanics was deterministic and his cat thought experiment was a dig against it being probabilistic as advocated by Heisenberg and others by illustrating the absurdity of applying quantum mechanics to objects on a macroscopic scale.
The probabilistic interpretations of quantum mechanics could lead to nonsensical situations when scaled up from subatomic particles to macroscopic systems.
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