Complexity Classes
Complexity Classes courtesy Wikipedia

P≠NP Problem

The Astounding Link l the P≠NP Problem and the Quantum Nature of Universe. How can a particle be decaying and not decaying at the same time? Quantum mechanics does not allow that to happen.

As Doug Gill pointed out in a Facebook post, “The half-silvered mirror experiment (illustrated in Penrose’s book – Shadows of the Mind) gives the simplest explanation of why a quantum state cannot be superposed for a classical cat. The very fact of the cat (as a classical-level disturbance) interferes in a quantum state means that it will be collapsed to classical. As soon as the cat, as a detection device, interferes on one of the paths of the superposed photon, the photon will collapse to one of the paths. Every EPR experiment supports this conclusion. For the radioactive particle version, the cat has no effect on when the quantum state will collapse. What is not understood on the relationship between correlated quantum and classical states is that each constitutes a separate level of dimensional complexity. At the quantum level, “time” in the classical sense is not supported as separate. Rather it is the direction in the space associated with (square root -1). True “orthogonality”, at 90 degrees, does not exist – instead, it is 180. Both time, at the classical level, and sqrt-1 are imaginary…”

“…Great to hear someone with similar thoughts on this. There is a very large caveat with accepting that “orthogonality” is not fixed dynamically (and mathematical representation is fixed as consistent). Mathematics must have consistency. To explain, using a very simple reference to the Argand plane, mathematics navigates this issue very successfully by just assigning [sqrt -1] to the y-axis. the problem is that to get back to a classical version of the unit circle you have to use a squaring operation. The import of this is that the quantum and classical states do not share a common dimensional framework. They have paradoxical constructions. Introduction of sqrt-1 confirms this (it is internally paradoxical to the classical definition of square root). The short of this is that the process of dimensional development in the universe (as a process) and the mathematical tools we have to represent it … are paradoxical! (the exclamation symbol is appropriate). This shows up when we attempt to represent infinity in our formulae. Our representations fail.” Click this link to go directly to this facebook thread.

If you do not understand the P≠NP problem, then you need to learn some quantum physics or you need a refresher in quantum physics, to start with.

Let’s start with the quantum mechanical operators, mathematical formalism and experimental and quantum mechanical 2 state vector mathematical physics.

Quantum 2 state vector:

Bra-ket (pronounced bra the same as bra is pronounced in the word bracket and ket is pronounced the same way that the ket in the word bracket is pronounces) is a quantum mechanical two-state vector which is symbolically written as:


Sabine Hossenfelder: Understanding Quantum Mechanics: It’s not so difficult!

where the bra state <Φ| evolves backwards from the future (-t) and the ket state |Ψ> evolves forwards from the past (+t).

Click here to learn more about student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations after 7 semesters of undergraduate and graduate level quantum physics 1 at 4 universities.

Two-state vector formalism (Wikipedia)

If you want to learn more about notational quantum 2 state vector’s +t and -t mathematical directionality in space using Dirac notation (<Φ||Ψ>) then click here to download this excellent PDF file. 

Experimental and Quantum Mechanical 2 State Vector Mathematical Physics:

Click here for experimental quantum 2 state vector notation mathematical physics PDF format file download.

If you want to learn even more about quantum 2 state formalism then I recommend downloading Quantum Physics II, Lecture Notes 2 – MIT OpenCourseWare PDF by clicking here.

I will be adding more to this article.

Keep checking back….

Written by Rickey Estes