Quantum mechanics

Quantum mechanics is the body of scientific principles that explains the behaviour of matter and its interactions with energy on the scale of atoms and subatomic particles and how these phenomena could be related to everyday.
Classical physics explains matter and energy at the macroscopic level of the scale familiar to human experience, including the behaviour of astronomical bodies. It remains the key to measurement for much of modern science and technology. 

Mathematical formulations
In the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac David Hilbert, John von Neumann,and Hermann Weyl the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors"). Formally, these reside in a complex separable Hilbert space - variously called the "state space" or the "associated Hilbert space" of the system - that is well defined up to a complex number of norm 1 (the phase factor).

Mathematically equivalent formulations of quantum mechanics
There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the "transformation theory" proposed by the late Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics—matrix mechanics and wave mechanics. 

Interactions with other scientific theories
The rules of quantum mechanics are fundamental. They assert that the state space of a system is a Hilbert space, and that observables of that system are Hermitian operators acting on that space—although they do not tell us which Hilbert space or which operators. This "high energy" limit is known as the classical or correspondence limit

1.The standard model
The most developed quantum theory to date is known as the "standard model", and is considered to be the most accurate physical theory ever created. It has been proved to be valid to a very high precision. 

2. Weird and spooky
Some of the phenomena of quantum mechanics, such as entanglement were described by Albert Einstein as "spooky" because, at the sub-atomic level, physics as we think we know it breaks down and becomes almost incomprehensible

3.Core principles
There are a few basic core principles for understanding quantum mechanics and the supposedly spooky oddness that goes on at the level of atoms. It is very important to remember one key thing: quantum mechanics is not classical mechanics. 


The Photoelectric Effect
In the late nineteenth century, James Clerk Maxwell formulated a theory of electromagnetism that described a wide range of electrical phenomena, and in particular described light as an electromagnetic wave. Despite the success of this theory, the early twentieth century found it unable to describe certain aspects of the photoelectric effect.

Quantisation of energy
Prior to quantum theory, energy was thought of as necessarily analogue; taking any value indiscriminately and acting as a smooth transition. In the macroscopic world, this observation remains fairly true. Like a hosepipe that can deliver whatever amount of water you like by turning the tap in small amounts.

Particle-wave duality
Classical mechanics treats particles and waves as different things. A particle is a point, a speck with mass and an exact location. A wave is a little more abstract but it has wavelength - it's spread out, with frequency and speed. In quantum mechanics there is no distinction. Particles can be waves and waves can be particles - although really they're something else entirely with some, but not all, of the properties of both. We've evolved in a macroscopic world where we can see a distinction, but there isn't in the quantum world.

Uncertainty
With the wave-like nature of quantum mechanics established, problems began to arise in figuring out the location of particles. Waves do not have a specific location; they're spread out over an area and aren't described the same way as particles. Thus the "uncertainty principle" was established; in short it means you cannot know the location and momentum of a particle to the same degree of accuracy. 

Interpretations
There are many attempts at intuitive interpretations of quantum mechanics, and a minor industry of physicists coming up with them. These attempt to come up with an intuitive framework to explain the equations - essentially, trying to get them to "make sense" because, frankly, they really don't. 

Copenhagen interpretation
The Copenhagen interpretation, favoured by quantum mechanical pioneer Neils Bohr, envisages that the wavelike behaviour of particles "collapses" upon observation. It proposes that superpositions of states should be taken extremely literally and that a wavefunction is nothing more than an abstract concept that just reflects our uncertainty and lack of knowledge prior to an observation. 

Conscious observation
"Observation," in the sense of the Copenhagen interpretation is really just short-hand for any form of interaction with a quantum system. There are some, however, that seem to take it as requiring conscious observation, i.e., observation by a human mind. This is highlighted in the intentional absurdity of Schrödinger's cat experiment, where the cat and the detector itself act as "observers."

Quantum woo
Quantum physics is a difficult subject and people without science degrees are rarely expected to understand it — even those with the degrees are usually expected to have a working knowledge and not a full appreciation of every aspect of it. Its difficulty is further increased by the fact that, in many cases, there really are no decent lay explanations of how it works, so more accurate and nuanced explanations are lacking in popular science. 

Quantum consciousness
Scientists have some partial understanding of quantum physics but frequently disagree with each other while ordinary people are regularly mystified. Similarly the reason for consciousness is, given current scientific knowledge, impossible to understand.

Applications:
Quantum mechanics had enormous success in explaining many of the features of our world. Quantum mechanics is often the only tool available that can reveal the individual behaviors of the subatomic particles that make up all forms of matter (electrons, protons, neutrons, photons, and others). 

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