Quantum Mechanics also reveals that the heavier some wave function related observable is, and the faster it moves, the smaller it's wave length.

In Philosophy of Physics: Quantum Theory, Maudlin gives a look into the philosophy of the most unique and peculiar aspect of Physics: Quantum Mechanics, covering specifically, de Broglie-Bohm Theory, G.R.W. Theory, and the Many Worlds Theory.

A main issue is the fact that General Relativity is a system based on Classical Mechanics, yet Quantum Mechanics puts us in a situation where we have to ask, from where does a particle, that can be in two places at once, attain its gravity? The answer to this question is often called a Theory of Everything or a Theory of Quantum Gravity."

The ideas and laws contained within are elegant, and it would seem that they could not be altered without ruining the benefits of them, however, it is possible and necessary to do so, in order to describe events at the atomic scale, which we call Quantum Mechanics.

Quantum Mechanics

The problem, is that Quantum Mechanics, as with gravity, does not quite agree with the classical perspective on time:

Here, we will analyze the best description of matter: Quantum Mechanics.

In QM, time is strict, and not flexible in the way that time is from the perspective of relativity, which states that time is not absolute for two observers, depending on certain conditions.

In fact, with regards to Quantum Mechanics, Physics is already there, with questions about the fundamental nature of time and Space- it would be foolish not to interact with the field built upon people who think and have thought deeply about these very questions.

One of the premiere mathematical structures of Quantum Mechanics is the Hilbert Space. Here, we can think of Hilbert spaces as a state space in which all vectors representing quantum states exist. The difference between these spaces, and typical vector spaces, is that Hilbert space comes equipped with an inner product, an operation that can be performed on two vectors, that returns a scalar.

Within quantum computation, we tend two encounter two types of matrices, Hermitian and Unitary matrices. The former is more related to Quantum Mechanics, but still has some relevance, whereas the latter is the bread and butter of quantum computation.

Quantum Mechanics and Relativity theories, have made obvious how peculiar the nature of time, leaving nothing but paradoxes left in some cases.

In 1926, a theory to explain the new types of behavior observed in electrons, was developed, referred to as Quantum Mechanics.

A main issue is the fact that General Relativity is a system based on Classical Mechanics, yet Quantum Mechanics puts us in a situation where we have to ask, from where does a particle, that can be in two places at once, attain its gravity? The answer to this question is often called a Theory of Everything.

Because it does not conform to Naturalness, or their ideas of beauty in Mathematics, physicists have actually sought to poke holes in Quantum Mechanics, which has one of, if not the best track record of any theory.

The Lagrangian is key in Dirac and Feynman's path-integral formulation of Quantum Mechanics, where the classical action can be used to derive the relative probability amplitude for a path.

That description, of course, is Quantum Mechanics.

The deep irony here is that eventually, Einstein reneged on this very belief of his, refusing to accept Quantum Mechanics, and searching for a Unified Field Theory, despite QM being highly successful with predictions, as well as informative about nature, and despite there being little success with developing a UFT: there were facts of experience set forth by external conditions of the field of science and the associated knowledge that he couldn't incorporate into his conceptual world, and thus likely missed out on potentially many more opportunities to put his mark on science via taking great strides forward, where the pathways were clearer, and less obstructed.

Paul Adrien Maurice Dirac, was one of the fathers of Quantum Mechanics, and mathematically, balanced upon a ”dizzying path between genius and madness”.

[Hilbert Space] was established systematically by von Neumann, summarized in his book. The book was based on three papers, published in 1927. Of these three papers, the first introduced the notion of abstract Hilbert space, and presented the "eigenvalue problem", of self-adjoint operators having a continuous part in their spectrum, in a mathematically rigorous form, without making use of Dirac's delta function. The complete, analysis of the spectral theorem was worked out in a following paper in 1930.

Quantum Mechanics entertains the notion of Superposition, with regards to states (of systems) that bear information, and the real utility of this must be understood. Parallelism in Quantum Computation is one potential application, and will be critiqued.

Quantum Mechanics

Max Born, one of the fathers of Quantum Mechanics, stated "...Statements like a quantity x has a completely definite value (expressed by a real number and represented by a point in the mathematical continuum) seem to me to have no physical meaning ".