Quantum mechanics is the theory that we use to describe the microscopic world, which the classical Newtonian mechanical theory is unsuccessful at explaining. The microscopic world is the realm of atoms, photons, nuclei, electrons, neutrons, and a whole host of other subatomic particles. These particles are the “building blocks” of our universe, in the sense that everything that is observable in the macroscopic world that we can see and feel around us is the result of the interactions of these elementary particles.
The initial seed that was to later grow into the quantum theory that we have today was
Max Planck’s postulate that energy is quantised, or comes in discrete packages, as opposed to existing in an infinitely continuous series of states. He put forward this postulate in order to explain the frequency dependence of a black body. CHECK.
MORE ABOUT PLANCK’S CONSTANT HERE.
In 1905, Albert Einstein used the idea of quantised states to explain the photoelectric effect. He explained the observed frequency dependence of the emitted photons by postulating that light energy too comes in quanta. He called these light packets photons.
A paradigm shift was beginning. In 1913 Neils Bohr was able to explain the observed spectral lines of a hydrogen atom by quantising the atom. He postulated that electron/electrons? CHECK surrounding the hydrogen nuclei could only exist in states of certain definite energy, with no electrons ever existing in between these certain energy levels. MORE NEEDED HERE.
And in 1924, Louis De Broglie showed that matter itself had wavelike properties.
MORE HERE.
The explanations put forward by these scientists correctly explained the observed phenomena. A more rigorous theory was soon to emerge, extending and developing the work of Planck, Einstein, Bohr, De Broglie, and others.
In 1927, Werner Heisenberg developed his uncertainty principle, which states that you cannot know both the momentum and position of a particle at the same time with absolute certainty. A more rigorous statement is that you cannot have an eigenstate of a wave function of both momentum and position. CHECK.
And in “DATE”, Neils Bohr formulated an interpretation of quantum mechanics that said that nature itself is inherently deterministic, and the uncertainty in our measurements is not due to the limits of our measureing apparatus, but due to the indeterministic nature of the particles themselves.
MORE HISTORY?
In 1925 the concept of spin was introduced by Ralph Kronig. Spin is the intrinsic angular momentum that a microscopic particle possesses, although the concept of spin is a bit different from what it means in classical mechanics. In classical mechanics, an objects angular momentum is due to its rotation around its central axis, or around an extended axis.
Spin angular momentum in quantum mechanics does not arise from a particle actually spinning like a top, rather it is an intrinsic property of a particle, like its mass. An important thing to note is that spin is quantised. It can only have discrete values. For example, protons, neutrons and electrons are all “spin half” particles, that is, they

have spin values that are one half H BAR SYMBOL, where H BAR = h/2

, and h =
Planck’s constant. A hypothetical particle that will play a large part in the conflict between general relativity and quantum mechanics is the graviton. This as yet undetected particle is a spin two particle, meaning two times H BAR. CHECK.
Let’s look at what quantum mechanics has to say about the fundamental forces. The fundamental forces are: The strong nuclear force, The weak nuclear force, the electromagnetic force, and gravity.
The strong nuclear force is…FILL IN.
The weak nuclear force is…FILL IN
The electromagnetic force is…FILL IN
And gravity is the attraction that all masses feel toward each other. The first three forces have been successfully explained by quantum mechanics as arising from the exchange of sub-atomic particles, “force carriers”. CHECK. For example, the electromagnetic interactions between objects can be explained by assuming quantised photons CHECK are being continually created and destroyed by charged particles, and the interactions between these photons result in the electromagnetic force that objects can feel. MORE THEORY HERE. BE SURE ON FORCE CARRIERS.
Similar force carrier particles are postulated for the strong and the weak nuclear force
DETECTED BY EXPERIMENT YET?
Consistency would indicate that a force particle must also exist for the force of gravity, the graviton. Since the other three forces have been successfully explained by assuming force particles, it makes sense that gravity would also be the result of some particle exchange.
So the graviton was postulated, with the expectation that a quantum gravity theory would quickly pop out, one that is consistent with general relativity. REWRITE.
However this was not to be. Conflicts and inconsistencies soon arose due to the fundamental differences between relativity and quantum mechanics, which will be elaborated on in later pages.
One fundamental difference is that general relativity says that spacetime is warped due to the presence of masses, and the force of gravity is not the result of any particle, but due to the curvature of spacetime. WHAT IS SPACETIME? Thus no force particle is needed in general relativity.
FOR BEGINNING.
A quantum mechanical wave function is…
A quantum mechanical state space of a system is a Hilbert space and the observables are Hermitian observables that act on that space, but do not tell us which Hilbert space or which operators ( Wikipedia/Q.M. )
Correspondence principle.
Quantum field theory is the theory that attempts to unify special relativity and quantum mechanics. Since fields play such a critical role in classical mechanics, a quantum field theory is needed. FIRST SENTENCE, REWRITE.

Quantum field theory is necessary because the schrodinger equation is a nonrelativistic equation, in that it reduces to classical mechanics instead of relativistic mechanics in the correspondence limit.
The schrodinger equation: FILL IN, MAYBE DIRAC NOTATION.
Has the classical kinetic energy term on the left, rather than the relativistic term for kinetic energy.
In quantum mechanics time is thought to have a fixed, non-dynamic structure as opposed to relativity. Time exists as an absolute quantity, like in Newtonian mechanics; it is the background on which quantum mechanical interactions take place. In quantum mechanics time does not vary with differing frames of reference
CHECK. IS TIME CONTINUOUS?
MORE ABOUT WAVE FUNCTION
MORE ABOUT ABSOLUTE POINTS IN SPACE IN Q.M. AS OPPOSED TO G.R.
WHERE IT’S RELATIVE.
“THREE ROADS TO Q. GRAVITY”
MENTION SCHRODINGER EQUATION SOLUTION TO WAVE FUNCTION.
EIGENVALUES ARE QUANTISED ENERGY?
WHEELER DE WITT.
PLANCK LENGTH.