REWRITE INTRO TO SOUND BETTER.
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 presence and interactions of
these elementary particles.
A LITTLE HISTORY
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.
END OF HISTORY.
BASIC QUANTUM DEFINTIONS HERE.
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. We
have known since Newton’s time what forces are. A force can basically be defined as
something that causes the state of an object to change; whether it is a change in the
object’s motion, temperature, electrical charge, or potential energy, a force is
responsible. However Newtonian mechanics does not specify any mechanism by
which force is transferred, except in the most basic sense. It tells us that when an
object is in contact with another you have some force between them. Newton’s laws
tell you what the effect of a force is, and how to calculate the magnitude of a force,
but they do not have much to say about what actually happens at the microscopic
level when forces act, the actual mechanism by which a force acts.
Quantum mechanics gives us that mechanism. It says that forces are the result of the
exchange of force particles that transfer force from one object to another. FORCE
FIELDS HERE, MORE ABOUT FORCE PARTICLES. WHAT THEY ARE.
It has been discovered that all interactions between objects can be reduced to the work
of four fundamental forces. Those fundamental forces are:
The strong nuclear force, The weak nuclear force, the electromagnetic force, and
gravity.
The strong nuclear force is the force that holds together protons and neutrons in an
atomic nucleus.
The weak nuclear force is responsible for things like radioactive beta decay, which is
when a neutron turns into a proton, with an electron and an anti-neutrino being
emitted in the process. MORE MAYBE.
The electromagnetic force is the force that acts between electrically charged particles.
This includes all electric and magnetic forces which arise from the motion of charged
particles, and also from stationary electric charges. This force is responsible for most
of the phenomena we see around us, such as light, friction, and the structure of
elements and molecules. This force can be both attractive and repulsive.
Gravity is the attraction that all masses have for each other. It is the weakest of the
four forces, but it is always attractive, and has the longest range of all the forces.
Every interaction in the known universe can be explained by the exchange and effect
of force particles.
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? NECESSARY?
WHEELER DE WITT.
PLANCK LENGTH.