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. WHAT IS QUANTUM BEHAVIOUR?
First, 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 phenomena of blackbody
radiation. He postulated that an electromagnetic wave can only interact with matter in
integer multiples of h, where  is the frequency of the wave, and h is a quantity
known as Planck’s constant. Planck’s constant has a value of h = 1.05457  10-34 Js,
which is an extremely small number, and it is because the value of Planck’s constant
is so small that we don’t ordinarily notice any of the behaviour associated with
quantum mechanics in the macroscopic world around us. Only by probing the
microscopic world do we encounter the strange and mystifying behaviour of subatomic particles.
In 1905, Albert Einstein used the idea of quantised states to explain the photoelectric
effect. He explained the observed frequency dependence of the emitted particles by
postulating that light energy too comes in tiny discrete bits, or quanta. These discrete
light packets, or photons, also come in integer multiples of h, with  here being the
frequency of the light.
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 atoms
could only exists in states of discrete energy, and that any interaction between a
hydrogen atom and any surrounding radiation could only happen as integer multiples
of h. For example, the hydrogen atom can only be raised to the first excited energy
state from it’s ground state if it absorbs exactly one times h. Likewise it can only be
raised to it’s second excited state from it’s ground state if it absorbs exactly two times
h, and so on. Bohr’s quantisation of the hydrogen atom successfully explained the
problems that the classical model could not.
In 1924, Louis De Broglie showed that matter itself had wavelike properties. He
derived the equation,  = h/p, that related a particle’s momentum with an associated
wavelength. This equation tells us that all matter has wavelike properties, and must in
some cases be thought of as existing as a wave, rather than as a discrete particle.
The explanations put forward by these scientists successfully explained many
outstanding problems, and only by assuming quantised states. However these
explanations were not based on any underlying theory, instead seeming to be quite
arbitrary explanations for the PROBLEMS REWRITE. A more rigorous theory was
needed, and soon emerged, extending and developing the work of Planck, Einstein,
Bohr, De Broglie, and others. This theory came to be known as quantum mechanics.
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.
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.
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. )
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.
And 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 , where  = 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 . CHECK.
END OF HISTORY.
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 has been determined after much
smashing of particles together 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.
Every interaction in the known universe can be explained by the exchange and effect
of force particles.
A wonderful and elegant discovery relating to forces has been 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. It is a very short range force, with it sphere of influence FILL IN.
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. SPHERE OF INFLUENCE? 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.
Consistency would indicate that a force particle must also exist for the force of
gravity, and has been dubbed 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. For example, a planet circling the sun appears
to be in orbit due to the gravitational force exerted by the sun, but general relativity
tells us that the planets motion is FILL IN. Thus no force particle is needed in general
relativity. The nature of spacetime will be explained in the general relativity section
of this website.
An interesting thing happens when we try to probe the microscopic world at greater
and greater levels of magnification; space becomes more and more turbulent, or
frothy. Space loses its “smoothness” in that any values we measure for
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.
CORRESPONDENCE LIMIT.
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.