Quantum theory consists of a mathematical formalism together with a vast amount of information
concerning how to apply that formalism to electrons, atoms, radiation, field, etc.
As an instrument for predicting the results of experiments, it is enormously successful.
However, despite this, it says little if anything about the electrons, and such that produce
the results.
From its inception, it has been a theory in search of an interpretation.
In order to understand where the ideas of the Quantum world came from it is important
to understand the strange discoveries and see the connection between photons and matter.
In 1859 Gustav Kirchoff proved that the energy emitted from a blackbody depends only on the
temperature and the frequency of the emitted energy.
He wrote the formula as follows, where E is the energy, T is the temperature and v the
frequency of the emitted energy.
He then challenged physicists to find the function J.
Twenty years later Josef Stefan performed a number of experiments and based on these
he proposed that the total energy emitted by a hot body was proportional to the fourth
power of the temperature.
Five years later and totally independently Ludwig Boltzmann would reach the same conclusion
using thermodynamics and Maxwell's electromagnetic theory.
Today we know the results of these two ideas as the Stefan-Boltzmann law.
The problem is that it does not fully answer Kirchoff's challenge as it does not address
specific wavelengths.
In 1896 Wilhelm Wien proposed a solution to Kirchoff's challenge.
His experimental results would show that for small values of the wavelength it matched
extremely well but for anything, in the far infrared it did not.
When Max Planck saw the experimental results he made the outrageous guess that the total
energy was made up of indistinguishable energy elements, or quanta of energy.
He was not entirely happy with this guess.
Not for the first time theory had now deviated from experiment and was based on a hypothesis
with no experimental basis.
In 1905 Einstein proposed a quantum theory of light based on experiments of the photoelectric
effect.
The experimental results disagree with classical electromagnetism, which predicts that continuous
light waves transfer energy to electrons, which would then be emitted when they accumulate
enough energy.
If there was a subsequent change in the intensity of the light there should theoretically be
a change in the kinetic energy of the emitted electrons.
If the light source was sufficiently dim it should cause a delay in emission.
The experiments showed that electrons are dislodged only when the light exceeds a certain
frequency, regardless of the light's intensity or duration of exposure.
This demonstrated that light could not be treated as a simple wave but instead a swarm
of discrete packets known as photons.
Einstein realised that the energy changes occur in a quantum material oscillator in
jumps which are multiples of hv where h is Planck's reduced constant and v is the frequency.
In 1913, Niels Bohr proposed a new model of the atom and would explain the spectral lines
of hydrogen using the idea of quantisation.
In his model, the hydrogen atom is pictured as a heavy positively charged nucleus orbited
by a light, negatively charged electron.
The electrons are only able to exist at specific locations or orbits determined by their angular
momentum which is restricted to be an integer multiple of the reduced Planck constant.
Emission lines would be explained by the transition of electrons between orbits.
Based on Bohr's model and Planck's quantum theory it allowed for the calculation of the
electron's magnetic moment.
The problem was that these theories were not derived from first principle and there was
no justification for why quantisation would occur in the first place.
In 1923 Louis de Broglie put forward a theory which would allow particles to exhibit wave
characteristics and waves to exhibit particle characteristics.
It was derived from Special Relativity and based on a single particle.
Two years later in 1925, Werner Heisenberg presented a treatment of electron behaviour
based on discussing only 'observable' quantities, meaning the frequencies of light that atoms
absorb and emit.
Based on this Max Born made the leap that the classical variables of position and momentum
would instead be represented by matrices.
Erwin Schrodinger presented an equation that treated the electron as a wave, and Born discovered
that the way to successfully interpret the wave function that appeared in the Schrodinger
equation was as a tool for calculating probabilities.
In 1927 Heisenberg formulated an early version of the uncertainty principle.
He created this by analysing a thought experiment where an attempt is made to measure an electron's
position and momentum simultaneously.
At this point, no definition was given about what the uncertainty actually meant in the
measurement.
That same year Paul Dirac made an incredible leap in unifying quantum mechanics with special
relativity by proposing the Dirac equation for the electron.
It achieved the relativistic description of the wave function of an electron that Schrodinger
failed to obtain.
It also predicted electron spin and the existence of antimatter or more specifically the anti-electron
or positron.
Heisenberg had been an assistant to Niels Bohr at his institute in Copenhagen, where
they helped formulate the theory of quantum mechanics.
At the 1927 Solvay Conference, a dual talk by Max Born and Heisenberg declared "We consider
quantum mechanics to a closed theory, whose fundamental physical and mathematical assumptions
are no longer susceptible of any modification!"
In 1929, Heisenberg gave a series of invited lectures at the University of Chicago explaining
the new field of quantum mechanics.
These served as the basis for his book 'The Physical Principles of Quantum Theory'.
This would be published the following year in 1930.
In the preface Heisenberg wrote the following: "On the whole, the book contains nothing that
is not to be found in previous publications, particularly in the investigations of Bohr.
The purpose of the book seems to me to be fulfilled if it contributes somewhat to the
diffusion of that 'Kopenhagener Geist der Quantentheorie' if I may so express myself,
which has directed the entire development of modern atomic physics."
The irony is that this implies something more than just a spirit and the fact is that the
writings of Bohr and Heisenberg contradict each other on several important issues.
Bohr and Heisenberg never totally agreed on how to understand the mathematical formalism
of quantum mechanics, and Bohr distanced himself from what he considered Heisenberg's more
subjective interpretation.
Bohr offered an interpretation that is independent of a subjective observer, or measurement,
or collapse.
Instead, an irreversible process caused the decay of quantum coherence which imparts the
classical behaviour of observation or measurement.
Bohr also disagreed on wave-particle duality.
He felt that the type of experiment and its setup would determine whether the result was
a particle view or a wave view.
Heisenberg thought that every mathematical formation was capable of both wave and particle
interpretations.
There is no uniquely definitive statement of the Copenhagen interpretation.
The term encompasses the views developed by a number of scientists and philosophers during
the second quarter of the 20th century.
It contains a set of rules of thumb for relating the elements of theory to what can be observed
in the laboratory.
Some of the high-level principles can be described as follows:
1.
Quantum mechanics is intrinsically indeterministic 2.
The correspondence principle.
This states that the behaviour of systems reproduces classical physics in the limit
of large quantum numbers.
So for large orbits and for large energies, quantum calculations must agree with classical
calculations.
3.
The Born rule.
In its simplest form, it states that the probability density of finding a system in a given state,
when measured, is proportional to the square of the amplitude of the system's wave function
at that state.
The wave function is not directly observable; however, it gives the probability that, when
a measurement is made, you will find the system in a particular state.
These systems can be elementary particles such as electrons, protons, atoms or even
larger molecules.
Upon measurement, the wave function and its probabilities collapse to the measured value.
4.
The collapse of the wave function.
In the act of measurement, the wave function of a system can change suddenly and discontinuously.
Prior to the measurement, the wave function includes the probabilities for the different
potential outcomes of that measurement.
Once the measurement is made, no traces of the other remain.
5.
There is no reality aside from the calculation of probabilities.
There is no underlying deterministic later; there is no hidden machinery that registers
what will be measured before the measurement is taken.
These probabilities do not reflect our lack of knowledge, as in classical statistical
physics, because there is nothing to have knowledge about.
There is only probability.
What the Copenhagen interpretation says is vague, obscure, and maybe even inconsistent.
Nevertheless, it became the orthodox interpretation and has been taught to generations of physicists
as the only correct way to think about quantum theory.
It is vague in that it does not tell us exactly which interactions are measurements.
And yet its laws specify that non-measurements evolve through Schrodinger's laws and measurements
a different way through the collapse.
The exact boundary between the quantum mechanical world and the classical is also left unspecified.
It is obscure in the way that it asserts that a particle can possess a determinate velocity
but no determinate position, or vice versa.
The relationship between measurement and determinate reality is especially obscure.
Why does a measurement initiate a collapse, making it determinate?
A measurement of a part of a system at one location can instantaneously change the physical
situation of far-distant parts of that system.
It is inconsistent in that on the one hand it makes assertions about the nature of quantum-mechanical
reality while, on the other hand, it denies that anything can be known about that reality.
One of the statements made in the Copenhagen interpretation is that an object does not
have a definite value before being measured.
Elsewhere it mentions that states are probabilistic and therefore it is only possible to talk
about probabilities before measurement.
This is very different from saying it has NO definitive value.
Let's just consider an unstable atom.
If we never observe its decay, does that mean it does not have a decay status?
It also says nothing about what counts as a measurement.
Does it have to be conscious?
A common assumption is that the measurement device must be outside the system.
At first, this makes perfect sense.
If we consider 1 particle, then we would expect to find a wave function of that one particle.
The wavefunction function essentially maps the energies, momenta and locations of the
particle into another dimension, the axis of the wave function.
As we increase the particles in the system this wavefunction would hold the information
of these multiple particles within it.
This essentially contains all possible configurations of a system.
In theory, it would be possible to create a wave function that contained every single
particle in the universe.
In this case, if we wanted to measure it we would have to be outside the system, but in
this case, that is the universe.
So in order for the wavefunction of the universe to collapse someone outside the universe would
have to measure the universe.
How would you then measure the measurer in that case?
You would once more need someone outside that system.
This leads to an infinite regression.
Saying that what happens before we measure is not relevant as we are not measuring that
is self-defeating.
Quantum mechanics talks about probabilities before measurement so we cannot simply ignore
this.
The problems go deeper than this - down to a metaphysical level.
The idea that observation would create a different kind of reality than the one that existed
before was something that Einstein found wholly unacceptable.
Reality somehow existed in a different way while under observation than it did in itself.
Is there an escape from the quantum realm?
Are there alternative theories of Quantum Mechanics that approach the problem in a different
way and yet still provide the same results?
In the next part, this is exactly what we will examine.