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Introduction to the strange world of Quantum Physics

Terminology Note: Quantum physics, quantum theory, quantum mechanics and wave mechanics all refer to the

same field of study in physics. Quantum physics deals with the world on microscopic level.

The discovery in the 1920s of quantum theory bought about the biggest revolution in physics since the time of Isaac

Newton. To understand the full impact of quantum theory we also need to have an understanding of the important

features of what is known as classical physics.

A health warning: “Anyone who can contemplate quantum mechanics without getting dizzy hasn’t understood it.”

– Niels Bohr

Classical Physics

A Brief History of Classical Physics:

Newton published his volume on physics called principia (three editions between 1687-1726) and

established the field of physics called ‘mechanics’ which enabled scientists to describe the motion of objects

using mathematical techniques.

James Maxwell towards the end of 19th century found it was possible to link electricity and magnetism

together in one set of mathematical equations even though electricity and magnetism appeared different in

nature. Maxwell realised that his mathematical equations for electromagnetism have solutions which were

wave like and the velocity of these waves was the speed of light. It was demonstrated that light was made

up of electromagnetic waves.

The theories of Newton and Maxwell are the two main theories on which all of ‘classical physics’ (as it is now

known) is built. Their descriptive power was so great that at the end of the 19th century it was thought that

all the major problems in physics had been solved and it was just a matter of using the existing theories to

describe the world with greater and greater accuracy.

Characteristics of Classical Physics:

In Newton’s mechanics, the laws of motion are written in terms of particle trajectories.

There are no restrictions on the values of physical properties (e.g. energy, speed, position etc.) that

something can possess. Quantities are allowed to vary continuously.

Physical quantities such as velocity and location can all be known with arbitrary precision – you just have to

make better measurements.

There are two basic physical phenomena in classical physics which are mutually exclusive. Objects can either

have the form of an extended field (or wave) or a localised particle but not both. Fields (or waves) and

particles are different and independent phenomena, however they can interact with each other e.g.

electromagnetic wave interacting with a charged particle.

The interaction of fields tails off with distance and therefore classical physics is essentially a locally based

theory which means an object can only be affected by things it’s the immediate neighbourhood.

Classical physics is a completely deterministic view of nature. If you know the values of all physical quantities

describing a situation then you can accurately say what the values of the physical quantities would be at

some later point in the future AND you could say what they would have been at some point earlier in the

past. There is a casual link between past, present and future.

o e.g. using Newton’s second law of motion: Force = mass x acceleration

o IF you know all: particle masses, particle positions and velocities at specific time and the forces

acting on all particles at all times.

o THEN you can predict the motion of the particles accurately for all time.

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o The picture of a clockwork universe: A link to deism. God set the universe in motion and then leaves

it on its own.

The quantum revolution

However cracks began to appear in the classical physics picture of the world:

Physicists studying the behaviour of what is known as a ‘black body’ using classical physics found a disturbing

problem with their mathematical predictions. A black body in physics is one which is a perfect absorber, it

absorbs all electromagnetic radiation that falls on it and then re-emits it. Classical physics predicted a black

body should emit at infinite intensity at high frequencies of radiation. This did not agree with experiments!

The assumption in classical physics was that the black body was absorbing electromagnetic radiation

continuously. Max Planck provided the solution to the problem by suggesting that radiation was emitted and

absorbed from time to time in packets of energy of a definite size. The energy of these so called ‘quanta’

(energy packets) would be proportional to the frequency of radiation. The greater the frequency the greater

the energy of the quanta. This was the first indication that light may not be a continuous wave but small

packets.

The idea that light came in small ‘quanta’ was reinforced when Einstein came up with an explanation for the

photoelectric effect which Hertz had discovered in 1887. Here electrons are emitted from a metal when

exposed to electromagnetic waves.

The problem was that classical physics predicted that the whatever kind of electromagnetic radiation you

exposed the metal to, if it was intense enough, electrons should be emitted

However, experiments showed that the emission of electrons depends on the frequency of the

electromagnetic waves rather than the intensity. There is threshold frequency below which no electrons will

be emitted however intense the electromagnetic waves are. Over this frequency electron emission happens

and even a weak intensity beam can eject some electrons.

Einstein used Planck’s theory of quanta to give an explanation for the photoelectric effect therefore showing

that electromagnetic radiation is a beam of individual quanta or discrete packets of energy like a particle.

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Diagram of the maximum kinetic energy of electrons emitted as a function of the frequency of light on zinc

Diagram from: http://en.wikipedia.org/wiki/Photoelectric_effect (Accessed 16/9/2014)

Another nail in the coffin of classical physics came when in 1911 Ernest Rutherford discovered that atoms

had a central core made up of a positive charge. This suggested a ‘solar system’ model for the atom, with a

positive charge at the centre and electrons orbiting around the outside at any distance from the centre.

However classical physics predicted that the orbiting electrons as they move around the centre should emit

electromagnetic waves and therefore lose energy. As they lost energy the electrons would collapse towards

the centre of the atom and the atom become unstable.

Diagram from: http://en.wikipedia.org/wiki/Bohr_model (Accessed 16th September 2014)

The solution to this problem was suggested when Neils Bohr in 1913 following Plancks idea of discrete

energy packets proposed that electrons could only exist at a certain number of discrete distances from the

centre. An atom had a lowest state of energy and when the electron was in this orbit it could not lose any

more energy, therefore the atom became stable and did not collapse in on itself. If an electron moved

between orbits it did so by emitting or absorbing a discrete amount of energy (quanta). Bohr’s ideas turned

out to be right, but he had added an ad hoc idea to what was essentially a picture based on classical physics.

It took about another ten years before a fully quantum mechanical picture of the atom would be formulated.

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Louis de Broglie made the suggestion that if light had particle-like properties as well as wave-like properties,

then we can expect particles to have wave-like properties. This is known as wave-particle duality –

sometimes a microscopic object will behave like a wave and sometimes it will behave like a particle.

Quantum mechanics was fully born when in 1925 Erwin Schrodinger discovered his so called wave equation

which describes microscopic phenomena of particles:

( )

( ) ( ) ( )

( )

Quantum mechanics has been a very successfully theory and the reason we have mobile phones and laptops

we can carry around today are all because of the principles of quantum mechanics. Our understanding of

mathematics and consequences of the quantum mechanical picture had developed radically since the early

years of the theory.

The consequences of the quantum revolution

The quantum revolution bought about a radical change in our view of the world. Classical physics still works well at

the macroscopic (large scale) level we experience in everyday life but quantum mechanical effects become more

important at the microscopic level (small scale). What are some of the characteristics of quantum theory?

Physical properties of particles can vary continuously or be limited to discrete values.

An object could be anywhere in space, therefore its position can vary continuously.

An object (e.g. in the case of an atom which we mentioned earlier) can only take on discrete energy values.

Probability

Whereas classical physics spoke about certainties, quantum physics talks about probabilities. Classical physics would

say a particle is actually at a specific place at a specific time, but standard quantum physics speaks about the

probabilities of particles being found (or measured) at a specific place at a specific time.

The probability of a particle being found (or measured) at position, x, at time, t, = | ( )| (known as the Born rule)

Standard quantum physics says that there is some kind of probability built into the way nature works.

The Heisenberg Uncertainty Principle and complementarity

It turns out that the wave-like nature of particles means that there is a deep connection between the physical

property of momentum (in overly simplistic terms we can consider this a measure of particle speed) and position.

The more accurately we measure the position of a particle, the less accurate its momentum is. The more accurately

we measure the momentum the less accurate its speed is. This is known as the uncertainty principle which was

discovered by Heisenberg in 1927. It says that we cannot simultaneously determine both position and momentum of

particle at the microscopic level with arbitrary precision. The inability to determine both position and momentum at

the same time is not because of the inaccuracy of our measuring device but is inherent in the wave properties of

matter. This different to classical physics where a particle’s position and momentum can be measured to arbitrary

precision.

The Heisenberg uncertainty principle is an example of what is known as complementarity. In quantum physics some

physical properties of matter form complementary pairs. Any attempt to measure one property of a pair will lead to

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uncertainty in the complementary property. Another example of a complementary pair of properties in quantum

physics is time and energy.

Wave-particle duality and complementarity

Another kind of complementarity spoken about in Quantum physics is linked to the complementary properties of

matter or wave-particle duality. Niels Bohr emphasised that we should take the wave-like and particle-like properties

of matter together and not assume they implied a contradiction. Each picture complemented the other rather than

conflicting. The emphasis was they each picture corresponded to different and mutually exclusive sets of

experiments. You could set up experiments to explore the wave-like properties of matter and you could set up

experiments to explore the particle like properties of matter but you could not do both at the same time. We think

of an electron as having both wave-like aspects and the particle-like aspects. These are different ‘forms’ of the same

material object which we call an electron. It is how we interact with that electron which determines which aspect

(particle-like or wave-like) we see exhibited.

Superposition of states

In classical physics a particle could only be in one state, but in quantum physics a particle can be in a mixture of

many states at the same time. The story is told that Paul Dirac who is important in the early development of

quantum physics described it like this:

“He took a piece of chalk and broke it in two. Placing one fragment on one side of his lectern and the other on the

other side, Dirac said that classically there is a state where the piece of chalk is ‘here’ and one where the chalk is

‘there’, and these are the only two possibilities. Replace the chalk, however, by an electron and in the quantum

world there are not only states of ‘here’ and ‘there’ but there are also of whole host of others states that are

mixtures of these possibilities – a bit of ‘here’ and a bit of ‘there’ added together.” (Polkinghorne, Quantum Theory:

A very short introduction, p.21)

This is counterintuitive but this it is what distinguishes the quantum world from the classical world. This is known as

the superposition of states and is responsible for quantum phenomena we can see. This can be demonstrated by

what is known as the double slit experiment:

Fire a beam of electrons at a double slit and detect them on a screen the other side.

Diagram from:

http://cherrypit.princeton.edu/donev/Samples/QuantumPhysics/QuantumPhysics.html (Accessed

16th September 2014)

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If only one electron is arriving at the screen at a time, which slit did the electron go through?

From a classical physics perspective, because an electron is a particle it can only go through one slit at a time. If it

went through the top slit then we could ignore the bottom slit and temporarily close it up and this would have no

effect on the experiment outcome.

However from a quantum physics point of view if we close a slit, the probability of an electron being detected at

specific point on the screen is different from if both slits were open. The presence of the other slit is significant and

affects the results of the experiment. In quantum physics we have a superposition (mixture) of the states for the

electron both going through the top slit and the bottom slit which makes the electron behave like a wave and

produce the characteristic pattern of light and dark shades on the screen.

In some way we have to say the electron went through both slits. From a classical physics perspective this is

nonsense, from a quantum physics perspective it makes perfect sense. The consequences of a superposition of

states can be huge!

Determinism and Indeterminism

In classical physics if you know the all the quantities which describe the state of a system. You can describe how the

system evolves in time. The previous state of the system determines the later states.

In quantum physics where you work on the microscopic level it is different. The superposition principle means that

you mix together two mutually exclusive possibilities (e.g. electron being ‘here’ or electron being ‘there’) until you

make a measurement. Quantum physics then says that in this mixed state you can only predict the probability of

measuring states 1 or 2 rather predicting exactly which state you will find when you make a measurement.

Quantum physics therefore introduces indeterminism into physics. Quantum indeterminism says that we cannot

always predict with certainty the outcome of a measurement from our previous knowledge of the state of the

system. Sometimes we can only give the probability of measuring the different possibilities.

Determinism says that what comes before determines what comes afterwards in a casual way. However, we must

not say that quantum physics is completely indeterministic as the wavefunction (or quantum state) evolves

deterministically according the Schrodinger equation between measurements.

( )

( ) ( ) ( )

The Measurement Problem and wavefunction collapse

In classical physics when you measure something you simply measure what is already the case in reality. The

observer does not impact or change the situation by any significant degree when they make a measurement e.g. you

can measure the speed of car without having any significant impact on the speed of that car.

Assume you have a superposition of two states:

What happens to the state of the system after a measurement? The standard interpretation of Quantum mechanics

is that after you measure state 1 or 2 you no longer have a superposition state. One part of the wavefunction

collapses (this is known as wavefunction reduction or wavepacket collapse) so that the measurement is repeatable.

The state of the system has changed into being just one of the mutually exclusive states . The measurer

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effectively alters the state of the system by their measurement and causes irreversible change. We cannot describe

the observer who makes a measurement in the same detached and objected way as we do in classical physics.

Generally the laws of physics are reversible (meaning they make evolve continuously if we run them backwards or

forward in time), but quantum physics implies an irreversibility when we make a measurement.

One of the big debates in quantum physics (known as the measurement problem) is when does this wavefunction

collapse take place? i.e. when does the wavefunction change? Does it change when the actual measurement

happens or at some earlier point? What determines that we measure state 1 or state 2 this specific time?

Some propose that it is human consciousness that causes the wavefunction collapse, when a human being becomes

conscious of the results of the experiment it settles into a definite state. However, this causes problems. Consider

Schrodinger’s famous thought experiment, his cat.

The cat is placed in a box with a radioactive source with has a 50-50 probability of decaying in the next hour. If it

does decay it will trigger the cat being killed either by poisonous gas (a hammer hitting the bottle causing release), a

gun etc. There are many versions along the same idea. If human consciousness is the thing that causes wavefunction

collapse then at the end of the hour the cat is in a superposition of states of both dead and alive before anyone looks

in the box. This sounds bizarre because the cat is not aware of its own death before we open the box!

Another bizarre proposal called the ‘many-worlds interpretation’ is that at measurement we select one of number

of possibilities, but all possibilities are realized because the universe splits into many parallel universes and each

possible measurement outcome is realized in one of these universes. i.e. the observer is cloned. There is a world

where I open the box and the cat is dead and there is a parallel world where I open the box and the cat is alive. The

problem is that this proposal is unprovable because we cannot detect the other universes.

In standard quantum physics it is assumed that the wavefunction provides the most complete description of reality

that is possible. The wavefunction all the physical information that is accessible to us and therefore a superposition

of states (cat dead + cat alive) describes the actual state in the real world. A third proposal to solve the measurement

problem is that there is a ‘hidden variable’ (eg. particle position) not described in the mathematics of quantum

which determines the situation in reality. This hidden variable is correlated to the wavefunction and the

wavefunction guides the development of this hidden variable. However when we measure we are always revealing

this hidden variable. Returning to Schrodinger’s cat, the radioactive source does have ‘hidden variable’ of the actual

particle position. The wavefunction guides how the particle moves and never actually collapses. If you repeated the

experiment many times in some cases the wavefunction will guide the particle such that it causes the cat to die and

sometimes it won’t. It is the particle position rather than the wavefunction describes the reality of the system, so the

cat itself is never in a superposition of states in reality but the supposition of states guides the particle. This

introduces determinism back into quantum physics but in what seems like an ad hoc way. There have been some

good proposals for hidden variables theories (e.g. The de Broglie-Bohm theory) but none have been fully convincing

yet.

Non-locality

Classical physic is local theory, which means things like particles are only influenced by those things in the immediate

surroundings. Einstein’s theory of Relativity says that the fastest speed than anything including information can

travel is the speed of light.

Quantum theory is known as a non-local theory as it is possible for two particles to influence each other faster than

the time it takes light to travel between them. There is a kind of ‘spooky action at a distance’ as Einstein called it.

Suppose we have two particles which are in a superposition (mixture) of states e.g. either particle could have a

velocity of +1 or -1 but they can’t have the same. We have the super position of states:

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[Particle A = velocity +1; Particle B = velocity -1] + [Particle A = velocity -1; Particle B = velocity +1]

Make the particles so far apart that when you measure particle A and you can measure particle B before anything

could travel at the speed of light between the two positions. If particle A has velocity+ 1, how does the particle B

know to have velocity -1? The implication is that measurement at point A causes instantaneous change at point B.

Experiments demonstrate this is what actually happens and that it not just about our lack of knowledge. Quantum

mechanics is a non-local theory.

Holism

We have seen that quantum physics is a non-local theory and therefore there is what John Polkinghorne calls

‘togetherness-in-separation’ (Polkinghorne, Quantum Theory: A very short introduction, p.79 cf. p.90). The focus in

quantum physics is on the microscopic aspects of nature but this doesn’t mean nature can be solely reduced into

small independent bits. There is an indivisible unity in the world at a microscopic level. The picture of reality in

quantum physics is one of an integrated reality rather than separate parts working independently. An object and its

properties at the quantum level of matter mutually and indivisibly interlinked with the systems it interacts with and

with the environment. There is a form of relationality built into nature.

Bibliography:

Bohm, D., Quantum Theory, (Mineola, NY: Dover Publications, 1989)

Greiner, W., Quantum Mechanics: An Introduction, 3rd edn, (Berlin: Springer-Verlag, 1994)

Polkinghorne, J., Quantum Theory: A very short introduction, (Oxford: Oxford University Press, 2002)

Polkinghorne, J., Science and Theology: An Introduction, (London: SPCK, 1998)