Introduction to the strange world of Quantum Physics

Transcription

1 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 ) 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 19 th 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 19 th 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. Page 1 of 8

2 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 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. Page 2 of 8

3 Diagram of the maximum kinetic energy of electrons emitted as a function of the frequency of light on zinc Diagram from: (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: (Accessed 16 th 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. Page 3 of 8

4 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 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 Page 4 of 8

5 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: (Accessed 16 th September 2014) Page 5 of 8

6 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 Page 6 of 8

7 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 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: Page 7 of 8

8 [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, 3 rd 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) Page 8 of 8