Quantum Theory



Quantum physics deals with tiny, indivisible units of energy called quanta.
The Quantum Theory can be summarized by these four main ideas:
  • The world at the level of atoms is entirely different than what is familiar to us.
  • Energy is not continuous, but comes in tiny, discrete units called quanta.
  • Elementary particles behave like particles and like waves.
  • It is impossible to know both the position and the momentum of a particle at the same time. The more precisely one is known, the less precise the measurement of the other one is.
Mechanics is the study of energy and motion. Quantum mechanics is a theory that extends the ideas about motion that Isaac Newton developed, helping to describe the motions of sub-atomic particles where Newton's equations don't work. Quantum mechanics also helps unify our ideas about motion with the laws of electromagnetism at the atomic level.

The foundations of quantum mechanics were established early in the 20th century by various scientists, including Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Paul Dirac, Wolfgang Pauli and others.



You may have learned that an atom is made up of three particles; here's a summary of what you might already know about atoms, as first described by Rutherford almost 100 years ago:
  • Protons - these are positively charged and contain, along with neutrons, most of the mass of atoms.
  • Neutrons - these are neutral particles with a mass similar to protons but with no charge.
  • Electrons - these are much smaller than protons, with a negative electric charge equal to the charge on a proton.
The protons and neutrons form the center of an atom (called the nucleus), and the electrons revolve around them. It is the outer electrons that interact when atoms combine with other atoms, and the outer electrons that are stripped off to form electric currents. The number of protons in a nucleus determines how many electrons there should be. This proton number (called the Atomic Number) determines how the atom behaves; changing the number of protons in the nucleus changes the type of element. (Hydrogen atoms have one proton and one electron; helium has two of each, etc.) The electrons are held in orbit by the positive-negative attraction between them.

This is the Newtonian (or Classical) description of an atom, and scientists have known since the early 1900's that it is wrong. In his Nobel Prize winning paper on the Photoelectric Effect in 1905, Albert Einstein showed that electrons can orbit a nucleus only at certain distinct energy levels; the energy of each level is 'quantized'. Moreover, electromagnetism (as described by Maxwell in the late 1800's) could not explain how an atom could possibly be stable ... an electrically charged electron that is changing direction as it orbits around the nucleus should be radiating energy away until it falls into the nucleus. This doesn't happen ... atoms appear to be stable. In addition, the orbital model of an atom does not explain radioactive decay.

Isaac Newton thought that light was a stream of particles; Thomas Young thought it was a wave.You will learn about these two differing theories in Physics 30, and how physicists in the 20th century came up with a new idea about how matter is put together. It was discovered that both light and matter particles share properties of both particles and waves. A quantum (or packet) of light can be considered both a particle and a wave, and so can an electron!

Tiny elementary particles like electrons sometimes act like particles ... but at other times they act like waves. A single electron passing through a single slit in a double-slit diffraction-type grating, for instance, will create an interference pattern just as if a wave front had passed through both slits.

A physicist named Neils Bohr assumed that an electron could be a wave, and worked out the wavelength of an electron moving around the nucleus of an atom. He found that an orbit, to be stable, had to be a whole multiple of the electron's wavelength. Orbits that include fractions of waves were not possible, so the electron could not orbit at those levels. In other words, an electron could have a stable orbit ... it wouldn't lose energy and spiral into the nucleus. Moreover, if an electron absorbed or radiated energy, the energy would have to be in certain discrete amounts.

When you measure an electron's wave-like properties, it appears to be a wave. But when you measure it's particle-like qualities, it appears to be a particle. What you see depends on what you are attempting to measure.

This 'wave-particle duality' idea is true for both matter and energy. For example, the location of an electron as it circles the nucleus is given by a probability. Electrons exist only in certain discrete energy states. They can absorb energy, but only in discrete amounts (called quanta), and when this happens, the electron disappears, appearing instantly at a higher energy level.
Electrons are no longer considered to be little balls orbiting a nucleus. Rather, the orbit of an electron is a cloud of probability around the nucleus. The electron at a certain energy level is everywhere at once; when it jumps to a new level, it does so instantaneously.

At the left, the old view of a simple atom. At the right, the modern view.


Particle behaviour can be described mathematically by equations called 'wave functions'. They can describe how an electron can move from one place to another ... and there are only a certain finite number of possible paths. When the electron is not being observed, the electron takes all the routes. But when you're watching it, it's forced to choose one and follow that path.

Put another way, if you try to determine an electron's position with some precision, you will be much less certain of its momentum. Alternately, if you try to determine its momentum, you won't be able to find its position precisely. This idea was first proposed by Werner Heisenberg in 1925, and has been named the Heisenberg Uncertainty Principle ... although a description that best matches the German word as Heisenberg used it would be the 'Indeterminability' Principle.

The smaller the object, the greater the uncertainty is. For a moving baseball, we can determine its position to a high degree of certainty, and still measure its momentum very precisely. But for tiny particles like electrons, we can't do both at the same time.

The probabilistic nature of quantum mechanics (where a particle's position, for example, is a region of space where 'its probability of being there' is measured) is one of the most difficult concepts in quantum physics to understand. The probability comes from the act of measuring; when a quantum system (eg: an atom) interacts with a measuring device, their individual wave properites become 'entangled', so that the original quantum system is changed.

"God does not play dice" was what Albert Einstein said when he learned about the Uncertainty Principle. He was unable to believe that it could be true, and spent much of his life after 1925 trying to find a way to determine both the position and the momentum of a particle. He wasn't able to.

Another idea in quantum theory is that energy must come in small bundles, called quanta (one bundle being a single quantum). This was proposed by Max Planck in 1900. He suggested that electromagnetic energy is a multiple of the number 6.63 X 10-34 joule-seconds (later referred to as Planck's Constant h). The energy of one quantum can be calculated using the equation E = h·v, where v is the frequency of the energy. This means that energy is not continuous, but only comes in certain finite-sized packets based on Planck's constant.

This explains why electrons (which in Planck's time were still thought to orbit around the nucleus like a planet around the sun) can only exist at certain energy levels. Ironically, it was Einstein who had given support to this idea with his explanation of the photoelectric effect.

Quantum equations describing particles using mathematics were proposed by Erwin Schrödinger in 1926. They described particles that jumped from one quantum state to another, just as electrons seem to move from one orbital level to another.

By combining Planck's constant with what we know about gravity and the speed of light, it seems that not only energy is quantized. There is also a quantum of length (about 10-35 meter) and a quantum of time (about 10-43 seconds). These are called Planck's length and Planck's time. They are quantities of length and time that cannot be broken up into smaller pieces. (This is why there are only a certain finite number of possible paths for an electron to follow).

The 'Schrödinger's Cat' puzzle illustrates a problem with quantum theory that physicists have been unable to overcome. Imagine a box containing a radioactive substance, and a cat.
You may know that the decay of atoms causes radioactivity, and that there is no way to predict when any individual atom will fall apart; the best we can do is to make a statistical prediction like 'there is a 50-50 chance that a radioactive atom will decay in a certain period of time'. This uncertainty can cause seeming paradoxes in the larger world.
Now imagine also that there is some sort of device that will kill the cat if it detects a radioactive atom decaying. The radiation from the radioactive decay is set to be released such that there is a 50-50 chance of it occurring. The box is closed.
You wait a while. Is the cat now dead or alive?
The only way to tell if the cat is still alive is to open the box. As long as the box remains closed, it is impossible to predict if the cat is dead or alive. Quantum theory says that the best you can say is that there is a 50-50 chance of either, but there is no way of knowing for sure, as long as the box remains closed.
Before you open the box, the cat is both dead and alive. The box contains a 'half-dead cat'.

Some consequences of the quantum theory:
  • The Uncertainty Principle implies that there is a built-in uncertainty in the world. It is possible for particles to be created out of nothing, if you wait long enough. On the level of atoms it is impossible to precisely locate a particle's position and speed at the same time. Using the 'Schrödinger's Cat' example, it looks as if there may be things in our world that are unknowable; we can assign probabilities of certain events occurring, but there is no way to predict actual results ... at least, on the sub-atomic scale.
  • Zero energy is impossible, since this would be a precisely measureable state. As a result, nothing can be cooled below -273 degrees C (Absolute Zero). An atom must have at least one quantum of energy, which means nothing can ever be completely at rest.
  • Because mass and energy are equivalent, there is a finite probability that in certain circumstances, particles can appear 'from nowhere'
  • Subatomic particles have a property called 'spin'. When two particles are separated by any distance, determining the spin of one of them automatically and instantaneously fixes the spin of the other, no matter how far away it is.
(Instantaneous transfer of information was another property of quantum physics that Einstein objected to. He believed it impossible that one particle could instantaneously influence another, trillions of miles away, since this could necessitate speeds greater than the speed of light, something forbidden by his Special Theory of Relativity. However, the instantaneous transmission of information was actually demonstrated by particle physicists in 1997. How it works remains unknown.)

Quantum effects are not noticeable in your everyday surroundings; they only become visible when things are very small, such as for atoms. Nevertheless, their effects are important in many branches of science. Quantum physics is used to understand and describe radioactivity, semi-conductors, solid-state computer chips, radiation from black holes, and many other phenomena. Much of modern technology works on the level of atoms where quantum effects are significant; examples include lasers, electron microscopes, and magnetic resonance imaging. Quantum mechanics is important for understanding how individual atoms combine to form molecules ... the application of quantum mechanics to chemistry is known as quantum chemistry.

On the frontiers of quantum research, scientists are attempting to develop quantum computers, which will be able to perform many computational tasks simultaneously, and exponentially faster than ordinary computers. Much more esoteric is the notion of quantum teleportation, which deals with techniques to transmit quantum states over arbitrary distances instantaneously.

Quantum physics provides probabilistic results because our universe seems to be probabilistic rather than deterministic, seen at the level of individual atoms. Most scientists think that quantum mechanics provides a true description of our physical world, but recent research has indicated that quantum mechanics may in fact not work near black holes, where its predictions seem to conflict with the theory of general relativity. The question of whether the principles of quantum mechanics (which describe the world of the tiny particle and subatomic forces) and general relativity (which describes the world of the very large and gravitational forces), can be brought together into one overall theory is the subject of current research in this area of physics.