Quantum Mechanics: An Introduction

You've probably heard that quantum physics is strange and weird and doesn't obey the laws of physics that you are used to. This is certainly true to a large extent. There is a reason physicists had to develop a new theory and not rely on the old ones to explain what happens in the world of the extremely small.

In this introduction to quantum mechanics you will learn how scientists approach quantum behavior and quantum phenomena as well as where these ideas came from.

There is indeed a lot of weirdness in the quantum world. Quantum mechanics is the branch of physics that attempts to explain that weirdness and provide a framework that allows for predictions and explanations of observed phenomena.

Fundamental aspects of quantum mechanics include the notion of quantization. That is, there exists a smallest unit of something that can't be broken down further. Energy is quantized, meaning that it comes in discrete units.

The size of quantized units are usually written in terms of Planck's constant, ​h​ = 6.62607004 × 10^-34 m²kg/s.

Another aspect of quantum mechanics is the notion that all particles actually have particle-wave duality, meaning that they sometimes act as particles and other times act as waves. In fact, they are described by a so-called wave function.

Quantum weirdness includes the notion that whether a particle is acting like a wave or not somehow depends on the way you decide to look at it. Also, certain properties of a particle – such as the orientation of its spin – do not seem to have a well-defined value until you measure them.

That's right, it isn't just that you don't know until measurement, but the actual distinct value does not exist until measurement.

Quantum mechanics might be best understood by comparing it to classical physics, which is the physics of everyday objects that you are likely more familiar with.

The first major difference is which realms each branch applies to. Classical physics applies very well to objects of everyday sizes, such as a tossed ball. Quantum mechanics applies to objects that are very small, such as protons, electrons and so on.

In classical physics, particles and objects have a distinct position and momentum at any given point in time, and both can always be known precisely. In quantum mechanics, the more accurately you know an object's position, the less accurately you know its momentum. Particles do not always have well-defined position and momentum. This is called the Heisenberg uncertainty principle.

Classical physics assumes that the energy values something can have are continuous. In quantum mechanics, however, energy exists in discrete chunks. Subatomic particles such as electrons in atoms, for example, can only occupy distinct energy levels and not any values in between.

How causality works is also different. Classical physics is completely causal, meaning that knowledge of initial states allows you to predict exactly what will happen.

Quantum mechanics has a different version of causality. Particles are described by a quantum mechanical wave function, which gives relative probabilities of what it might do when measured. That wave function follows certain laws of physics in how it "evolves" in time and leaves you with predictable "probability clouds" of what measurement might give.

Many famous scientists contributed to quantum theory over the years, and many won Nobel Prizes for their contributions. Indeed, the discovery and development of quantum mechanics was revolutionary. The beginnings of quantum theory can be traced back to the 1800s.

•Physicist Max Planck was able to explain the phenomenon of black body radiation by the quantization of energy. 
•Later, Albert Einstein developed an explanation of the photoelectric effect by treating light as a particle instead of a wave and giving it quantized energy values.
•Neils Bohr is famous for his work on the hydrogen atom, where he was able to explain spectral lines in terms of quantum mechanical principles. 
•Louis de Broglie presented the idea that particles that are small enough – such as electrons – also display particle-wave duality.
•Erwin Schrodinger developed his famous Schrodinger equation, which describes how wave functions evolve in time.
•Werner Heisenberg developed the uncertainty principle, which proved that neither position nor momentum of a quantum particle can be known with certainty.
•Paul Dirac predicted the existence of antimatter and made steps towards reconciling general relativity theory with quantum theory.
•John Bell is known for Bell's theorem, which proved that there were no hidden variables. (In other words, it isn't just that you don't know a quantum particle's spin or other property prior to measurement, but it actually does not have a well-defined value prior to measurement.)
•Richard Feynman developed the theory of quantum electrodynamics.

Because quantum mechanics is so strange and so counter-intuitive, different scientists have developed different interpretations of it. The equations that predict what happens are one thing – we know they work because they are consistent with observations – but understanding what they really mean is a more philosophical matter and has been subject to much debate.

Einstein characterized the different interpretations based on four properties:

•Realism, which pertains to whether properties really exist prior to measurement.
•Completeness, which addresses whether or not current quantum theory is complete.
•Local realism, a subcategory of realism that pertains to whether realism exists on a local, immediate level.
•Determinism, which pertains to how well quantum mechanics is believed to be deterministic.

The standard interpretation of quantum mechanics is called the Copenhagen interpretation. It was formulated by Bohr and Heisenberg while at Copenhagen in 1927. In essence, this interpretation states that all that a quantum particle is and all that can be known about it is described by the wave function. In other words, all the weirdness of quantum mechanics is really that weird and that's how things actually are.

An alternate point of view is the Many Worlds Interpretation, which does away with the probabilistic outcomes of quantum observations by stating that all possible outcomes actually do occur, but in different worlds that are branches of our current reality.

Hidden variable theories state that there is more to the quantum world that would allow us to make predictions that aren't based on probabilities, but we need to uncover certain hidden variables that would give us these predictions. In other words, quantum mechanics is not complete. Bell's theorem, however, proved that hidden variables do not exist on a local level.

De Broglie-Bohm theory, also known as pilot wave theory, addresses the notion of hidden variables with a global approach not contradicted by Bell's theorem.

Unsurprisingly, many, many other interpretations exist because scientists have had over a century to try and understand the truly bizarre nature of the quantum world.

Many famous experiments have been performed along the way that both led to and proved different aspects of quantum theory.

One very famous experiment is the EPR experiment, named for scientists Einstein, Podolsky and Rosen. This experiment dealt with the idea of entanglement in a quantum system. Consider two electrons, both of which have a property called spin. Their spin, when measured, is either in the up position or the down position.

When measuring the spin of a single electron, it has a 50 percent chance of being up and a 50 percent chance of being down. The results cannot be predicted beforehand per quantum mechanics. In this experiment, however, two electrons are entangled such that their combined spin is 0. However, per quantum mechanics, we still cannot know which one is spin up and which one is spin down, and indeed neither is in either position and is instead said to be in a "superposition" of both states.

These two entangled electrons are sent off in opposite directions to different devices that will measure their spins simultaneously. They are far enough apart during measurement that there is no time for either electron to send some invisible "signal" to the other one to let it know what its spin is measured as. And yet, when measurement occurs, both are measured to have opposite spin.

Schrodinger's cat is a famous thought experiment meant to both illustrate the strangeness of quantum behavior and pose the question of what is truly meant by measurement and whether large objects – such as a cat – can display quantum behavior.

In this experiment, a cat is said to be in a box so that it cannot be viewed by the observer. The cat's life is made dependent on a quantum event – for example, maybe the orientation of an electron's spin. If it is spin up, the cat dies. If it is spin down, the cat lives.

But the state of the electron is hidden from the observer as is the cat in the box. So the question becomes, until you open the box, is the cat alive, dead or also in some strange superposition of states like the electron is until measurement?

Rest assured, however, no one has performed such an experiment and no cats were harmed in pursuit of quantum knowledge!

The 1900s was a time when physics really took off. Classical mechanics could no longer explain the world of the very small, the world of the very large or the world of the very fast. Many new branches of physics were born. Among these are:

•​Quantum field theory:​ A theory that combines the idea of fields with quantum mechanics and special relativity.
•​Particle physics:​ A field of physics that describes all fundamental particles and the ways they can interact with each other.
•​Quantum computing:​ A field that tries to create quantum computers that would allow for quicker processing and better encryption because of how the workings of such a computer would be based on quantum mechanical principles.  
•​Special relativity:​ The theory that describes the behavior of objects that move near the speed of light and is based upon the notion that nothing can travel faster than the speed of light.
•​General relativity:​ The theory that describes gravity as space-time curvature.