Werner Heisenberg and the importance of the uncertainty principle.
The Uncertainty Principle
In 1927, German physicist Werner Heisenberg was able to show that a ‘fundamental limit’ exists for the precision with which you can measure the position and momentum of a quantum particle. The more precise you want to be about one, the less you can say about the other. This isn’t down to the quality of your measuring equipment either; it instead speaks to the inherent uncertainty encoded in nature!
This counterintuitive result is popularly known as ‘Heisenberg’s Uncertainty Principle’. It once again reminds us that in quantum mechanics we simply can no longer talk about the location or the trajectory of a particle with any certainty.
Accepting the results of Schrödinger’s Equation means accepting a probabilistic view of nature as we no longer can have exact answers to previously straightforward sounding questions like ‘Where is the electron at time ‘t’?’ The absolute best we can get from the mathematical representation of a quantum state – the wave function – is a probability.
Wave Function Collapse
It’s been made clear by experimental observations that the phenomenon of quantum superposition disappears when we look at a particle. After all, nobody has ever explicitly seen a single particle in several places at once! So why then does superposition disappear upon measurement? And how?
These are still unanswered questions in the field, but somehow in this strange new world the act of measurement causes reality to ‘snap’ into just one of the countless possible outcomes. Put in a slightly different way, it is said that the wave function – which previously told us that the particle was effectively ‘everywhere’ with an assortment of probabilities of actually being in any one place at each time – ‘collapses’ by some unknown quantum mechanism upon observation to have a specific location or momentum.
Extending The Uncertainty Principle
Heisenberg’s Uncertainty Principle states that you can never measure both the position and momentum of a quantum object with perfect precision. The more precise you are about one, the less precise you are about the other. However, position and momentum aren’t the only ‘observables’ – as they are often called in quantum physics – that can’t be measured simultaneously with arbitrary accuracy.
The time elapsed and energy of a quantum system are in fact another such pair. In other words, the more precise you are about the time span an event in your quantum system happens over, the less precise you can be about the energy associated with the event! This is why particles can sometimes defy the rules of everyday life and acquire energy seemingly “out of nowhere” for a very brief moment of time, allowing for the bizarre phenomenon known as ‘quantum tunnelling’ in which a particle is said to ‘tunnel through’ what would normally be an unsurmountable energy barrier.
Quantum Tunnelling
One of the quirkiest repercussions of quantum theory and its insistence on wave-particle duality, an electron – or any other subatomic particle for that matter – can potentially cancel the effects of an energy barrier if the barrier is thin enough. This is due to the quantum reliance on probability. For example, we can interpret this more practically as a particle being able to traverse through walls and doors if the barrier is thin enough.
Quantum tunnelling like this is possible because when a particle behaves as a ‘matter wave’ it can focus a great deal of energy on the barrier, ultimately negating it. Clearly, the chance of macroscopic, everyday objects doing this is unthinkably small, but for subatomic particles or quarks – the even smaller ‘elementary’ particles which make up protons and neutrons – it is a very real and unsettling possibility.
Quantum Entanglement
Yet another popular example of quantum weirdness that often captures the public imagination is that of ‘quantum entanglement’, which arises as an implication of the wave function derived from Schrödinger’s Equation. It’s all down to the fact that a wave function – a solution to Schrödinger’s Equation for a given quantum system that gives you information about it – can be used to describe a system of many particles and not just one.
Often, it’s simply not possible to decompose an overall wave function for a multi-particle system into components that correspond to the individual particles. When that happens, the interpretation is that the particles involved have become inextricably linked, even if they were to move far, far away from each other.
The particles are said to be ‘entangled’, and when something happens to one of the particles, a corresponding thing happens to its distant partner. Einstein famously described this phenomenon as “spooky action at a distance”.
An Example of Quantum Entanglement
There’s a uniquely quantum property that all particles possess known as ‘spin’ which can either be in the ‘up-spin state’ or ‘down-spin state’. It has nothing to do with any physical rotation and is instead a property that results in a particle having ‘angular momentum’, without it rotating. For this reason, it’s usually called ‘intrinsic angular momentum’.
A laser beam fired through certain crystals can cause individual photons to split into a pair of ‘entangled’ photons, with opposing spin states. Once entangled and separated by a vast distance, actions performed on one can affect the other.
If Photon A is observed and takes on an up-spin state, entangled Photon B – now far away – mysteriously takes up a state relative to that of Photon B, in this case a down-spin state! This transfer of state between the entangled photons has been known to take place at a speed of at least 10,000 times the speed of light.
