Talk : When the Uncertainty Principle Goes up to 11

For April's Uni of Nottingham Public Science Lecture, Professor Philip Moriarty from the School of Physics & Astronomy at the University Nottingham talked about "When the Uncertainty Principle Goes up to 11".

@Gav Squires was there and has kindly written this guest post summarising the event, with some linkage added by NSB.

There is a deep and fundamental link between quantum physics and heavy metal. This is a real thing unlike the huge industry that people like Deepak Chopra have built up around quantum woo, trying to link eastern mysticism and quantum physics. Despite what Deepak and his ilk will have you believe, we actually understand quantum physics remarkably well - it is a theory of waves. We don't know what those waves mean yet but we can do the mathematics behind them. At the minute, there are around twenty interpretations of quantum mechanics. As Richard Feynman said, "if you think you understand quantum mechanics, you don’t".

Metal Bands and Physics

Heavy metal is not considered to be the most cerebral of genres but there are a number of bands that are embedding science themes in their music. David Robert Grimes, from Oxford University, has written a paper on string-bending and there is also a published paper entitled, "Collective Motion of Humans in Mosh and Circle Pits at Heavy Metal Concerts" (it turns out that the people behave in exactly the same way as molecules in a box) So, scientists are already writing about the physics of music. Mathematician Gottfried Wilhem von Leibniz (1646-1716) even said, "music is the pleasure that the human mind experiences from counting without being aware that it is counting" There is an equivalence between fractions and musical notation such as quavers, semi-quavers etc. Musical theory is based around the concept of intervals - thirds, fourths, fifths, octaves. Music has notations and maths has notation and we can simplify both of them.

Moriarty playing the guitar

We can use our knowledge of waves in the real world to tell us about the quantum world. If we confine a particle to a finite space it will have a wave like characteristic. This is similar to a guitar string. What happens when a wave can't propagate? It reflects. With two nodes, you get very simple waves where it doesn't vibrate rather than the mess that you might expect. A low note has a low wavelength, while a high note has a higher pitch and a higher rate of oscillation.

Why does an "E" on piano sound nothing like an "E" on guitar? It's the harmonics. If every wave produced just looked like a standard sine wave you wouldn't be able to tell the difference between different instruments. The real waves are much more complex, even though they are still regular and repeating. Whistling is a lot more similar to a "standard" sine wave.

Different Harmonics possible with a single string

How a harmonic may oscillate

The amplitude is the period of a wave, how many times it repeats per second. The frequency can be represented as 1/T, where T is the amplitude. This is "reciprocal time" - converting from one quantity to its reciprocal is incredibly important in physics. The frequency will change with the pitch. On a guitar, there are multiple spikes even with just one note, so we know we have a range of frequencies.

You can get any pattern that is relevant in the real world by adding together different sine waves. As Jean Baptiste Joseph Fourier said, "mathematics compares the most diverse phenomena and discovers the secret analogies that unite them." The guitar string can vibrate in a number of ways. However, we always know that it has two nodes. By adding your finger to the string at a node, you can dampen out any waves (harmonics) that don't have a node at that point.

With particles and waves, you're looking at localised versus delocalised. When an electron moves on silver you get standing waves, just like with guitars. These days it is child's play to manipulate individual atoms on a surface, you can just point and click. Electrons create waves but rather than these being actual waves, they are probability waves, all to do with the probability that you will find an electron. If you create a string of iron atoms and then look at the distribution of the electrons then you can see that the same ideas that we have on a guitar string can be ported down to this level.

Electron Waves 

Heisenberg's Uncertainty Principle has been incredibly mis-interpreted throughout the years, not least by Heisenberg himself. You could say he was uncertain of how it worked! It is different from the observer effect, where if you interact with a system then you change the evolution of the system. Anything can be an observer - in the famous case of Schrödinger's Cat, even the box is an observer, so the cat has been observed long before you actually open the box. We see the Uncertainty Principle all the time in the real world.

For example, when you mute a guitar string with your palm. If you look at the peak for the fundamental - the lowest frequency peak, it is wide in time but narrow in frequency. By muting the string with your palm, you get narrow in time but wide in frequency. This comes from classical physics but it is the Uncertainty principle.

You can also have a spatial frequency - number of stripes per metre. Then you look at the reciprocal space - how often does it repeat? This ties back in with momentum in the Uncertainty Principle. High definition means high spatial frequencies, while a narrow spectrum gives much greater uncertainty in space.

The Public Lecture Series returns on May the 18th where Professor Frazer Pearce will be talking about Adventures In The Goldilocks' Zone - The Search For Other Earths. For more information visit the website: www.nottingham.ac.uk/physics/outreach/science-public-lectures.aspx

Image Sources
Standing Waves, Others by Gav Squires.