A few people have asked me why I needed such extravagant equipment (ping-pong balls, a torch and a metre-ruler) in my lecture on Thursday night.
I did only use one ping pong ball in the talk but I found the local budget shop Eurosaver only sells them in packs of twelve (for the princely sum of €3) so I now have plenty of spares. The metre ruler was borrowed from the Department of Experimental Physics (who have expertise using sophisticated measurement devices) and returned on Friday morning. The torch was procured from Tesco along with two batteries.
One of the things I wanted to do in my lecture was to explain some of the difficulties about measuring cosmological distances. I started by holding up a ping pong ball (radius 2cm) and asking if the ping pong ball were the Sun (radius 7 × 108 m), on the same scale how far away would be the nearest other star (Proxima Centauri)?
To cut a long story short – and you can do the arithmetic yourself – the answer surprises most people who haven’t seen this demonstration before. It’s not the back of the lecture theatre, nor is it the town centre, nor the next town. It’s 1200 km away. That’s as far from Maynooth as, say, Geneva, or Copenhagen. The distances between stars is huge, even in the relatively dense part of a Galaxy, such as where the Sun is situated. The Universe is very big and very empty, even in the places that look crowded.
The torch and the metre rule were used to demonstrate two ways of possibly measuring astronomically large distances. I had a student stand up at the back of the theatre holding the metre rule. I explained that I could measure the distance to the student using geometry by measuring the angle subtended by the ruler if I knew its length (which I do). This is the principle behind the angular diameter distance; the metre rule is called a “standard rod”.
The torch is used to illustrate the luminosity distance. If I knew its power output I could measure the intensity of light using a lightmeter and infer the distance from that using the fact that it follows an inverse-square law. The torch is thus a “standard candle”.
Of course in cosmology we don’t have perfectly standard rods or candles but we can apply the principle of the angular diameter distance to features in the galaxy distribution or the cosmic microwave background or gravitational lenses and supernovae can provide us with accurate luminosity distances.
There are additional complications. Objects at large distances are receding with the Hubble expansion so light from them is redshifted, affecting their apparent luminosity. Einstein’s theory of general relativity allows for the possibility that light rays don’t travel in straight lines either (because space is curved), affecting the angular diameters. That means the two methods don’t necessarily give the same distance unless these factors are taken into account.
In the Dark 