The Significance of 18 Magnitudes

I wrote this in 2007 and thought about it again today (June 2015) and thought I would share it.

OK some of you will know I have a physics degree.
When I was at University I was influenced by my mentor, Professor Ditchburn.
His expertise was everything to do with optics and light. For me an extension of optics was crystallography the study of the physical structure of solids. The significance of this was my fascination about scale.
In quantum mechanics we were taught about a wave particle duality or the significance of the wavelength of radiation caused by the vibration of atomic particles.
The link between mass and the speed of light identified by Einstein fascinated me too. Again the speed of light was the fastest speed available and the speed of light never changes.
Hence distance could be measured in light years – the distance light would travel in a year.
This way I realised that the phrase “order of magnitude” gave me a way of imagining scale.
I just want to explore this with you dear reader if you can try and stay with me
If you start with a unit of 1 and our normal mathematical base as 10, then scales could be measured simply. So something an order of magnitude bigger than another is ten times bigger, if it is 3 orders of magnitude it is 10 x 10 x 10 times bigger, that is a thousand times bigger.
Now when I was at University the smallest particle imaginable was the Quark. The size of the quark is theorised to be 10^-18 metres (a metre being about a yard for us over 50’s – actually a yard is .91 metres).
10^-18 metres is 1 metre divided by 10 eighteen times. Not easy for us humans to picture is it?
Perhaps it would help if we pictured this the other way round and try to imagine 10^18 metres.
Let’s start by picturing a piece of string that is 1 metre long. An order of magnitude bigger is 10 metres – an athlete doing the long jump cannot quite reach that distance.
The next order is 10^2 a 100 metres which is the length of a soccer field, then 10^3 – 1,000 metres (a kilometre), then 10^4 10 Kilometres – The English Channel is 33 Kilometres at its narrowest.
At 10^5 we need to begin to think globally 111 Kilometres is the equivalent of 1 degree latitude.
By 10^6 you need to think of nearly one third the diameter of the moon.
At 10^7 we are close to the diameter of the earth itself. That is 7 out 18 do you see where this is leading to?
10^8 or 100,000 kilometres is harder to imagine. Jupiter is 12 times bigger than the earth (142,984 kilometres to be exact).
By 10^9 we are “half way” through this journey. Nearly the diameter of the sun.
So what is 10^10? 10,000,000 kilometres. Light is the fastest anything can go and light would take about 33 seconds to cover this distance.
The mean distance between the earth and the sun is known as one astronomical unit. That is 93 million miles to you and me. 10^11 is two thirds the way between the earth and the sun.
We have now reached two thirds of the way through the journey. 10^12 and we have almost reached the distance between Jupiter and the sun.
10^13 – the Voyager 1 spacecraft was launched September 5th 1977, nearly 30 years ago and it is still going. In its 30 years of travel it has covered just 1.5 times 10^13 metres.
To picture 10^14 takes another leap of imagination. Voyager 1 will not reach that distance for another 180 years at its current speed.
In one year light travels 9,460,730,472,580.8 km which is 9.46 x 10^15 metres.
10^16 takes us three quarters of the way to the nearest star Proxima Centauri from which light takes over 4 years to reach us.
100 times bigger than this is what 10^18 actually means.
So my comparison of the smallest known particle when I was studying physics was the quark at 10-18 metres is comparable to 1 metre as is 1 metre to 70 times the distance of the nearest sun.
Since 1968 Atomic Physics has ventured downscale from 10^-18 to 1.6×10^−35 metres which is almost the same orders of magnitude smaller again.
And whilst I am on the subject going back up in scale from 10^18 to 10^36 which carries the same order of magnitudes again we reach the outer limits of the theoretically known Universe.
Do you see where I’m coming from?


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