There's no doubt that the long winter nights before Christmas (the winter solstice) are a time for hot crumpets and deep reflection.

As usual we can see the life threatening madness of our modern culture going on all around us – climate change, pollution, extinction, war and more..... These concerns pop up in the conversation of any gathering of “normal” people but recently I was pleasantly surprised to hear a different story. It came from a wise old 'cellist who joined up with us to play Beethoven's 8th symphony a couple of weekends ago. “No, no” he said, “surely you must see that all this is just part of a much larger plan. Part of a long evolutionary journey in which our present human civilization is only a small and perhaps temporary player. Life on Earth will certainly go on – with or without us. Humans are only making all this fuss because they think they're so important!”

My friend gave a wry smile, took a sip from his beer and asked for another mince pie. There was a quiet moment whilst the group tried to take in the enormity of what had been said. We soon got back to our music and the technical and creative challenges created all those years ago by the mischevious genius of Beethoven. What would he have made of it all, I wonder!

Now, as some of you may know, I am by training a theoretical physicist. The reality I see through my rain spotted window consists of magical vibrations in the fabric of space and time. We know enough about these to be amazed that such “vibrations” seem to follow mathematical laws (yes – all over the Universe). We know enough to understand that the “vibrations” seem to be constantly trying to organise themselves into beautiful patterns. (We won't try to define “ beautiful” because we know it when we see it.) These patterns too are magical because the molecules they create also like to organise themselves into beautiful patterns. Many of these patterns are constantly trying to make more of themselves – and we call this “LIFE”.

The “Earth” we live on is the local vessel which contains a great selection of this “LIFE” but there is certainly much more of it battling away in every corner of the cosmos.

So – I ask myself – why is it that the magic of Harry Potter exerts such an attraction for the billions of humans who are fascinated by his story yet the same people are strangely ignorant of the real magic which surrounds them on every side? Somehow the foundations of belief which underpin our mass human culture seem to have got stuck in the deterministic mechanical world of Descartes! The much more exciting (and scary/magical) world of relativity and quantum theory which physicists have been playing with for more than 100 years, has simply not percolated through into our upbringing, education or cultural way of doing things.

This sad state of affairs was brought home to me during a conversation I had with a bright young physics teacher who had just bought my partner's lovely old piano. Did he, I asked, teach anything about relativity or quantum theory to his teenage students. “Oh no”, he replied, “such things are considered much too hard to understand and are only taught at University level”. So this is the knub of the whole problem. Of course relativity and quantum theory ARE impossible to “understand” - that's the whole point. Those of us with the right training can predict their effects through the medium of mathematics - but we certainly cannot “understand” them, just as we cannot “understand” why we are here and why life on Earth is behaving as it does.

So my message at Christmas is this: - **I believe that the human species will never be able to behave in more life enhancing ways until it does see and marvel at the “MAGIC” of life and the cosmos all around it at every moment. When you live in a “magical” world you would be wise to understand that you cannot “control” events although you may try to influence them. You would be wise to respect the complex power of the natural world which can destroy as well as create. With our amazing brains and capabilities, we humans are an important part of the magic** – but understanding its ultimate destiny will always be beyond us.

So how do we earthly physicists get our message across? Like Beethoven, Einstein was a free thinking man who did not simply follow convention. He worked at the Swiss Patent Office trying to understand different ways in which clocks could be synchronised to ensure train timetables worked properly This was why he became interested in wider questions about time and space. Einstein became convinced that the seemingly perverse implications of the famous (and very elegant) equations, derived by the scottish genius Maxwell from the electrical experiments done by Faraday, were in fact correct. The equations implied that light must always travel at the same speed whatever its moving frame of reference – a result so bizarre that most scientists believed it was an error. Einstein figured out that if Maxwell was right then there must be significant implications for the measurement of time, mass and size as relative speeds became large. For years his conclusions were rejected by the establishment until finally experiments showed his formulae really were correct! This was the genesis of “Special Relativity”.

So when I saw my golfing partner looking carefully at his GPS rangefinder last week I wondered whether he knew that the exact yardage he was seeing could only be calculated accurately because of Einstein's insights! The small computer on his wrist was finding his position by comparing the exact timing of radio signals from at least 4 satellites moving at 14000 miles an hour 20,000 miles away in space. The atomic clocks ticking away in his computer and in the satellites have an accuracy of 1 nanosecond (1 billionth of second). The relative times of signals from different satellites must be within 30/40 nanoseconds in order to predict his position on Earth within 5 yards. (Radio waves travel about 1 foot each 1 nano-second – 10 yards in 30 nano-seconds.)

The effect of Einstein's special relativity means that the fast moving clocks on the satellites will appear to be going slower when seen by a stationary observer on Earth. Yes – they really will! In fact the mathematics shows the slowing to be about 7 microseconds per day (7000 nano-seconds). This is an error which would totally swamp the 30/40 nano-seconds required for accurate positioning. But this is just the start of the problem.

Einstein went on to think even more about the wider consequences of his insights. He had already shown that space and time can flex and bend because of movement. He went on to show how mass (how big stuff is) must “bend” the space around it and this is what makes the thing we know as “gravity”. Just as a ball will roll downhill so any mass will be attracted to any other (as Isaac Newton predicted) because each mass “bends” the space around it, making a gradient just like the hill for the rolling ball. So here again there are important consequences for our golfer's GPS receiver. The little receiver on his wrist is 20,000 miles closer to the massive centre of the Earth compared to the atomic clock ticking away out in space. The tighter curvature of space near the Earth makes the wrist clock run slower according to the mathematics of General Relativity. This is an even bigger effect (about 38 microseconds per day) than the opposite effect we calculated (7 microseconds) because of Special Relativity. The makers of the GPS wristband have to take account of the net effect of both types of relativity by adjusting the atomic clock on the golfer's wrist (by about 30 microseconds perday) so its time matches the clocks on the satellites.

I hope you find this reality quite impossible to understand! The maths really works – but it produces a magic which is certainly incomprehensible - and that's the whole point. The important step which all of humanity needs to take is to realise that we will never be able to “understand” the cosmic processes of nature. All we can do is appreciate their “magic” and try to live our lives accordingly.

I should add that when we get to quantum theory, the “magic” of reality becomes even more weird. The mathematics implies that things can be in two places at once and even the exact position of something has to be calculated as a matter of chance. Once again we can use the mathematics to predict outcomes. We can understand the maths but we can never “understand” the magic of reality itself.

So this Christmas just take a moment to reflect on the fact that the human brain you carry with you is probably the most complex ordered structure which the magical reality of the cosmos has produced after 14 billion Earth years of evolution. You don't have to understand it but the “magic” is certainly all around us for those that have the wisdom to see it.

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