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A Really Long Time

I want to go back to the theme of big numbers in this entry, particularly in relation to an interesting web site which describes the different ways the world might end. The web site is Exit Mundi and the URL for the specific article I’m describing is http://www.exitmundi.nl/eternity.htm. Before I go any further I want to emphasise that I haven’t checked up on the credibility of this article although it does cite two references and seems reasonable based on the existing knowledge I have of the topic.

First, some background. There is a phenomenon known as vacuum fluctuation where mass can appear spontaneously from a complete vacuum for short periods of time by “borrowing” energy from “nothingness”. This seems strange but its real and has been observed in experiments. Single particles continuously appear for really short times, then disappear again everywhere, but its also theoretically possible for combinations of these events to produce macroscopic objects, perhaps even a whole Universe!

This is the future of the Universe portrayed at the site. First, in one hundred trillion years the sky will be black. All the stars in our galaxy will have burned out and all the other galaxies will have moved out beyond our visible range, even if they are still producing light.

A bit further in the future, in one hundred million trillion years, our galaxy will be gone completely. All the objects left will have been captured by black holes. Other galaxies will suffer similar fates.

Form there things get really serious. Subatomic particles themselves aren’t stable over really long periods of time (at least according to this site because this theory is far from proved). In 100 billion trillion trillion years particles like protons, and in about 1 thousand billion trillion trillion years, photons will also simply evaporate! There will be nothing left except the black holes.

But even the black holes themselves will evaporate through a process called the Hawking radiation process. They will turn into photons which will then decay themselves. At this point there really is nothing left… except for the vacuum fluctuations I mentioned near the start.

As I said above, vacuum fluctuations provide a way for mass/energy to be created from nothing and for no reason and, if you wait long enough, anything can result. There has even been a calculation for how long we would need to wait until a whole new Universe was created through another big bang.

This is how long we would expect to wait for a big bang to spontaneously appear: 10^1056 years. That’s so big I hardly know how to describe it in words. I usually use quadrillion as the biggest word to describe a number, but even that is hopelessly inadequate here. I need to revert to the good old googol, that word which people use to describe a really big number. A googol is 1 with one hundred zeros after it, that is: ten thousand trillion trillion trillion trillion trillion trillion trillion trillion. Based on that, the number of years we would need to wait for a new universe would be one hundred million trillion trillion trillion trillion googol googol googol googol googol googol googol googol googol googol.

Assuming time is infinite this doesn’t seem like too long to wait, but compared with anything else it seems a ridiculous amount of time. But it does mean there is an unlimited supply of universes basically guaranteed to continue forever… if you are patient!

Note. After researching big numbers I have noticed that, in the past, I have used the words trillion and quadrillion inconsistently. There are two meanings for most of these words: the American and modern British version, and the European and traditional British version. I used trillion in the US sense (1 followed by 12 zeros) but I used one quadrillion in the European sense (1 followed by 24 zeros). This isn’t completely incorrect but its obviously very confusing! I have used the US versions consistently in this entry.

Obviously for serious scientific work numbers should be specified using digits such as 1 x 10^12 instead of potentially confusing words like trillion or difficult to follow sequences of zeros like 1 000 000 000 000.

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