## Tuesday, January 11, 2011

### Living on the hillside

I grew up on the side of a hill. There was always a view ahead of you wherever you were in the garden, and a steep bank behind you. Streams always ran downwards towards the view, ahead of me the future path of the water, and behind me the past.

When asked where the water in the stream came from I might have answered “from further up the stream”, and if questioned further I may have said “well from even further up”. From my knowledge of the garden where I played, and from my friends’ houses it would have been hard to comprehend how the streams could have a beginning and an end… and this isn’t surprising because almost all houses in hilly areas are on the side of the hill, very few indeed are right at the top or right at the bottom, very few places show where a stream actually starts.

As adults we sometimes think of time as flowing like a stream, it always comes from somewhere and goes to somewhere else. And here lies a puzzle for us… what was the first moment in time? And what came before that?

People answer in several ways, some say it’s impossible to have time before the big bang, others say there was just nothing before that, others suggest that there was a big crunch before the big bang, giving way to infinite repeated cycles of universes, so time goes on indefinitely. I would like to explain why I think it is probably none of these.

Just like growing up on a hillside, we are all on a different kind of hill, we are descending from order into chaos. I don’t mean this as dramatically as it sounds, this simply means that things are very very slowly becoming more disordered, it is called the 2nd law of thermodynamics and the chaos is measured as entropy and is slowly increasing.

Unlike what is often quoted of this law, there is not an inevitable march into chaos, but from the high perch of order that we are on in this universe each step in time is highly likely to increase disorder.

In this post I show how the total landscape of possible evolutions of the universe follows a fractal pattern which looks much like a hilly terrain through time, perched on the side of a hill looking downwards to a slowly more disordered future. When we look back towards what we think of is the beginning of the universe we are actually looking up to the top of this hill. As we try and look back deeper into the past the cause and effect of events will become less clear, and a description of why each event happened will be less apparent and more contrived, more and more events will seem to just emerge due to luck from a more chaotic state. This tipping point is the top of the hill.

If we could look back further the events would seem almost magical, things would seem to emerge by change, you might see a chaotic galaxy splitting neatly into two ordered ones, in short it would look like time in reverse. This is because newton/einstein’s physics is time reversible.
So a good way to make sense of this is to distinguish objective time (the horizontal axis below) from subjective time, which always points down the hillside:

Why should subjective time run downhill?
It guarantees that entropy/disorder will increase over time. Otherwise, it may take some clever experiments to explore the relationship between entropy and time, but I will hazard a theory here…

Our perception of time is probably mostly to do with us having memories of the past and being able to store and then re-simulate them in our heads. If you keep memories of up the slope then this has more order and an event uses less information, whereas down the hill events would take more information than our current experience. There is a sense that you can fully know the uphill (past) but are not able to understand downhill (future) as it is more complicated than your current state.

You might even use this idea to come up with a unit of subjective time, the time taken for you to be able to store an event twice in the space that you can currently store an event. This idea lets us answer a second puzzle, how long does the universe last?

If time is perceived in proportion to increase in entropy, then as you near the bottom of the hill, the gradient probably drops off and time will pass faster… i.e. the universe won’t “get boring”… at some point you will hit another upwards hill and you won’t perceive time after that.