20.08.2006 18:19
PS on sheep
Hey, that's it. It's then obvious that this matter of "counting sheep until you fall asleep" does never work. Because you just cannot count them.
19.08.2006 21:39
Inflation and sheep
Last week as part of the concluding conference of the NBI Summer institute there was a very nice talk by Paul Steinhardt from Princeton University on "the origin, structure and future of the universe".
According to the standard model of cosmology there was a big bang, where everything, the universe, space and time began. Shortly after our universe entered a period of inflation, where it expanded at an exponential rate. Inflation accounts for the homogeneous microwave background which we measure nowadays (COBE, WMAP) This background radiation is very uniform, it is 3 K everywhere modified by tiny quantum fluctuations as you can see from that fameous WMAP pictures. According to Steinhardt this process can be modelled by a scalar field which moves in a potential. Classically, the scalar would be developping towards the minimum of the potential where inflation eventually stops, and the universe is flat and uniform as we see it. But due to quantum fluctations there will allways be regions where inflation goes on. (The scalar field jumps "back up the potential".) Since these regions expand exponentially most of the universe in fact continues expanding. In the end we have an eternally inflating universe full with causally disconnected "bags" where expansion has stopped. This theory is called "eternal inflation". Steinhardt said that he finds this idea very disturbing because apart from explaining how the part of the universe we see, came about, it tells as that indeed most of the universe is not at all like the place we live in and there must be infinitely many other "bags" in the universe of every physically possible type. However since there is no causal connection they are out of our reach.
I like the picture. First of all I have never understood why there shouldn't be any other worlds where physics is very different? Many physicists search for a ultimate theory which explains for every constant that there is, why it has the value it has. The goal is to explain that it could not have been otherwise or at least that every other solution would be very improbable. I never really understood why there should be such a theory at all. I suspect that behind this quest there is an anthropic principle lurking: Since if there is no other possible way the universe could develop then it is necessary that mankind came into existence. Why shouldn't it be just coincidence? Due to a quantum effect at the very beginning somewhere? And suppose that quantum physics is objectively random, then we are just a coincidence. Of course in an eternally expanding universe there are so many "bags" that there will be a whole lot of them where some kind of living creatures developped. There might even be infinitely many universes which are very similar to ours, which contain men and fish and sheep.
Now the sheep: Some days ago, I claimed that there can be at most
sheep, since sheep are discrete things and I intuitively thought that a set of discrete things just cannot be uncountably large (Do you know any mathematical set, i.e. set of discrete number which is larger than 
. But in view of eternal inflation I must admit that there are possibly many more sheep. Since it seems to me that there might well be uncountably many such bags in the universe which contain sheep. So even if there was only one solitary sheep in each of them, that makes them many many more in total.
