Now, your homework assignment is to really think about this, to contemplate what it means. Carl Sagan once famously said that in order to make an apple pie, you must first invent the Universe. But he was not right. In Boltzmann’s scenario, if you want to make an apple pie you just wait for the random motion of atoms to make you an apple pie. That will happen much more frequently than the random motions of atoms making you an apple orchard, and some sugar, and an oven, and then making you an apple pie. So this scenario makes predictions, and the predictions are that the fluctuations that make us are minimal. Even if you imagine that this room we are in now exists and is real, and here we are and we have not only our memories, but our impression that outside there is something called Caltech and the United States and the Milky Way Galaxy.
It’s much easier for all those impressions to randomly fluctuate into your brain than for them to actually randomly fluctuate into Caltech, the United States and the galaxy. The good news is that, therefore, this scenario does not work, it is not right. This scenario predicts that we should be in minimal fluctuation, even if you left our galaxy out, you would not get a hundred billion other galaxies. Feynman also understood this, Feynman says: “From the hypothesis that the world is a fluctuation, all the predictions are that if we look at a part of the world we have never seen before, we will find it mixed up, not like the piece we just looked at.” High entropy. “If our order were due to a fluctuation, we would not expect order anywhere, but where we have just noticed it. We therefore conclude the Universe is not a fluctuation.” So that’s good, the question is then, what is the right answer?
If the Universe is not a fluctuation, why did the early Universe have low entropy? And I would love to tell you the answer but I’m running out of time. Here is the Universe that we tell you about versus the Universe that really exists. I just showed you this picture, the Universe is expanding for the last ten billion years or so, it’s cooling off.
But we now know enough about the future of the Universe to say a lot more. If the dark energy remains around, the stars around us will use up their nuclear fuel, they’ll stop burning, they will fall into black holes. We will live in a Universe with nothing in it but black holes. That Universe will last 10 to the 100 years, a lot longer than our little Universe has lived. The future is much longer than the past.
But even black holes don’t last forever, they will evaporate, and we will be left with nothing but empty space. That empty space lasts essentially forever. However, you notice that since empty space gives off radiation, there’s actually thermal fluctuations and it cycles around all the different possible combinations of the degrees of freedom that exist in empty space. So even though the Universe lasts forever, there’s only a finite number of things that can possibly happen in it, they all happen over a period of time equal to 10 to the 10 to the 120 years.
So here are two questions for you: number one, if the Universe lasts for 10 to the 10 to the 120 years, why are we born in the first 14 billion years of it, in the warm, comfortable afterglow of the Big Bang? Why aren’t we in empty space? You might say, there’s nothing there to be living, but that’s not right.
You could be a random fluctuation out of the nothingness. Why aren’t you? More homework assignments for you. So, like I said, I don’t actually know the answer, I’m going to give you my favorite scenario; either it’s just like that, there is no explanation, it’s a brute fact about the Universe that we should learn to accept and stop asking questions. Or maybe the Big Bang is not the beginning of the Universe. An unbroken egg is a low entropy configuration and yet when we open our refrigerator we do not go: “How surprising to find this low entropy configuration in our refrigerator.” That’s because an egg is not a closed system. It comes out of a chicken. Maybe the Universe comes out of a Universal chicken. Maybe there is something that naturally, through the growth of the laws of physics, gives rise to a Universe like ours in low entropy configuration. If that’s true it would happen more than once, we would be part of a much bigger multiverse. That’s my favorite scenario.
So the organizers asked me to end with a bold speculation; my bold speculation is that I will be absolutely vindicated by history, and 50 years from now all of my current wild ideas will be accepted as truths by the scientific and external communities who will all believe that our little Universe is just a small part of a much larger multiverse, and even better, we will understand what happened at the Big Bang in terms of a theory that we will be able to compare to observations. It’s a prediction, I might be wrong, but we’ve been thinking, as a human race, about what the Universe was like, why it came to be the way it did, for many many years. It’s exciting to think, we may finally know the answer some day. Thank you.