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PG: Well, sometimes what pulls toward prediction may not pull in the same direction as explanation. Theories that are purely predictive, that don’t give us a sense of understanding, can be valuable in some moments. That kind of positivist urge was part, though not all, of what Einstein was trying to do with special relativity.
He said, “It’s all very well to try to understand what’s going on inside of an electron and to wonder about the dynamics of the ether and whether it moves around like little gyroscopes at each point. But this is beyond what we can know. Let’s start with something that we can touch and measure. We’ll say the measure of space will be laying down rulers, and the measure of time will be what I can see on my watch. And we’ll build up from these founded principles.”
Other times it’s the explanatory force of something that drives us even where prediction is difficult. Einstein’s later work with general relativity, for example. When he saw that the motion of Mercury as it went around the Sun violated everything people knew from very accurate calculations based on Newton’s theory, he wrote a postcard to his mother, saying, “Something snapped inside me.” He knew at that moment this theory was right. He had one measurement — an old measurement, at that.
This play between prediction and explanation is a tension that lies very, very deep inside the history of physics. There are moments when, by turns, one plays a more dominant role than the other. Of course, we’d like to have both.
PS: But at least in the history of science up until the present, there’s always been the thought that we’re working toward a positivist-type solution. We hope to eventually find a theory that explains what we know and that predicts new things we haven’t measured.
The kinds of theories we’re talking about now explain after the fact, or are designed to match what we already knew. It seems to be a different kind of paradigm as to what science is, what even constitutes a valid, an acceptable, theory.
PG: Right. So there are splits in science where people disagree about something that’s predicted. But there are also splits where one side says to the other, “That’s not really science. It’s not the project we should be engaged in.” And that’s a deeper, far more unsettling moment.
We have that sort of split right now among the string theorists. One side says, “Look, what’s really scientific is to say there’s this infinite or very huge number of craters to be imagined in some landscape, each of which carries different physical particles and different physical laws and so on. And we happen to live in one of them.”
But the other says, “You’ve given up! You’ve given up the historical project of science. We went into string theory because we wanted to produce a theory that had one parameter, or very few movable parts. And now instead of a glider you’ve got a helicopter with 10,000 little pieces that have to move exactly the same way. If the slightest thing goes off, it falls to the ground in a heap of burning aluminum.”
It’s really an interesting moment in that way.
PS: I think it’s historic. There’s a certain community that feels, “This is an ‘aha’ moment. Science has to change. We have to accept that science has limits. There’s only a certain amount that we’ll be able to predict. Beyond that we’re going to accept that we live in some special corner of space in which seemingly universal laws — including Newton’s law of gravity — are just local environmental laws that aren’t really characteristic of the whole.”
Other groups say, “Hold it, this is failure. We either find ways of fixing the problems in those theories, or we scrap them and replace them with something else.”
OUT OF BOUNDS?
PG: There was a huge debate in Germany in the 19th century called the Limits of Science debate. The question was, “Is there a limit to what you can explain with science?” Not just the current science, but science in general. Was it a matter of ignoramus, that we don’t know, or ignorabimus, that we cannot know?
For some people, it was a protection of science against the mystical or the religious, a guard against intrusions of the nonscientific into the scientific domain. It said, “Here are the limits of science; everything within this domain is ours, and beyond it, do what you want, but it’s outside of what’s really going to be explained by science.”
PS: You mean ever?
PG: In principle. Of course, a boundary keeps one side away from the other, and vice-versa. So certain figures on the religious side said, “Oh, the limits of science are a good thing.” It says that there is a domain that is inherently mystical or spiritual and science won’t intrude on it.
But the assertion of the limits of science was also criticized. For some people it was outrageous that you would say there’s anything outside of science. This was certainly the view of the scientists who helped form the Vienna Circle — the beginnings of the philosophy of science — after the first world war. Their view was that you could put things in logical form based on observation combined with the new formal logic. If you couldn’t, you were dealing with errant nonsense.
That’s such a hard and fast line that it was inadequate for many scientists, like Einstein, who said that science has to go beyond the simply observable. By the end of his life, he became increasingly convinced that reality could be ascribed to phenomena beyond what we observe.
PS: So Einstein brings up the issue of space and time, which is something I want to revisit. Because although in relativity we’re used to them being on equal footing, in cosmology they really aren’t.
When we say the universe is 14 billion lightyears across, it’s somewhat unclear exactly what we mean. But, roughly, there’s a certain finite patch of space we can observe because that’s the greatest distance from which we can see light. We believe that the universe extends much farther than that, and it may even extend infinitely farther.
So here’s the question: Is it finite — does it eventually close on itself — or is it really infinite? All that we can tell from measurements in our own patch, especially recent measurements by the WMAP satellite, is that we can’t tell. We’d need to be able to go way beyond what will ever be visible to be sure.
So we must ask ourselves: Is this question — whether or not space is finite — even a scientific one? If it’s forever beyond our realm of testing, is it science? Is it metaphysics? Is it even an important question?
PG: Is it in principle beyond the realm of testing?
PS: When the universe is filled with matter and radiation, the expansion of the universe continually slows down. Because of that deceleration, we are able to see the light from greater and greater distances as time goes by. At any given time, of course, there’s a horizon, a limit to how far we can see. The universe is only about 14 billion years old, so the current horizon is 14 billion light-years. But in principle as long as the expansion rate is slowing down, we can see more and more space.
That whole view has recently been upended because we’ve discovered that beginning about five billion years ago, the expansion of the universe has begun to speed up again. When the universe undergoes acceleration, the opposite happens — we will actually be losing sight of the space that we’re seeing today.
The billions of galaxies we see now, almost all of them beyond Andromeda, will eventually recede from view forever and our patch of space will become a wasteland.
So, whether or not there’s an infinite amount of stuff out there, as both eternal inflation and the cyclic model would suggest, is therefore not testable as a matter of principle. Accepting this kind of limit seems like something new.
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