My attitude towards the landscape problem had been based on pragmatic neglect. I can't figure out what this discussion is good for, so why bother? The landscape problem, in one sentence, is that a supposedly fundamental theory does not only deliver the description of the one universe we inhabit but of many, maybe infinitely many, universes in addition. The collection of all these universes is often called the multiverse.
There are many versions of such multiverses, Max Tegmark has layered them in 4 levels and Brian Greene has written a book about them. String theory infamously won't let its followers ignore the inelegant universes, but everybody else can still ignore the followers. At least that was my way to deal with the issue. Until I heard a talk by Keith Dienes.
Dienes has been working on making probabilistic statements about properties of possible string theory vacua, and is one of the initiators and participants of the "string vacuum project."Basically, he and his collaborators have been random sampling models and looked how often they fulfilled certain properties, like how often did one get the standard model gauge groups or chiral fermions, and where these features statistically correlated. I can't recall the details of that talk, you can either watch it here or read the paper here. But what I recall is the sincerity with which Dienes expressed his belief that, if the landscape is real, then in the end probabilistic statements might be the only thing we can do. There won't be no other answer to our questions. Call it a paradigm change.
Dienes might be wrong of course. String theory might be wrong and its landscape a blip in the history of physics. But that made me realize that I, as many other physicists, favor a particular mode of thinking, and the landscape problem just doesn't fit in. So what if he's right, I thought, would I just reject the idea because I've been educated under an outdated paradigm?
Now, realizing that I'm getting old didn't make me a multiverse enthusiast. As I argued in this earlier post, looking for a right measure in the landscape, one according to which we live in a likely place, isn't much different from looking for some other principle according to which the values of parameters we measure are optimal in some sense. If that works, it's fine with me, but I don't really see the intellectual advantage of believing in the reality of the whole parameter space.
So while I remain skeptic of the use of the multiverse, I had to wonder if not Dienes is right, and I am stuck with old-fashioned, pragmatic paradigms.
I was trying to continue to ignore string theorists and their problems. Just that, after trying for some while, I had to admit that I think Tegmark and Greene are right. The landscape isn't a problem of string theory alone.
As I've argued in this post, every theory that we currently know has a landscape problem because we always have to make some assumptions about what constitutes the theory to begin with. We have to identify mathematical objects with reality. Without these assumptions, in the end the only requirement that is left is mathematical consistency, and that is not sufficient to explain why we see what we see; there is too much that is mathematically consistent which does not describe our observation. All theories have that problem, it's just more apparent with some than with others.
Normally I just wouldn't care but, if you recall, I was trying not to be so pragmatic. This then leaves me two options. I can either believe in the landscape. Or I believe that mathematics isn't fundamentally the right language to describe nature.
While I was mulling over German pragmatism and the mathematical effectiveness of reason, Lee Smolin wrote a paper on the landscape problem
- A perspective on the landscape problem
The paper excels in the use of lists and bullet points, and argues a lot with principles and fallacies and paradigms. So how could I not read it?
Lee writes we're stuck with the Newtonian paradigm, a theme that I've heard Paul Davies deliver too. We've found it handy to deal with a space of states and an evolution law acting on it, but that procedure won't work for the universe itself. If you believe Lee, the best way out is cosmological natural selection. He argues that his approach to explain the parameters in the standard model is preferable because it conforms to Leibniz' principle of sufficient reason:
- Principle of Sufficient Reason.
For every property of nature which might be otherwise, there must be a rational reason which is sufficient to explain that choice.
That reason cannot be one of logical conclusion, otherwise one wouldn't need the principle. Leibniz explains that his principle of sufficient reason is necessary "in order to proceed from mathematics to physics."
Lee then argues basically that Leibniz's principle favors some theories over others. I think he's both right and wrong. He is right in that Leibniz's principle favors some theories over others. But he's wrong in thinking that there is sufficient reason to apply the principle to begin with. The principle of sufficient reason itself has a landscape problem, and it is strangely anthropocentric in addition.
As Leibniz points out the "sufficient reason" cannot be a strictly logical conclusion. For that one doesn't need his principle. The sufficient reason can eventually only be a social construct, based on past observation and experience, and it will be one that's convincing for human scientists in particular. It doesn't help to require the sufficient reason to be "rational," this is just another undefined adjective.
Take as an example the existence of singularities. We like to think that a theory that results in singularities is unphysical, and thus cannot fundamentally be a correct description of nature. For many physicists, singularities or infinite results are "sufficient reason" to discard a theory. It's unphysical, it can't be real: That is not a logical conclusion, and exactly the sort of argument that Leibniz is after. But, needless to say, scientists don't always agree on when a reason is "sufficient." Do we have sufficient reason to believe that gravity has to be quantized? Do we have sufficient reason to believe that black holes bounce and create baby universes? Do we have sufficient reason to require that the Leibniz cookie has exactly 52 teeth?
Do we have any reason to believe that a human must be able to come up with a rational reason for a correct law of nature?
The only way to remove the ambiguity in the principle of sufficient reason would be to find an objective measure for "sufficient" and then we're back to scratch: We have no way to prefer one "sufficiency" over the other, except that some work better than others. As Popper taught us, one can't verify a theory. One can just not falsify it and gain confidence. Yet how much confidence is "sufficient" to make a reason "rational" is a sociological question.
So in the end, one could read Leibniz principle as one of pragmatism.
That way reassured in my German pragmatism, I thought going through this argument might not have been very useful, but at least it will make a good blogpost.