Why Multiverses don't help with Fine Tuning
It's often said that the idea of a multiverse helps to solve the supposed problem of “fine tuning”. The apparent unlikeliness of the values of physical constants in our universe, the values that seem to be required for life, should be no surprise if there are a multitude of other universes in which the values are different. The set of universes provides somehow a larger domain within which the very unlikely is bound to happen. But what does this really mean? Does it make sense. No, it doesn't.
To see why, here is a thought experiment. A spaceship is in orbit around a very large black hole (very large black holes are more gentle in terms of the forces nearby to them). In the black hole is a robot programmed to play cards. It's got stuck in “shuffle and deal” mode. Many, many times a second, it shuffles a deck, and deals out the cards. Bored with trying to fix it, the crew have gone to sleep. The robot is still shuffling the next morning (or what counts for morning on such a spaceship). “Throw it out with the trash” says the Captain. The robot is still shuffling cards as it is dropped out of the garbage chute and falls towards the black hole. Within a minute, the shuffling robot fades out of view. The crew take a routine look at the ships internal security cameras, and what they have been viewing. One of them notices the robot dealing out a deck with all the cards in order. “What a rare thing it must be” says the first office. “Yes”, says the Captain, “but the robot is still shuffling even now, within the black hole. It will be days before it is finally crushed. All that shuffling means that unlikely arrangements will tend to turn up more.”
Is the Captain right? From the “point of view” of the robot, it is still falling and shuffling cards. However, black holes do odd things to space and time. From the point of view of the crew the robot never entered the black hole, it seemed to slow down as it approached, and, if they could still see it, it would be frozen still at the very edge of the hole – the “event horizon” - the place from which nothing can return. If we forget the messiness of quantum mechanics, the robot will take forever to reach the black hole. It will be seen to resume shuffling “beyond eternity”. Objects within the black hole are effectively in another reality, another space-time, another universe.
It seems clear that in the strange case of the card-shuffling robot it doesn't make sense to include the card shuffles within the spaceship and those within the black hole as part of the same set. Card shuffles within the black hole can't have any influence or connection with those outside. They are in different universes.
This rather contrived example has a point, which is to show how difficult everyday ideas get when we try and deal with different space-times. This is what we try and do if we are shuffling physical constants and dealing out universes. There is no card table called the “multiverse”, because existence only makes sense within a realm of space and time. Other universes in a multiverse are as isolated from us as an object within a black hole. Just as there is no position where one can stand to see both within and outside a black hole, there is no position where one can see a multiverse. Just as what has fallen in a black hole is "beyond eternity", other universes are separate from ours in ways that it is hard for our language to deal with.
So now, let's get back to fine tuning. What does “rare” mean regarding a universe? What does it mean for a universe to be “unlikely”? These questions seem to lose their foundation, because rarity and likeliness require us to be able to look at some overall domain, some “card table” to see what has turned up, what hands have been dealt.
After the physical constants have been shuffled, if that is indeed what happens, each universe goes it's own way, it has its own future, its own events. Various stages may appear, such as star systems and galaxies, and on some of those stages self-aware actors may appear, such as humanity.
But, each universe has its own space and time, it is its own story in its own space-time book, but there is no library. There is no shelf on which universes can be seen arranged in order, from which ours can be picked from the section labelled 'life-friendly'. As there is no library, there cannot be a sampling of universes. To mix metaphors, there is no position in the library where it is possible to stand to throw darts and see if any have hit the bullseye. A point of view beyond space and time makes no sense, and that is where such a library would have to have its foundations.
Some theories of physics suggest the possibility of knowing at least all possible book titles. String Theory may describe ten to the power 500 or more. But that doesn't help even if there were some meta-universal library, as it doesn't tell us how many copies of each book there are. Even if it did, what does it mean to pick a particular book and take it off the shelf? Does it only count in some way if it the book is the book of our universe, or will a book that is in some way close to ours do just as well to help with discussions about fine tuning?
It has been said by some scientists (particularly Peter Atkins) that “Why” questions can be meaningless. It is also the case that some “What if” questions are similarly mistaken. “What if we were in a different universe?” may be one of these. Questions can lose meaning if they wander outside of space and time. There may be questions about Fine Tuning, but they may not be the questions we have been asking: “Who did it” is almost certainly wrong, and so might be “what if?”.
I believe that we don't yet have the right language to discuss the matter of fine tuning. We may never do. Perhaps it isn't a question that makes sense. One thing is for sure – when dealing with such extreme and extraordinary situations as the origins of universes, common language fails us. We may end up with unintelligible descriptions in obscure mathematics, and we may have to be satisfied with that. Multiverses may not fit within our minds.