I hope to swash an oft repeated criticism of the multiverse theory saying such a result depends on a speculative inflation model such as one caused by some ad hoc scalar field.

This is all you need to just about guarantee an eternal multiverse:

- That some superluminal inflation actually took place. (We have lots of evidence for this.)
- That it was caused by a quantum process. (And what in nature fundamentally isn't?)

That's it, that's all you need and this is why:

- If a quantum process it, like every other quantum process, has a finite probability of happening again.
- If it was quantum, it had to emerge from some pre-existing thing other than a singularity.
- Whatever this thing was, (pre-existing universe?), since it went through a superluminal expansion, there is literally exponentially more of it which has the probability of happening again.

Let's use some numbers to do a back of the envelop calculation. We know from data that our own universe experienced an exponential expansion of greater than 60 e-folds.

So pretend this thing was some small 3D box of space time. Now, assume some quantum process made our box go through a 60 e-fold expansion.

What do we get? We get a new universe filled with 10^78 boxes identical to the first, each just as likely to inflate as the first was.

*How on earth could you justify an event, which happened, to not happen again when such an event is now 10^78 times as likely to occur? It's like saying: suppose every time a neutron decays, 10^78 more neutrons are created. Should we expect to see another neutron decay?*

And this is very conservative. I assumed inflation stopped everywhere after 60 e-folds which is the bare minimum assumption I can make given the data.

The odds are it happens again, and again and again creating an eternal multiverse. It is really very robust and you don't need scaler fields, colliding branes, etc... All you need is a superluminal expansion, governed by a quantum process, to occur even once.

Interesting, especially since I don't know much about cosmic inflation.

ReplyDeleteI was just reading about the Banach-Tarski paradox, in which a single 3-d ball can be broken into many non-overlapping pieces, which can then in turn be reconstructed into two balls each identical to the first. Of course this can't be done with a material ball, since such an operation doesn't conserve volume. But for an ideal ball the pieces are simply collections of geometric points.

Thus, since space-time is literally geometric, your argument seems to agree with the Banach-Tarski result.

Ben, that's really interesting and yes it does seem to be analogous.

ReplyDeleteTo me, how space-time, and the quantum fields within it, can grow without violating some conservation principle is intriguing. Physicists point to the fact that in quantum field theory the vacuum energy is technically infinite so there is plenty of energy to go around.

Still, it is crazy to think that the universe is like this.

"We get a new universe filled with 10^78 boxes identical to the first, each just as likely to inflate as the first was."

ReplyDeleteI think that is what makes me most uncomfortable with this whole multiverse idea - how do you know that each new box is just as likely to inflate as the original one if you don't know how they inflate in the first place? And arguing that since string theory allows for different physical laws those laws are just as valid as the laws of physics in our current universe assumes string theory is correct. There are a number of non-physical solutions to Maxwell's equations, for example, but I don't think one could base a prediction about multiple universes on that theory, much less on string theory which completely lacks experimental evidence.

Nick,

ReplyDeleteCome, join me on the dark side. :)

"how do you know that each new box is just as likely to inflate as the original one if you don't know how they inflate in the first place?"

This is another subtle assumption in all quantum theories, much like the equivalence principle in relativity: We do assume that the fundamental physics of the universe is the same at every point.

In quantum field theory language this means that every point in space has the same vacuum structure and quantum fields whether they are excited or not.

I *agree* I am making the subtle assumption that as the universe inflates the "new points" points have the same underlying quantum structure as the "old ones", both in terms of vacuum states and fields, and therefore inherit all the same quantum possibilites as the "olds ones." If this assumption is wrong a lot more than inflation is on shaky ground.

"And arguing that since string theory allows for different physical laws those laws are just as valid as the laws of physics in our current universe assumes string theory is correct."

I have made no references to string theory. This argument just as valid/(invalid?) whether or not string theory is true.

In some sense this is my point, you don't need something complex like string theory to have a multiverse. But I admit you need your fundamental theory to be quantum in nature.

However, adding the complexity of string theory does open even more possibilities. Those extra possibilities require something like string theory, but not the minimal idea that there may be a multiverse of some type.

Just watch Nick, one day you will be a convert. Or maybe its one day I will look like a big fool. I've still never said the multiverse *is* correct, only that I think there is a strong case to be made that it probably is.

Let me also as this, the robustness of a multiverse does not stand on this "back of the envelope" calculation. After reading your last comment I realized many other subtle points you could bring up to attack my claims.

ReplyDeleteHowever, l'll just say to first order I believe this argument should be good enough for someone who doesn't need all the details.

People a lot smarter than me, like Guth and Linde I have quoted, have come up with much more compelling arguments for the robustness of a multiverse.

However, on a practical level, I hope my overly simplistic argument sheds light on some basic reasons why one would expect something like a multiverse indeed comes from inflation.