ultraviolet-divergence:
natalieironside:
Fellow science assholes and science enthusiast assholes: Hit me with your favorite wildly unguarded speculations about what conditions were like before the Big Bang. Bonus points if the crankery includes dubious math; we love reading about dubious math.
I enjoy the French bread model of chaotic cosmic inflation- before our Big Bang, there had already been many (infinitely many?) other Big Bangs, each leading to their own local universes. These other universes continue to exist around us, but because each creates its own expanding spacetime metric, we will never observe them. Note, this is different from the boundary of our own observable universe, about 14 billion light years away and increasing with time, which is only a function of where we happened to evolve and how old the universe is.
But within these different bubbles of cosmic inflation, new spacetime is being created too quickly for them to come into contact with one another. Or, alternatively, there is no spacetime between these bubbles, and so they can’t come into contact with one another, as there is no dimension for such an interaction to occur in.
These other universes share some, but not all, of our physics, because our physics is an outcome of certain symmetries breaking while our universe chaotically cooled down after our big bang. Certain fundamental constants will vary in these other universes, such as the mass of some fundamental particles or the relative strengths of different forces, whereas some will not, such as the speed of light. They may also have a different number of dimensions!
For additional dubious speculation, please see further in Max Tegmark’s hierarchy of different multiverses (the above is what he describes as level II)
I’m not even sure it’s wildly unguarded so much is perfectly reasonable and quite grounded speculation which needs more mathematical exploration, but it’s really fun, so…
This will take some background first though.
So. Thestandard model of the universe as we currently understand it is a variety of quaternion topological structures laid over a manifold with three dimensions of space and one dimension of time.
What that means in somewhat simpler terms is that spacetime is squishy and stretchy but does not tear, and has three dimensions which are negative, and one dimension which is positive. What this means is that if you go an equal distance in one direction in space and in time, they cancel each other out and the effective distance is zero. If you’ve ever heard that light doesn’t experience time, or that somebody moving fast relative to you experiences less time than you do, this is why. The distance you travel in this case is how much internal “time evolution” you experience, and (to simplify things) we are all moving in the time dimension at the same speed. So if someone moves really fast relative to you, you see their time evolution distance as being smaller than yours. But light is moving so fast relative to you that it appears to have no time evolution at all.
Then at each point on this hyperbolic (name for positive and negative dimensions together) spacetime, we can define a variety of numbers and these numbers are quaternions. So, complex numbers are numbers which have one real component, and one imaginary component. So like 3 i. Quaternions are like that but they have one real number and three different flavors of imaginary number. Like 3 i-2j 4k. Each imaginary number acts like i does, so j^2=k^2=-1. But also there’s ij=k and ji=-k. They’re fun and also for complicated reasons, extremely useful for describing three-dimensional rotations so they show up in a lot of graphics programming.
Now these numbers show up in complicated ways. For instance, let’s imagine a circle. Now we’re going to add a line from 0 to 1 attached to each point on the circle. That makes a cylinder right? Well sure, but it can also make a Möbius strip. The lines don’t have to be attached to their neighbors in a way that makes a cylinder. At one point on the circle we can have two of the lines be connected upside down creating a Möbius strip. Well these, both the cylinder and the Möbius strip, are what are known as topological structures.
Except in the standard model, instead of having a circle as the foundation, we have a hyperbolic spacetime. And instead of a simple line from zero to one, we have line segments of quaternions and infinite lines of quaternions and planes and volumes and hyper volumes of quaternions, and also real and complex numbers which can be made out of quaternions. And instead of just being able to attach things so that they look like cylinders or Möbius strips, there is so much weird stuff you can do with these structures.
And those weird structures are things like the electromagnetic field, the gravitational field, strong field, weak field, and the higgs field. And there are certain properties of those fields which create structures which tend to persist even when acted on by other forces, and those are particles.
Now this theory is incomplete, we know some ways it doesn’t quite match reality. One theory for why is that we need to extend the quaternion number structures to include octonion number structures, which have seven types of complex number. Unfortunately the math for this is so hard that in 45 years only one person (Cohl Furey) has made any meaningful progress on this theory, and that only recently. An attempt at a simpler to solve model is string theory, where each point in space-time is a circle instead of a point, but it’s run into a lot of trouble.
Anyway, that is the background necessary to understand this fun theory about what happened before the Big Bang. See, remember how I said space time has three negative dimensions and one positive? Yeah that’s not necessarily the case. You can also have three positive dimensions and one negative and get something very close to the physics we see. The difference is just that you swap a lot of the right hand rules for left hand rules, Like rules about how a curling magnetic field generates an electromagnetic force, where in this flipped spacetime the force would go the other direction.
So the question is, why do we see right-handed forces instead of left-handed forces? Why is the universe one way instead of the other? Well the answer this theory proposes is that it’s not, it’s both. On one side of the big bang you have positive time moving in one direction, and on the other you have negative time moving in the other direction. So on the other side of the Big Bang is just a mirror to our universe with differently handed physics rules.
The trick is that you need some weird math to describe the connection between the two sides right next to the Big Bang. I don’t mean this in the sense that stuff could be transferred from one side to the other, but in the weird abstract mathematical way where one connection defined a cylinder and another connection defined a Möbius strip. And it turns out that some of the mathematical connections proposed to make this work happen to come with interesting solutions to some perplexing bits of cosmology.
The authors of this theory are very reasonable and grounded about it, and will be the first people in line to comment that not enough work has been done to evaluate this properly as a theory yet, or even to construct a full theory which can be evaluated. But they also point out, quite rightly I think, but this is a much simpler and more sensible solution to some of our cosmology issues than string theory is, and think we should be investigating similar mathematical structure implications of the standard model before we go replacing the whole thing with string theory.
