Help a lay person understand this theory of the multiverse

[wagersmith]

Hi, I don't know any physics, but I wondered if I could get a physicist to indulge me by telling me the most obvious things that are wrong with this theory of the multiverse (please excuse my profound ignorance of your field):

Lets say our universe uses three dimensions out of the total mathmatically possible 11. Let's say in the center of a black hole, the gravitational force gets so high that at some threshold, the pressure collapses those three dimensions and unfurls some subset of the remaining 8 curled up dimensions. Let's say that as the first clump of strings gets popped into this new configuration, it makes it easier for the rest of the matter in the back hole to assume the same new dimensions. So we've got matter from the black hole of our 3 dimensions bursting into a new set of dimensions. This would be manifest by a reduction in matter in the black hole and a big bang into a new universe with the new set of dimensions. So black holes are cosmic vaginas through which new baby universes, made of different dimensions than their parent universes, are born.

Thanks for taking the time to share your fascinating knowledge with lay people.
Warm Regards,
Karen

 

[kurros]

Haha, a few years ago Lee Smolin was going around saying things not all that unlike what you are saying, although with different motivation (http://arxiv.org/abs/hep-th/0612185). Not sure what the status of it is these days.

 

[julian]

Smolin talked of a Darwin type production of universes from black holes in a general context. Thing is there was a paper by Pullin and Gambini "Discrete quantum gravity: a mechanism for selecting the value of fundamental constants":

"Smolin has put forward the proposal that the universe fine tunes the values of its physical constants through a Darwinian selection process. Every time a black hole forms, a new universe is developed inside it that has different values for its physical constants from the ones in its progenitor. The most likely universe is the one which maximizes the number of black holes. Here we present a concrete quantum gravity calculation based on a recently proposed consistent discretization of the Einstein equations that shows that fundamental physical constants change in a random fashion when tunneling through a singularity."

Also Bojowald has recently put forward the idea that multiverses may come about with inhomogeneity within the context of LQG which involves a transition from elliptic to hyperbolic equations (and correspondingly a failure of propagation of information) that could resolve the special boundary conditions of our universe:

"A loop quantum multiverse?"

 

[julian]

Bojowald is referring to the boundary condition of the big bang rather than the fundamental constants. Multiverse ideas are usually considered to be abstract and the domain of wild physicists like Smolin, but actually they may be predictions of mundane theories like loop quantum gravity. Obviously inhomogeneity could seed regions of spacetime that collapse and then bounce first and will be causally disconnected from the rest of spacetime. But Bojowald is saying intuition from inhomegenieus models is hinting that there is not a simple bounce but at high densities there is a signature change in spacetime taking you from hyperbolic to elliptic equations (it is only with hyperbolic equations you have propagation of information). It sounds a lot like the Hawking-Hartle no-boundary condition. Penrose has been saying for years that a theory of quantum gravity should be time-asymmetric but hasn't been taken seriously as classical GR is time-symmetric and it is not obvious that QM would change this. And he has said that this should be as much a part of physics as determining the dynamical laws. Seems like Bojowald might be predicting such a scenario from mundane LQG. An opportunity to mention this paper again a few months later...

 

[mitchell porter]

The string theory description will possibly be that the black hole (the big ball of strings and branes created by gravitational collapse) loses most of its energy over time by shedding Hawking radiation, and also shrinks until it's smaller than the curled-up dimensions - at which point it will be as small as an ordinary string, and all the space dimensions around it will look "big" to it - and then it just blows up into a few ordinary strings. This is discussed briefly in an appendix of http://arxiv.org/abs/hep-th/0507219 - but it's still just something of an idea, apparently the real math still hasn't been done.

In string theory, people now generally don't believe that black holes produce baby universes, because of the "AdS/CFT correspondence", which says that string theory in "AdS space" has an alternative, totally equivalent description - the "CFT" - which is self-contained, therefore the strings can't ever be creating new degrees of freedom that aren't in the CFT, like a new universe. And then the presumption is that this must apply to string theory in any space, even if we don't know the counterpart of the CFT description for our sort of space.

But even in AdS space, the study of how black hole processes correspond in detail to the CFT description is still quite schematic. It does occur to me that ultra-high-energy virtual processes in the CFT might correspond to the branching off of a closed universe on the AdS side. This is a loophole which has to do with how modern quantum theories work.

To get the probability of starting with some observed physical situation A, and later obtaining another observed physical situation B, you do Feynman's sum over all possible histories starting with A and ending with B - the path integral - and it's a bit like ordinary probability (where you add the probabilities of the individual possibilities, in order to get the total probability), except that you use complex numbers and so different histories can cancel. So this is the mystery and scandal lying beneath the empirical success of quantum mechanics, that we have this procedure for generating empirically relevant predictions - probability of B given A - but we don't know what the hell it means that we have "cancelling possibilities" in between. I actually don't think the idea of cancelling possibilities makes sense in reality, so there must be some other picture of reality that provides an alternative justification for the success of these Feynman calculations.

But even putting that issue side, there are also mathematical technicalities to Feynman's procedure which mean that when it is actually done, it's not as straightforward as it sounds. Suppose you're doing a sum over histories for a vibrating string. You're supposed to include "all" possibilities. Does that include histories where the string is fractally bent, down to infinitesimal scales, and not just where the string is smoothly curving? It ought to, but there are severe mathematical difficulties in defining the path integral over "all infinitesimally jagged string configurations". And the analogous problem arises for fields - in this case the problem comes from peaks and troughs in the field intensity, that have that same infinitesimal jagged fractal quality.

So in practice, these sums are only done over limited classes of configurations, and then there will be some recipe for approximating or ignoring everything else. If this recipe works, meaning that you can still get meaningful answers from a procedure consisting of "sum over histories but throw away the infinitely jagged ones", the theory is called renormalizable (since you "renormalize" various quantities in the cutoff theory, in order to extrapolate what the full theory would have said) and it's considered a mathematical success.

I've gone on quite a tangent, but the point is that a full sum over histories for branching and joining strings should include outcomes that look like finite baby universes - it's important that they are finite, so there aren't extra degrees of freedom at the final stage, the B that follows the A. But it seems like you ought to be able to have arbitrarily big baby universes in the path integral, and that they ought to correspond to ultra-high-energy fluctuations in the alternative, CFT description. And it may be that this aspect isn't even addressed by the nature of the approximations that are used in concrete investigations of the AdS/CFT correspondence.

That digression aside, it's also true that the ultimate outcome of black hole collapse and evaporation is still just unknown, even as a matter of theory, and it's likely that even your specific notion of some dimensions shrinking while others expand could be the basis of a concrete model, because it resembles a known type of oscillation in general relativity, I think called a Taub oscillation, where one direction of space shrinks while another expands.

The situation in physics about these questions might be remotely analogous to consciousness in neuroscience - there's a lot of data (here the data would be concrete calculations made within specific frameworks) but it's also still very unclear how it will all fit together. The picture that I started with (black hole shrinks to a single heavy string, shedding energy as it goes, and then the final remnant blows up into a handful of ordinary strings) seems appealing and plausible to me, but that's just a tentative judgement call and I wouldn't absolutely rule out the baby universes yet.

 

[julian]

The idea that quantum mechanically only fields of a distributional in nature should be considered is fairly general. Interacting field theories fail to be well defined as they usually involve distributional valued operators evaluated at the same point and need regularization to be well-defined. This implies that the measure of integration in functional integrals should be concentrated on distributional fields because otherwise the action appearing in the functional integral would be well-defined and there would be no need for regularization! I think the space of continuous configurations is completely insignificant compared to the space of distributional configurations. This is the case in LQG where the connection field is distributional. A physical ramification of this is that quantum mechanically an isolated horizon has independent degrees of freedom from the bulk field - if the bulk field were continuous it would completely determine the field on the isolated horizon and it would have no independent degrees of freedom to account for black hole entropy.

 

[julian]

That such theories as LQG are finite and well defined is because diffeomorphism invariance of GR says small and large distances are gauge equivalent. So actually at the end of the day you can remove the regulator, work with distributional fields, and everything is fine.

 

[Jason_0]

Julian,
I don't think this is correct as far as the current LQG bh model is concerned. The IH is not quite independent from the bulk as there are boundary conditions, which have to be fulfilled to recouple the bulk and surface dof. It is rather that the diffinvariance of a graph embedded in the 3-mfd gets broken/modified through the horizon encrypted by the boundary condition. this leads to the bh entropy in this particular model.

 

[julian]

Hi Janson_0

Yep, you are right that their is an intertwining of surface dof and the bulk dof - which comes from the definition of the IH as I think you were explaining and so not completely independent of each other.

I think my comment came from quotes like that of Ashtekar in living reviews http://relativity.livingreviews.org/open?pubNo=lrr-2004-10&page=articlesu16.html:

"Recall next that, because of the horizon internal boundary, the symplectic structure now has an additional surface term. In the classical theory, since all fields are smooth, values of fields on the horizon are completely determined by their values in the bulk. However, a key point about field theories is that their quantum states depend on fields which are arbitrarily discontinuous. Therefore, in quantum theory, a decoupling occurs between fields in the surface and those in the bulk, and independent surface degrees of freedom emerge. These describe the geometry of the quantum horizon and are responsible for entropy."

But we are going off on a tangent here. Maybe should be a new thread.