Just Geometry

I've been hearing lately from people who say they found The Grand Design, the new book by Stephen Hawking and Leonard Mlodinow, easier to digest because of the advanced concepts I had already eased them into through my writing. Thanks for your kind words, everyone!

At the end of our last blog entry, Extra Dimensional Geometry, we talked about how we could work the hard determinist viewpoint into the idea that we are ultimately each just navigating within extra-dimensional patterns that already exist. In The Grand Design, the authors suggest that free will is an illusion. They say that the system of inevitable cause and effect outcomes leading from the big bang to the creation of life to the evolution of humans to an individual such as you or I right "now" is so incredibly complex, saying that we have "free will" works as an effective interpretation, but is ultimately not the correct one. I think the authors are trying to have their cake and eat it too on this point, but we'll return to that thought in a minute.

The Grand Design is a summary of mainstream cosmologists' thinking about the nature of reality, targeted towards an audience with little knowledge of the subject. Some readers may be frustrated by the book's repeating references to M Theory as being the best candidate for the ultimate Theory of Everything, while spending comparatively little time explaining any more about M Theory other than to say that it combines the five other versions of string theory.

(Here's an amusing Venn Diagram example from flickr)

M Theory, which relies on ten spatial dimensions plus one of time, can be thought of as a Venn Diagram: draw five circles which overlap in various ways, they represent the different versions of string theory, and M Theory provides a framework for showing how these different theories fit together and overlap. Hawking and Mlodinow invoke the interesting concept of "model-dependent realism" in their book, which we can sum up like this: reality can be interpreted in a number of ways, and the frame of reference from which you describe reality can make one theory or another appear to be more relevant while your viewpoint is within that frame. One of the more often-quoted examples from this new book appears in Dwight Garner's New York Times book review:

They write about a city in Italy that, a few years ago, barred pet owners from keeping goldfish in curved bowls. Why? Because it is cruel, the city council argued, to give the fish “a distorted view of reality.” We’re quite similar to those goldfish, the authors suggest. Our perceptions are limited and warped by the kind of lenses we see through, “the interpretive structure of our human brains.” Digging deeply into quantum physics, they argue that our universe “doesn’t have just a single history, but every possible history, each with its own probability.”

Which is where I believe the authors are having their cake and eating it too. In my book and this blog, one of the keys to understanding the multiverse is Feynman's "sum over histories" or "sum over paths" concept. Hawking and Mlodinow also talk about this important idea: the wave/particle duality underlying our reality means that there are many many paths a particle could have traveled to get to its current position. When you add all those paths together, you get the path that is most likely, but that is not the path that was necessarily taken. Hawking and Mlodinow say free will is an illusion because of the existence of this "most likely path" for every particle in the universe, which contradicts Feynman's theories and the evidence provided by numerous double-slit experiments clearly showing that particles do indeed take all paths, not just the most likely one provided by Feynman's sum over histories.

(image from Wikimedia Commons)
This double-slit experiment has shown that when a particle passes through a barricade having either one or two slits, when one slit is opened the resulting pattern shows (as you would expect) that only one path was taken. But when two slits are opened an interference pattern results: a particle is going through both slits simultaneously! Each particle interferes with itself as it passes through the two openings.

Now, the common objection to the relevance of all this is that the quantum world is completely separate from our classical reality. I've taken the opposing view, insisting that this is all part of the same continuum, and there really is no dividing line between the one layer of reality and the other.

Hawking and Mlodinow talk about how the double slit experiment has been successfully demonstrated with "buckyballs": molecules created from 60 carbon atoms. A buckyball passing through two slits simultaneously would already be moving uncomfortably far into our classical world for some people: but no more so than the "spooky action at a distance" entanglement experiments being demonstrated with increasingly large molecules over increasingly large distances that we've talked about in past entries.

I use the phrase "just geometry" in my book a number of times, here's an excerpt from chapter 8:

The idea of the moment you are experiencing at this instant as being “just geometry” means that there are multiple paths which could have caused you to arrive at this particular moment, and the path that you remember as being your personal history is only one of many which could have brought you to this present moment in time (as you will recall from the discussion of Feynman’s “sum over paths” theory which we first looked at in chapter four). The image of the extraordinarily extravagant multiverse that is inferred from this concept is something we discussed in the Introduction, as this ties directly to Everett’s “Many Worlds Theory” and “decoherence”, both of which have been enjoying renewed support in the last few years. And finally, we should always be mindful of the double-edged sword that is implied by the idea of the current instant of time being “just geometry”: while this means that the potential for this instant of time has always existed within the tenth dimension (as have all the potential moments to come and all the ones that could have already occurred), it does not mean that our path is somehow carved in stone and unavoidable. As creatures with free will, we are constantly moving through the fifth dimensional paths that are available to us, selecting one of those paths as our personal timeline. The path that we have been on makes the next possible choice the more likely one (and that would be the one predicted by the sum over paths method), but a life-changing decision or event that breaks old habits and old patterns will certainly direct a person’s life to a new trajectory, making other future paths more likely to be followed from that point on.

I hope that the concept of "model-dependent realism" shows another way that my own approach to visualizing the dimensions can be juxtaposed with other theories of reality: it works as a frame of reference, it has its uses because of that, but it is only one way of many systems for describing how our universe fits into the biggest picture of all. We're going to continue this exploration next time in an entry called "Thinking Biggest".

Till then, enjoy the journey!

Rob Bryanton