Category Archives: topology

The Feel of Space

(left:eRiK, right:me)

That’s my friend eRiK. My mother emphatically titles him “eRiK the Dane.” eRiK and I studied Physics and Math together as undergraduates at The University of California at Berkeley. We share a great love of understanding, and whenever something’s puzzling me, from Set Theory to counting cards in BlackJack, I turn to him.

He’s been singing the praises of the show RadioLab on NPR lately and he was particularly stricken by a comment made by the well known Columbia University Physicist Brain Greene. Dr. Greene was discussing the expansion of the universe, and, this is hearsay now, he said that there is no center to the expansion. No origin, no point away from which things are expanding. This is, as eRiK said, unsettling. If you were blowing a bubble with chewing gum, bubble swelling from your mouth, the rate of expansion would be greatest at your lips where the mass of sticky stuff was being stretched into a sheet. If you were pulling a rubber band with your index fingers the rate of expansion would be highest near your digits and lower elsewhere. The point I’m trying to get across is that it’s difficult to think of examples of isotropic expansion of objects. This means spatially and directionally uniform expansion. A pizza pie made from a lump of dough is expanded into a sheet in a roughly constant spatial manner, but the spread is not directionally uniform, it is expanded radially, out from the center. Dr. Greene’s comment means that there is no direction or origin associated with the universes growth. As astrophysicists and astronomers watch stars getting farther away from eachother, it appears to be happening in the same way everywhere. At the very least this means that the universe itself must behave differently from every object in it.

There is one example that is a bit comforting : imagine that you lived on a line, confined to one dimension. Further, lets say this line was connected at the ends, an infinite hoop of 1D existence. If “something” caused this circle to grow radially out from the center (which wouldn’t be a part of the line itself of course), to those living on the line segment, it would appear as if everything was expanding isotropically. We could extend this idea to a 4 dimensional space-time as a hoop embedded in a higher dimensional space, but this is pure speculation.

This brings us to the topic that motivated the title of this post. What would it feel like to come to the edge of a universe? I don’t know that such a boundary exists or not, but we can certainly conceptualize a space like our own with well defined boundaries. This is not like being in a room with boundaries. The repulsive forces that we experience as a result of encountering walls are just that: fields of force. A boundary of space must be very different. There wouldn’t necessarily be any repulsive force, I imagine it more like asking a person to reach into the 14th dimension or backward in time. It doesn’t even make sense to try and conceptualize it. There is simply nothing to try or do or a direction to move in or a place to point to or anything. This is the closest thing I can imagine to arriving at a boundary to space. Not only would there be nothing there, our perceptual abilities would probably be quite stymied by such a thing. Again I have found myself in the slippery slope of speculation, and I invite others to weigh in on this. I’m not sure that anybody has the required personal experience to comment on this but I am sure that somebody could, in the great tradition of doing so in physics, suggest a thought experiment which would shed some light on the subject.