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Time Dimension To Become Space-like
KentuckyFC writes "The Universe is about to flip from having three dimensions of space and one of time to having four dimensions of space. That's the conclusion of a group of Spanish astrophysicists who have calculated that observers inside such a Universe would see it expanding and accelerating away from them just before the flip (abstract, full paper pdf on the physics arXiv). 'We show that regular changes of signature on brane-worlds in AdS bulks may account for some types of the recently fashionable sudden singularities. Therefore, the fact that the Universe seems to approach a future sudden singularity at an accelerated rate of expansion might simply be an indication that our braneworld is about to change from Lorentzian to Euclidean signature. Both the brane and the bulk remain fully regular everywhere.'" Update: 10/09 16:06 GMT by Z : A few readers have written in to point out that the article is not peer-reviewed; your mileage may vary.
Lets say I told you we had two spatial dimensions. You would imagine a plane with perpendicular x-y axes everyone knows and loves. If I asked you to draw the set of points that were equidistant from the origin, you would probably assume the geometry was Euclidian and would probably instinctively draw a circle (a good guess!). It is commonplace to hear "time is the fourth dimension." As first pass to visualize this, you might try to draw a two dimensional space-time plot: an x axis and a perpendicular time axis in a plane. If I then asked you to draw all the points equidistant from the origin, you would probably again draw a circle in this x-t plane. It seems to make sense, but is only true of time is a "space-like" dimension like "y" in the x-y plane. This is way Newton thought of things and it seems to be what the authors of the paper are advocating. But, unbeknownst to some people who cite "time as the fourth dimension," according to the theory of relativity, the set of equidistant points from the origin on a x-t graph would actually be hyperbole, not circles. This is because in relativity space-time is a Minkowski geometry, not Euclidian. All the weird stuff in special relativity like time dilation and length contraction come about because of this weird geometry. In fancier language, time has an opposite sign than space in the metric. The metric determines how distances are calculated in a given geometry. If time has the same sign as space in the metric, then space-time becomes Euclidian and one would say that time was a space-like. The article is probably extra confusing to non-physics people because most probably didn't know time wasn't space-like to begin with.
i\hbar\dot{\psi}=\hat{H}\psi
When I first heard that the rate of the universe's expansion was actually accelerating, I came up with a weird hypothesis after a few days...
Time in our frame of reference is slowing down.
The only way that seemed possible was if we were traveling at speeds close to c, but that didn't sound feasible since we were observing objects that were moving away from us, in all directions. Then another weird thought occurred to me...
Our observed universe is self-contained within the event horizon of a giant black hole.
We're closer to the singularity, and accelerating towards it faster than objects closer to the edge of the event horizon. Time will move slower for us, and far away objects will appear to speed up. An outside observer (if such a thing could possibly exist) would perceive our universe as shrinking, but in our current frame of reference, we still think of it as expanding.
One other observation that lends to this possibility is the fact that we have not seen evidence of other "Big Bangs" or other "Universes". If the Big Bang happened once, shouldn't it be a repeatable occurrence in the limitless void of space?
Okay, that's my rant. You can slap the straitjacket on me now and ship me off to the funny farm.
Solomon Chang
"Twice half-assed makes an ass whole." --Solomon K. Chang