We humans seem to experience time in a very specific way. Our notion of time as linear and oriented (that is, the direction of time matters) is very strong. But is this necessarily the case?
Now first I want to state that I have very little understanding of general relativity, which presumably answers some of my questions about the nature of time. So in my discussion here I will restrict myself to the methodology of thought experiments, without trying to delve into the mathematics of relativity too much. Furthermore I have no doubt that in the process of explaining my thoughts I will expose more ignorance of physics than should be expected of a physics major, but I hope these ruminations will nevertheless be interesting as the simple musings they are.
First, must time be one-dimensional? We certainly experience time as one-dimensional. We are only conscious of tracing out time in a single dimension, and in that dimension, in a single direction. But as we go through our lives, do we not also only trace out a single dimension in space? Our past and future existence in space can be drawn as a line. To use mathematical terminology, it is a one-dimensional manifold immersed in the (locally) Euclidean 3-space. Might our path through time also be a one-dimensional manifold embedded (i.e. we don't seem to experience the same moment twice) in higher dimensions?
These thoughts fail Occam's Razor, unless there is a reason that extra dimensions of time would solve problems presented by physical theories involving just one dimension. Furthermore it isn't clear to me it matters whether the extra "unseen" dimensions so popular with today's theoretical physicists need to be specifically identified as dimensions of time or space; in fact, I suspect such identification is unnecessary. Time is considered separate specifically because we experience it in the unique way we do, so calling extra dimensions that we do not experience dimensions of time would be confusing.
A perhaps more interesting question, is that if we experience time as an oriented one-manifold (i.e., it looks linear when you zoom in), what kind of one-manifold is it? Assuming it's connected, there aren't that many options. It could be an infinite line (time has no beginning or end), a ray (time has a beginning (or end) but no end (or beginning)), a finite line segment, or a loop.
The Big Bang indicates that 13.7 billion years ago, something important happened, but it isn't clear that was actually the start of time. It could simply be a singularity in the space-time manifold, in which the spatial dimensions collapsed but the time dimension did not. For example, take a donut and squish part of it down to a point. The donut still is 3-dimensional everywhere but the squished point. Suppose now that the dimension that goes around the donut hole is time. As time goes by, we are travelling around the donut. We can see the two spatial dimensions that are perpendicular to the time dimension at any point except for the squished point. This point is a singularity.
If this is what the Big Bang was, there's no real reason to believe the donut is squished in only one place. In fact it isn't clear we will every be able to know anything about the other side of the singularity. But this is my blog, so I'll go ahead and say I like the picture of the once-squished donut. If I'm not mistaken, this is similar to the notion of time proposed by those studying Loop Quantum Gravity. My next question would be, is the loop that describes the time dimension smooth? If it isn't, it would seem that we really have no hope of learning anything about the other side of the singularity.
The primary curiosity about time is why we experience it in such a different way from the other dimensions. I suspect that the squished donut just exists, and that our voyage around it is an illusion. Our existence in the dimension is no different than our existence in each dimension of space, but for some reason while we can look in the mirror and see ourselves from head to toe, we cannot at once see ourselves from birth to death. Even our language doesn't allow it; without a second thought I just stated that we cannot at once see ourselves from birth to death, nearly without perceiving the tautology. An understanding of time such as this would have many fascinating consequences. For example, my death would be no more profound a notion than the top of my head.
But for now we'll have to wait for the neuroscientists to give us a little more to go on. Not that lack of information will stop anyone from philosophizing.
