Time dimensions • m*******e@a****.***u.edu 03/12/1997 00:00:000 UTC I have been wondering what would happen if there was more than one time dimension. Now, on the real number line the numbers are arranged in a unique sequence. But if you add a dimension to get the complex number plane, there is no longer a single, unique ordering for the numbers. If you add further dimensions to get "supercomplex" numbers the situation gets even worse. So one might expect that in a universe with multiple time dimensions there would be no unique sequence of events, and the concepts of a past and future would become meaningless. But we know that in out universe there is a fundamental difference between the time dimension and the space dimensions: the universe is compelled to constantly move along the time dimension. So if we had two or more time dimensions, the universe would constantly move along all of them, tracing out a one-dimensional path through some N-dimensional "timespace". We could define a unique sequence of events by comparing to the ordering of each event along that curve. So the situation collapses back to a one-dimensional case. It appears that there is no way to distinguish between a universe with one time axis and one with many time axes. --- Brian • -=(JC)=- 02/12/1997 00:00:000 UTC Brian McGuinness wrote in message <6629o3$ol6$*@g*****.***u.edu>... >I have been wondering what would happen if there was more than one time >dimension. Now, on the real number line the numbers are arranged in a unique >sequence. But if you add a dimension to get the complex number plane, there >is no longer a single, unique ordering for the numbers. If you add further >dimensions to get "supercomplex" numbers the situation gets even worse. So >one might expect that in a universe with multiple time dimensions there would >be no unique sequence of events, and the concepts of a past and future would >become meaningless. >But we know that in out universe there is a fundamental difference between the >time dimension and the space dimensions: the universe is compelled to >constantly move along the time dimension. So if we had two or more time >dimensions, the universe would constantly move along all of them, tracing out >a one-dimensional path through some N-dimensional "timespace". We could >define a unique sequence of events by comparing to the ordering of each event >along that curve. So the situation collapses back to a one-dimensional case. >It appears that there is no way to distinguish between a universe with one >time axis and one with many time axes. >--- Brian Hmmm...What you're talking about is really familiar. You're sort of supposing half of what you say in advance. Two dimensional time is like what they talk about when they say that every possible event in the universe happens in all its subsets. Like when you flip a quarter, you'll see it come up, say, tails. There is just under a 50% chance of this happening. There is a slightly higher chance that you would have gotten a heads (bit of trivia, though I might have it backwards: the head of a quarter contains more upraised bits, so it is very slightly heavier and will more likely, by a usually unnoticeable factor, land facing down). Some people like to theorize (or fantasize) that when events at the quantum level happen, every single outcome happens, if you will, in a spontaneously generated universe (or perhaps just an otherwise parallel universe where Mr. Quark spun left instead of right). A somethingetician two years back or so put together a method using quantum effects of some order which acted as a computer that could return infinite results on simple problems that would normally take a mundane cpu forever to compute, like finding all primes or certain factors, that sort of thing. That guy claimed that the reason the system works theoretically was because every possible event actually happens. But others tend to think of other reasons not so seemingly far-fetched. Some think he's a crackpot. But his ideas work. Hmmm... But getting back to your paragraphs, I thought it cool that you were relating to an n-dimensional coordinate system. The way you described it makes it seem to me that the path of the universe in timespace would work best in infinite (or nearly so ) dimension, with a total state of the entire universe at one slice of time being definable as a really (read "infinitely") big set of coordinates. By reading the curve so far attained, we could approximate the future state of the entire universe with accuracy based on how high dimension we used to calculate, kind of like a Taylor Series, but with more than one variable (many more). From that, extrapolation of individual events would take a while, I guess. In fact, on the micro scale like that events would probably be completely wrong unless you approximated to a level so high that you would probably get your result. Hmmm...wouldn't what you said mean that time isn't actually another dimension, it not being at a right angle to the others? Basically that there is a set of dimensions that include our own two (three...sorry, brain fart), but only orthogonal to space, space, and space (my pet names for the other three dimensions we experience)? And time is just a length of the line that's traced through the graph (probably starting from all variables [i.e.."dimension values"] being zero and sort of generally spiraling upwards). Hmmm...this reminds me of Sphereland (a sort of follow up to Flatland, wherein an analogy to curved space is explained in terms of a two dimensional universe). -JC (we can all tell I have no idea what I'm talking about, but I swear to you that the stuff I talked about above is at least vaguely true) • j********o@***.com 05/12/1997 00:00:000 UTC In article <6629o3$ol6$*@g*****.***u.edu>, m*******e@a****.***u.edu (Brian McGuinness) writes: >... But if you add a dimension to get the complex number plane, there >is no longer a single, unique ordering for the numbers. If you add further >dimensions to get "supercomplex" numbers the situation gets even worse. So (Of course, complex numbers are merely a handy way to represent multidimensionality.) >one might expect that in a universe with multiple time dimensions there would >be no unique sequence of events, and the concepts of a past and future would >become meaningless. >But we know that in out universe there is a fundamental difference between >the time dimension and the space dimensions: the universe is compelled to >constantly move along the time dimension. So if we had two or more time >dimensions, (as we are presumed to have within the event horizon of a black hole (Brian knows this, but I point it out for the general elucidation)) >the universe would constantly move along all of them, tracing out >a one-dimensional path through some N-dimensional "timespace". We could >define a unique sequence of events by comparing to the ordering of each event >along that curve. So the situation collapses back to a one-dimensional case. >It appears that there is no way to distinguish between a universe with one >time axis and one with many time axes. This seems sensible when applied to a totally isolated particle, but replaces the linear cause and effect of time with a mere mono-temporal parameterization. We could similarly assert that an ordinary object moving along a curved path in two dimensional space is in fact travelling along a one-dimensional line: both descriptions abnegate the essential qualities we associate with "time" and "line," respectively. Maybe in a black hole (perhaps this is why you didn't make the point), the newly inexorable passage of radial distance fallen may become identically mapped to the passage of time, so no higher dimensionality of time would be evident despite the loss of a spatial dimension? If we assume that we are adding dimensions to ordinary matter, we have the same problem of Flatlanders in our space: that things naturally have extension, so they couldn't have been truly flat to start with. If, as in a black hole, we are transmuting an existing spatial axis into a temporal one, the radial axis becoming timelike, so the extension problem doesn't appear to present itself. The object would seem to be sliced into an infinite set of newly two-dimensional systems - I can't imagine the transformation of the physics, though. Maybe prior physical extension would matter somehow, after all? In the more general case, let us examine our framework of time: I'd submit that it is the (necessary and sufficient) causal evolution of a spatial or state configuration. At the most obvious level, additional time dimensions would appear to allow a less linear causality and a greater interconnection of a system's history - the evolution of a system from a particular event could be influenced by not merely the immediately "preceding" event but (directly) by earlier states. For example, whether an electron flips its spin orientation in a particular interval might now be influenced by how long it was in the preceding state. Likewise, particles might appear to skip forward in time as they pursued shorter paths than our own. Ok, so let's start with a system which naturally has such higher time dimensions. Either evolution along both time dimensions is obligatory, in which case I say that they reduce to one, or they are not. In the latter case, the only idea that pops to mind is that a system is obliged to evolve along one or the other axis (a taxicab geometry): this can be visualized by the two axis being parallel and identical or being inclined in a range which includes orthogonality and anti-parallelity (oppositeness). In the orthogonal case, it would seem that elements in a system would (from one axis of experience) be able to evolve instantly: thus, the cue ball strikes the racked balls and the next instant, some balls are flying away while others are already bouncing back from the sidings. If the inclination is less than orthogonal, sequences in the other axis would appear to merely be sped up. If the inclination is beyond orthogonality, then things travel backwards in time along the other axis (a further case of the greater connectedness alluded to earlier). All this would effectively speed up complex interactions involving both axes. The phenomenological outcome depends upon the population of these axes and the dynamics of axial exchange: if this operated routinely at a microscopic level, there might be no substantial qualitative change in how the universe was perceived to work. If the effects were rare or could be employed macroscopicly (for example, if they were discovered as a hidden fact of our universe), we might get some cool effects, like ultrafast computers or accelerator spheres. Gorno • j********o@***.com 05/12/1997 00:00:000 UTC In article <662jgj$of9$*@w*****.****.*****s.com>, "-=(JC)=-" <**@b****m.com> writes: >A somethingetician two years back or so put together a method >using quantum effects of some order which acted as a computer that could return >infinite results on simple problems that would normally take a mundane cpu forever >to compute, like finding all primes or certain factors, that sort of thing. That guy >claimed that the reason the system works theoretically was because every possible >event actually happens. But others tend to think of other reasons not so seemingly >far-fetched. I would differ with his characterization of the process: a good analogy is the design of a network of irrigation canals - instead of numerically iterating through possible series of in and outflows in the individual canals, one builds a model and lets the water flow! Similar flow of quantum probability fields could be employed, taking advantage of the quantum nature of the effects to solve such mathematical problems (in a cleverly fashioned apparatus). Gorno