George Levy writes:
> Hal Finney wrote:
> >http://space.mit.edu/home/tegmark/dimensions.html , specifically
> >http://space.mit.edu/home/tegmark/dimensions.pdf .
>
> Wouldn't it be true that in the manyworld, every quantum branchings that
> is decoupled from other quantum branchings would in effect define its
> own time dimension? The number of decoupled branchings contained by the
> observable universe is very large. Linear time is only an illusion due
> to our limited perspective of the branching/merging network that our
> consciousness traverses. While our consciousness may spread over
> (experience) several OMs or nodes in that network, it can only perceive
> a single path through the network.
Tegmark's idea of multiple time dimensions was more general than this.
As with multiple space dimensions, you could travel about in the
time dimensions.
In relativity theory, there is a "light cone" that restricts which
direction is "forward" in time. You can change your direction but are
constrained to always be going forward relative to your light cone.
This keeps you from turning around and going backwards in time, because
you can't exceed the speed of light. However with 2 dimensional time the
geometry is different and you actually go backwards in time. Your own
personal clock goes forward but you can end up back before you started.
I'll give you a mental visualization you might find useful and
interesting. There is a conventional way to think of a light cone which
is what gives it its name. Imagine a 2+1 dimensional universe, 2 spatial
dimensions and 1 of time. To think of it, start with an x-y plane with
the x and y axes. We'll call the y axis time, positive being upward.
This is a 1+1 dimensional universe. Now imagine the lines x=y and x=-y,
in other words the two lines running at 45 degrees and crossing at the
origin. These can be thought of as the paths of light rays emitted by or
received at the origin. Now imagine spinning the whole thing around the y
axis, where the new z axis will be another spatial dimension. The crossed
lines become a pair of cones that represent possible light beams being
emitted from or received at the origin. These are called light cones.
At each point in space we could imagine a pair of such cones existing,
future and past. Objects are constrained in their movements to only be
going upward, they have to stay within their light cones.
Now for the variant, with a 1+2 dimensional universe: 1 spatial dimension
and 2 time dimensions. Again we will start with the x-y plane, y is time,
and we draw the crossed 45 degree lines. This time we spin around the
x axis, to again produce two cones, but they are pointed right and left
rather than up and down. In this model z is a time dimension like y,
so we have 2 time dimensions. Now, objects again are constrained in
their movements not to cross the cones, but the cones are pointed to
the side rather than upward. This means that objects are not stuck
inside the cones but are in effect outside of them and are able to move
much more freely. You can see perhaps how an object could start at
the origin, move in a loop in the y-z plane and return to the origin,
all without ever passing through the cones.
This is the nature of the 2-dimensional time explored by Tegmark.
It is pretty different from the MWI. I would not say that the MWI
has multidimensional time any more than it has >3 dimensional space.
Technically the MWI all happens in one spacetime area, it is all
superimposed and squashed together. There is merely a mathematical
separation which occurs when states become decoherent, such that their
future histories are causally independent. But technically they are still
using the same space and time, they are just invisible to each other.
Hal Finney
Received on Thu Jul 21 2005 - 13:47:13 PDT