Russell Standish wrote:
What I was asking is why you think "time-area" should be proportional to length. I can't see any reasoning as to what it should be proportional to.
Thanks for your interest in this. I did not make this any easier by bungling the initial concept a little in my first post. To directly answer your question, I am assuming space-time is a single entity, with time representing the spatial area of the multiverse. Therefore, the question you pose really wouldn't make sense. It would be like drawing a square and asking why height is proportional to length. The relationship is necessary.
Going back to all of our multiverse stacks with the cube on it, all these stacks would equal the time-area. This is the "depth" of the cube in the multiverse, that would allow the cube to store 10^300 bits of information. The time area equals the cube in it's totality in the multiverse. So why, in our universe, can we only store information equal to the surface area? Well we know we don't have access to the whole cube, because we are not in all of the universes that this cube exists in. So we have to divide the cube by something to represent the fact that we are only on one stack. The proper divisor would be the length of the cube, because we are existing on a time-line. The information that can be stored is limited to a single set of outcomes- a line along the plane of the time area (a stack of pictures).
This leaves us with the Holographic principle.
Please note this is an interesting concept (to me) I am proposing because the geometry of it makes sense when I picture it mentally. You or others much smarter than I will have to explain why this works or doesn't work mathematically in QM or TOR. Colin Bruce suggests in his book that the cube volume contains multiverse information (as a speculative ending to his book), and when I started thinking about it I realized if you take the "multiverse block" concept seriously, and consider time a spatial dimension through the multiverse, a cube of space would only provide a full content of information before it was seperated out into all of the individual outcomes as it moved through time (or how about "multiverse space"?).
A cube of space really does hold it's volume in information. But we have to divide by time. Particularly, the length of the time plane because the rest of the time area has been lost to the other outcomes/universes/stacks (or whatever allows you to conceptualize it the best). This is speculative (obviously). I'd like to hear some feedback, as this explains a lot (to me anyway) if the concept is right.