Rotation and Time, Part 2       

            The following is highly speculative in detail. Even if my premises about time and rotation are correct, the idea developed below, while roughly plausible, is based on incomplete knowledge of the subject and is not likely to be more than a starting point. But, hey, it’s fun!           

            NOTE – I will be using a progression of concepts through universes of lower to higher dimensions. This device is by no means original with me. It has been a standard way of developing understanding of higher dimensions for more than a century. 

            I’ll start with a one-dimensional universe: a line of some sort. 

            I want to remember a couple of basic principles I discussed in Pencils 2019 – 03 “Time and the Origin of the Universe”. One is that for something to exist it must have a non-zero magnitude in each dimension of its universe. The other is that the fundamental concept of the physics of a universe is momentum. Momentum combines mass, space, time, and motion. None of these exists without all three of the others. Momentum essentially creates a universe. 

            Immediately, my one-dimensional universe is in trouble. It can’t exist without momentum. That means there must be mass moving along the line, which requires time. General Relativity tells us that time is just a preferred dimension of a multi-dimensional spacetime universe. Fundamentally, then, existence already requires at least two dimensions of spacetime, one of space and one of time. 

            Ok. Now I have a two-dimensional spacetime universe that has crystallized into one dimension of space and one dimension of time. We have one-dimensional masses (and/or creatures) moving along a line universe and through time. Actually, by my first principle above, any mass or creature is two-dimensional. They have length and also duration—a lifespan—as they move. They also have a past and future. But what defines past and future? They can move forwards or backwards along their one-dimensional line universe, but only forwards in time. 

            All I did was add another spacetime dimension. Why can’t they move forwards and backwards in the timelike dimension as well as in the spacelike dimension? The physics seems to allow it. What could make a difference between the two possible directions? It’s the same problem we have in our universe, and I’ll solve it the same way I’m proposing for us, by a rotation. 

            But something else is needed before rotation can happen. That something else is another dimension. Rotation is defined by something moving in a plane (and/or parallel to that plane) around a rotational center. There are no planes in a universe with one spacial dimension, so I’ll add another dimension. I now have a line universe embedded as a sub-universe of a two-dimensional plane universe plus time. I have a total of three spacetime dimensions in a Minkowski space. (I’m still treating it as Euclidean.) 

            There is another difference with a line universe existing in two spacial dimensions. Though it may appear to be just like the one spacial dimension line, this line must have a non-zero magnitude in the 2nd spacial dimension. It has a breadth, like a tiny ribbon. This breadth may be very small and imperceptible to the physicists living in this universe, but it will be there, or nothing, including the physicists, would exist. 

            Now I want my line universe to rotate in the plane. Having an infinite line universe and starting it rotating around some random point on it isn’t how this would happen. I need to get this universe started and see how rotation might develop. 

            Remember that momentum creates a universe. Momentum is a vector. It has mass and motion (made of space and time) with direction. I have a potential universe, but until there is momentum, there is no universe. This is the Big Bang moment. There is no line yet. According to my current model there will be three potential spacetime dimensions, all equivalent at the start, and momentum will create the line. 

            As my universe begins, it propagates as momentum in two opposite directions along one spacial dimension, a line, using one dimension of time. That leaves one of the original three spacetime dimensions to appear as another spacial dimension partially present as a tiny breadth to the line universe. 

            This is where the rotation starts. Instabilities in the forces of the Big Bang on the newly created mass-energy cause the line universe plus time to rotate in a plane in this 2nd spacial dimension (3rd spacetime dimension) as the line grows in length in both directions. This rotation defines the plane and causes the three original spacetime dimensions to appear as two of space and one of time. 

            The rotational plane is orthogonal (perpendicular) to the time dimension and would differentiate between the two possible directions of travel along the time dimension because of the opposite directions of the apparent angular velocity of rotation. Going one way, the rotation appears as clockwise, and going the other way, it appears to be counterclockwise. One direction would be past and the other future. Which one is which and how that determination is made are questions for another day. The important point now is they are observably physically different to a traveler through time, which we all are. 

            Once determined, the line universe grows at both ends. Travel is possible in both directions, though travel away from the origin will be easier than toward the origin because of going with or against the direction of propagation. From this point of view, three is the minimum possible number of spacetime dimensions for existence in space and time as we know it because of the requirement for rotation. 

            Note that the plane in which the line universe rotates is mostly outside of that universe. Except for the tiny unperceived breadth of the line, the rotating line universe does not occupy that plane at all. The physics of the line universe is unaffected by its 2nd spacial dimension. It is wholly one-dimensional. This will be important to us later. 

            I will extend this 1d (spacial) universe into our 3d (spacial) universe, but first I want to introduce another way the line universe could expand into the plane universe, which is more analogous to how we believe our universe expands. 

            It may have occurred to you that, given two potential spacial dimensions, there is no obvious reason why a universe would be limited to expanding in only one dimension. Also, the image of a stringlike universe growing at both ends and rotating into a spiral shape with all the mixed up forces the inhabitants must experience seems inelegant to put it one way. I can’t completely address that, but this revised model seems more useful. 

            Instead of expanding from the Big Bang in opposite directions along a line from the origin point, the line universe could expand as a circle from the origin point. This universe expands from the beginning in both available spacial dimensions. It would still be a 1d line universe (with a tiny 2nd dimension) growing in time and embedded in a plane that is mostly outside of it, and it would still be rotating in the plane (like a wheel rim) with the direction of rotation creating the same apparent distinction between directions in the time dimension. No more dimensions are required in the model. The circular line would increase in circumference and radius from the momentum of its mass and expand as a wave on a pond does from the point where a rock has splashed into it. Creatures living in the circle line universe could still travel backwards and forwards along the curved line of the circle moving forward through time (like living on an expanding smoke ring). They would of course not know they were on a circle. They can’t perceive the curvature in the 2nd dimension. 

            There are other important differences from the rotating stringlike line universe. One is that the origin center is outside of the universe, not a part of it. The interior of a circle, including the center, is not part of the circle. Another difference is that the line universe is now unbounded. A propagating stringlike line universe has two ends which are moving further from the point of origin, but is always finite in length, and a creature in that universe could in theory travel to either end of it. A creature living in the expanding circle universe could travel forever in one direction and never reach the end. A circle doesn’t have an end even though it is also finite in length. 

            Another important difference is that travel along the circle line universe would be simpler for the creatures than in the rotating stringlike model. Rotational forces would be transverse to the line, and the linear expansion of the universe would be equal everywhere as if every point were the center of expansion. Neither effect would create any point to point differentials within the line, so neither would affect the movement of the creatures. Since they do not perceive a 2nd spacial dimension, they won’t even think of looking for it, at least not for a long time. Once again, this relates to the way we have come to understand our universe. 

            NOTE – If there is one circle universe expanding from the origin point, there may be others, just as there is usually more than one concentric circular ripple expanding from a rock splashing into a pond. These would be independent non-communicating universes. 

            This will be my starting point to try to bring all this into the context of our actual universe. We’ll see how it goes in the last part to be published next week. 

Hugh Moffatt 
Watertown, Massachusetts 
November 14, 2020