LeeE,

Is there speculation particles move one plank unit via a separate dimension? Could time in that dimension change according to momentum of the particle so that it reapears at the next plank unit at the appropriate time, thus displaying a corresponding 3D velocity?

Sorry, missed this when first posted.

If someone speculates about it then there is speculation [

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The trouble with the time dimension is that, from our point of view, it clearly and obviously seems to be quite different to the spatial dimensions. However, relativity indicates that space and time cannot be separated, and furthermore, some of the relativistic phenomena, such as relativistic time-dilation indicate that they are the same (the phenomenon of relativistic time-dilation can be explained by saying that the sum of the spatial and temporal vectors always equals 'c', and because the two vectors can be so summed suggests that they are the same).

As to whether time in another dimension could change according to the momentum of a particle; well, I'd say it would be possible if a mechanism could be found/conceived to make it happen. That is, yes it could happen, but only if there's a reason for it to happen. Just speculating about whether it does happen, or not, without first finding a causal mechanism to make it happen, doesn't really get you anywhere though.

This, and your next post, seem to me to be moving towards something I have thought a lot about; the fundamental nature of change. Although I've mostly been thinking in terms of change of location within a dimension, whether it be spatial or temporal, it seems to apply rather more widely than I initially thought.

A model for dealing with space-time, unless it is to be restricted to the specific four-dimensional space-time that we appear to exist within, must be able to deal with both more than and less than four dimensions using the same rules; a five-dimensional environment should be describable in the same terms as a two, three, four or n-dimensional environment. In the model that I've been thinking about, something that exists within an n-dimensional environment does not need to occupy space in every dimension of that environment i.e. it may have zero-size in one or more of the dimensions of the environment it occupies, and this in turn leads to two quite distinctly different modes of change, or in other words, movement through dimensions. If something has zero-size in a particular dimension then its position in that dimension can be precisely defined, and if it is precisely defined then any change of position to another position will leave it a precise distance away from where it was. Thus, any change of position would seem to require a discrete 'step'. Conversely, if the object has non-zero size in a dimension, or more specifically, if the boundaries of the object cannot be precisely defined, we cannot know precisely how far it has moved when it changes position and so cannot define a discrete 'step'; in fact, the best solution would seem to be a super-position of positions i.e. the 'blurry' object is occupying several positions, to greater or lesser degrees.

You can also see this effect with numbers. If I ask what is the difference between 1.4 and 1.5? the answer is 0.1. This answer is only possible though, because 1.4 and 1.5 are precisely defined, as is the difference between them, but if I were to ask; what is the difference between the ranges of

*approximately* 1.4-4.2 and 3.3-5.3? the answer cannot be a single precise value without qualifying the answer to a specific set of conditions i.e. you could resolve the two ranges to single precise values by a number of methods, let's say by ignoring the approximation and then averaging them, for example, and then get a single precise value for the difference between the two resolved values, but this would be akin to collapsing a non-zero size to a zero-size, and would not match the reality of what it was you were trying to measure.

Sorry for going a bit off-topic here, but the post isn't easily addressed without some background.