Dear Inger,
Thank you so much for your interest, and your investment of time and attention. I am certainly happy to attempt to answer your questions.
You said:
"Does this mean that the smaller object is less acrual than the larger one, in a 3-dimensional frame of reference? This is how I intepret your schema. "
I suspect you might have meant "actual" (at least that way I can understand your question). Well, this is a bit tricky for me to answer because a full explanation depends on ideas that I have not yet publicly discussed or disclosed anywhere and introducing them here informally without detailed background information (as in a paper) does not seem such a good idea. I have already experienced the reactions of people who hear a really strange sounding idea without sufficient backing sufficiently often to know better.
Within the context of the paper and everything else I have discussed so far, the answer is no. The gradations in existence as I have discussed in my paper only apply to actualizable objects. For actual objects, existence is still binary: Either an object actually exists or it doesn't actually exist. Actualizablity, on the other hand can take on intermediate "ontological values", where by ontological value I mean this:
0- it doesn't exist
1- it exists
I did present a fuller description of this in my post above on Sept. 10th 18.36 in response to Jerzy Krol, and hope you don't mind if I refer you to that for more details as it was a bit long.
Having said that the answer is no, I will also mention that I believe that the answer is ultimately a qualified yes. I actually don't believe that actual existence is binary, but a quantity. Explaining my reasons for believing this at this point would take me too far. Suffice it say that if you can have quantitative gradations between actual existence, then of course it implies that some objects can be less actually existing than others, and you could create situations in which smaller objects are less actual than larger ones, but I would like to emphasize that in this case size is not the relevant factor, rather it is the energy-momentum associated with the object. Again, if this sounds really strange, just ignore this paragraph until I have had time to present my argument in a detailed paper at some future date.
What the schema does is to present a broad pattern into which we might be able to fit our current theories to obtain an overview of how they relate to each other. while there is a definite relation between size and dimensionality, the boundaries between the integer dimensionalities have to be abrupt to keep the domains of the theories apart. I envision this very much in analogy to phase transitions. As you heat, say, a quantity of water under constant pressure its temperature only increases up to a certain point, beyond that it becomes something that is macroscopically totally different, even though it is composed of the same basic building blocks.
You said:"
Analoguously, of two 2-D objects of same shape but different size, the smaller one has more units of length per unit of area than the larger one, which can be interpreted as the smaller object being more 1-dimensional than the larger one.
Does this mean that the smaller object is less actural than the larger one in Flatland - and even less actual in a 3-dimensional frame of reference? Would this be the reason behind quark confinement?"
Well, here I can only give a metaphysical speculation, but it does not seem unreasonable to me to believe that when 2-dimensional objects are observed in a 2-DFR, the same kinds of distinctions and relations apply as those between 3-dimensional objects as observed in a 3-DFR.
It would be very foolish of me to speculate on any direct relations between this framework at this stage of development and quark confinement. The task ahead to seriously answer this question is as follows:
1. Find the underlying physical description that gives rise to the SU(2) symmetry of the weak force and the SU(3) symmetry of the strong force (I believe that the mechanism I described, namely that the phase factor exp{tau/tau_A) arises from an indirect mechanism for comparing distinct proper times already gives an underlying physical description to the U(1) symmetry, as it can be directly related to the phase factor and a change in the gauge associated with the potential of the relevant field).
2. Once the underlying physical description for the symmetries is found, map the associated Lie Algebra to underlying physical processes in lower-dimensional analogs as observed by higher-dimensional observers.
3. Discover (hopefully!) a fundamental reason why quark confinement must arise as a direct consequence of this deeper physical understanding (rather than as a "patch" which one could uncharitably say how it was originally discovered).
So connecting my framework to quark confinement is far from a trivial task. It may well take me years (if it is even possible).
You said: "In your schema, you place dark energy in the fourth dimension of observed event (box 4.3). How would we, in our 3-dimensional frame of reference, experience a 4-dimensional phenomenon? I have read somewhere - but unfortunately forgot where - that we would experience its impact equally in all directions. The accelerating expansion of the Universe is equal in all directions. As is also the CBR.
Would placing the CBR in the same box as dark energy (4.3) facilitate an alternative to the Big Bang theory?"
As to how we would experience a higher dimensional phenomenon, the honest answer is that I don't know. However, I can offer a speculation based, again, on an analogy with phase transitions: From the perspective of a molecule sized observer it would seem very strange that above a certain average random motion, the molecules forming a substance suddenly seem to be a lot less constrained and literally fly off in all directions. An observer our size has no trouble with this: We might just say that the substance changed, say, from a liquid state to a gaseous state. In this analogy, one could imagine that we are like the molecule sized observer, and the human-sized observer is like the observer with a 4-DFR.
The point is, we might not see any direct "extra" objects, but instead unexpected behavior of objects we already have observed at very large scales, which indeed we do.
The CBR is most fundamentally an aggregation of photons, so it should properly be placed in the (2,3) box. However it can be a marker of what, in a sense, is going on in spacetime. The visual analogy of here might be that if you spill some paint on a balloon, and then expand the balloon, the paint spots will increase in size but become less dense.
i hope I was able to answer your questions, If you have more, don't hesitate to ask (It may take a few days for me to respond, due to my combined school and work schedule).
Thank you again so much for your interest,
All the best,
Armin
