Glad to be of help. I'll respond one question at a time:
Thanks for making this more understandable for me Richard. Are all these dimensions set as a set of whole numbers 0,1,2,3...., or it is "on off" or "1 or 0". No such thing as partial or negative dimensions?
********Set of wholes excluding zero. There is no 0 dimension. Partials, rather fractional dimensions only occur as effective dimensions, like effective fractional charge in models of physics. However, dimensions may be disconnected. The three space dimensions go in a more or less straightline in the + and - directions. The remaining dimensions are not off but rather they disconnect and roll up on themselves and essentially look like particles of space. So they are not 0 or 1. They are always in existence. Only the configuration changes. We know from GR (General Relativity) that space can curve. Compactified space is just a curvature extreme. Good question.
So that for everything in the Universe has to have 26 discrete "traits" so-to-speak.
********Interesting that you say traits. In the Hebrew kabala, in the Book of Creation supposedly written by Abraham, it is written that God made the universe using the 22 letters of the Hebrew alphabet, each having a different trait..... These could be metaphor for the 22 compactified dimensions- plus 3 space and 1 time makes 26. This same book also speaks of the universe being created in 10 dimensions, each dimension bearing a name of god. The really cool thing, if a 68 year old is allowed to say that, is that the book desacribes how 6 of the dimensions roll up. To begin with there are three dimensions in each direction. That the east-west dimension. The two extra dimensions roll upeast to west, and the other west to east, in opposite curvatures. That is one of the possible compactification models in string theory. That book surfaced in the 1600s, I believe, at the beginning of the classical period of physics. I find that amazing.
Are you saying that this Dark Matter would not occupy the obvious space we are familiar with, but would have an effect with space? Is there always an interaction with space through gravity?
**********Dark matter is all around us and within us, and within the earth, and the solar system in a more or less uniform density profile.
It occupies the same space as the galaxy, our Milky Way and most all other galaxies, and even extends beyond our galaxy. But it appears that there are distinguishable globs of dark matter associated with every galaxy......
That is, every spiral galaxy. There seems to be no dark matter associated with spherical galaxies. Why???? Well, whether or not spherical galaxies have none is questionable, based on astronomical observations. But already at least three scientists have proposed gravitational theories that predict that spherical galaxies have no dark matter. That's because these models predict that dark matter does not exist.
In short, dark matter is a theoretical mistake first made by Newton and carried forward by Einstein. The claim is that there is a hidden assumptuion of spherical symmetry in both Newton theory of gravity and Einstein's GR. The field eqautions have one or more terms left out.
The first guy to point this out was John Moffatt, now a university prof in Canada, who was a consultant of mine at MIT Lincoln Labs in the 1960s. No one took him seriously. Then Reginald Cahill, a pr0of from Australia camme to the same conclusion by a very different path studying Process Physics. Some took notice and showed that Cahill's model could not explain gravitational lensing of star or quasar light. But fiannly, last year I recall, Berenstein, a prof from Israel on sabbatical at Harvard, who is about as well respected as a physicist can be, produced a theory along the same lines, but that also explained gravitational lensing, and predicted based on his analysis of astronomical data that dark matter does not need to exist. But most astronomers refuse to give up on dark matter.
Are these axions forever "lost" to familiar observations by humans?
************* No. There are theories for axions that would allow experimental detection. But so far none have been detected where they were expected, in support of Berenstein's theory.
For any future experiments that may be dreamed up, will conditions be reachable to where you could "show" some of these non-apparent "traits"?
************Not likely. These traits are in the realm of religion. But who knows?
Do these dimensions have to be demarcated in the sense each is unique and non-interchangeable?
*********In physics it seems that so far all compactified dimensions are treated as alike. The three space dimensions and time are definitely distinguishable. But your question raises an interesting issue. What has stymied string theorists is that there are thousands (maybe infinite number)of possible solutions to how the dimensions could compactify. They find a lack of uniqueness.
But why could not each dimension compactify in a different way from any other, with all those possibilities, why not. Then each compact dimension could carry a different set of information, like DNA carries info, which might be called a trait. That thought just occurred to me as a result of your question. That's what I like about this forum. There is enough freedom to be creative.
If 25 of the dimensions say 0, and one dimension says 1, that discrete trait describes a definite thing or state, so the "on" trait doesn't switch between the other "off" dimensions?
*************This sounds like DNA based thinking. My first reaction is that the compact dimension are always on, just because space always exists- compact space exists. But you are essentially asking what the influence of compact space is, and designing an exp req'd to measure the effect of each trait.
In that tv show by Greene, I saw those discrete strings vibrating; are they conserved in the sense that they remain dicrete but can change? All these strings are exclusive from each other? I'll leave it there...thanks again.
*********Strings are like any point particle, say an electron or quark. Electron appear to be descrete until they interact with the environment where they can change, energy level for example. However, most electrons are not free. The electrons in an atom are bound and as a result, they do not seem to have precise locations.
This raises the question of quantum mechanics and whether fields or particles or both exist. All the conundrum about wave/particle duality also applies equally well to strings. We know for sure that in superconductors and superfluids, it's all waves, as they can pass right through each other. Yet you can do a theory, as Feynman did quantum electrodynamics, assuming that only particles exist.
It seems that whether wave or particle depends on circumstance- so strings may not always exist. If dark matter exists and if it is a superfluid, as it would be if composed of axions, then only waves exist in dark matter and no strings. That may be why axion particles are so difficult to detect. BTW axions are a superfluid because they are essentially stationary in space (heck, they are space) and therefore at absolute zero. In fact, our 3-d space is also stationary, and if composed of loops or particles, they are a superfluid. So gravity is like a superfluid, which is saying all of space acts as if it were one big particle. That is why static gravity or space propagates perturbations instantly. There is no speed of light barrier within a single particle, as proven by the EPR experiments. That is one way to think of gravity escaping a black hole. The gravity due to its mass propagates instantly. Some describe this with virtual particles which have infinite speed.
Fields travelling faster than light have been verified experimentally when the field is not in a wave-like state, but rather is decaying exponentially. Such fields behave like static fields. Suppose an EM wave is being attenuated in an insulator, a flat surface with thickness. It's been shown exp that any field perturbation on the front surface is instantly propagated to the back surface. That is how gravity works.
Well, I got carried away there. But I hate to leave a thought 8incomplete, esp the new ones.
I have noy proof read this
Thanks again for the questions