judiefletcher said:
We live in Minkowski space with Lorentzian signature with the dimensions of space and one dimension of time. Ignoring time, we live in flat Euclidean space. String theory postulates that there are actually 10 or 11 spacetime dimensions, with the extra dimensions compactified on an internal manifold, such as a Calabi-Yau threefold. Whether our space is flat or curved, general relativity does not assume that our universe is embedded or suspended within higher dimensional space. It would have been easier to formulate if we had assumed that. When physicists say space is “flat”, they mean something different than the average person’s usage of the word “flat”. It has to do with the fact that parallel lines to do not intersect. Also, there are theories such as brane world cosmology that assume that our universe is within higher dimensional space. According to the traditional Big Bang, the Big Bang was the beginning of time, so there was no such thing as “before the Big Bang” However, more recent theories such eternal inflation postulate that time extends infinitely backwards. A Calabi-Yau manifold is a Kahler manifold with vanishing first Chern class. We use Calabi-Yau with SU(3) holonomy, which is 6-dimensional. 10 - 6 = 4, which we identify with the four spacetime dimensions we observe. If you start with E8 x E8 superstring theory, and compactify the extra dimensions on the correct Calabi-Yau, you get something similar to the Standard Model. The details of the topology that the extra dimensions are compactified on determines the low energy physics. If you are asking, why are the extra dimensions compactified on that manifold, the answer is that we chose to compactify the extra dimensions on that manifold in order to get a result that is as close as possible to the real Universe. If you are not satisfied by that, you could say there is a multiverse with an infinite number of universes, and our universe is anthropically selected, so for example, universes where the extra dimensions are compactified on different manifolds have no observers.
Thanks for the insights. Yesterday i was reading a thread about the simulation hypothesis with amusement. I googled to read what is the latest and i saw this paper.
https://arxiv.org/abs/1011.5499
"Background
A hundred years of research have validated quantum and relativity theories in sub-atomic and cosmic domains, yet they conflict at the core. The quandary is that:
1.Quantum theory assumes an objective space background, which relativity specifically denies. For quantum theory to satisfy relativity it must be background independent, i.e. not assume, as it currently does, that quantum states arise in a fixed space and evolve in a fixed time [3].
2.Relativity assumes objects exist locally, which quantum theory specifically denies. For relativity to satisfy quantum theory it must be foreground independent, i.e. not assume, as it currently does, that localized objects move relatively through space-time.
These two great theories contradict because each debunks an objective reality assumption the other still clings to. Quantum theory challenges the objective reality of foreground objects, but still assumes a fixed background. Relativity theory challenges space and time as objective backgrounds, but still assumes fixed foreground objects. Both theories rebelled against the idea of objective reality in different ways, so each exposes the other's conceptual baggage but ignores its own.
To reconcile, both theories must abandon entirely all objective reality assumptions, i.e. reject objective space, objective time, objective existence, objective movement and any similar ideas. The prime axiom here is that nothing in the physical world exists of or by itself, so while it seems substantial and self-sustaining, both its foreground and background arise from processing. One can't "half-adopt" this theory, so it has no fixed space or time that quantum states exist in, nor any fixed entities that move relatively. The only constant is information processing, with space, time, matter and energy just outputs. In this model, not only is matter-energy calculated by "space" as Zuse suggests [4], but space itself is also calculated. "
Just for sake of discussions. Let's say it were true. Does it mean there is no longer a need for quantum gravity? If still needed, why?