I once got into a debate concerning the issues of spatial dimensions on a astronomy board. The argument was concerning the need for a dimension to have a length to be real. If there wasn't a length to the dimension then it did not exist. Well the issues were even deeper than just does a dimension needing a length to exist. Considering some of the problems in trying to utilize the concept of dimensions to describe matter, I felt that the QM approach would provide a more effective solution. The way I handle space is by making it an attribute of matter, a degree of freedom that a particle can manifest as. This concept can be described by the Schrodinger equation.(although the Strodinger equation assumes matter is in space-time not creating it) Now if we allow for a fourth spatial dimension how is it that we never experience it? A fourth dimension could exist virtually, in other words its value is always zero! But the other individual in this debate argued that if it is zero then it does not exist and therefore does not influence space-time at all. But he did admit it could be very small. So I thought about this and came up with an idea as to how space could wrap around a point. I drew a picture of a torus with its center collapsed and could see clearly how a fourth dimensional point could be apart of the Reimann manifold.
Viewing space as this world space that encompasses everything is very much like Einstein's idea of space. Schrodinger space (this is my term) is not that kind of space. Schrodinger space is the probability realm of a particle that is a unique frame with a virtual dimension, the universe is an aggregate of over lapping probability realms or frames. Therefore it does not bend in the same sense as Einstein space; it can only skew as a result of particle's realm through interactions with other particles.
Below is a crude diagram of how space-time could be described with a virtual fourth dimension. The area described as 3d space could be thought of as the volume space defined by the degree of freedom or probability of a particle's space-time realm.
So what observational evidence could give a clue to this virtual dimension? Einstein's inability to accept quantum mechanics was the key. There is a strange paradox known as the Einstein, Podolsky and Rosen paradox. When two particles are entangled if one is affected so is the other. This phenomenon transcends the speed of light. Theoretically no matter how far apart the two particles are this effect still works. Recently many papers have been written to take advantage of this effect and fall under the heading of teleportation. With Schrodinger space entanglement can be viewed as the unique frame of a particle dividing into two with a common virtual dimension. It's like two condos sharing the same wall only in this case it is a virtual dimension. The shape of the particles' probability realm is not skewed or shaped because of entanglement. The twin pairs each are interacting with matter independently and therefore each particle's division of the frame can be constrained to a shape, but the mutual dimension is unaltered. So space-time is not curved to form this link between entangled particles, it is not a micro-worm hole in the essence of General Relativity. It is more like a partitioning of space that is wrapped around a virtual point. The common bond through the virtual dimension merges the space-time of the two particles to a point. This merging in the case of electrons would apply the Pauli exclusion principle. In the case for photons the two interfere with one another producing opposite polarization when measured. To have a better visualization of this idea you can think of each particle's section of the frame hinged on a 4th dimensional point like the axis of a clock and each section of the frame are like the hands of the clock. As the particles move through 3d space they pivot about the virtual dimension. So no matter how far apart the particles are in 3D space they are still local to one another through the common dimension. Just as a reminder: every particle has its own unique virtual dimension as a part of its frame, but only entangled twin pairs share the same virtual dimension of a divided unique frame.
Now since space-time is an attribute of matter and all attributes exist simultaneously prior to an interaction (measure or energy exchange of particles), then there is no time until a particle is measured! Space just as a volume is not inclusive of time. Time is an attribute of matter in the form of a space-time coordinate relative to some reference only when matter is measured. Now notice I say time does not exist until there is an interaction. This is not the same as saying time is zero relative to some reference. If you can imagine a particle that by definition has various qualities and those qualities can only be perceived by other particles via a reaction through space-time, then without time all qualities of a particle would exist simultaneously, super imposed on one another. Not until time manifests do the attributes define to a particular state! So when visualizing a particle's Strodinger volume, the particle is everywhere in its probability realm and only when there is an exchange of energy does it realize to a specific space-time coordinate.
Just to clarify a little more on time, essentially when dealing with time, when two particles exchange energy a frame is formed and time is created spontaneously. Time in this sense is virtual. Time as we measure it is really a series of reactions that we can count and make a comparative measure, so many X counted compare to Y count. This is why time can be negative to some reference. Time should be viewed as the means energy can turn into work and therefore is more of a dimension that realizes into an absolute value. So time is really discontinuous and discrete, a facility for energy and not the string of events as we perceive it to be.
So we can view this model of matter as having five dimensions, three measurable spatial dimensions, one virtual dimension and one spontaneous temporal dimension. The next question is how can you integrate matter and space with GR? When one says energy is required to bend space how is that done? Does space just react to matter magically? At least with this interpretation of space-time as a product of matter, which is represented by the Schrodinger Volume, it integrates space and energy. This allows for a consistency of force carriers (with the exception of nucleonic forces) to be in the form a photon and could implicitly prove gravity to be such.
A probability realm can have FTL reactions. Its a matter of whether or not a particle has enough energy (whether through tunneling or otherwise) to span a probability curve that is large enough to cause a reaction with another particle that is at a distance that would other wise require FTL ability. Such is the case of the "Big Bang", before the expansion all of the matter's probability curves constrain to the greatest probability of existence to within the event horizon. When the black hole opens the probability curves expand well beyond the event horizon instantly. It is the interactions of particles with gravitons that slow this expansion to something that is still faster than light.
To expand on this FTL further, if we take this idea of the Schrodinger Volume to describe space-time and change the constant of c to describe wave-length with a more generalized idea of quantum states to be frequency nodes. Then nature can change the mass of a particle not only by it wave-length with c as constant, but also by changing its probability curve and maintaining its frequency. This means there can be instances where particles can travel faster than light! There really isn't an understanding of QM that limits how a particle's probability curve can change. So not only does this interpretation change the sense of space-time but also the notion of c being constant in every situation. It also opens up the idea that particles can take on just about any mass, that means we will always find some new species of particles given enough energy to increase the probability of its possibility. The question now arises when we experiment with accelerators when are we creating matter as opposed to breaking up matter into pieces? A question that could radically change the views of the standard model!
Finally GR could be achieved statistically. Probability curves of matter in a cool universe could have inter-particle reactions that would conform to the velocity of light. When something like a space ship is propelled to some percentage of c, the nature of the distribution of energy of the particles making up the ship does not necessarily result in changing the particles Schrodinger volume. In fact statistically results in the emission of energy as photons. Remember the Schrodinger volume is a degree of freedom a particle has in distributing energy in particle interactions. The ability to convert or distribute energy in the form of other particles is also a venue. So GR and SR can be a statistical products of this interpretation of matter and conform to QM observations.