How we know about the dimensions given in sensations? At the level of our feelings three dimensions are not more than orientation of body in respect to the local gravitational field. Take off the gravity the dimensions will disappear in our feelings, so that is not good source of knowledge about the world's dimensions. Then, as always, will turn to the physics experiments. From there we know that any quantum field (perhaps except scalar which we have no in a stable form in reality) are built in a way to respect the symmetry of the 3+1 dimensional world and does depend on the 4 coordinates (which are in general is simply human way to mark a point, there are no any coordinate as physical quantities in reality). Nevertheless, we need 4 coordinates for fields of 4 dimensional world and that works absolutely perfect in any physical experiment description. Now let's speculate. Let's assume that there is no such thing as spatial dimensions (will not talk about the time arrow right now) and the dimensions are simply a human way to handle a position of our bodies in an external gravitational fields. How it can work? First of all, what about the fields, why they respect a symmetries of 3+1 world? The answer can be simple in fact. These fields do respect the symmetry 0f 3+1 world but they are do not request an existence of 3+1 dimensions of Universe as a unique and only option. In some extend we talk about the 3+1 dimensions of whole Universe simply because the fields we explore have this structure. Namely, take a world without the gravity, make experiments, make conclusions about the structure of the world. The simplest conclusion will be that we can handle and feel only that kind of fields and corresponding matter, but the conclusion that the whole Universe has that 3+1 structure is a kind of not necessary logical jump. We simply made of and observe that kind of matter that respect the symmetries of 3+1 physical bubble but nothing more. Now will consider a gravity field. First of all, classical gravity field has a form of metric of 3+1 manifold, so it must be a proof 3+1 world's structure for the first sight. But, quantum gravity is not a geometry as it seems right now. So, if we will consider a metric simply as a spin 2 quantum field it will not be related to a geometry at all. We can replace all physical geometrical notions by the notions of interplay of quantum fields without introducing spatial dimensions, instead the dimensions we will have a number of components of the spin 2 field. In this picture is assumed, we can imagine that we live in big something where each physical event we can observe is defined by particular matter fields and their mutual interactions. Namely, the law of physics we have are dictated by the fact that we and the world we explore are made of the same matter and we can feel, observe and handle only that particular reality made from the particular particles and fields. Of course, two questions remain then, what is time dimension and why we so perfectly isolated from other possible phenomena of possibly more complicated general Universe. I do not like an anthropic principle as an answer.
I already answered the question of the 3+1 dimensional reality in my paper:
Article The Geometrical Meaning of Time
The argument relies on linear stability of the Lorentz metric with respect to the Einstein equations. However, limited space-time domains can be Euclidean or any other signature. Please see:
Article The Primordial Particle Accelerator of the Cosmos
Dear Sergey Bondarenko
The 3 + 1 dimensional "mechanics" in relation to the model of spacetime as described in the theory of Special and General relativity is not a scientific concept. It is a "trick" to make calculations easier. This kind of "tricks" are well known in engineering. That is not strange, because what we actually do in physics is reverse-engineering phenomenological reality with the help of observations and measurements.
In quantum field theory Einstein's theory of Special and General relativity are not really helpful. Quantum time is a universal constant - because of the universal constants h and c - and the concept of spacetime has no direct relation with the geometrical structure of the basic quantum fields. The universal electric field is a topological structure under invariant volume, the corresponding magnetic field is a vector field and the Higgs field is a universal scalar field (lattice structure).
So we can describe the basic quantum fields in Euclidean space with the geometrical concepts volume, surface area and lines/points. There is no need for the "trick" to use 3 + 1 dimensions.
Gravity as a force field shows to be an emergent field and the consequence is that the force of gravity is mediated by one of the basic quantum fields. So spacetime and its 3 + 1 dimensional "mechanics" has no direct relation with phenomenological reality. It is a model and we can use it to calculate observations and measurements, mostly in the macrocosm.
So I agree with the introduction of your discussion.
With kind regards, Sydney
We can get 3 space dimensions from observation of our own body, no need for gravity. These are ``dimension'' because we can go forward and backward. Time is not a dimension. So, time is only NOW. What exists now if the matter particles and the forces (the STOE suggests these forces are from the gradient of a continuous plenum which exists). Our memory establishes a model of ``past'' positions of matter. Hence, consciousness is related to or brain's memory.
Beyond the 3 space dimensions is only math. The additional space like dimensions are used to add parameters to the math. That is, there are unmodeled characteristics underling the observations of which we are ignorant. So, the advance of physics is to use only the 3 space dimensions, consider the universe as Machian, and to use causality for the memory (time) of past to now. Use of more space-like dimension is going in the wrong direction.
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size