# How many dimensions compose reality?

1. Sep 16, 2006

### Duhoc

I have heard as many as eleven. But I vote for 4 and only 4. What is the evidence for more than 4? Or logic?

2. Sep 16, 2006

### setAI

dimensions are an emergent metric of relationships determined by the degrees of freedom of the interactions of elements in a causal network- they are wholly arbitrary based on the dynamics of the system- there are universes of limitless spacelike and timelike dimensions that can emerge from the spectrum of possible physical rule-systems [take the M-Theory Landscape as just one example: 10^500 possible universes ]

3. Sep 16, 2006

### Duhoc

I just thought they were this or that, or so much this and so much that. Up down, right left, in out. I am aware of the very tiny geometries of superstring theory that are required to enact the vibrational patterns of elementary particles, but I am curious as to why they qualify as dimensions. They might only be approximations of dimenions, but anyway, how would you determine precisely what they are scientifically?

4. Sep 16, 2006

### marcus

there is no evidence for more than 4
and there is no logical reason that there must be more than 4

string theory has so far as I know not made contact with reality
so there is no reason to suppose that it describes nature,
therefore if some version of string theory requires 11 dimensions
this does not yet say anything about nature, and may never.

IMO it is important to notice one thing about spatial dimensionality.
Spatial dimensionality is an OBSERVABLE.
There are various ways to MEASURE IT!

e.g. the "Hausdorff dimension" way and the "spectral dimension" way.

One is by experimentally comparing radius and volume and see how they depend one on the other, as a practical matter.

One is by experimenting with DIFFUSION PROCESSES like the random walk followed by smoke particles

Both these ways of measuring dimension depend on the SCALE. and they can give fractional answers. The dimension of space at large scale can be different from the dimension at very small sub-atomic scale.

==============

Renate Loll has made this point very clearly----when we finally get a quantum theory of spacetime which is truly background independent, then the dimensionality will be a QUANTUM OBSERVABLE.

It will no longer be a static mathematical assumption with some fixed value but will be a dynamically varying quantity that one will have to measure in conjunction with other quantities. It may indeed have different expectation values at different scales. It could even evolve with time or in connection with matter.

So one should probably not think of spatial dimension as some integer like 3, fixed by God for all eternity at all times and scales for reasons best known to Himself. But also even less should one imagine as some string theorists do, that it is a different integer like 10.

Last edited: Sep 16, 2006
5. Sep 17, 2006

### Duhoc

I like string theory

I believe it is true. But your point about scale is very interesting. Maybe when you get down to a certain level of smallness you cannot distinguish reality by length. Only some type of curvature enacted by a string can distinguish between 1 of 2 states. And these states may only border our universe not reside in it. In any case I will read up on the references you provided.

Duhoc

P.S. What is your opinion on only four dimensions in our universe?

6. Sep 19, 2006

### Chronos

Perhaps the most fundamental building blocks of the universe reside in fractional dimensions whose emergent properties macroscopically appear to be 4 integer dimensions.

7. Sep 19, 2006

### EL

What is "fractional dimensions" (in physics)?

8. Sep 19, 2006

### Chronos

Renate Loll's CDT model, for example.

9. Sep 19, 2006

### MeJennifer

Perhaps I miss something but to me it seems we cannot measure space at all. It seems that we can only infer space by measuring collisions and calculating trajectories of particles or bigger objects.

10. Sep 20, 2006

### Duhoc

query

I asked if there were 4 dimensions in our universe, but what I really meant to ask was are there exclusively 4 dimensions? That is, is everything four dimensionsal, and what we observe as one, two, three, five, six ... dimensions merely apprximations. Just as two dimensions can depict three dimensions, can four depict all of the others? But here is an even more interesting question. Suppose space is composed of something (strings), as string theorists assert. What happens when someone walks down the street, through space. Are these little strings pushed aside, or is the person part of the matrix of strings? I'll give you a buck if you can answerr that.

11. Sep 21, 2006

### Chronos

The operative question, IMO, is how many dimensions do you need to make testable predictions? I can make a powerful case that only 4 are necessary to quantify any prediction. Mathematical artifacts aside, the burden of proof is upon you to falsify my model, not me.

I'm only challenging the argument, not the messenger. Both of you raise interesting questions I perceive as sincerely motivated. I have made the mistake of not pointing this out in the past - and offended people I regarded as kindred souls who are well intended and curious. I like to think we are all here to learn and polish our knowledge.

12. Sep 21, 2006

### Duhoc

The Alphabet

Well lets take the alphabet as an example. We know letters, we use the letters. We can recite them in order. But where is the alphabet? And I think the same principle applies to space. I think as you rightly point out, it may be in the same place the alphabet is, and I suppose it really doesn't matter where it is, provided we can use the relationships its existence implies, whatever that existence is. But on the other hand, space seems to have "physical" properties, or maybe it's the "letters" which exhibit the realtionships of space that have them. So I guess any physical process can define space depending on how we define it (how many dimensions) as the letters do the alphabet and therefore in order to have space a physical process must be present wherever space is. But I was thinking, and I think this is in essense what string theorists assert, that actually the converse is true, that it is space that defines phsical processes by the resonance of these strings which are arrayed in four dimensions.

Duhoc

13. Sep 26, 2006

### Chronos

I understand your argument. I only question if every placeholder in this alphabet scheme is meaningful - i.e., has observational support. I tend to otherwise regard them as mathematical artifacts. I fully embrace all mathematical solutions as plausible, but view them with suspicion until validated by observation.

Last edited: Sep 26, 2006
14. Sep 26, 2006

### bchui

So, does the concept fractional dimension plays any role in copsmology or string theory?

15. Oct 9, 2011

### waterpump

Duhoc and Chronos have initiated a fascinating discourse.

There are deep issues here. Re the alphabet metaphor - This alludes to dimensional partitioning / expressed and unexpressed potentialities. The alphabet exists in the realm of our consciouness, it has no existence in spacetime. Sure, we can draw letters, make marks on surfaces or displays, but these realities are mere patterns with boundaries, 'models' if you will, their meaning (as patterns on surfaces or displays) are unexpressed wrt our conscious understanding of alphabet, the marks on surfaces or displays are 'unexpressed potentialities'. The reality and the recognition of the meaning of the alphabet lies in (the dimensionality(?) of) our consciousness where the meaning is fully expressed.

So we have the issue of the 'model' and the 'reality'. We can model the 3 dimensional space we exist in, calculate, make geometrical transforms, and construct shapes, planes and curves in Euclidean 3 space, but not a single atom of (three dimensional) physical reality can exist in E-3 space.

I would argue that is not simply a matter of 'how many dimensions' but what is the 'quality' or 'attribute' of those dimensions? What is the quality or attribute of 'spaceness' in spacetime as opposed the quality of 'spaceness' in Euclidean 3-space that allows atoms to exist in one but not in the other. Obviously the influence of 'time' has something to do with it!

So although we can accurately model three dimensional space and perform calculations to accurately predict certain behaviours of bodies and phenomena in spacetime, surely we cannot assert that the 'models' (quantum / GR / string / M or whatever), and hence the nature of or quality of dimensionality of these models, is the same as the reality of our universe, although its the best set of (evolving) models we have?

Again this is not directed towards personalities, i'm just trying to engage with the debate.

16. Oct 9, 2011

### Staff: Mentor

Waterpump this thread is over 5 years old and thus is too old to revive.