What made the universe have 3 dimensions, instead of some other number?

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The discussion centers on why the universe has three spatial dimensions, exploring various theories and principles, including the anthropic principle and string theory. Participants speculate on the implications of having more or fewer dimensions, questioning the stability and existence of life in higher-dimensional spaces. The concept of dimensionality is framed as either arbitrary or constrained, with arguments suggesting that three dimensions may represent the simplest arrangement for observable phenomena. The dialogue also touches on the role of time as a fourth dimension and the potential for extra dimensions posited by string theory. Ultimately, the consensus is that while three dimensions are observed, the true nature of dimensionality remains uncertain and complex.
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I think because the number 3 is still pretty low it isn't so suspicious to people, but imagine we lived in some universe with, say, 186 dimensions (that miraculously supported intelligent life, so there's someone to ask the question - I know about the anthropic principle). Wouldn't we have asked ourselves something like "Hey wait a minute, 186 seems pretty arbitrary, what's so special about this number that it should be the number of dimensions in our universe?".

I know that string theory says there's 10 or 11 dimensions (or was it 26?), and space-time is really 4d not 3d, so let me generalize the question. What made the universe have the number of dimensions it happens to have, whatever this number happens to be?

I'm wondering if maybe there was a dimension-making mechanism, like the Higgs mechanism is supposed to create mass.
 
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Higher-dimensional spaces become unstable essentially, we aren't sure why but this is in the context of String Cosmology (http://en.wikipedia.org/wiki/String_cosmology) and String Gas Cosmology (http://arxiv.org/abs/0808.0746). String Gas Cosmology attempts to explain the compactification processes with regards to inflation/inflaton, dilaton field/dilatons, string gases, the string landscape and String Winding Modes. 26 dimensional String Theory is Bosonic String Theory (http://en.wikipedia.org/wiki/Bosonic_string_theory) and is used in String Cosmology models.
 
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3 is a nice number because quaternions are still associative. So, perhaps, the answer is in the http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_%28normed_division_algebras%29" . All the rest, like stability of matter, may well be its (hidden) consequence.
 
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Thanks for the replies. Another question: Any idea why is the universe not zero-dimensional? Zero is just a more fundamental number than 3. I'm wondering if there could be a cause that's different than the anthropic principle.
 
satuon said:
Any idea why is the universe not zero-dimensional?

Perhaps because you should not divide by zero? By the way, perhaps it is zero-dimensional. But it feels like three-dimensional, and we like to have science that corresponds to our feelings. We are then motivated to develop it.
 
I think it's fair to say that the beliefs about how many spatial dimensions the universe is composed of vary in the semi-mainstream from 2, to 10+. After all, while String Theory is still young, it posits a glut of extra spatial dimensions that we don't experience... which goes to arkajad's last post. The Holographic Principle goes for 2 embedded... so really , we don't know. It APPEARS that there are 3 spatial dimensions, and if there are more or less, it is yet to be demonstrated.

I would just add, beyond the fact that dividing by 0 is a no-no... wouldn't a 0 dimensional universe... not exist, or at least, not in a manner that could allow ANY degrees of freedom that we observe?
 
Dimensions per se do not exist, any more than miles, yards, inches etc.. They are communicable tools of concept that have been devised to allow us to better understand, and explain, our surroundings. Three appear to be adequate for this, whilst the passage of events, time, is regarded as the fourth.
 
Peter Watkins said:
Dimensions per se do not exist, any more than miles, yards, inches etc.. They are communicable tools of concept that have been devised to allow us to better understand, and explain, our surroundings. Three appear to be adequate for this, whilst the passage of events, time, is regarded as the fourth.

That's true for colloquial descriptions of dimensions, but in terms of Relativity, and String Theory they are in fact REAL things. If they were not, then gravity would also be merely a concept... that is not what we observe to be the case.
 
So, do we assume that an the 3 dimensional space (+ 1 dimension for time) needs to be in-place before the Big Bang for the laws of physics to work - placed there by an Act of God? Or did the Big Bang itself create 3 dimensions + 1 time from (zero dimensional) nothing? I do the physical laws predict that the known Universe can be created starting from a zero-dimensional universe?

Perhaps because you should not divide by zero?
Could you please elaborate. I couldn't find much about zero-dimensional spaces, but there is one article in http://en.wikipedia.org/wiki/Zero-dimensional_space" about zero-dimensional spaces but it doesn't mention about that problem. I was wondering if the equations for General Relativity can be adapted to work for any number of dimensions, and what would happen if you tried with 0, but I really don't have the knowledge to try it or even know if I'm talking sense.

Stephen Hawking in his book 'The Grand Design' says that the universe came from Nothing - did he mean a 3-dimensional Nothing or a 0-dimensional Nothing? I hope that his book wouldn't be just metaphysics but maybe has some mathematics in it.
 
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  • #10
arkajad said:
3 is a nice number because quaternions are still associative. So, perhaps, the answer is in the http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_%28normed_division_algebras%29" . All the rest, like stability of matter, may well be its (hidden) consequence.

I agree with those like Baez who feel that the normed division algebras tell us something important about self-consistent dimensionality, but quaternions don't seem a good explanation of 3D, or even 4D. Why stop at 4 when 2 and even 1 dimensional algebra is even more regular in its behaviour? It would seem more likely that by this argument we should make more of the absence of trionions.

But perhaps you have some specific argument or reference in mind here? As I say, it does seem the right way to start thinking about the reasons why dimensionality is so low. This was Baez's essential point. Algebra could have an infinity of dimensions, but it only starts to produce self-reinforcing patterns as dimensionality becomes strongly constrained.
 
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  • #11
I believe that someone rolled the dice and ended up with a 2 and a 1.

But really, your question is pretty difficult to answer. We live in a 3d universe because it happens to be 3d for whatever reasons. Where did it come from? NO ONE KNOWS!
 
  • #12
Drakkith said:
I believe that someone rolled the dice and ended up with a 2 and a 1.

But really, your question is pretty difficult to answer. We live in a 3d universe because it happens to be 3d for whatever reasons. Where did it come from? NO ONE KNOWS!

Grrr... Einstein no like, EINSTEIN SMASH! :wink:


Your last point seems to be the most convincing however unsatisfying it may be, especially if some form of MWI holds; it's 3D because we wouldn't be here if it were not... elsewhere it's more or less, but we're not there to observe it.
 
  • #13
Maybe because there is a cross product in 3D. In higher dimensions you can't form a cross product that takes vectors to vectors - you have to take vectors to bivectors (or whatever they are called).

without a cross product (e.g. in 4D or 5D) how will you build a bicycle!
 
  • #14
least_action said:
Maybe because there is a cross product in 3D. In higher dimensions you can't form a cross product that takes vectors to vectors - you have to take vectors to bivectors (or whatever they are called).

You can do it in 7D - using octonions.
 
  • #15
You can rule out some configurations just by the anthropic principle. <2 dimensional beings would have a hard time pondering the nature of the universe. Even 2 dimensional animals couldn't have traditional digestive systems (as any path through them would split them in half). In other configurations, the relationship between forces is probably such that life as we know it couldn't form (for example if there were many more dimensions and gravity were significantly weaker, we might not get star birth).
 
  • #16
least_action said:
Maybe because there is a cross product in 3D. In higher dimensions you can't form a cross product that takes vectors to vectors - you have to take vectors to bivectors (or whatever they are called).

without a cross product (e.g. in 4D or 5D) how will you build a bicycle!

This is the key I believe as well. 3D is the simplest possible arrangement of degrees of freedom, if degrees of freedom need to be shaped by a measuring context.

It is like the way in network theory, all more complex networks (with many edges meeting) reduce to just networks of three edges.

You can take two positions: either the number of dimensions is arbitrary, any number being possible, or the number of dimensions is constrained for some reason.

If the number is random and all arrangements probably exist "somewhere", then we indeed have only an anthropic explanation for why we find ourselves in a 3-space.

But if instead dimensionality is subject to the principle of constraint, then it seems only logical that one solution, one arrangement, can count as the "most constrained" - the lowest possible dimensional minima.

Given we exist in an incredibly low-D realm (just 3 when there could have been any number up to infinity?) should suggest that the second view is the more likely.

And least action has touched on exactly the reason why the minima would be 3-space and no lower. The least amount of context needed to measure/constrain the least amount of event is 2D to measure/constrain 1D.

If you just take dimensionality to exist, then there is no reason to take this view. But if you see crisp degrees of freedom arising by way of contexts that constrain, then 3D has obvious unique properties.

Time then arises as "fourth dimension" in this approach as unfinished business. Constraint being an active process implies a gradient. To create a flat 3-space "everywhere", it has to expand. Which takes time.
 
  • #17
apeiron said:
This is the key I believe as well. 3D is the simplest possible arrangement of degrees of freedom, if degrees of freedom need to be shaped by a measuring context.

It is like the way in network theory, all more complex networks (with many edges meeting) reduce to just networks of three edges.

You can take two positions: either the number of dimensions is arbitrary, any number being possible, or the number of dimensions is constrained for some reason.

If the number is random and all arrangements probably exist "somewhere", then we indeed have only an anthropic explanation for why we find ourselves in a 3-space.

But if instead dimensionality is subject to the principle of constraint, then it seems only logical that one solution, one arrangement, can count as the "most constrained" - the lowest possible dimensional minima.

Given we exist in an incredibly low-D realm (just 3 when there could have been any number up to infinity?) should suggest that the second view is the more likely.

And least action has touched on exactly the reason why the minima would be 3-space and no lower. The least amount of context needed to measure/constrain the least amount of event is 2D to measure/constrain 1D.

If you just take dimensionality to exist, then there is no reason to take this view. But if you see crisp degrees of freedom arising by way of contexts that constrain, then 3D has obvious unique properties.

Time then arises as "fourth dimension" in this approach as unfinished business. Constraint being an active process implies a gradient. To create a flat 3-space "everywhere", it has to expand. Which takes time.

This is a good argument for experiencing only 3 spatial and one temporal dimension, and for having no less than 3+1... but does nothing for the existence of extra dimensions we don't experience as with String Theory or the like. Would you agree, or am I missing your point?
 
  • #18
I'm sympathetic with Peter Watkins. No observations to date suggest the need for more than 3+1 dimensions to adequately describe its position in space-time - at least so far as the macroscopic [GR] universe is concerned. String theory is the main driver in the search for extra dimensions, and the LHC is currently testing this proposition. It is worth noting the 'universe' may have been dimensionless prior to the big bang.
 
  • #19
Chronos said:
I'm sympathetic with Peter Watkins. No observations to date suggest the need for more than 3+1 dimensions to adequately describe its position in space-time - at least so far as the macroscopic [GR] universe is concerned. String theory is the main driver in the search for extra dimensions, and the LHC is currently testing this proposition. It is worth noting the 'universe' may have been dimensionless prior to the big bang.

I'm personally not a fan of String Theory, but I felt the need to mention it in this context, I am by no means trying to promote it.
 
  • #20
nismaratwork said:
This is a good argument for experiencing only 3 spatial and one temporal dimension, and for having no less than 3+1... but does nothing for the existence of extra dimensions we don't experience as with String Theory or the like. Would you agree, or am I missing your point?

No, that is a sharp question. And indeed, six compactified dimensions would be a prediction of a constraints-based logic.

If you are interested in a fuller explanation, perhaps PM me.
 
  • #21
Chronos said:
It is worth noting the 'universe' may have been dimensionless prior to the big bang.

Or I would describe it as "vague". In a constraints-based approach to dimensionality, our initial conditions would have to be maximally UN-constrained. So we would presume that "in the beginning" there were infinite dimensions. Or rather potential degrees of freedom. And where everything is happening at once, nothing is really happening. It is an equilibrium state, a perfect symmetry - though obviously, as results showed, an unstable one.

Then when symmetry breaks, when there turns out to be a gradient of development (towards more constrained dimensionality), you end up with a more limited state of something. Again, by logic, if the initial conditions are imagined as a state of maximal lack of constraint (ie: a vagueness), then the final state is one of maximal possible constraint.

You can't have one end of this story (a 3+1+compactified D, expanding and cooling realm that is essentially the creation of a big fat nothingness, a heat death) without having the other (initial conditions which are a big fat everythingness, an infinity of dimensional potential).

It is a sum-over-histories approach. Everything "exists" as a potential dimensional arrangement, but most of it self-cancels away to leave what cannot be self-cancelled away.
 
  • #22
Another way to explain why there are 3 dimensions (+time) is that spacetime was created by the Big Bang. Since the Big Bang started from a singularity, that singularity could have been actually an initial 0-dimensional universe. That might seem far-fetched, but it is the only way to account for the fact that there are dimensions instead of no dimensions at all.

Then there are two scenarios - The Big Bang created many (probably disconnected) universes with varying configurations of parameters (like dimensions, fine structure constant, etc.). That would account for the fine-tuning problem.

Or our spacetime might be the only one, because the physical process that created it had some sort of *constraints* about the type/number of dimensions.
 
  • #23
apeiron said:
So we would presume that "in the beginning" there were infinite dimensions

I especially like the idea of infinite dimensions, because it is the only other sensible 'number' of dimensions apart from zero for the initial state of the universe before the Big Bang. I personally feel that the dimensions themselves must have been created by the Big Bang, i.e. they weren't a prerequisite for the universe to be created.

apeiron said:
In a constraints-based approach to dimensionality

Could you explain more about the constraints-based approach to dimensionality? What is it, exactly?
 
  • #24
How do 'extra' dimensions defeat any cosmological model?
 
  • #25
Could it be that we perceive only 3 spatial dimensions as this is the minimal amount of dimensions that we need to exist?
There are more dimensions but we do not observe them because we don’t need them. Similar to the electromagnetic spectrum, we only observe the light part of the spectrum as this is the part that we need.
 
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  • #26
Dragonetti said:
Could it be that we perceive only 3 spatial dimensions as this is the minimal amount of dimensions that we need to exist?
There are more dimensions but we do not observe them because we don’t need them. Similar to the electromagnetic spectrum, we only observe the light part of the spectrum as this is the part that we need.

The problem would be that if extra (non-compact) dimensions actually exist, then why does our energy not drain away into them?

One of the things many say is special about 3D is that gravity and EM fade only gradually - at the square of the distance. Raise the dimensionality and interactions would drain away at the cube, the fourth power, etc.
 
  • #27
apeiron said:
The problem would be that if extra (non-compact) dimensions actually exist, then why does our energy not drain away into them?

One of the things many say is special about 3D is that gravity and EM fade only gradually - at the square of the distance. Raise the dimensionality and interactions would drain away at the cube, the fourth power, etc.

In essence, some of the extra dimensions in string theory are meant to account for the relative weakness of gravity, but only when these dimensions are compact. It makes one wonder if all dimensions "curl" back on themselves, but the 3 we're familiar with just happen to have (relative to us) the largest spatial extent.
 
  • #28
apeiron said:
The problem would be that if extra (non-compact) dimensions actually exist, then why does our energy not drain away into them?

One of the things many say is special about 3D is that gravity and EM fade only gradually - at the square of the distance. Raise the dimensionality and interactions would drain away at the cube, the fourth power, etc.

But, it also seems mathematically possible that interactions occur in a manner that exhibits a 1/r dropoff in 4D which we see as a 1/r^2 dropoff in 3D because of the effect of the extra 4th dimension.

I see this as implying that the limit to spatial dimensions could also be 4.
 
  • #29
arkajad said:
3 is a nice number because quaternions are still associative. So, perhaps, the answer is in the http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_%28normed_division_algebras%29" . All the rest, like stability of matter, may well be its (hidden) consequence.

Occam's Razor. "Pluralitas non est ponenda sine necessitate." Three is all that's required.
Your position in the universe, any other position and the time relative to the speed of light between them,
 
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  • #30
In string theory, an 11 dimensional universe is uniquely singled out as both a minimum and maximum number of dimensions to unify all known forces.

Furthermore, it has been demonstrated that the only stable configurations of these 11 dimensions are either 4 macroscopic dimensions and 7 compactified dimensions, or 7 macroscopic and 4 microscopic.

It could very well be that we see only 4 dimensions because that is just one of only 2 possible stable configurations of 11 dimensions.
 
  • #31
To be honest I see extra dimensions as a cop out way trying incorporate a gravity into a theory of everything.

I could easily solve the problem of the non-compatibility between relativity and quantum mechanics by simply saying: the reason we can't determine both the velocity and location of particles at the same time if that particles move in and out of non-observable dimensions, therefore quantum mechanics is not a complete theory and needs to be worked on before any sort of unification takes place.
 
  • #32
schteev said:
To be honest I see extra dimensions as a cop out way trying incorporate a gravity into a theory of everything.

I could easily solve the problem of the non-compatibility between relativity and quantum mechanics by simply saying: the reason we can't determine both the velocity and location of particles at the same time if that particles move in and out of non-observable dimensions, therefore quantum mechanics is not a complete theory and needs to be worked on before any sort of unification takes place.

I truly think some people on this forum should learn about theories incorporating extra-dimensions such as Superstring Theory before merely stating it's a cop out because you don't fully understand the implications.
 
  • #33
Kevin_Axion said:
I truly think some people on this forum should learn about theories incorporating extra-dimensions such as Superstring Theory before merely stating it's a cop out because you don't fully understand the implications.


Perhaps I should clarify. I see the adding of more dimensions in the same light as adding the "ether" when our theories don't entirely explain everything that they're intended.

I'm hoping that we can attempt to explain the universe without having to resort to adding extra dimensions to fit our (great attempt at a) grand unifying theory, if one exists.
 
  • #34
String theorists don't add dimensions, superstring theory requires the dimensions mathematically, they appear in the equations. I understand your perspective in just placing values in and ideas without motives which is what a lot of the Standard Model is (the physical constants). Superstring Theory doesn't do that and in fact it doesn't have any adjustable parameters.
 
  • #35
Kevin_Axion said:
String theorists don't add dimensions, superstring theory requires the dimensions mathematically, they appear in the equations. I understand your perspective in just placing values in and ideas without motives which is what a lot of the Standard Model is (the physical constants). Superstring Theory doesn't do that and in fact it doesn't have any adjustable parameters.

The fact that m-theory or other types of string theory require extra dimensions mathmatically to me means that, while we are not arbitrarily adding constraints ala Newton/einstein, our theory needs to be improved so that it does not mathmatically require these extra dimensions in the first place.

I could be wrong though.
 
  • #36
schteev said:
The fact that m-theory or other types of string theory require extra dimensions mathmatically to me means that, while we are not arbitrarily adding constraints ala Newton/einstein, our theory needs to be improved so that it does not mathmatically require these extra dimensions in the first place.

I could be wrong though.

Is time a dimension? What makes Einstein's addition of time as a dimension any different from adding other dimensions?
 
  • #37
Jack21222 said:
Is time a dimension? What makes Einstein's addition of time as a dimension any different from adding other dimensions?

Arrow of time.
 
  • #38
Jack21222 said:
Is time a dimension? What makes Einstein's addition of time as a dimension any different from adding other dimensions?

Well, he redefined something that's been in our common experience. Nobody disputes that time exists, and defining it as a dimension actually makes a lot of sense, never mind the good physics we get from that. Recognizing that time and 3 spatial dimensions are subject to warping by mass is what makes Relativity.

schteev: I have issues with string theory, but what you're talking about isn't one of those issues nor do you make sense. You're acting from a biased point of someone experiencing 3 spatial and one temporal dimension, much as people were skeptical about time as a dimension and not some absolute measure. The issue with string theory is confirmation of a prediction, not extra dimensions. If that confirmation ever comes out, then the dimensions would naturally follow... no more or less, much as with GR. Is this any odder than the notion of quantum behaviour at small scales?
 
  • #39
In my opinion, dimensions are simply a theoretical degree of freedom. There is no reason why there shouldn't be an infinite number of possible degrees of freedom. However, actual geometrical structures don't generally have an infinite number of dimensions. They have some finite number of dimensions that places boundaries and limitations on things.

The geometrical object you happen to inhabit forms the "space" in which you live, along with its limiting dimensional structure. If you live on a line, your space is one-dimensional, if you live on a plane your space is two-dimensional. If you live in spacetime, you have four dimensions. You can't assume that the geometrical object is embedded in a higher "space".
 
  • #40
closet mathemetician said:
If you live on a line, your space is one-dimensional, if you live on a plane your space is two-dimensional. If you live in spacetime, you have four dimensions. You can't assume that the geometrical object is embedded in a higher "space".

But physics is not about my space or your space. It is about the objective reality. And the objective reality may well be different from the subjective one experienced by our senses.
 
  • #41
arkajad said:
But physics is not about my space or your space. It is about the objective reality. And the objective reality may well be different from the subjective one experienced by our senses.

Yes our senses are limited, which makes it hard for the average human to get their head around these sorts of concepts, just like it's hard for the average flatlander to comprehend a three-brane world.

I tend to think a simple explanation is a better fit than something that is needlessly complicated. Yes, in the language of our universe string theory (all of them) makes sense and goes a long way to at least trying to unify our great theories.

I just think that we should spend time trying to explain what's happening in our own brane world first before getting too far ahead of ourselves. Let's work out what is keeping stars in galaxies, and where all this unexplained energy is coming from first. Let's work out dark matter with a simple explanation.
 
  • #42
The extra-dimensions to some extent simplify the mathematics. Also possibly the answers to your questions such as dark energy and dark matter will be discovered in superstring theory.
 
  • #43
Kevin_Axion said:
The extra-dimensions to some extent simplify the mathematics. Also possibly the answers to your questions such as dark energy and dark matter will be discovered in superstring theory.

I hope so, but I think we are a long way from answering these questions.

It certainly doesn't hurt to try though.
 

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