Dimensions Creation: Theory or Always Existed?

[cam875]

out of curiosity is there any theory on how dimensions that we exist in were created? or are they always said to have existed.

 

[starkind]

This is close to the origin problem. I believe it is still open.

But what do you mean by theory? If your definition is fuzzy enough, you will allow yourself to call creationism a theory. Then there must be a creator and all of that.

I am sure that for as long as anybody has thought it worthwhile to speculate, dimensions are said to have existed. But have they always existed?

By the way, I like that word, "always.' What does it mean to you? It seems you can follow the Hubble contraction back to any point, or every point if you like, in the conceivable Universe(s). Is that The Beginning?

(By the by, have you read Douglas Adams story about the philosophic engineers who built the ultimate computer (-1, actually it was only the penultimate, but it did create the actual ultimate computer, the one that has the answer, sort of the Aleph-null of computers.,)

 

[cam875]

im in no way insinuating creationism as a theory but what I am saying was before our universe was created there were no dimensions and than once it was created there was 3 spatial and one time and who knows there could be more if string theory works out. I am asking how the dimensions came to be and why there are a specific amount and all that and if there is a theory on this.

 

[starkind]

Do you like mathematics?

 

[starkind]

Perhaps not.

Well, it is a stubborn problem. Space and time are inextricably linked. Einstein and others have seen fit to call them equivalent, which leads to some potential lines of thought. So, "back in time" may be analogous to some direction, say, "West." Then the question of what there was before the beginning is like asking what exists if you go all the way West, and then a few more steps...

Of course you can't go all the way West, because no matter how far you go there is still more of it. Or maybe North. Since there is a North Pole, there is an end to North. The beginning of North would be the South Pole, then. So if you go back in space beyond the South Pole, where are you? This might be difficult. But you see, the difficulty is in the question, not in the shape of the globe. It isn't a good enough question to have a good enough answer.

The universe is thought to be curved, in a four-dimensional sense, something like the globe is curved in the sense of a three dimensional sphere.

I know this is unsatisfactory. It doesn't really satisfy me, anyway. But it won't do to go "off-globe" and pretend the universe is really perfectly flat. Let's see what happens.

We are pretty sure the universe has no boundary. That means you can look to the West at sunset, and then, pointing West, go 'off-globe', arriving in due time at the Sun. Then you just keep going. You go on in a straight line forever, past the Sun, the planets, the stars, the galaxy, the local galactic cluster, the great wall, the great attractor, and keep on going. Now maybe you can keep on going forever. Let's say you did. Then, since the universe is infinite in every direction, you would have gone an infinite distance, in which you might have passed by all sorts of things. By probability, in infinity, anything might be able to happen. If it didn't, you just keep on going until it does. So eventually you come to a star with a nice Goldilocks planet that looks exactly like Earth on the day you left town. It even has an exact copy of you, just now leaving toward the sun. Have you gone 'all the way 'round the universe? Never mind what happened to all that time that went by while you were away traveling. Or, have you just come to one of the inevitable infinite repetitions of Earth on the day you left?

I suspect, given that you have asked the question the way you have done, that you haven't done the necessary ground work to get a better answer than this. It turns out that a lot of people have thought about the problem of origin, but unfortunately all the better answers have involved better math than is taught in most high schools.

Or you could just say God did it, and humans are too little to understand the purposes of God.

 

[cam875]

thanks for the answer, and yes you're correct I am in senior high school math so I don't expect to understand the equations of cosmology just yet, but thanks for your insight into this problem and sorry if I didnt word it correctly.

 

[jal]

Read some of my blog entries.
https://www.physicsforums.com/blog.php?b=271
jal

 

[starkind]

ok, no problem. I don't mean to discourage you. But words are very slippery, even when defined as well as possible.

The Big Bang theory comes from work Edwin Hubble did, showing that the galaxies are all moving away from us. If you then trace their trajectories back in time, it seems they all intersect about 13.7 billion years ago. I used to think that was a large number before the current economic crisis.

However, when we measure the light from the most distant galaxies, it seems clear that they are around 40 billion light years away...in other words, they started sending light in our direction way before the Big Bang. How can that be?

The answer seems to be cosmic inflation. The distance between us and the far distant galaxies was a lot less when that light was sent, but expanding space got in between us and the far distant galaxies in between times. So it has taken 40 billion years for light to travel 13.7 billion light years. That seems a little slow for light, especially since the speed of light is generally held to be a constant. Why did it take so long to get here? Anyway I thought the speed of light was the same for all observers.

I don't really have any talent for math, but you can go get popular books by people who are so talented, and they make the math gentle enough for most interested parties. Lee Smolin, Brian Green, Michio Kaku. I have a whole shelf full of them. Unfortunately, they do not make your question go away. Smolin talks about a big bounce instead of a big bang, where the initial singularity is avoided and maybe something came before that. So you are not asking a dumb question.

Also, I hope you are not put off by my suggesting you need to think about the terms of the question. Natural language can only do so much. Really, mathematics is the proper language for these things. I don't know what they are teaching in high school these days. Maybe you already understand tensor math, which has been giving me a headache for lo these many years. I wish you well in your endeavors, and recommend you stick around this forum as much as you can. There are some people here who actually know what they are talking about. Some of them, I think, even wrote the books.

Good luck to you.

R.

 

[Naty1]

See my recent thread: emergent Quantum Spacetime

https://www.physicsforums.com/showthread.php?t=294666

Also, I am just about to post a similar discussion, this time from a string theory perspective...Should be up in an hour or less: Space from Strings

 

[cam875]

alright thanks a lot for this info.

 

[apeiron]

There are some alternative stories around that don't seem to get much discussion.

The mainstream approach, metaphysically speaking, is to attempt to construct dimensionality from the bottom-up. So with causal triangles and other grainy quantum stories, we begin with something as small as possible - as near to a zero-D point as can be -then start gluing them together,

This was the approach right back to Euclid. First the point, then the 1D line, then the 2D plane, etc. Build upwards from some fundamental grain.

This has many problems of course. We can ask why a zero-D point should have a (plankian) grain. Why logically should three dimensions be flat(ish) and any further dimensions be compacted?

But you can instead take the complete opposite starting conditions and see what kind of counter-metaphysical story emerges.

In short, instead of assuming we must start with nothing (or zero-D points, which are as near as dammit nothing) we start with the presumption that an everythingness exists. An infinity of dimensionality (which can be modeled as an infinite symmetry, another story).

So we begin with a "solid block" of dimensional freedom just as a sculptor might start with some infinite block of materiality. And an infinity of degrees of freedom are the same as nothing when you think about it.

Then instead of constructing upwards from 0-D bricks, we constrain - we apply a top-down or contextual causality (much as advocated by process physicists with their soliton models).

So for some reason, this block of infinite dimensionality, or infinite symmetry, begins to self-organise, its dimensionality becoming constrained, reduced. The infinite symmetry becomes broken.

For the moment - as we are doing metaphysics - we don't have to say why this self-constraint is occurring. Just accept it and see where the idea leads us.

Anyway, to jump to the end of the story, we can start to see why three dimensions may be special as the least number of dimensions that total all-out constraint can produce. Once every degree of freedom has been constrained, just three remain unsuppressed, and so existent.

The argument goes like this. It takes a minimum of two dimensions to constrain any third. This is the minimal way you can have both a figure and a ground, a global context that constrains and then a remaining degree of freedom to mark what is not successfully constrained.

Picture it as two dimensions making a flat plane. Between them, they can constrain any remaining dimensionality to a dot-like point, a zero-D coordinate on the plane. So they disappear all other available degress of freedom.

But aha. The plane cannot "see" into the orthogonal axis, a straight line set at exact right angles to the plane. So as far as the plane is concerned, everything has been constrained to localised points. But then any point can freely extend in a straight line.

The causal trick is then that this is a self-constraining situation. Each pair of dimensions constitutes a plane of constraint that is helplessly then creating an unseen, therefore unconstrained and free, third dimension.

You can tie this approach into network theory and the fact that all network topologies reduce to triangular connections (and hence, you can begin to recover spin network approaches to quantum gravity, and other good SO stuff) from this general metaphysics.

As with network theory, four or more extended dimensions would be unstable and self-reduce to just three.

And a reduction to zero-D cannot work as this would leave absolutely no context (where could all that "energy" represented by a collapsing infinoverse go?).

A reduction to 1-D cannot work as how could a point be fixed to a location on a line. It is free to wander about unless a second dimension cuts across the line and thus locates it.

A reduction to 2-D cannot work because a plane can now act as a minimum set of co-ordinates, but by definition there is now that single remaining possibility which is unlocated, unconstrained, by the point-like co-ordinate - the now free third dimension.

So 3D can be shown to be a special case once you accept the metaphysics of an infinite dimensionality (instead of "a leap out of nothingness") as your initial conditions, and a causality based on constraint (instead of construction) The suppression of all freedoms that finally leaves the unconstrainable free to exist, and thus be real dimensions.

String-type entities could be fitted into this picture as secondary features. If there is some natural Planckian limit to the constraint, then each of the three dimensions would not be zero-thickness lines but instead have a certain tube like fatness. They would thus be able to carry resonances. With two compactified degrees per dimension (transverse and longitudinal ripples of the "tube") that adds up to six extra degrees of freedom in the 3D system.

All highly speculative perhaps. But it is important to note that there are alternatives to the standard model metaphysics, the presumption that dimensions are constructed by additive acts working upwards from some fundamentally small grain.

You can instead believe that the beginning was fundamentally large (and wildly free) then became as constrained and small as possible. But there exists a logical limit to the constraint of freedoms. And what cannot be constrained must therefore be what freely exists.

 

[starkind]

I am not sure CDT is entirely as you say. I have heard they start with a small but not infinitely small triangle, overlaying the manifold of interest, then in the manner of differentiation they reduce the size of the triangle to get closer approximations to the real surface, which of course is expected to be curved. So it seems to me they are not entirely constructing dimensions from the point upward.

Also, in higher dimensional approximations, the ratio of the volume of the n-sphere to the superscribed n-cube decreases as more dimensions are added. So more dimensions, at least in this ratio, seems to me to cause the n-sphere to get smaller, not larger. (Wikipedia, n-sphere, under the heading 'volume of the n-ball.)

And, you say the remaining dimensions cannot be constrained. Surely this cannot be correct. I can easily constrain a piece of paper, which has thickness, to consider only one of the two conjoined two dimensional surfaces.

I think your writing is of good quality, but the development is not rigorous.

Do you like math?

 

[apeiron]

I am not sure CDT is entirely as you say.

It is a bit hybrid in its metaphysics as you say :-0.

But essentially, it falls back on an atomistic ontology. Strings say take the smallest loop (or now brane). CDT says take the smallest triangle. LQG and other network or foam stories are saying take the smallest connected space. So all these are about atomised form - shapes with slightly more complexity than a zero-D point (which has the too-simple symmetries of a sphere, not enough shape to explain higher level emergent properties).

So it remains about construction - the additive effects of gluing together fundamental components.

Though CDT - like strings - also have a flavour of the alternative, top down causality, I am talking about.

So a lot depends whether you are mentally picturing these things as located entities or internal resonances so to speak. Is the string a little wiggly object floating in a void (an atom) or is it more like the holes in swiss cheese, the inner boundary where the cheese (the universe) finishes and the hole (a sub-planckian realm) begins?

Either view can be valid as both would lead to equivalent, formally complementary, models. And we also know that the bottom-up atomistic modelling, the traditional mechanistic approach, is a very efficient modelling approach. Well proven through many mechanics from classical to relativistic to quantum. But then there is still the largely unexplored alternative (though I see the process physics guys trying to work out how it might apply fruitfully).

Also, in higher dimensional approximations, the ratio of the volume of the n-sphere to the superscribed n-cube decreases as more dimensions are added.

Not sure how this would be relevant. And I would add that there is a further metaphysical novelty that would have to be introduced to discuss the n-dimensional realm that I dub the infinoverse here. The standard assumption is that it would be a "crisp" realm - that it would be a countable infinity of actual dimensions. But this way of thinking only works if you tie it to the notion of (ontic) vagueness. So the n-D realm would be ultimately vague - and as such, distinctions between cubes and sphere geometries would become "lost in the fog". They would "exist" as potential distinctions, but not as actual distinctions.

I don't want to throw too many novelties into the discussion at once, but vagueness has recently been resurrected as an important metaphysical notion (Russell killed it off a century ago, but now again a community of thinkers in philosophy and a few fringe quantum theorists have tried to employ it).

And, you say the remaining dimensions cannot be constrained. Surely this cannot be correct. I can easily constrain a piece of paper, which has thickness, to consider only one of the two conjoined two dimensional surfaces. .

Yes YOU can constrain it as you are acting from a larger context, a higher geometry. And here you seem to be achieving your effect by constraining your observational location - standing only to one side (or are you suggesting a moebius strip story - which does not work for other obvious reasons).

The question would be can a plane self-constrain itself to something smaller? Even say if the paper were highly elastic, could it contract one of its dimensions and end up a 1D string of no width?

This is really the sort of question we are asking about black holes. Three dimensional space get knotted up into a singularity, the model says. But then we find it cannot be naked. It has an event horizon. Which is another way of saying it is formed as the inside of a larger context - the hole in the cheese argument again.

I think your writing is of good quality, but the development is not rigorous. Do you like math?

I would like it if there existed the math that could express the metaphysical notions here rigorously! In fact that is largely where I am at at the moment, looking into the available approaches.

For example, hierarchy theory is one way of modelling the causal topology of what I am talking about here - systems that arise out of self-organising constraints.

So we have seen in physics attempts to apply network theory to modelling the Planck-scale realm - quantum foam, spin networks, etc. But a hierarchy is in effect a "networks of networks". And this has recently started to be modeled with real maths - scalefree networks.

So yes, I am very mathematical in my approach I hope. It is just not the usual maths applied in the domain of fundamental physics.

 

[starkind]

I know a way that 3-balls can be seen to self-organize into complicated structures, and I feel like I'm getting close to the maths. Wikipedia is becoming comprehensive enough now to be a useful independent study tool in learning the mathematics. Sometimes I think it would be good to discuss with other people. But this board is jealous of speculation and theory development.

 

[oldman]

out of curiosity is there any theory on how dimensions that we exist in were created? or are they always said to have existed.

A thought-provoking question to which the simple answer is "nobody knows". You're implying that things may have once been different: e.g. that 'once' there may have been no dimensions (whatever a dimension is). Or maybe there may have been different numbers of dimensions. Or their relative magnitudes may have been different (some rolled up tight, others spread out). To all these possibilities the answer is still 'nobody can answer these questions'.

But this is not to say there aren't thought-provoking changes going on. There is a great deal of evidence to support one kind of change with a mysterious origin -- namely the expansion and possible inflation of the universe. It seems evident that the universe was once a very different place from what it is now -- much hotter, most probably without all the people, atoms, stars and stuff that are here now.

When this change is described by the best theory of gravity we can muster -- Einstein's General Relativity -- it turns out that onee can give a rational and persuasive description of change which explains the evolution (but not the creation) of just about everything we can observe. But also much more that we can't observe, like the still-mysterious "dark sector" stuff that has become part of conventional wisdom.

It is universally believed by mainstream folk that GR 'expansion' is what is going on --- change is the 3 space dimensions all getting bigger equally and together. But if you look carefully at how space and time are gauged, namely with the 'metric' -- essentially a flexible kind of Pythagoras's formula that can change dynamically over combined spans of space and time according to how mass/energy is distributed--- you find that an alternative description of change could be that only one dimension, time, might change: unfold, as it were.

I have no idea whether an attempt to describe our changing universe in this way would succeed, or whether it's a crackpot notion to be dismissed out of hand in an 'I've got a dollar, don't need more' fashion, but I'm surprised that nobody has even tried to do this (as far as I know).

The question raised in the OP is one worth asking, even if it can't yet be answered!

 

[marcus]

out of curiosity is there any theory on how dimensions that we exist in were created? or are they always said to have existed.

im in no way insinuating creationism as a theory but what I am saying was before our universe was created there were no dimensions and than once it was created there was 3 spatial and one time and who knows there could be more if string theory works out. I am asking how the dimensions came to be and why there are a specific amount and all that and if there is a theory on this.

You really should read the 2008 Scientific American article on CDT, a comparatively new kind of quantum geometry/gravity. I have the link always in my signature---small print at bottom of post, article by Loll. Let me know if the link doesn't work. It's an easy read. Well illustrated, understandably written. But the ideas are deep.

The CDT approach is very successful in that they run simulations in the computer where small universes emerge and evolve according to simple rules. And they can get inside and study. Take an imaginary random walk. Measure stuff like distances and volume.

These universes have no predetermined or well-defined dimensionality. They only appear conventional at large scale. The tiny microscopic elements are allowed to goof up at small scale. Fractal-like foam. Unpredictable. There is geometric uncertainty (as there must be in a quantum mechanical system).

In your post you assume that dimensionality is given, pre-specified uiniform fixed in the math model we make of the world. This may be so in the various string theories, but it should not be in a more fundamental theory. And it is not.

Dimensionality is something that can be measured, around any given point. It may differ from place to place and according to what scale you measure. In a successful model the large scale spatial dimension should always turn out 3D everywhere you can measure. This is how it turned out in CDT. But it doesn't have to be, and at small (Planckian) scale it turns out different. Dimensionality is not a given---it is what is called an observable.

If you were a tiny Planck-scale being you could measure the dimensionality at some location in your world simply by comparing radiuses and volumes. If the volume increases as the cube of the radius around some point then your space is 3D at that point. If it increases as the 2.5 power of the radius then your space is 2.5D at that point. And spaces can have fraction dimensionality like 2.5 (for instance some fractals do.) So dimensionality is something to test, to measure, to observe. It is not postulated by Mother Nature

Loll stated that clearly in a 2005 technical paper, and it has been supported by continued research by a number of different people.

It sounds complicated but it isn't. It is explained rather well just with words and pictures in the 2008 Sci Am article.
Some other approaches to quantum geometry/gravity have also converged with CDT on this and come to similar conclusions.

You may not want the 2005 technical paper, but in case anyone does here it is:
http://arxiv.org/abs/hep-th/0505113
Spectral Dimension of the Universe
J. Ambjorn (NBI Copenhagen and U. Utrecht), J. Jurkiewicz (U. Krakow), R. Loll (U. Utrecht)
10 pages, 1 figure; published in Physical Review Letters
(Submitted on 12 May 2005)
"We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional at short distances. We conclude that quantum gravity may be 'self-renormalizing' at the Planck scale, by virtue of a mechanism of dynamical dimensional reduction."

The main thing is if you are interested in the emergence of dimensionality you should read the 2008 Sci Am article. From there on, if you want to pursue it, there's plenty more (it has actually become a hot research topic! )

 

[Naty1]

When considering where space time may originate, it's interesting to consider the weather... who would have ever thought, or been imaginative enough to develop a theory for...the origination of thunderstorms, or hurricanes or tornadoes...even we never experienced them? How can such things "self organize" when right now I'm looking out my window and all I see are clouds and calm breezes...seems rather incredible.

and I may be mistaken here: but I don't think there are yet reliable models for predicting any of these natural phenomena, although we are getting closer. At least I know they can't predict weather more than about three days distant with any high degree of certainty...

 

[apeiron]

Actually there is plenty of math modelling if you are interested. And it would be relevant to potential new approaches to dimension creation.

Vortexes are a class of dissipative structure. Benard Cells can give you an introductory insight to how they arise... http://en.wikipedia.org/wiki/Bénard_cells

Then "weather" is vortexes over all available scales. So a fractal chaos of vortexes.

If you are willing to phrase the question as "how could dimensionality self-organise to form the stable equilbrium system we see?", then you would naturally want to look to the literature on dissipative structures.

 

[oldman]

When considering where space time may originate, it's interesting to consider the weather...I know they can't predict weather more than about three days distant with any high degree of certainty...

Yes indeed. This is why success in physics requires theory to be in close and continual contact with observation and experiment. We just aren't imaginative enough to predict, say from non-linear interactions (think Navier-Stokes equations), such complicated structures as the thunderstorms, hurricanes and tornadoes you mention. "Mother nature" has to rub our noses in fact, so to speak, before we can make real progress.

These days computational modellling is indeed a great help in deciding what assumptions are needed to explain structures, for example the filamentary structure of the universe or clouds, and Apieron's comment:

Then "weather" is vortexes over all available scales. So a fractal chaos of vortexes.

is very apt. But there's nothing like looking out of the window to see what the weather is actually doing, rather than trusting the forecasts!

As for dimensions, the observation that we live among four dimensions must a great help in devising schemes (like those of Loll's group mentioned by Marcus) of why this is so (causality?).

 

[cam875]

very interesting, this is the kind of stuff I love. I am happy that there is actual mathematics behind it as well and a whole area of theoretical physics devoted to the research of this kind of stuff.