String Theory: 6 extra dimensions

  • #26
apeiron
Gold Member
2,013
1
I agree


No - it does not require these specific geometries! And that's exactly the problem. ST can be formulated with any number of non-compactified or large dimensions.
Which is where adding constraints to the mix could help?

Constraints produce emergent results from complex brews like the ST landscape. Constraints select some particular equilibrium outcome.

What would this look like in this case? It would demand some kind of interaction between dimensions. So the construction approach takes each dimension as a non-interacting direction. This is atomistic in that each dimension just is, and gets glued additively to make whatever is seen to exist.

But if there is interaction between dimensions, then we would expect a self-organisation into some more particular arrangement. There could be a development from a landscape of possibilities towards some minima that is the least energy conformation.
 
  • #27
Fra
3,097
144
It is also interesting that you explicitly *construct* dimensionality by gluing new dimensions at right angle to the existing ones. I can see this is the normal mathematical way to think about it (building up from simple spaces to complex spaces by additive steps), but does anyone instead take a *constraints* based approach to the creation of dimensions as far as you know?
Based on our past discussions I loosely think I know what you mean. This is what I am partly trying to do, but I have still alot of work to do. They way I envision a dynamical dimensionality is that the underlying structures is just a set of distinguishable elements. But when it comes to the representation encoding of this information, some re-arrangements are more fit, because they represent a form of datacompression. This is how I envision the reason for particular dimensions. New indexes (dimensions) are created in my vision, from emergent measures on the underlying dimension that exploits "patterns". Then the information can be transformed into another form, like a phase transition.

The most problematic thing for me is to motivate the transformations the define the transitions. I imagine them a result of evolution, this is why also the transformations themselves are information and must have inertia.

But there are plenty of issues here to sort out.

IMO the constraints you talk about are imo evolving as well. You can associate them with the phase transition transformations.

String theory as far as I know does not have a sufficiently sophisticated rule for explaning dimensions. Main problem is that they lack the evolutionary rule, instead they are lost in a landscape.

/Fredrik
 
  • #28
The 6 extra dimensions being the 3d spatial in the past and 3d spatial of the future.
Can someone debunk this please?
 
  • #29
arivero
Gold Member
3,306
60
The 6 extra dimensions being the 3d spatial in the past and 3d spatial of the future.
Ok, the debunk is as plain as: "it does not follow from the setup of string theory".

Now, I think can understand this idea, and I played with it when young but in a different interpretation (no extra dimensions, but extra generations). The point is to wonder how to reduce second order differencial equations to "0th order". We all know that we add dimensions to reduce n to n-1. And we can see that, in a discrete interpretation of a second order equation, we need the value of the function not only at x, but at other two points, x-delta and x+delta.

So one could expect that a general theory of [discretisation of?] partial differential equations will produce extra dimensions.

But on other hand it seems an excesive overrequisite, if you think that the time coordinate could be already giving you the extra values you need. Really I feel that all of this should have been worked out by mathematicians time ago, and that it is not connected at all with the extra dimensions of string theory. Still, not 99.999%sure.

While at the topic, there is another source for a need of extra dimensions that Motl and myself loved to discuss centuries ago: the generalisation of Nash embedding to non euclidean (and towards minkowskian) spaces.
 
  • #30
5,601
40
No - it does not require these specific geometries! ..... The requirement comes "only" from our observation, not from the theory.
good clarification...I agree.
 
  • #31
Ok, the debunk is as plain as: "it does not follow from the setup of string theory".

Now, I think can understand this idea, and I played with it when young but in a different interpretation (no extra dimensions, but extra generations). The point is to wonder how to reduce second order differencial equations to "0th order". We all know that we add dimensions to reduce n to n-1. And we can see that, in a discrete interpretation of a second order equation, we need the value of the function not only at x, but at other two points, x-delta and x+delta.

So one could expect that a general theory of [discretisation of?] partial differential equations will produce extra dimensions.

But on other hand it seems an excesive overrequisite, if you think that the time coordinate could be already giving you the extra values you need. Really I feel that all of this should have been worked out by mathematicians time ago, and that it is not connected at all with the extra dimensions of string theory. Still, not 99.999%sure.

While at the topic, there is another source for a need of extra dimensions that Motl and myself loved to discuss centuries ago: the generalisation of Nash embedding to non euclidean (and towards minkowskian) spaces.
Thanks, but I understand that string theory valid science and more/less philosophical inference at this point. Which not to say that the 6 extra dimensions are 3d spatial past and future are valid science but on the same level; just a logical alternative. What I'm looking for is the logic that negates that these dimensions that is mathematically necessary in string theory not be described as extra physical dimensions in the here/now, as opposed to the dimension of what was then and what will be in the future.
 

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