# A Max number of extra dimensions

1. Nov 17, 2017

### MathematicalPhysicist

Is there an upper bound for the number of curled-up extra spatial dimensions and perhaps also temporal dimensions?

I just wonder how many more theories with extra dimensions are possible... infinite?

2. Nov 17, 2017

### jerromyjon

M-theory uses 11 dimensions and covers everything in the known universe, what would be the point of more?

3. Nov 17, 2017

### MathematicalPhysicist

Well F-theory has 12 dimensions.

I don't see even the point for more than 3+1 dimensions, but some physicists look for extra dimensions.

4. Nov 17, 2017

### jerromyjon

No one who only believes in only what they see around them does, because that is all we need to explain our sense of reality. When physicists find new features which can't fit into (x,y,z,t) dimensions the only option is to add dimensions to model the new degrees of freedom.

5. Nov 17, 2017

### jerromyjon

Well, you learn something new everyday... I did! Thanks for the heads up...

6. Nov 17, 2017

### MathematicalPhysicist

But then one asks himself, why stop at some finite number of dimensions?

7. Nov 17, 2017

### jerromyjon

Because "anything" doesn't happen in physics. Laws constrain what occurs, and dimensions encompass the math to describe it. What point would there be to a model that describes "way more than could ever occur in nature"?

8. Nov 17, 2017

### MathematicalPhysicist

@jerromyjon but how do we know there aren't more dimensions?

This is why I asked in my OP what is the max possible number of curled up dimensions?

Why did we stop at 11 or 12 (assuming there aren't new theories I am unaware of with more dimensions).

9. Nov 17, 2017

### jerromyjon

We don't. There just isn't any evidence or need for them.

10. Nov 17, 2017

### MathematicalPhysicist

Well there isn't even evidence for more than 3+1 dimensions.

As I said if string theory could bypass somehow the anomaly it has in 3+1 dimensions that will be better than postulating more tiny dimensions.

In the future I'll read Zweibach and I'll see if I have an idea as to how to do it; if it's possible of course.

11. Nov 17, 2017

### rootone

Occam's razor indicates that an infinite number of dimensions is unnecessarily complicated as a way of explaining what we observe,

12. Nov 18, 2017

### MathematicalPhysicist

@rootone they want a theory of everything, who said it would be less than "complicated".

13. Nov 18, 2017

### haushofer

It can also bypass that anomaly by postulating one spatial dimension less. In 2+1 dimensions the rotation group becomes abelian.

14. Nov 18, 2017

### haushofer

That's nonsense and depends on you theory. Does Occam's razor also falsify statistical mechanics because one needs an enormous amount of molecules?

15. Nov 18, 2017

### MathematicalPhysicist

But obviously we have at least 3+1 dimensions. :-)

16. Nov 18, 2017

### haushofer

I'm sorry, whut? We don't even know what M-theory is in the first place.
Well, maybe we live in 2+1 dimensions but one spatial dimension emerges. Who knows. :P

17. Nov 19, 2017

### Fra

I would argue that this deceptive argument about out sense or reality implying we live in 3D+1 seems fallacious in the first place.

If i look at what our senses actually does from the point of view of physics and how neuroscientist understand the brain. They actual sensory signals are merely electrical signals conducted via afferent nerves towards the CNS and the brain, and in the brain the information in all electrical signals seeme to be processed encoded in a way that makes predictions of the future accurate and resposive. That is simply the task of the brain from the evolutionary perspective.

So it is clear to me, that our intuitive perception of our world, in particular dimensionality is very FAR from direct. Instead i think the most honest description of the situtation is that that "map of reality", that evolution created for us, encoded in our brain, has AT BEST a holographic connection to actual reality. But this connection might well represent and equilibrium or tradeoff between structural accuracy and dynamical accuracy because the purpose of the BRAIN is not be a truthful map(however one would operationally define that without using another brain?), the purpos is to make the host survive. So an effective map, that is good enough, but easier to make predictions with, will have an evolutionar advantage.

Incidently this insight from how our brain processes input, to produce actions during a race condition that evolutio is, do have parallells to some ideas in physics as well. As we know some of the dualities (AdS/CFT) relate spaces of different dimensionality with each other - BUT sometimes the "COST" of stronger couplings and higher computational costs. And if we thinkg about this just for a couple of seconds, the intuition here is clear why there can be a preference for developing a higher dimensional map. It simpy a "reformulation" and restructuring of a processing task, in order to optimize computational speed. IMO this is right way of using inuition from our senses to understand physics.

This also actually implies that the "actual dimensionality" of our universe might be a matter of perspective! I is actualyl possible that the same universe have different dimenstionality depending on the observer. And - given holographic correspondencs - this is by no means a contradiction.

It may well be another fallacy to think that the dimensionallty "must" be a fixed value. There is in fact NO justified argument for this that i can think of. It is just one part of old conceptual baggage we carry that are not serving us well anymore.

So from a mathematical perspective only, i cant see how there can possible be an upper bound to dimensionality. Mathematics alone can no solve this, as they only guid there are questional arguments like "simplicity" and "beauty". I instead argue that we must see it in the above perspective, and there the "selective principle" is not "beauty arguments" but evoulutionary arguments.

I am simplyfying grossly here, but just to formulate the toy argument to illustrated the idea:

Too low dimesionality of the map, mean the code is very compressed, and the process to infer the future expectation from the self evolution of the map will be one of many computational steps.

Too high dimensioanlity of hte map, will requied a bigger encoding structure (more memory) but it will be more uncompressed, and the computational resources to infer the future evolution from this lower.

So there is somewhere for a given structure and environment encoding a map of its environemnt an optimal "balance" of dimensioanlity thta we should be able to EXPLAIN, rather than put in by hand when we claim to understand this and have the mathematical theory ready.

Our laws and maps may be seen as "optimal codes", taking into account not only the footprint of the code, but also the computation resources to decode it.

/Fredrik

Last edited: Nov 19, 2017
18. Nov 19, 2017

### gianeshwar

Theoretical possibilities are the torch bearers.Advanced algebra gives many possibilities like may be in Hilbert space.

19. Nov 24, 2017

### David Lewis

The point of additional dimensions is to unify and simplify the laws of nature.

20. Nov 25, 2017

### kodama

bosonic strings 26 dimensions

in what way are timelike dimensions different from spacelike dimensions on the planck scale?

21. Nov 26, 2017

### haushofer

In the case of string theory we have a double strike: extra dimensions which can give extra gauge fields a la kaluza klein, and extra gauge fields in the RR-sector.

22. Nov 29, 2017

### vortextor

@Fra
Our brain is part of our existence, our world, our reality.
If the "map of reality" encoded in our brain, is just a holographic
connection to actual reality and any argument about the sense of
reality implying dimensionality of our physical word seems fallacious
-as you say-the same reasoning will be applied to any assertion with
reference to our brain.

23. Nov 29, 2017

### Fra

Yes, the argument in principle works both ways, but my point was this:

The "at best" holographic picture of the environment, an observer has, is a rational view originating from inference based upon incomplete and uncertain information. And the map of reality is constantly evolving.

It is not a fallacy to act as if our world is roughly 3D, it is in fact rational. The fallacy of the theoretical physicists is to mistake the probable opinion for an absolute observer independent and timeless truth, that we see as a logical constraint. It "looks like 3D", just like our brain "looks like" a bunch of neurons communicating via electricity. But done right, these "soft" statements will converge, to effective reality. But to understand the effective reality, IMO at least i think a key is to understand the inference made. Inductive or abductive inference is not deductions. Its more like a guided random walk, all we need to make sure is that the random walker is converging and not gets lost.

/Fredrik

24. Nov 29, 2017

### jerromyjon

From a 3D being in a 4D spacetime forced to exist in a 2D plane of mobility, it is irrational that we don't see scale as another dimension unto itself. The vastness of space and the vastness of microscopic complexity are both just out of reach of consciousness but almost everyone believes they are there, with barely a care to their relevance...

25. Nov 30, 2017

### Fra

Not sure what you mean here as you talk about consciousness? My reference to the brain, was not the main point. The main point in my first post was the dimensionality of state space vs computational complexity.

Also 3D space of course just relates to the apparent dimensionality of relations between remote objects. If we talk about internal spaces and theory spaces its a different case, but less "intuitive" of course.

About scales, I think in terms of several scales, the UV scale, IR scale and the observer complexity scale. In current theories however, the complexity scale of the observer is effectively infinite, as its typically seen as an "information sink" or classical background that are never "saturated" with information. This is why current frameworks are unable to cope with "observer complexity scaling".

The scaling done in RG flow, is rather seen as a kind of scaling of the observational RESOLUTION, but still with a fixed (infinite) CONFIDENCE. Ie the observer still sits in a classical boundary embracing the "system" under observation. This is the situation in HEP.

A generalisation of this would be need a generalized framework for measurement theory that can handle "inside observers" and it would also imply an interesting generalisation of renormalisation. Then renormalization should not be seen as something of releveance to curing technical problems in perturbation theory, but a way to understand how theories evolve as you tweak its parameters.

What if if flip the coin here and consider a small observer embraced by a vastly larger system under observation? Then what we get is a cosmological theory, but formulated from the inside. This is the missing part in current formalism. And it is also why its fallacy to APPLY the framework from HEP to cosmology. It is a conceptually fallacy. Howver the mathematics of HEP has seduced us.

Lee Smolin calles this the cosmological fallacy.

/Fredrik