# Just imagine

#### rushil

Just imagine!!!

Suppose every phenomena in this universe (of course most are reducible to some particular general ideal ones - basically I'm talking about those!) could be described as disturbances/waves/ripples/tensions in a $$\mathbb{R} ^ n$$ field. Is this possible? Can we find $$n$$ ?

Basically, I came up with this when I studied that General theory of relativity explains gravitation as a distrubance/tension in a 4-dimensional field of space-time. Basically, I'm asking whether the entire universe can be described as such? Do you have any research article in mind on this topic!!!

#### Alamino

rushil said:
Suppose every phenomena in this universe (of course most are reducible to some particular general ideal ones - basically I'm talking about those!) could be described as disturbances/waves/ripples/tensions in a $$\mathbb{R} ^ n$$ field. Is this possible? Can we find $$n$$ ?
Basically, I came up with this when I studied that General theory of relativity explains gravitation as a distrubance/tension in a 4-dimensional field of space-time. Basically, I'm asking whether the entire universe can be described as such? Do you have any research article in mind on this topic!!!
I think that Kaluza and Klein had this idea to unify electromagnetism and gravity and this is also related to the interpretation of the many dimensions in string theory.

#### Cexy

Disclaimer: I'm only a student, not a researcher, and my understanding of quantum gravity is limited to having read the first hundred or so pages of Polchinski's string theory book!

General Relativity is described in a four dimensional space, but that space isn't $$\mathbb{R}^4$$. Instead it's a much more general space which in its 'flat' limit, i.e. with no mass, looks like four dimensional Minkowski space.

Minkowski space is the space whose distance measure is $$ds^2=dt^2-dx^2-dy^2-dz^2$$. Compare this to standard four dimensional Euclidean space, which has a distance measure $$ds^2=dt^2+dx^2+dy^2+dz^2$$.

In 1920-something Kaluza and Klein realised that if you tried to formulate GR in a five dimensional space, whose fifth dimension was a circle, then you got an extra set of equations to deal with - and that set of equations turned out to be the relativistic form of Maxwell's equations, which describe electromagnetism.

Nowadays, string theorists like to think they'll eventually be able to describe everything using the one theory, which only makes sense when it's formulated in ten dimensions - which are the four standard dimensions from GR, plus another six dimensions which are 'curled up', like the circle that Kaluza and Klein used. As far as I understand it, M-Theory has eleven dimensions, but I don't know what the eleventh one is.

So there you have it - n could be 10 or 11, but equally well could be neither of those. Nobody knows yet!

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#### hossi

rushil, brilliant question. Try to make more precise what you mean with 'phenomena' and whether 'disturbances/waves/ripples/tensions' is sufficient. E.g. does 'phenomena' cover 'chiral fermion' and how would you describe that through 'disturbances/waves/ripples/tensions' which sounds like these were tensor fields? What do you do with gauge charges, how do you describe interactions...

However, I don't think the answer is really clear. What is clear, is that KK theory comes along with several problems. The most famous one being: if it takes extra dimensions, how do we get rid of them? However, the whole concept of the question changes when you change your idea of what spacetime is (don't ask me, I don't know).

#### rushil

Thanks... but i'm sorry I dont know much of the terms you used and have no idea on how to quantify my thought! I'm a high school student with a highly wavering mind!!!

#### hossi

rushil said:
Thanks... but i'm sorry I dont know much of the terms you used and have no idea on how to quantify my thought! I'm a high school student with a highly wavering mind!!!
Doesn't matter. Keep it in the back of your head, someday it will make sense.

#### Careful

First of all, we are students for our entire life that does not change when PhD is in front of your name (actually I never use this word). Second, I percieve your question in two ways: (a) can our physical theories be poored into this classical view (b) does nature satisfy this picture? (b) is the most tricky question and the matter has not been settled yet. (a) is more easy to answer :
- No, QM cannot be described as such (at least if I understand your intention well)
- Spin is much more delicate (I do not like spinors, I will just give you that) ; alternative descriptions of spin are semiclassical spinning fluid models which you can find in Einstein Cartan theory, or simply spinning Kerr solutions to the Einstein Maxwell equations, or classical spinning rods. I do not know how far the know models reproduce the spinor picture (it is even doubtful they should do that in the first place). However, AFAIK there is for sure no no-go theorem against the existence of an appropriate classical model. Perhaps Hossi (or someone else) knows more about this ?

Cheers,

Careful

#### hossi

Careful said:
First of all, we are students for our entire life
I wish you were right. There are people who definitly stop being students once they are permanent...

Careful said:
I do not know how far the know models reproduce the spinor picture (it is even doubtful they should do that in the first place). However, AFAIK there is for sure no no-go theorem against the existence of an appropriate classical model. Perhaps Hossi (or someone else) knows more about this ?
Not sure, but don't think so. What should it be based on? But there are surely several critical points one would need to overcome and not very much perspective right now.

Take Care,

Sabine

#### rushil

I'd just like to ask this.... is my idea worth further study and analysis to see if something can be figured out...or is it outright 'wrong!!''....also, since i'm not aware much on this subject,,,,can somebody probably give a clearer statement of the problem I am thinking about( as you have understood it!!) Thanks!

#### rtharbaugh1

Hi rushil

It seems your idea is worth study and analysis, based on the fact that several serious workers here (I do not include myself, as I am a mere dilletante) have chosen to reply. The tools needed to think about these ideas are partly plain language, such as I have to use, and partly mathematics, which I try to use but am not very fluent. Plain language suffers from slippery definition and can only take you part of the way, or so I have found. It seems that mathematics is required for deep understanding of these matters.

Here is a link which you might find useful, which I have from a post by Careful. It starts with high school level maths and goes on beyond my understanding.

http://www.phys.uu.nl/~thooft/theorist.html

Your curiosity is good, and your ability to analyse seems ok. Now you need to aquire the tools for clear thought and discussion. Study the maths and use this most valuable tool, the internet, to search on terms with which you are not familiar. For example, you might enter "chiral Fermion" into one of the search engines, such as are provided freely by google and yahoo, among others.

Good luck, and I hope you have the good fortune to remain a student throughout your lifetime, may it be long and prosperous.

Richard

#### garrett

Gold Member
Hey Rushil,

As others have pointed out -- this idea that everything is describable as higher dimensional ripples of spacetime is very pretty and has a well developed history. The first incarnation, and the broad heading under which most of these theories are classified, is Kaluza-Klein theory. The germinal Kaluza-Klein idea is that we can mathematically consider how general relativity would work in five dimensional spacetime and see that if the fifth dimension is wrapped up (compactified) into a circle of constant scale (the cylinder condition) then the equations we get out are the equations of four dimensional spacetime coupled to an electromagnetic field. Objects moving in the compact direction have an electric charge corresponding to that momentum. This works perfectly, and it gets even better when we consider symmetric spaces more complicated than circles. It turns out there is a seven dimensional symmetric space with symmetries that give all the standard model force fields: electric, weak, and strong. So, at first look, the answer to your question is n=11 -- all the forces of the standard model and gravity can be treated as the ripples of an 11 dimensional fabric, with 7 of the dimensions wrapped up small in a special way.

But there are problems. To complete the correlation with the standard model, we need to also find geometric descriptions of a scalar Higgs field and spinor (electron, quark) fields within this higher dimensional space idea. The Higgs fields can be found by getting rid of the cylinder condition -- letting the symmetric space wiggle and change scale a bit. But getting the spinor fields to pop out right from this picture is harder. (I've worked a little on that.) Things don't work correctly when we use the most obvious extension of spinors over the 7 dimensional symmetric space. This is the "chiral spinor" problem that hurt Kaluza-Klein theory in the late 80's. Also, if one does allow the symmetric space to wiggle, there are all sorts of other particles predicted that we don't see (the tower of KK modes). So, the Kaluza-Klein idea doesn't work perfectly when done the most obvious way.

But one can tweak things to try and get everything to come out right. One interesting thing to try is to add torsion -- which is a geometric field describing a twist of spacetime. Using this means giving up the equivalence principle of GR in its familiar form -- a price most aren't willing to pay. But if you do use torsion, which fits well with GR mathematically, you can get chiral spinors out, and get the standard model nicely using only a four dimensional symmetric space (called CP2). But, as I said, this takes some messing around with the original premise. And there are still problems.

String theory relies on Kaluza-Klein theory as a background in which the strings dance around. And people spend a lot of time playing with theories of surfaces and strings moving around together in various spaces. But this sort of thing requires a lot of outlandish speculation and doesn't work very well to produce the standard model or gravity -- which are the two theories solidly backed by experimental verification.

Really, quantum field theory already sort of describes things as ripples ON spacetime and works spectacularly well to describe almost all particles and interactions. (So one has to learn that first before dabbling properly in these wilder ideas.) But your idea, and Kaluza-Klein theory, is about getting fields as ripples OF spacetime.

And then there's the subject few want to touch. Our universe is fundamentally quantum. So what you'd really like to see pop out of these geometric theories of dancing higher dimensional spaces is a quantum field theory that matches up with what we know works. Almost no one works on this -- it's currently taboo. And I don't think anything will come together properly until people work on this too, in order to have a chance of seeing the whole thing at once.

Well, that's more or less a ramble on the subject... hope it's more than just confusing. And, of course, to really make sense of this, or anything in physics, you have to do the math.

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