[Newbie question] Quantum gravity in fractal spacetimes?

[C. Tellermann]

This came out of a philosophical discussion last night. It is probably
stupid from a physicist's point of view, so please forgive my ignorance.

Can a quantum theory of gravity (string theories?) live in a fractal
spacetime? In other words, the separation between two points in
spacetime wouldn't be constant, but instead vary as a function of
location and direction, the gaps ranging from infinitesimal to
arbitrarily large with a certain periodicity.

Is such an idea sound, or is it complete mathematical nonsense? Do any
such theories exist, and if so, are they common or uncommon? Where can
one find more information?

Of course, if this is a silly question, I'm perfectly happy with being
referred to an appropriate FAQ entry.

Thanks,
Chris

[Oh No]

Thus spake C. Tellermann <ctellermann@yahoo.de>
>This came out of a philosophical discussion last night. It is probably
>stupid from a physicist's point of view, so please forgive my ignorance.
>
>Can a quantum theory of gravity (string theories?) live in a fractal
>spacetime? In other words, the separation between two points in
>spacetime wouldn't be constant, but instead vary as a function of
>location and direction, the gaps ranging from infinitesimal to
>arbitrarily large with a certain periodicity.
>
>Is such an idea sound, or is it complete mathematical nonsense? Do any
>such theories exist, and if so, are they common or uncommon? Where can
>one find more information?
>
There have been such theories, studied by a few but not generally taken
that seriously by most. You could start by looking at these

http://arxiv.org/abs/hep-th/0511021
http://arxiv.org/abs/hep-th/0203086
http://arxiv.org/abs/hep-th/0004152


Regards

--
Charles Francis
substitute charles for NotI to email

[carlip-nospam@physics.ucdavis.edu]

C. Tellermann <ctellermann@yahoo.de> wrote:
> This came out of a philosophical discussion last night. It is probably
> stupid from a physicist's point of view, so please forgive my ignorance.

> Can a quantum theory of gravity (string theories?) live in a fractal
> spacetime?

This isn't quite the right question -- gravity doesn't just "live in"
a spacetime, but determines its geometry, including properties that
would be used to determine whether it is fractal. But you can ask
almost the same question: can the spacetime described by a quantum
theory of gravity behave as if it has a fractal dimension? For at
least some models, such as "dynamical causal traigulation," the
answer is yes. Look at http://arxiv.org/abs/hep-th/0505154 and
arxiv.org/abs/hep-th/0505113, for example.

Steve Carlip

[C. Tellermann]

carlip-nospam@physics.ucdavis.edu wrote:

> This isn't quite the right question -- gravity doesn't just "live in"
> a spacetime, but determines its geometry, including properties that
> would be used to determine whether it is fractal. But you can ask
> almost the same question: can the spacetime described by a quantum
> theory of gravity behave as if it has a fractal dimension? For at
> least some models, such as "dynamical causal traigulation," the
> answer is yes. Look at http://arxiv.org/abs/hep-th/0505154 and
> arxiv.org/abs/hep-th/0505113, for example.
>
> Steve Carlip


Thanks very much for your explanation (also to Charles), and sorry for the
late reply. Again, please forgive my superficial knowledge of the subject,
I have no qualification in physics, other than finding it colossally
interesting.

I've tried to read and understand the papers you gave me. While I've been
able to research and more or less make sense of most of the pure
mathematical equations given, I'm afraid I don't have the background to
come to any form of interpretation.

Maybe I'll try to reformulate my original question. Let's for one moment
imagine the absurdly over-simplified case where a small, more or less flat
region of quantized spacetime resembles the Cantor set. In that spacetime
there's an pair of entangled photons, going off in different directions
from the same source.

Is it conceivable that, while both photons travel the same distance through
spacetime as observed classically, the following is true: one photon has
ample opportunities to interact because it "encounters" possibly an
infinite number of spacetime quanta. The other photon, however, has no
chance of interacting at all as it remains "within" the same spacetime
quantum. All of this because, in the photon's histories, spacetime has
different units of quantization owing to its fractal nature.

If this construction is meaningful at all, are there any particular physical
implications arising from it? And is this, in principle, a valid
interpretation of hep-th/0505154?

I'm really sorry for bothering you with this. All of this came out of
discussion with my husband, a computer scientist, about whether it's
possible to build a computer that operates on the set of real numbers.
Please, don't hestitate to suggest a more appropriate forum for asking my
questions or to refer me to a book or website to teach me the basics for
figuring out these things myself.

Chris