What does QM say about the structure of spacetime?

[gib65]

What I'm really trying to ask is, does QM say that spacetime is quantum too, or is it still thought to be continuous? For example, we know that QM says that an object can only have discrete amounts of energy such that if something was accelerating from n km/hr to m km/hr, the increments in its velocity can be no smaller than some amount q - that is, as it goes from n km/hr to m km/hr, its velocity will change from n to n+q to n+2q, to n+3q, and so on, but it will never be n + cq + r, where c is an integer and r is some amount less than q.

 

So my quesion is: would QM apply a similar formula to the same object's position in space as it accelerated? Suppose, during the acceleration, it travelled from point x to point y. Is there some smallest increment in its position, say s, such that it could only be at points x + cs but never at x + cs + b (again, where c is an integer and b is some amount less than s)?

 

And how about for time?

[Martin]

What I'm really trying to ask is, does QM say that spacetime is quantum too, or is it still thought to be continuous? ...And how about for time?

 

Quantum Gravity theories attempt to build a quantum model of spacetime

 

there are several approaches to QG. no one is clearly successful yet.

 

the standard classical model of gravity is General Relativity which is a theory of spacetime and its geometry. so quantum pictures of gravity are apt to be a quantized version of Gen Rel. (or have Gen Rel as a largescale limit). the upshot is basically that Quantum Gravity MEANS a quantum model of spacetime and its geometry.

 

if you want to find out people's quantum models of spacetime, therefore, you should do a search with keywords "quantum gravity"

 

Loop quantum gravity (LQG) is one where area and volume measurments have only a DISCRETE range of possibilities. In LQG there is this famous result that the "area and volume operators have discrete spectrum". But LQG has not yet been tested.

 

So far LQG does not predict discrete time. but there is a related approach in which time proceeds in bitty (roughly Planck unit size) steps. this also could be wrong. Quantum gravity is a hard theoretical problem and none of the various approaches can yet claim to be tested experimentally.

 

I am most interested by a new approach that has just appeared in 1998 and become prominent in 2004, by achieving a run of surprising results. It has a basically new model of quantum spacetime where the CURVATURE can be quantum without the space or time being divided up into little bits. the spacetime continuum, in this approach, is not discrete or broken into little steps, but geometric things about it like curvature and dimensionality are subject to quantum principles.

 

there are no answers now. people hype various approaches, but it is good to be cautious and a bit skeptical. don't believe everything you read in Brian Greene books, and so on. good luck pursuing your interest

[rajama]

Martin

 

can I ask where I would find an overview of the 'new approach' you mentioned, or maybe what search terms would provide relevent hits?

[Martin]

Martin

 

can I ask where I would find an overview of the 'new approach' you mentioned' date=' or maybe what search terms would provide relevent hits?[/quote']

 

there is no "Brian Greene-type" popularizer for it

there are only lecture notes and research papers

but here is a reading list, and the first half of #6 is pretty readable

(it is lecture notes to introduce grad students to it in case they

might want to get into it and do a thesis, so it explains more):

 

1.

http://arxiv.org/hep-th/0105267

Dynamically Triangulating Lorentzian Quantum Gravity

J. Ambjorn (NBI, Copenhagen), J. Jurkiewicz (U. Krakow), R. Loll (AEI, Golm)

41 pages, 14 figures

Nucl.Phys. B610 (2001) 347-382

"Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated extensively in d less than 4, with promising results. It is based on a simplicial regularization of Lorentzian space-times and, most importantly, possesses a well-defined, non-perturbative Wick rotation. We present a detailed analysis of the geometric and mathematical properties of the discretized model in d=3,4..."

 

2.

http://arxiv.org/abs/hep-th/0404156

Emergence of a 4D World from Causal Quantum Gravity

J. Ambjorn (1 and 3), J. Jurkiewicz (2), R. Loll (3) ((1) Niels Bohr Institute, Copenhagen, (2) Jagellonian University, Krakow, (3) Spinoza Institute, Utrecht)

11 pages, 3 figures; final version to appear in Phys. Rev. Lett

Phys.Rev.Lett. 93 (2004) 131301

"Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically."

 

3.

http://arxiv.org/abs/hep-th/0411152

Semiclassical Universe from First Principles

J. Ambjorn, J. Jurkiewicz, R. Loll

15 pages, 4 figures

Phys.Lett. B607 (2005) 205-213

"Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over space-time geometries in nonperturbative quantum gravity. We show that the macroscopic four-dimensional world which emerges in the Euclidean sector of this theory is a bounce which satisfies a semiclassical equation. After integrating out all degrees of freedom except for a global scale factor, we obtain the ground state wave function of the universe as a function of this scale factor."

 

4.

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

SPIN-05/05, ITP-UU-05/07

 

"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."

 

5.

http://arxiv.org/hep-th/0505154

Reconstructing the Universe

J. Ambjorn (NBI Copenhagen and U. Utrecht), J. Jurkiewicz (U. Krakow), R. Loll (U. Utrecht)

52 pages, 20 figures

Report-no: SPIN-05/14, ITP-UU-05/18

 

"We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time."

 

 

6.

http://arxiv.org/hep-th/0212340

A discrete history of the Lorentzian path integral

R. Loll (U. Utrecht)

38 pages, 16 figures

SPIN-2002/40

Lect.Notes Phys. 631 (2003) 137-171

"In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach solves the problems of (i) having a well-defined Wick rotation, (ii) possessing a coordinate-invariant cutoff, and (iii) leading to_convergent_ sums over geometries. Although little is known as yet about the existence and nature of an underlying continuum theory of quantum gravity in four dimensions, there are already a number of beautiful results in d=2 and d=3 where continuum limits have been found. They include an explicit example of the inequivalence of the Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the cancellation of the conformal factor, and the discovery that causality can act as an effective regulator of quantum geometry."

 

Loll wrote this as an introduction to CDT for Utrecht graduate students who might want to get into her line of research. It is a good beginning. It is already 2 years out of date so it does not have the latest headline results but that is OK

[Martin]

Martin

 

can I ask where I would find an overview of the 'new approach' you mentioned' date=' or maybe what search terms would provide relevent hits?[/quote']

 

the signs are that this is going to quickly become a hot field of

quantum gravity research

 

even tho there are now only a halfdozen people working in it, it will be one of the highlights of the main quantum gravity conference this year, in Berlin in October

 

it is so new the name only recently stabilized----they now consistently call it Causal Dynamical Triangulations (CDT) whereas a few years back it was called various things (lorentzian quantum gravity, lorentzian dynamical triangulations, simplicial quantum gravity....)

 

One thing that is remarkable about the CDT people is that they do massive computer simulations of the evolving geometry of the universe and study the results-----they run a QUANTUM model of spacetime, starting with big bang (or a quiescent period leading up to)-----so far their model of quantum spacetime has about a third of a million building blocks in the computer----and they find out things from the computational model that they had not necessarily expected.

 

this is subtly different from the usual way pure theorists work. a lot of the headline CDT results in the past year or so come from their ("Monte Carlo") computer simulations of the spacetime geometry of the universe.

 

another remarkable thing is that their model does not use coordinate functions to calculate curvature and to implement the Einstein Gen Rel action. most people who do differential geometry are slaves to coordinate functions. their building block (or "simplex") method implements geometry by how the blocks assemble themselves, which can involve a kind of quantum mechanical randomness or uncertainty.

 

it is an interesting approach

the roots go back to 1960 and to 1985, but the final innovation that made it work was just in 1998

[rajama]

Oh My Goodness a computer simulation... I might actually understand 1/2 of the topic!

 

Many thanks

 

Ray

[Martin]

Oh My Goodness a computer simulation... I might actually understand 1/2 of the topic!

 

Many thanks

 

Ray

 

I hope so. I badly need someone who answers back and sometimes asks questions. I have been slowly finding out some detail about how the computer simulation is conducted----still far from being able to flow-chart it! Anything you read in these articles you want explained, try me (if I cannot explain I will say so).

 

I think quantum gravity is an outstanding problem that is now nearing some new stage or perhaps reaching a resolution. and this CDT triangulation method, with its concrete model of quantum spacetime where they can actually explore the dimensionality of the spacetime at various scales (as by the "diffusion process" simulation) this seems to me to be one of the most important recent developments. so i am very anxious to understand it better, and welcome questions

[rajama]

Martin

 

Just wanted to say thanks again for the papers - I'm afraid I only finished the first of them a week ago (the overview you recommended, reading at lunchtimes, late evenings, etc.) and I'm skimming the 'Reconstructing the Universe' paper as and when...

 

I really don't think I'll have any questions that are likely to extend your understanding of the topic - I spent most of my time following up Wick rotation (not just putting an i into time), Monte Carlo simulations (actually found something that may be useful at work in that little foray) and most of the other mathematical tools (Hausdorff dimension!) and other key concepts employed in the construction of the program.

 

Overall, very entertaining - still haven't gotten by head around the (what would you call) 'glue' that holds the steps together. This chap Loll really seems to have given a boost to an area of research that (to me) looks as if it wasn't going anywhere, but evaluating the (struggling here) usefulness (probably the wrong word) of the results must be fun... I mean, this simulation predicts causality and dimensionality at varying scales...

 

If I can phrase an inteligable question, I will. Actually, writing here, I think I already need to read the first paper again...

[DQW]

What I'm really trying to ask is' date=' does QM say that spacetime is quantum too, or is it still thought to be continuous? For example, we know that QM says that an object can only have discrete amounts of energy such that if something was accelerating from n km/hr to m km/hr, the increments in its velocity can be no smaller than some amount q - that is, as it goes from n km/hr to m km/hr, its velocity will change from n to n+q to n+2q, to n+3q, and so on, but it will never be n + cq + r, where c is an integer and r is some amount less than q.

 

So my quesion is: would QM apply a similar formula to the same object's position in space as it accelerated? Suppose, during the acceleration, it travelled from point x to point y. Is there some smallest increment in its position, say s, such that it could only be at points x + cs but never at x + cs + b (again, where c is an integer and b is some amount less than s)?[/quote']No, there is no quantization of space, as such. What QM does is impose an uncertainty in specifying the position of an object (repeatably) along with its momentum.

 

And how about for time?

Time is not an observable in QM (like position is); it is merely a parameter. And it is not quantized either.