Unraveling the Mysteries of Planck Scale Physics and Quantum Gravity

[stglyde]

Quantum Gravity only becomes a problem when we probe below the Planck scale. This is because we don't know what occurs inside a singularity in a Black Hole or in the initial condition of the Big Bang when the universe was supposed to be in Planck density. The Planck scale is also the origin of the trouble of what to make of a metric that is in quantum fluctuations.

So how come we don't just assume that minimum resolution of nature is the Planck scale. Meaning there is nothing below the Planck scale because the Planck scale is the minimum pixel of nature. Then there is no need to search for quantum gravity and no trouble about metric in quantum fluctuations.

But how come this is not simply assumed and the solution? What problems or other conflicts would come up if we simply assume this?

 

[marcus]

...So how come we don't just assume that minimum resolution of nature is the Planck scale?...

LQG is based on this kind of assumption (as regards measurement, and thus the definition of a quantum state of geometry). It is a quantum dynamics of geometry. There is a growing literature. A lot of smart people are working on it, and regularly report new results. I'm not sure one can reasonably ask for more.

But since you have thought about it, what would you like to be the minimal angular resolution?

It is not an obvious consequence of a minimal "pixel", i.e. a minimal nonzero length or area measurement. There is no "planck unit of angle". A moment of reflection will get you into considering a maximal length as well as a minimal.
Also if you have a minimal angular resolution then you probably are going to want to use a modification of the rotation symmetry group. People doing that tend to get into using the q-deformed version of SU(2), or a socalled "quantumgroup" in place of the classical rotations.

I don't mean to say this is a problem with what you say, or an obstacle. It is just an interesting aspect, little extra mathematical richness on the side. So you might want to think about angular resolution as well.

Here's some stuff on it.
http://arxiv.org/abs/1105.1898

 

[dhillonv10]

To OP, if we assume plank scale to be the end, that has no relevance to whether we look for QG or not. There is something interesting that happens at smaller scales, the smoothness of space (as in GR) disappears and its just ripples, well in some sense. At that scale physics is a little different, its quantum mechanics, and at macro scales we would use general relativity. So QG is an attempt in some sense to unite those theories, plank scale arises from the notion that strings in string theory are that small.

Also on that note, marcus posted here a paper just a few days ago on this topic that physics might not be all that different then we expect at smaller scales, perhaps that link would be relevant here as well?

QG: quantum gravity
GR: general relativity

 

[stglyde]

There is no "planck unit of angle"? Oh. I was thinking that SpaceTime in the language of Tensors and Wave functions in the Langauge of Hilbert Space are much like programming languages. In fact. I wonder what would happen if a computer student would create a computer simulations using those languages and mathematical formalisms. Planck scale then would be a pixel or smallest resolution of the program. Anyway. Hasn't there actually a computer student who has inputted GR and QM into a computer. Or maybe our computer are stone age because it can't even calculate the hilbert spaces of 5 particles with dimensions of more than 25. Hmm... such primitiveness.

 

[marcus]

...So how come we don't just assume that minimum resolution of nature is the Planck scale.

OK, the direct answer (repeating something I just said) is that many smart theorists DO research assuming that kind of minimum resolution. To give you a rough idea of the size of just one rapidly growing part of the relevant research program (LQG):

As of 17 December http://howlonguntil.net/ 351/365 of year elapsed
199*365/351=207

LOOP RESEARCH PAPERS BY YEAR (loop quantum gravity, loop quantum cosmology, spin foam)
2005 http://inspirebeta.net/search?ln=en...2y=2005&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (42 found)
2006 http://inspirebeta.net/search?ln=en...2y=2006&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (77 found)
2007 http://inspirebeta.net/search?ln=en...2y=2007&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (120 found)
2008 http://inspirebeta.net/search?ln=en...2y=2008&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (142 found)
2009 http://inspirebeta.net/search?ln=en...2y=2009&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (145 found)
2010 http://inspirebeta.net/search?ln=en...2y=2010&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (152 found)
2011 http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (207 annualized from 199 found)

You can click on any of the links and see the most highly cited papers that appeared that year. Clicking on "abstract"will normally get you a summary of what it's about and clicking "PDF" will often get you the full paper. Most are archived online.
This research DOES, in effect, what you are asking about: "why don't we do this...?"

If you look down the list you will see that many of the recent papers have to do with how to observationally test. Most of these papers focus on "footprint" features to look for in the ancient light of the CMB (cosmic microwave background.)
The researchers use both analytic and equivalent numerical models. That is they use equation models of the early universe which they can solve, and they use computer models of the early universe, which they an run. Unlike the classical models (which blow up and develop a singularity) the models do not blow up.

Observationally testing the new quantum cosmology models, by comparison with future CMB data, is probably the most urgent thing on the agenda at this point.

So in large measure what you seem to be talking about is already in progress. Computer modeling and all that. Pixels .

But you don't seem to be interested in minimal angular resolution---that is a side of things which has NOT been much researched. Curiously enough it relates to the cosmological constant, responsible for accelerated expansion.

In case you are interested in a taking a look at the corresponding listing for string, M-theory, AdS/CFT here it is:
STRING,MEMBRANE,AdS/CFT RESEARCH BY YEAR
(search terms "string model", "membrane model" and "AdS/CFT correspondence")
2005 http://inspirebeta.net/search?ln=en...2y=2005&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (988 found)
2006 http://inspirebeta.net/search?ln=en...2y=2006&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1029 found)
2007 http://inspirebeta.net/search?ln=en...2y=2007&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1050 found)
2008 http://inspirebeta.net/search?ln=en...2y=2008&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1128 found)
2009 http://inspirebeta.net/search?ln=en...2y=2009&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1132 found)
2010 http://inspirebeta.net/search?ln=en...2y=2010&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1046 found)
2011 http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (931 annualized from 895 found)

895*365/351=931

 

[stglyde]

I'm familiar with Loop Quantum Gravity having read Lee Smolin "The Atoms of Space and Time" in Sci-am. In addition there is String Theory which also smears the Planck scale by making the string as big as the Planck length. But when one takes a minimum Planck pixel. Does it automatically imply Loop Quantum Gravity. I mean.. why not just stay at General Relativity and Quantum Mechanics levels by saying they are really not unifiable because there is nothing below the Planck length without having to invoke Loop Quantum Gravity. Well. I'm exploring the theory of Brian Greene in one of his books where he stated that the whole universe could be output of a computer program. If so, GR and QM are just programming subroutines and don't have to be united and the Planck scale is the minimum pixel of the computer. This means one doesn't even have to assume Loop Quantum Gravity. Or is LQG automatically the case when you make the Planck length the pixel?

 

[marcus]

I'm familiar with Loop Quantum Gravity having read Lee Smolin "The Atoms of Space and Time" in Sci-am.

That SciAm article was published in 2003. Loop cosmology changed radically after 2006. I would not read anything from before 2009. Loop quantum gravity itself changed radically after 2007-2008 and the first decent survey papers describing its new form came out in 2010.
You must suit yourself as regards what you like to read.

There is a DIFFERENT approach to quantum gravity which does have a pretty good description in a SciAm artice. It is the "signallake" link in my signature, at the bottom of this post. This is not LQG but it is still pretty interesting and it does have an element of discreteness. The main author is Renate Loll. If you like SciAm articles you may like this very much. It could be just right for you. It is not as dumbed down as a lot of the SciAm stuff, but it is well illustrated and well written.

Renate Loll's approach to QG is not growing or changing as fast as Loop is. The job of summarizing and popularizing and giving a meaningful description in words is not so challenging. She's a good writer.

But basically you just have to suit yourself. I can't think of anything about LQG to recommend to you.
In general I'd urge staying away from verbal fantasy, metaphor, speculation. Try to steer towards approaches where they see how to test observationally.

You are wrong to assume incompatibility between GR and QM. Several lines of QG research have made remarkable progress lately and nothing has been shown that in principle prevents a successful quantum theory with GR as its classical or large scale limit.

Today's LQG does not say "space is made of atoms or grains of space" it says something about limitations of MEASUREMENT. I've been telling you that, have I not? Space can be as continuous as it pleases---or it can not even exist as Einstein said so emphatically. The covariance principle of GR "deprives space and time of the last shred of objective reality." What matters is how nature responds to (geometrical in this case) measurement. The web of geometric relations among events. There is as much continuum in LQG as there is in the classical GR mother theory that gives rise to it. And as little.

In the popular literature they make a big fuss about how difficult to reconcile GR and QM but I see various (non-string) approaches advancing towards that goal. The string program appears to me to have stalled for the time being, but that is only one QG approach out of several.

 

[stglyde]

That SciAm article was published in 2003. Loop cosmology changed radically after 2006. I would not read anything from before 2009. Loop quantum gravity itself changed radically after 2007-2008 and the first decent survey papers describing its new form came out in 2010.
You must suit yourself as regards what you like to read.

Are you saying that any attempt to make Planck length the minimum scale automatically becomes Loop Quantum Gravity? If not.. what are the other possibilities beside it and String Theory? I am thinking along Brian Greene book about the universe possibly a computer program like in the movie Matrix where the world is a computer generated virtual dreamworld. In such case, Loop Quantum Gravity is still necessary?

 

[marcus]

. what are the other possibilities beside it and String Theory?

Personally I'd suggest avoiding Brian Greene books. Over the years too often I see people show up here with misconceptions from the Greene kind of poetry---highly skilled verbal imagery and metaphorical presentation that gives the illusion of understanding. But you have to suit yourself. If you're math-inclined you have more options. If not, I don't know what to suggest.

There are several alternatives to Loop and String however:

Asymptotic Safe QG is one possibility. (Steven Weinberg's idea now much expanded by Reuter Percacci and friends)

Triangulations QG is another (see Renate Loll's SciAm I told you about, link in my sig)

Simplicial QG approach (a team of young researchers led by Bianca Dittrich)

A new thing called Shape Dynamics (see papers by Gomes and Koslowski)

There are several approaches to gravity inspired by condensed matter physics (see e.g. X.G. Wen's papers, and a recent one by Liberati Finazzi Sidoni).

Group Field Theory (Oriti and co-workers)

The quantization of Cartan's GR (new papers by Derek Wise and Steffen Gielen)

Erik Verlinde's entropic gravity (2009 not so much lately)

Petr Horava's anisotropic gravity (2009 not so much lately)

Verlinde and Horava were formerly prominent string theorists. Their alternative non-string QG approaches got a lot of attention a couple of years ago but not so much now.

This is not a complete list! Just some alternatives to Loop and String that I happened to think of prompted by your question. There are many ways up the mountain to QG, and several separate parties of climbers making progress towards the summit.

 

[stglyde]

Personally I'd suggest avoiding Brian Greene books. Over the years too often I see people show up here with misconceptions from the Greene kind of poetry---highly skilled verbal imagery and metaphorical presentation that gives the illusion of understanding.

You think Brian Greene has lost it? In the following it's not verbal imagery or metaphorical presentation.. he was describing our universe may be computer generated as when he wrote in the book "The Hidden Reality":

To simulate not just individual minds but also their interactions among themselves and with an evolving enviroment, the computational load would grow orders of magnitude later. But a sophisticated simulation could cut computional corners with minimal impact on quality. Simulated humans on a simulated Earth won't be bothered if the computer simulates only things lying within the cosmic horizon. More boldly, the simulation might simulate stars beyond the sun only during simulated nights, and then only when the simulated local weather resulted in clear skies. When no one's looking, the computer's celestrial simulator routines could take a break from working out the
appropriate stimulus to provide each and every person who could look skyward. A sufficiently well-structured program would keep track of the mental states and intentions of its simulated inhabitants, and so would anticipate, and appropriately respond to, any inpending stargazing. The same goes for simulating cells, molecules, and atoms. For the most part they'd be necessary only for simulated specialists of one scientific persuation or another, and then only when such specialists were in the act of studying these exotic realms. A computationally cheaper replica of familiar reality that adjusts the simulation's degree of detail on an as-needed basis would be adequate."

If it were true. I wonder if it would change any Planck physics programme meaning would there still be need for Loop Quantum Gravity inside the program or would GR and QM be merely subroutines?

 

[Naty1]

a great panoramic list from Marcus

Personally I'd suggest avoiding Brian Greene books.

I'd say instead that reading anyone authors perspective does not likely give
a complete picture. I included several of his books in my previous summer
reading and found them thought provoking.

Three Roads to Quanum Gravity by Smolin is also a good read and shows some
of the relationships among different approaches.

So how come we don't just assume that minimum resolution of nature is the Planck scale.

For specific approaches, that's fine as Marcus has posted. But as a general rule you don't
want to exclude any possibilities. Here are a few examples of why avoiding actual investigation is unwise:

'Heavier than air flying machines are impossible' (Lord Kelvin)

“High speed travel on trains will be impossible” (over 25 MPH people won’t be able to breath, late 1700’s)

“ We must avert a global catastrophe” (1970’s mantra about the coming ice age.)

'We are probably nearing the limit of all we can know about astronomy' (Simon Newcomb 1888 )

We also do not know if space and time are continuous or discrete... analog or digital. That
seems to a layman like me an interesting question. Also whether information rather than
say mass and energy might be the foundation of our universe. There have been several discussions here regarding that discrete versus continuous issue in these forums and in one paper cited there were hints that there is no difference!...kind of like digital sampling of information where an appropriate sample rate can reproduce all the continuous analog information...
Whatever the outcome, investigating an area of science even when that seems insurmountably difficult has proven over time to bear rich results.

 

[Naty1]

So how come we don't just assume that minimum resolution of nature is the Planck scale.

I wondered what Wikipedia had to say...some pertinent comments in the first section here:


http://en.wikipedia.org/wiki/Planck_scale

still lots to learn!

 

[D H]

You think Brian Greene has lost it? In the following it's not verbal imagery or metaphorical presentation.. he was describing our universe may be computer generated as when he wrote in the book "The Hidden Reality"

It's important to keep in mind that pop-sci books such as "The Hidden Reality" were written with the goal of understandability to the lay public in mind. This general understandability comes at the expense of correctness. (For example, pick any lay description of the big bang: the raisin bread analogy, the balloon analogy, inchworm on a rubber band. Each is incorrect to some degree.) The scientific references posted by marcus et. al. were written with the goal of scientific correctness in mind. This correctness comes at the expense of understandability to the general public. Correctness or understandability: Pick one. You can't have both.

 

[stglyde]

Even without going to Planck scale. I think the search for physics of wave functions of the metric is a separate thing, isn't it? Or how to quantize the metric.. this is not related to Planck scale, right?

 

[stglyde]

Personally I'd suggest avoiding Brian Greene books. Over the years too often I see people show up here with misconceptions from the Greene kind of poetry---highly skilled verbal imagery and metaphorical presentation that gives the illusion of understanding. But you have to suit yourself. If you're math-inclined you have more options. If not, I don't know what to suggest.

There are several alternatives to Loop and String however:

Asymptotic Safe QG is one possibility. (Steven Weinberg's idea now much expanded by Reuter Percacci and friends)

Triangulations QG is another (see Renate Loll's SciAm I told you about, link in my sig)

Simplicial QG approach (a team of young researchers led by Bianca Dittrich)

A new thing called Shape Dynamics (see papers by Gomes and Koslowski)

There are several approaches to gravity inspired by condensed matter physics (see e.g. X.G. Wen's papers, and a recent one by Liberati Finazzi Sidoni).

Group Field Theory (Oriti and co-workers)

The quantization of Cartan's GR (new papers by Derek Wise and Steffen Gielen)

Erik Verlinde's entropic gravity (2009 not so much lately)

Petr Horava's anisotropic gravity (2009 not so much lately)

Verlinde and Horava were formerly prominent string theorists. Their alternative non-string QG approaches got a lot of attention a couple of years ago but not so much now.

This is not a complete list! Just some alternatives to Loop and String that I happened to think of prompted by your question. There are many ways up the mountain to QG, and several separate parties of climbers making progress towards the summit.

Marcus,

In one of the quantum gravity books. It is mentioned that there are 4 roads to quantum gravity:

1. quantising General Relativity
2. quantising a different classical theory, while still having general relativity emerge as a low- energy (large-distance) limit.
3. having general relativity emerge as a low-energy limit of a quantum theory that is not a quantization of a classical theory
4. having both general relativity and quantum theory emerge from a theory very different from both

You have listings of many Quantum gravity models above. Are they part of the above or are they new additions? How do you sort or categorize each based on the above classifications?

I'm interested in 4. What models have you come across that is about both general relativity and quantum theory emerge from a theory very different from both, and which of them is your favorite, and why?

Thanks a lot for your help.