Quantum Gravity

[Martin]

What does he mean when he says that "matter couples to geometry"?

 

the perception that matter couples to geometry goes back to 1915 with the publication of einstein first Gen Rel paper

 

concentration of any type of energy (call it matter for want of better word) curves space

 

John Archibald Wheeler put it something like this: matter tells space how to curve' date=' and shape of space tells matter how to flow

 

so the shape of space and the density of energy are COUPLED

 

no one has explained WHY or by what mechanism they are coupled. why should matter curve space? what could be the mechanics of the connection? nobody has a clue. hopefully QG research will dig up something on this.

 

but the linkage is very SIMPLE it is just the main Gen Rel equation, the socalled Einstein Eqn.

 

curvature = (coeff) energy density

 

the coefficient is the reciprocal of a force and it can be written

8pi G/c[sup']4[/sup]

[Martin]

you should know about the units of the Einst. eqn.

 

curvature is measured as reciprocal area (one over distance squared)

 

 

multiply any curvature by a force and you get a pressure (force over area) and that is the same as an energy density (energy over volume)

 

so when you see einst. eqn.

 

G_ab = (1/F) T_ab

 

LHS is curvature, RHS is energy density (actually the stress energy tensor whose unit of measure is energy density) divided by a universal constant force F = c⁴/(8piG)

 

so what you are likely to see if you look on google for Einst. eqn is

 

G_ab = ((8piG)/c⁴) T_ab

 

that is our main equation describing gravity! all we know is that it works!

 

It was a Frank Wilczek article in Physics Today that first pointed out to me that the central coefficient in the Einst. eqn. was one over a force and that it wasnt newton's G it was newtons G times 8pi.

 

I think this force will turn out to be important in understanding how the concentration of energy bends the geometry of space.

[Johnny5]

the perception that matter couples to geometry goes back to 1915 with the publication of einstein first Gen Rel paper

 

concentration of any type of energy (call it matter for want of better word) curves space...

 

so the shape of space and the density of energy are COUPLED

 

 

Ok, supposing that the "shape of space" (call it space for lack of a better word) is COUPLED (good word) to the density of MATTER (best word)"

 

does space have inertial mass? In other words, is it a resistive medium?

 

If (assuming GR to be correct under some interpretation) I throw a baseball in outer space, will it slowly come to rest?

 

Thank you

[Martin]

...

does space have inertial mass? In other words' date=' is it a resistive medium?

 

If (assuming GR to be correct under some interpretation) I throw a baseball in outer space, will it slowly come to rest?

[/quote']

 

I dont think so. I am a physics watcher. I am interested in watching Quantum Gravity emerge, especially LQG and spinfoam approaches which have been growing and getting stuff done in cosmology lately. I am not an authority.

 

but bearing in mind that I am not speaking authoritatively I would say absolutely not!

 

the expansion of space stretches light out when it travels for a long time it gets redshifted due to this stretching effect, so over billions of years of travel light can lose quite a lot of energy, but it still goes the same speed AFAIK

 

and other things like baseballs sail along without losing any energy at all AFAIK

[Johnny5]

 

the expansion of space stretches light out when it travels for a long time it gets redshifted due to this stretching effect' date=' so over billions of years of travel light can lose quite a lot of energy, but it still goes the same speed

[/quote']

 

I have a serious problem with the underlined part. Can you isolate where in the mathematics of GR, this is for me?

[Martin]

I have a serious problem with [the expansion of space'] Can you isolate where in the mathematics of GR, this is for me?

 

eventually you should get familiar with the FRW metric which is the standard metric of cosmology.

FRW stands for Friedmann Robertson Walker IIRC

and you should get familiar with the Friedmann equation, which is the basic equation of cosmology

 

it is a gross simplification of the Einstein eqn of GR.

 

the Friedmann equation can be understood by anyone with firstyear college calculus. it is a simplification DERIVED from Gen Rel by assuming that on the large scale the universe is pretty smooth and uniform and looks about the same in any direction. Gen Rel is more complex because it is geared to handle all the bumpy lopsided cases that could arise as well.

 

the Friedmann equation shows you the mathematics of why space has to be expanding, or with a different choice of parameters, contracting.

 

In the meantime, did you read the March 2005 SciAm article by Charlie Lineweaver and Tamara Davis?

[Johnny5]

you should know about the units of the Einst. eqn.

 

curvature is measured as reciprocal area (one over distance squared)

 

 

multiply any curvature by a force and you get a pressure (force over area) and that is the same as an energy density (energy over volume)

 

 

This is easy enough to remember... (for my own edification)

 

1. 'Curvature' has units of 1/meter^2' date=' inverse area, inverse r squared... like a certain portion of the Newton gravity formula.

 

2. Pressure has units of force per unit area, so that Force times 'curvature' has units of pressure, which would be Newton/meter squared, also equivalent to Newton meter/meter^3 same as Joule/cubic meter.. which is units of "energy density"

 

 

so when you see einst. eqn.

 

G_ab = (1/F) T_ab

 

LHS is curvature, RHS is energy density (actually the stress energy tensor whose unit of measure is energy density) divided by a universal constant force F = c⁴/(8piG)

 

G_ab this is a tensor, is the whole tensor called 'curvature'? Can you explain tensors to me quickly, just enough so I can understand this one?

 

(of course an equation is just a tautology in the end, at any rate)...

 

So the curvature is equivalent to the RHS, there is a constant of proportionality (to be constant means I can differentiate this portion with respect to time and nothing happens right?) and that constant you are telling me is a force constant (but inverted)? Something with units of kilogram meter per seconds squared? (where did the factor of [math] 8 \pi [/math] arise?)

 

Why not lift it (the inverted force constant) to the other side, and divide the Maxwell stress tensor by the curvature?) ?

 

As for the stress energy tensor...

 

T_ab

 

After you explain the curvature tensor, can you explain the stress energy tensor briefly. Does it have something to do with stretching something? (And please don't say space) I will probably have a lot of questions about this tensor, if you do say space.

 

As for that 'force' constant, let me check out the units:

c⁴/(8\pi G)

 

c has units of meters/second, G is the Newtonian gravitational constant I presume... 6.672 x 10^-11 meter^3/kg s^2 so that, the force constant has units of...

 

(m^4/s^4)/ (m^3/kg s^2) = (m^4/s^4)(kg s^2/m^3) = (m/s^2)(kg ) = Newtons

 

ok at least that checks out, but where did the 8 pi come from, thin air?

 

 

so what you are likely to see if you look on google for Einst. eqn is

 

G_ab = ((8piG)/c⁴) T_ab

 

that is our main equation describing gravity! all we know is that it works!

 

 

How did we find out that it works?

[Martin]

http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=0009F0CA-C523-1213-852383414B7F0147

 

Lineweaver and Davis good popular feature article "Misconceptions about BigBang" from March 2005 SciAm

Here are some sample sidebars. Each has one or more visual diagrams with a wrong answer discussed and a right answer explained.

 

 

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p39.gif

What kind of explosion was the big bang?

 

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p40.gif

Can galaxies recede faster than light?

 

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p42.gif

Can we see galaxies receding faster than light?

 

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p43.gif

Why is there a cosmic redshift?

 

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p44.gif

How large is the observable universe?

 

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p45.gif

Do objects inside the universe expand, too?

[Johnny5]

 

In the meantime' date=' did you read the March 2005 SciAm article by Charlie Lineweaver and Tamara Davis?[/quote']

 

The long-distance thinker

 

Martin Bojowald is on a journey back in time to see what happened during the Big Bang. Quirin Schiermeier tags along for the ride.

 

 

Is that you? If it is, hello.

If not, no harm done.

 

Is that the march article you are talking about?

[Martin]

 

ok at least that checks out' date=' but where did the 8 pi come from, thin air?

 

 

 

How did we find out that it works?[/quote']

 

good for you for parsing the units and making sure it really is a force.

lot of folks dont get down to the nittygrit of actually doing that

 

about "where did the 8pi come from?" LOL you know Usenet

sci.physics.research also called SPR

about 2 or 3 years ago they had this long thread titled

"WHO PUT THE 8 PI IN THE BUMP TI BUMP BUMP?"

 

John Baez was moderator then and SPR was a meeting place for all these highpower academics and the archives can be very interesting.

 

they dont know why the 8 pi. well some of them have some ideas.

 

it is amusing to see humans scrambling around and scratching their heads and being essentially clueless. it is our historical condition.

 

About the "How did we find out that it works?" You should know that Gen Rel has had a long series of tests and has repeatedly passed with flying colors. People have been trying to invent substitutes for like 70 or 80 years but they havent been able to.

 

Classic Gen Rel is NOT QUANTUM and it should be possible to replace it with something that works even better that is quantum. That is what QG research is about. A successful QG model would get rid of the singularities which are the famous glitches in Gr where it breaks down and will not compute. Well guess what, Quantum Mechanics has been around since 1925 (with the schroedinger and heisenberg stuff) and ever since 1925 people have known that they had to quantize Gen Rel and they have been trying! That is 80 years and they still cant do it.

 

And Gen Rel keeps on passing all the tests and getting its predictions verified out to 6 or 7 decimal places with this uncanny accuracy. Beautiful.

 

But I do think that it will be quantized and replaced before very much more time has passed. the LQG papers I watch are getting very interesting

[Johnny5]

 

 

the expansion of space stretches light out when it travels for a long time it gets redshifted due to this stretching effect' date=' so over billions of years of travel light can lose quite a lot of energy, but it still goes the same speed

[/quote']

 

I have a serious problem with the underlined part. Can you isolate where in the mathematics of GR, this is for me?

 

 

Instead of expansion of space, can we just say that matter is moving away from the center of the universe?

[Martin]

The long-distance thinker

 

Martin Bojowald is on a journey back in time to see what happened during the Big Bang. Quirin Schiermeier tags along for the ride.

 

 

Is that you? If it is' date=' hello.

If not, no harm done.

 

Is that the march article you are talking about?[/quote']

 

No way. I told you I am a physics watcher. I am not a working relativist or quantum gravitist. I wish I were. great field, very exciting these days

 

but popular journalism sucks! I hate how they write about all this stuff for popular consumption. it is embarrassing. but actually there is some truth in it because they are pushing the model back further in time

[Martin]

Instead of expansion of space, can we just say that matter is moving away from the center of the universe?

 

why dont you take a gander at the Lineweaver SciAm sidebars I linked to?

might be illuminating

[Johnny5]

But I do think that it will be quantized and replaced before very much more time has passed. the LQG papers I watch are getting very interesting

 

Tell me what it is that appears increasingly interesting... something experimental, or theoretical?

[Johnny5]

No way. I told you I am a physics watcher. I am not a working relativist or quantum gravitist.

 

 

So then you don't understand tensor calculus, you are just a novice/fan of GR and QG?

[Johnny5]

why dont you take a gander at the Lineweaver SciAm sidebars I linked to?

might be illuminating

 

I'm reading it now. Thanks Martin

[Johnny5]

the perception that matter couples to geometry goes back to 1915 with the publication of einstein first Gen Rel paper

 

concentration of any type of energy (call it matter for want of better word) curves space

 

so the shape of space and the density of energy are COUPLED

 

no one has explained WHY or by what mechanism they are coupled. why should matter curve space? what could be the mechanics of the connection? nobody has a clue. hopefully QG research will dig up something on this.

 

 

 

SUMMARY: If GR is correct then (matter and space are coupled)

 

Martin, what do you think would happen if matter was UNCOUPLED from space in some local region of spacetime?

 

Maybe I should preface this question with, "How would one go about uncoupling matter from space?"

 

 

Thanks

[Martin]

http://arxiv.org/gr-qc/0503020

 

 

(mu is the discrete internal time parameter that arises in quantum cosmology) sample exerpt from page 5:

 

" The evolution dictated by this difference equation in internal time mu does not stop at any finite value of mu. In particular, we can uniquely evolve initial values for the wave function through the classical singularity situated at mu = 0. Thus, there is no singularity where energy densities would diverge or the evolution would stop. This comes about as a consequence of the basic loop properties: the discreteness of spatial geometry leads to finite operators for the inverse volume as well as evolution in discrete internal time. Both properties enter in the demonstration of singularity free evolution. Physically, this means that around the classical singularity continuous space-time and with it the classical theory dissolve. Discrete quantum geometry, on the other hand, still makes sense and allows us to evolve to the other side of the classical singularity. "

 

a physical model like QG can be run backwards in time to explore earlier conditions. Old GR broke down at the bigbang's "classical singularity". The new quantum model does not break down there.

 

what needs to be explored is what actually conditions are at or before the bang ex-singularity, and at the black hole ex-singularity.

the black hole classical singularity has also, it seems, been eliminated in the LQG model. there is a talk by Abhay Ashtekar about this that one can get online but the paper has not yet been published.

 

the relation between matter and spacetime geometry must (it seems clear to me) be extremely different in these places that used to be singularities (that is, where the classical theory broke down and generated infinities)

 

I can't help you with the question. it is a forefront research type question basically whats it like at the center of a bh? However I can see if I can find a link to Ashtekar's talk.

 

Ashtekar (with Smolin and Rovelli) was one of the originators of LQG and Bojowald studied with him as a postdoc until in 2003 he went back to Berlin. they appear to be writing a paper together on the quantum picture of the innards of a black hole

 

here is Ashtekar Fall 2004 seminar talk, audio and slides. unless your computer has good sound you may not understand his accent. the slides are very rough drawn, he uses Penrose diagrams of BH a lot, which may be confusing. basically this is what you get for asking an extreme question like what happens in situations where the ordinary relation of matter and spacetime geometry breaks down?

 

http://www.phys.psu.edu/events/index.html?event_id=934&event_type_ids=0&span=2004-08-20.2004-12-25

 

[Johnny5]

Thanks Martin

[Severian]

but popular journalism sucks! I hate how they write about all this stuff for popular consumption. it is embarrassing.

 

I agree

[Johnny5]

 

Ashtekar (with Smolin and Rovelli) was one of the originators of LQG and Bojowald studied with him as a postdoc until in 2003 he went back to Berlin. they appear to be writing a paper together on the quantum picture of the innards of a black hole.

 

 

You mention Rovelli in another thread, where I ask about Foucalt's pendulum. Are you a fan of his?

 

Regards

[Martin]

You mention Rovelli in another thread' date=' where I ask about Foucalt's pendulum. Are you a fan of his?

[/quote']

 

 

got to respect those with creative vision to find a way out of the QG wilderness

 

25 years of "string theory" has led to no string theory but

conservatively 10^100 different stringy vacuum states with different physics and no way of chosing.

the "Landscape" morass of umpteen vacua, and the anthropic lack of principles.

 

thus no present prospect that stringy theorizing can make any definite prediction about a future experiment that would allow it to be tested

 

by contrast, a small research effort (hundreds instead of thousands of researchers) initiated by rovelli, smolin, ashtekar, now with ashtekar's student bojowald also a major player-----this much SMALLER research effort has made impressive progress in the past 5 years.

 

right or wrong? WE DONT KNOW

we can only test a theory when it bets its life on a prediction of the outcome of a future experiment

if it has no predictive power then it is predictively empty, meaningless

to become a theory, something must be brought to the point of having measurable consequences

now, it appears, that Loop Gravity HAS

and Smolin has made some testable predictions that will be tried by a satellite gammaray observatory called "glast" in 2007 or 2008.

 

we dont know. LQG may live or it may die. but at least it has made some remarkable progress and is reaching testability (it has removed the bigbang singularity, and subject to some further checking also gotten rid of the black hole singularity, it actually predicts inflation, with a graceful exit into normal expansion, without extra assumptions, it finds a discrete spectrum of the area and volume operators......read about a couple dozen main results in Smolin's article "Invitation to LQG")

 

So yes I have to respect the guy. LQG is where the QG action is. String is in a muddle and is a waste of research resources on a grand scale. Rovelli helped get Loop started in the Nineties.

Because of the conformism of physicists (who for career sake tend to all work on the same approach, what is fashionable) it took real guts for those guys Rovelli and Smolin and their postdocs who went with it, for them to do that. We dont know how its going to turn out but I am watching and respecting the effort

[Martin]

but about the Pendulum business

I refer to Rovelli chapter 2

because it does both philosophy and math about the question

of "rotation with respect to what?"

 

I refer to that NOT because I am a Rovelli fan, which in a sense I am, but

because it is a basic philosophical/mathematical issue that is down at

the foundations of physics, and he does both equations and thoughtful paragraphs. I do not know anybody else who does a concise but thorough treatment. I suspect that this background stuff (which he happens to provide) can be helpful.

 

The first part of the book is not about LQG, it is about the foundations of physics and especially about Gen Rel.

rovelli has a second degree in the History of Science, and has taught that as well as classical Gen Rel , and QG.

When you read Chapter 2 of his book you are reading history of science, about newton and einstein and how they wrestled with basic problems and came up with their ideas.

so it is not a LQG tract, it is basic science history that is necessary (i think)

background to Foucault Pendulum and such.

[Johnny5]

What does LQG say about inertial mass, if anything? Is it equivalent to gravitational mass?

[ed84c]

Have a read.

 

Note: Im only 15, so be kind.

Quantum Gravity.doc