General Relativity + Quantum Mechanics = Error Buy Why?

[RyanJ]

General Relativity + Quantum Mechanics = Error Buy Why?

 

Hi all!

 

I've been reading an interesting book on string theory and I read that one of the reasons it was developed was to resolve the conflicts between merging general relativity and quantum mechanics but my question is what makes these two so incompatible in the first place?

 

My thought on this was that it had to do with relativity dealing with large and exact while quantum mechanics deals with small and probabilistic, in other words they are contradictory in some sence.

 

If that the reason or is it something deeper that blocks their intergration?

 

Cheers,

 

Ryan Jones

[Daecon]

I thought it had something to do with Gravity...?

[ydoaPs]

General Relativity + Quantum Mechanics = Error Buy Why?

 

Hi all!

 

I've been reading an interesting book on string theory and I read that one of the reasons it was developed was to resolve the conflicts between merging general relativity and quantum mechanics but my question is what makes these two so incompatible in the first place?

 

My thought on this was that it had to do with relativity dealing with large and exact while quantum mechanics deals with small and probabilistic' date=' in other words they are contradictory in some sence.

 

If that the reason or is it something deeper that blocks their intergration?

 

Cheers,

 

Ryan Jones[/quote']

maths that are beyond my current understanding. i'm sorry i can't help you any more. if i could, i would show you.

[RyanJ]

maths that are beyond my current understanding. i'm sorry i can't help you any more. if i could, i would show you.

 

Unfortunatly I am not that good at maths either so the maths too me would be useless right now

 

Although I am fine with some areas of maths some kill me outright

 

If anyone can explain this I would much appreciate it - the book does not really cover this aspect of the history unfortunatly.

 

Cheers,

 

Ryan Jones

[ydoaPs]

somehow, tensor calculus(GR) and the type of algebra used in QM are hard to make work togather. you get infinite probabilities. that's all i know.

[Daecon]

Infinite probabilities?

 

Wouldn't that make it a "definitely"?

[Martin]

 

My thought on this was that it had to do with relativity dealing with large and exact while quantum mechanics deals with small and probabilistic' date=' in other words they are contradictory in some sence.

 

If that the reason or is it something deeper that blocks their intergration?

[/quote']

 

People say that GR and QM are like a mismatch old married couple that sleep in the same bed but won't have sex.

 

Roger Penrose says that both Gr and Qm will have to be changed a little so they can be compatible. Getting them into one combine theory (including large and small phenoms) is a big challenge but also a bit HOPE FOR PROGRESS because it will make people rethink the foundations of physics and get more understanding of both theories and IMPROVE BOTH in order to make them fit.

 

they must fit because nature is one.

 

I will tell you what people say is the BIG STUMBLING BLOCK.

 

Ordinary QM depends on having some FIXED GEOMETRICAL BACKGROUND as a framework in which it can be constructed. This geometrical background can, for example, be the simple flat Minkowski space of special relativity. It does not have to be Euclidean. But there has to be a fixed BACKGROUND GEOMETRY of some kind to start with.

 

Quantum Field Theory (QFT) the basis for particle physics and understanding matter is "relativistic" only in the limited sense of SPECIAL relativity. It uses a set fixed space as a stage on which to operate.

 

The trouble is that Quantum Physics (QFT in particular) is not GENERAL relativistic. It does not meet the requirements of Gen Rel.

For example, Gen Rel is BACKGROUND INDEPENDENT. It is built on a space time without any fixed pre-conceived geometry!

 

the lesson Gen Rel teaches us is that space time geometry is dynamic and changeable--no absolute fixed geometry in which things happen. Spacetime geometry happens like everything else. Geometry is a field like other fields.

 

One place you can read about Background Independence is in the soft parts of Lee Smolin's online article

The Case for Background Independence

http://arxiv.org/abs/hep-th/0507235

(just click where it says "PDF")

 

A little terminology------the unification of QM and GR is sometimes called "quantum gravity" because Gen Rel, the theory of the dynamic geometry of space time is our theory of GRAVITY. Gravity is best described as the effect of the shape of spacetime, i.e. curvature caused by matter.

But a prominent Quantum Gravitist, Carlo Rovelli, describes the unification goal as a GENERAL RELATIVISTIC QUANTUM PHYSICS.

 

So there is a lot of different terminology and it is in flux----as new discoveries are made the words change. Some people say "Quantum Gravity" and some say "quantum gravity and matter" because matter is being more and more included in with quantum gravity. And some say "quantum spacetime dynamics" (like QED quantum electrodynamics except that it is spacetime geometry that is studied, not electo-stuff). And some say "quantum geometry" (because gravity IS geometry, so quantum gravity must be quantum geometry).

 

The field is boiling over with activity. dont be discouraged by the confusion of terminology. It will be a while before any of it is pinned down.

 

If you are curious about recent progress, you might want to look at an online article by Renate Loll called THE UNIVERSE FROM SCRATCH (also another more technical paper is called Reconstructing the Universe).

She and her colleagues SIMULATE QUANTUM UNIVERSES IN A COMPUTER according to a process they developed called "causal dynamical triangulations"----just one of several promising recent approaches to quantum gravity

 

Loll's people build their universes out a a simulated "quantum foam" or rather they let them GROW by a quantum version of Einstein's Gen Rel rules. In each case they can't tell in advance how the universe is going to turn out, or even what its DIMENSIONS will be. Even the dimensionality is not fixed and can turn out to be different at very small Planck scale from what it is at large macro scale.

 

Loll's stuff is very active and got a bunch new results last year (2005). The article is written for general audience----not for specialists---so it has some soft accessible parts---it is not all hard to read.

 

It is not the only thing to look at but it is at least something.

 

http://arxiv.org/abs/hep-th/0509010

The Universe from Scratch.

"A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19th-century founders of modern geometry contemplated the possibility that a piece of empty space that looks completely smooth and structureless to the naked eye might have an intricate microstructure at a much smaller scale. Our vastly increased understanding of the physical world acquired during the 20th century has made this a certainty. The laws of quantum theory tell us that looking at spacetime at ever smaller scales requires ever larger energies, and, according to Einstein's theory of general relativity, this will alter spacetime itself: it will acquire structure in the form of "curvature". What we still lack is a definitive Theory of Quantum Gravity to give us a detailed and quantitative description of the highly curved and quantum-fluctuating geometry of spacetime at this so-called Planck scale. - This article outlines a particular approach to constructing such a theory, that of Causal Dynamical Triangulations, and its achievements so far in deriving from first principles why spacetime is what it is, from the tiniest realms of the quantum to the large-scale structure of the universe."

 

for the full article, click on where it says "pdf"

[RyanJ]

WOA! Thanks for the thorough decscription of it Martin! I will also look at the links you posted - should provide me with additional information for my personal research

 

I think I understand the problems a bit more clearly now... do they just output rubbish answers when combined? As I remember it normally outputs something with an infinity in it, something you clearly don't want in most cases.

 

Cheers & thanks as always,

 

Ryan Jones

[Martin]

Hi Ryan,

Loll has not put matter into her model yet! We don't know yet, in that particular case, how things will work out. Outputting rubbish, or things that dont agree with experiment, is ALWAYS a possibility. these are relatively new research initiatives and any of them can prove to be wrong. But overall surprising progress is being made in QG.

 

An awkward fact I should warn you about. This is partly for Transdecimal.

 

In these areas nothing stays the same. In Quantum Gravity circles, string theory is ancient history. If you wanted to find out what is happening in new non-string Quantum Gravity you would not go talk with Brian Greene, for instance, you would probably go talk to some younger person like Laurent Freidel or Daniele Oriti or Hanno Sahlmann or Willem Westra. they are young and at the leading edge. Hanno and Willem are postdocs working with Renate Loll in Holland. Daniele is at Cambridge in the UK and Laurent is at Perimeter in Canada.

 

My choice would be clear, I'd go talk with Laurent Freidel. His December 2005 and January 2006 papers were remarkable. I am waiting for the next.

He is including quantized matter in with quantized geometry on the SAME FOOTING so that the matter is just an ASPECT OR FACET of the geometry. the same web of connections describes both, and describes how they interact----so that matter can tell space how to curve and space, in turn, can tell matter how to move----because they are both the same thing. Unlike some other approaches, Freidel's approach appears capable of making predictions which can be TESTED. Indeed, I expect he will come out with some this year that can be tested by satellite observatory in 2007 or 2008. In other words there will be, I confidently expect, an opportunity to FALSIFY, something which is an essential part of science.

 

(one of the troubles with some older theories, like string, is predictive weakness----insufficient testability---lack of exposure to falsification)

 

I see that Transdecimal wants babies.

 

If you want babies, Freidel wouldn't be so good because he is quite plain---he is skinny, gangly and unshaven, and a bit shy. For babies, the person would be Hanno Sahlmann. He is way better looking than Brian Greene and a good ten years younger than Brian.

[Norman Albers]

Very nice, Martin, thank you. I happen to be mucking about in the foundations of quantum vacuum theory and I think it is HERE that we will change things. I state so in my paper on photon localization and dark energy. Norman Albers

[Norman Albers]

argh

[Severian]

Actually, they are not really incompatible. You can build a quantum theory of gravity using local supersymmetry. It has a graviton and at first order in an expansion of the coupling gives answers that are reasonable and makes reasonable predictions.

 

The problem is that it is a non-renormalizable theory. What this means is that if you work out the quantum corrections to these processes, you get infinte contributions because the high energy physics does not decouple. This is the 'infinite probabilities' that Yourdadonapogos mentioned.

 

However, this need not be the fault of the theory. This could be the fault of the physics - it may be that the physics at very high energies just doesn't decouple. We have always had decoupling in the past (eg. you don't need QM to use Newton's laws) but decoupling is just an assumption. Then we would need a proper theory of everything to make quantum gravity predictions beyond leading order.

[Norman Albers]

I am saying that it is a mistake to posit a necessary quantum ground state of one-half in the radiation field. I put in a statistical exponent which eliminates the high-energy blowups, no? I think there should be more 'fiscal responsibility' in our vacua!!!

[Martin]

... Then we would need a proper theory of everything to make quantum gravity predictions beyond leading order.

 

this is Ryan's thread so I can't speak for him, but if it was mine I would encourage you to say a bit more. do you want to elaborate? or have you a picture of what that "proper" theory might possibly look like?

 

if I understand your brief post, the theory would be non-perturbative---I think your assumption is what if Mother Nature adamantly refuses to be expanded in a perturbation series (except as largescale approximate or effective theory)

 

so spacetime and matter fields are not being expanded around some fixed background (are not being approximated by successive modifications of some fixed framework---there is no set "flat" case, or "vanilla" situation that you try to match to reality by bending and trimming)

 

is this a fair gloss, Severian?

 

In case you have some notion of what a nonperturbative fundamental theory of spacetime and matter might look like (don't laugh ) I would certainly like to know, even if it is a very vague sketch or hunch.

 

If not, that is OK, it seems very hard----people's efforts to date seem to have run aground in the shoals of their own complexity

[Norman Albers]

To state the existence of a tapered Gaussian wave packet of single frequency in propagation is to state the existence of a diffuse manifestation of charge and current which literally are the phased-array antenna (co-moving) which keeps it nondispersive. To allow such local response as I have cleanly characterized to first-order xpand, only, must lead logically to the realization that overall packet amplitude (total energy and total ang. mom.) is arbitrary. Locally energy density and ang. mom. density differ by omega. Now atoms emit only certain sized packets, namely our familiar quanta of h-nu. It is they which have selection rules of unit change in ang. mom., no? This does not say that fractional packets are not also possibilities of the field. I call this dark energy. . . . . . . . . . . . . . . My question of QM is, what is their virtual manifestation? I am saying that charge density is available at very small levels if there are packets. This allows reconsideration of the whole concept of vacuum fluctuations, which is somewhat of an embarassment, I feel. What magnitude was that ZPE?

[Norman Albers]

The xpansion I do is in saying there are many oscillations (wave vector k) in the Gaussian exponential envelope which falls off relatively slowly (length scale of "a", where a<<k). This bepeaks the strength of response from the not-vacuum, and I assume this changes at "high" energy. Since densities increase rapidly one would think some kind of saturation happens somewhere, but in which direction? Toward fewer or greater "cycles per packet", which is to say greater or smaller (a/k)?

[Norman Albers]

Electrons are like crystals of light. They can be seen as another phase state of the EM field. You can poke at ice on a cold bench and you will not find water until you learn to see water as angled molecules with different phase states at differing temps and pressure. Energy goes around in a phase-less wave; I call it the "frozen-yogurt" state. Stable shelf-life below maybe five billion degrees or so.

[Severian]

this is Ryan's thread so I can't speak for him' date=' but if it was mine I would encourage you to say a bit more. do you want to elaborate? or have you a picture of what that "proper" theory might possibly look like?

[/quote']

 

I have no idea. It would have to do something to cure the non-renormalizability though.

 

if I understand your brief post, the theory would be non-perturbative---I think your assumption is what if Mother Nature adamantly refuses to be expanded in a perturbation series (except as largescale approximate or effective theory)

 

Not necessarily. The infinities are arising because you are allowing the momentum in loops to go to infinity. You could cut off the integrals at some high energy (ie. decoupling) but this doesn't work because the theory is non-renormalizable (i.e. you need to renormalize the theory for every different observable, which makes it unpredictive).

 

But there is no reason in principle why the higher scale theory could not do something to tame the divergences, and this could be a purely perturbative theory.

 

We actually have one example of this already: Fermi's theory. Fermi came up with a theory for the weak interactions which involved interactions of four particles at once. It gave good agreement with the data at tree-level (leading order) but was found to be non-renormalizable (the quantum corrections blew up). This is exactly the state we are in with quantum gravity.

 

Eventually people figured out the 'true' theory of the weak interaction, introducing W and Z bosons which 'spread out' the Fermi 4-particle interactions into 2 different 3-particle interactions separated by a W or Z. We found that the W and Z were particularly heavy, which is why they were hard to see, and indeed, at low energies they move very slowly so are not dynamical. In fact, one can 'integrate out' the W and Z modes from the 'true' theory and Fermi's theory drops out. The reason why Fermi's theory gives the wrong answer for loops is that the momentum running around the loops can be very big, and so the heavy W and Z again become important and shouldn't be ignored.

 

so spacetime and matter fields are not being expanded around some fixed background (are not being approximated by successive modifications of some fixed framework---there is no set "flat" case, or "vanilla" situation that you try to match to reality by bending and trimming)

 

Well, this will be true in cases of large gravitational field, so as one approaches the Planck scale you will have to expand about some non-flat classical solution of Einstein's filed equations. Then you will have difficulty because the gravitational coupling is large. But in principle you should be able to do perturbation theory at low energies because the gravitational coupling is very small.

 

In case you have some notion of what a nonperturbative fundamental theory of spacetime and matter might look like (don't laugh ) I would certainly like to know, even if it is a very vague sketch or hunch.

 

If not, that is OK, it seems very hard----people's efforts to date seem to have run aground in the shoals of their own complexity

 

If I had any idea, I would be writing a paper, not posting at SFN. (But let me say this: i wouldn't be surprised if space-time itself was quantised. This woud act as a regulator, cutting off all loop integrals and make everything finite. It would have to be quantised on some trans-planckian scale though.)

[Norman Albers]

Please understand that I come sort of from nowhere and am poorly trained at where you speak but am quite ready to apprehend I hope. You know, over the years I have said quite a few times, "This is my nth approach to quantum mechanics. Surely this time I will see further." Well, n=about 7, now, and things are coming together. I am honored to talk with you. What do you mean by trans-Planckian? I see smoothness until ultimately small wtf.

[Severian]

What do you mean by trans-Planckian?

 

I mean at energies higher than the Planck scale. Or alternatively the space-time lattice separation distance would have to be shorter than the Planck distance.

[Norman Albers]

When I understand all that you offer me, the cows will come home and it will be a nice evening. Norm

[Norman Albers]

I don't mean that at all as a blowoff, either. This is what I came for. What if our quantum vacuum theory is not complete because the field is not necessarily quantized?

[Severian]

Which bit were you having trouble following?

[Martin]

I have no idea. It would have to do something to cure the non-renormalizability though.

...

...

 

If I had any idea' date=' I would be writing a paper, not posting at SFN. (But let me say this: i wouldn't be surprised if space-time itself was quantised. This woud act as a regulator, cutting off all loop integrals and make everything finite. It would have to be quantised on some trans-planckian scale though.)[/quote']

 

Severian, thanks so much for the extensive and thoughtful response! I just now saw it---missed it when you posted on the 22nd, already a couple of days ago.

 

the idea that (sub-) plancksize quantization of spacetime might cure infinities----provide a cut-off----is surely a reasonable thing to hope.

 

"I wouldn't be surprised if" sounds like a mild non-commital form of "I expect". I think I share that expectation (or hypothetical lack of surprise:-) ) I will see if I can come up with cases where that possibility has been studied in the literature.

 

that is, take a particular candidate model in which spacetime geometry is quantized and study exactly how it provides a cutoff and tames some infinities in field theory. (which is not to say that any of the candidates have been confirmed)

[Norman Albers]

The uncharitable could say I should be embarrassed to even speak here because I am not well trained at the level on which you speak. I have spent time at the semi-classical level because I found it producing useful results, as stated in my two papers. At one point where I was tempted to give up because quantum mechanics can be so intimidating, I finally realized I am doing something parallel and possibly different. Either the physics I depict mathematically is answered to in QM or not, but no one is saying!