What is Quantum Gravity and the Curvature of Spacetime and how is it all relevant to one another?
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Actually how quantum gravity relates to curvature of space-time seems like an interesting question. Is it really impossible to give some overview on the general approach on how to introduce backgound independence into quantum theory?
Because my main interest was in understanding what is known about black holes, i began reading on the properties of black holes. in the article that i was reading Quantum Gravity is mentioned. now i am reading on Quantum Gravity and how it what occurs when Quantum Gravity Meets the Quantum Theory, my problem now is this equation and what it means in relation to Quantum Gravity and to the properties of a black hole.
"In general relativity, mass and energy are treated in a purely classical manner, where ‘classical’ means that physical quantities such as the strengths and directions of various fields and the positions and velocities of particles have definite values. These quantities are represented by tensor fields, sets of (real) numbers associated with each spacetime point. For example, the stress, energy, and momentum Tab(x,t) of the electromagnetic field at some point (x,t), are functions of the three components Ei, Ej, Ek, Bi, Bj, Bk of the electric and magnetic fields E and B at that point. These quantities in turn determine, via Einstein's equations, an aspect of the ‘curvature’ of spacetime, a set of numbers Gab(x,t) which is in turn a function of the spacetime metric. The metric gab(x,t) is a set of numbers associated with each point which gives the distance to neighboring points. At the end of the day, a model of the world according to general relativity consists of a spacetime manifold with a metric, the curvature of which is constrained by the stress-energy-momentum of the matter distribution. All physical quantities — the value of the x-component of the electric field at some point, the scalar curvature of spacetime at some point — have definite values, given by real (as opposed to complex or imaginary) numbers. Thus general relativity is a classical theory in the sense given above."
Oh, I did not see your most recent post. This is a reply to your original post.
Juan, the first thing to understand is the classical idea of the curvature of space, from back in 1915 before quantum theory entered the picture
it was Einstein's insight that what we experience as gravity is really geometry, and the Einstein equation of 1915 shows how the distribution of matter determines the shape of space around it-----this is the main equation of Gen Rel
a famous physicist later put that equation into words: "Matter tells spacetime how to curve. Spacetime tells matter how to move."
starting in 1919 the geometrical theory of gravity (Gen Rel) was tested---repeatedly and with increasing precision. It really does predicts what will happen more accurately than non-geometric theories----theories in which space is a rigid rectilinear framework and gravity is explained by force vectors
so after 80 years of testing Gen Rel, we pretty much accept that space is a dynamic, changing, active thing-----its shape changes as matter moves around in it.
fortunately it doesnt change very much except for very dense massive things, so we dont notice------it is still approximately the foresquare rigid spacetime that Newton imagined, so for practical purposes we still think of it like that.
quantum theory comes in when you try to give this dynamic geometry, interacting with matter, a QUANTUM description-----that means using stuff like wave-functions, and having uncertainty built in.
it doesnt mean that space has to be divided up into little bits:rofl:
(sometimes people think space must be made of quanta)
it means that things that you observe and measure about the geometry of space----like SURFACE AREA, and ANGLE, and VOLUME, and even the dimensionality itself-----are no longer fixed definite things but are instead quantum observables (which can incorporate uncertainty)
For example, in a quantum model of a region of spacetime, the curvature is allowed to have some uncertainty---and depend on the quantum state of the system.
that's all I can provide as an introduction. the main thing is to understand the pre-quantum 1915 business first-----when that is assimilated it is easier to think about shifting to a quantum version of it.
If and when someone can do it I suppose they might, but being able to give a correct way to start would mean you knew were you were going.
Smolin in his book and Perimeter Institute papers seem to show they have tried several approaches and are still looking very hard.
Personally I do not think they will succeed in combining the background independence of GR with QM or the Standard Model.
Thank you, this clears up a lot. But how is it all relevant to a black hole and it's properties?
Several people are around here who could reply well to that. I will give someone else a chance.
juan_rod:” What is Quantum Gravity and the Curvature of Spacetime and how is it all relevant to one another?”
marcus:” a famous physicist later put that equation into words: "Matter tells spacetime how to curve. Spacetime tells matter how to move."
“it means that things that you observe and measure about the geometry of space----like SURFACE AREA, and ANGLE, and VOLUME, and even the dimensionality itself-----are no longer fixed definite things but are instead quantum observables (which can incorporate uncertainty)
For example, in a quantum model of a region of spacetime, the curvature is allowed to have some uncertainty---and depend on the quantum state of the system.
that's all I can provide as an introduction. the main thing is to understand the pre-quantum 1915 business first-----when that is assimilated it is easier to think about shifting to a quantum version of it.”
It seems that nature like follow to something very exceptional. In addition to
Marcus suggestion and in accordance with him look also the elliptical geometry in S7 E.Cartan “sphere” which admits an absolute parallelism.
juan_rod:” But how is it all relevant to a black hole and it's properties?”
I have no idea.
Hence my problem... thanks a lot everyone.
Wait, Juan and Anonym, I will try to reply. I thought some other people would like to reply, but they didn't.
You ask what BH has to do with classic 1915 Gen Rel and also with QG.
I think maybe you know the answer or part of the answer.
everything that has been observed about BH so far is simply consistent with classic Gen Rel and has nothing to do with QG
I think you will agree. If not, please say how I am mistaken. Astronomers have no observation of BH hawking radiation or BH evaporating. So there is no empirical data about relation of QG to BH!
By contrast there is a large amount of empirical data about stuff observed falling into BH and the minimal stable orbit radius----and the redshift of X ray from iron very close to hole----and so on. Wonderful empirical data. Stars have been observed orbiting the central BH in our galaxy and so on. All that is wonderful but perfectly classical.
So your question about what is relevance of QG to BH has a peculiar status. Unless we get some new observation, the question concerns something about which there is no empirical data, but is a rather more speculative question, purely about theory.
Well you seem more advanced than I thought your OP indicated.
I’d recommend considering what you already know about the fundamentals behind the two ideas: “Quantum Gravity” “Curvature of Spacetime” and how they are relevant to each other, before you worry about how they may be relevant to a Black Hole.
“Quantum Gravity” - Fundamentally based a quantum approach, utilizing QM (its derivatives or equivalents) and uses the Standard Model including the idea of particle exchange of gravitons (yet to be discovered) to account for gravity.
“Curvature of Spacetime” – Fundamentally linked to GR and accounting gravity by curves or warping in a 4D Dimensions (some claim 5) with our view of 3 dimensions and time along with gravity being the result. Note the lack of need or use of particle exchange.
Most see these two ideas, as completely incompatible. I agree with the view (but not all do) that they cannot be combined. As in, at least one must be shown as wrong (but they both work so well) some day! Hence my opinion that Smolin will not succeed in combining the background independence of GR with QM or the Standard Model.
Got to hand to those with the persistence to keep trying to combine them, IMO they are working on the core of your question.
Parampreet Singh in Ashtekar's group at Penn State has proposed a new phenomenon to look for in Gammaray Bursts (GRB) that would have a QG signature. I heard this in a recorded Penn State seminar talk
you see, I have to stretch very hard to reach some contact with empirical observation. He says that some instances of gravitational collapse would release a GRB with a distinctive lightcurve. I don't remember, the lightcurve would have some peculiar feature that astronomers could be told to look for.
In QG, gravitational collapse is different because gravity actually turns repulsive at near-Planck density. Some extreme cases might look different.
My apologies----I do not know if this work of Singh has even been published.
I will try to think of some more cases. If one has no observational check then there is no certitude of talking about something real---it could all be just weaving words about the artifacts of theory.
From my basic understanding of QG and QM, i know that quantum leaps from within electrons in the matter surrounding and in front of a BH make it seem as if time curves and or slows down. i also understand that space-time curvature helps both find and identify a BH.
if any of my assertions are wrong please share some insight.
Marcus:” Wait, Juan and Anonym”
“everything that has been observed about BH so far is simply consistent with classic Gen Rel”
Sorry, when I was a student, I attended the seminar given by Y.Zeldovich at Moskow Stecklov Institute. The issue was not a particular problem or particular solution of some problem. Y.Zeldovich presented analysis whether the Einstein GR contains essential singularity. If I understood him correctly, the answer was no.
However, I agree to wait
Of course, what happens to RT at this singularity?
With regards to this question I am interested to see what the members here think of integrating quantum theory with the priniciple of general covariance. Is it at all possible or would it indicate a fundamental flaw in at least one of the theories?
DocN:” what happens to RT at this singularity?”
I beg your pardon for my ignorance, what RT stands for?
I think he means "renormalization theory" or something like that
[EDIT: correction, I see from DocN next post that he may have meant "relativity theory"]
Anonym, I was interested by what you said here:
I agree that classical Einstein GR with a positive cosmological constant Lambda can have a bounce that begins the expansion phase. It does not absolutely need to have a cosmological singularity there. But I am not sure that I understand what you are reporting from Zeldovich.
I was glad to hear that you were attending seminars at the Steklov. This is to be congratulated as a kind of good fortune. Very famous institute. I hope your present location is also stimulating and has plenty of ideas.
doestn't relativity theory "collapse" at the singularity just like all physics laws?
What is it that you mean exactly by "collapse", and how do all the laws of physics "collapse" at the singularity?
a singularity is defined in the context of some particular theory---as a place where that particular theory breaks down (i.e. produces meaningless results)----so a singularity, or breakdown, in the theory helps define the limits of applicability of the theory.
A breakdown in Gen Rel would not, AFAIK, imply a breakdown in actual physical reality (however one defines that :-) ) or a necessary breakdown in other physical laws.
One way to say this is "singularities do not exist in nature, as far as we know, they are glitches in theories".
I think you may very well agree with what I just said. If you don't please offer us some physical evidence of the existence of the big bang singularity, besides just the fact that one theory, Gen Rel, breaks down there.
Assuming you DO agree with what I just said, let me try to answer the question you asked, that was quoted here.
"Doesn't Gen Rel break down at the cosmological singularity?"
Yes, by definition. The cosmological singularity is defined using Gen Rel, as a place where Gen Rel breaks down. So yes.
"...just like all other physical laws."
How do we know other physical laws break down at the beginning of expansion? Other theories constructed to replace Gen Rel do NOT predict infinite pressure, curvature, density, temperature. I don't know of any empirical evidence yet to say who is right. I would assume that much of physical law would have to be CORRECTED to be applicable at very high (Planck) temperature and density. Perhaps one would need radically new law or perhaps extensive quantum corrections. I simply don't know. But I have no scientific reason to suppose that ALL physical law simply "collapses" and ceases to apply.
Marcus:” I think he means "renormalization theory" or something like that
[EDIT: correction, I see from DocN next post that he may have meant "relativity theory"]”
“I agree that classical Einstein GR with a positive cosmological constant Lambda”
“everything that has been observed about BH so far is simply consistent with classic Gen Rel and has nothing to do with QG”
Let define what we are discussing. I suggest:
1.classic Einstein GR means without cosmological term;
2.GR means “relativity theory”;
3.nothing to do with QG means "renormalization theory" is not relevant.
I am outsider here. I jumped into discussion since juan_rod originally posted his thread in Quantum Physics. I was sure that you laughing in me (and I deserve it).I was ready to quit. However, perhaps, I misinterpret you.
Now I guess that DocN refered to Ch.12-14 of the later edition (6) of L.D. Landau, E.M. Lifshtz “Field Theory” which I never read untill today. It turns out that E.M.Lifshtz desided to improve L.D.Landau. However, Y. Zeldovich et al are discussed there in details. I refer to seminar since I hadn’t reference in hand ( by the way, this is the only seminar at Steklov I was attending. Occasionly I jumped to Moskow and was invited to listen “as a kind of good fortune”).
I interpret the negative answer of Y.Zeldovich as a statement that BH may be “gauged” away from GR in contrast with your statement.
Why I am here I will explain in the next post.
DocN:” doestn't relativity theory "collapse" at the singularity just like all physics laws?”
And what are substitutions? Hollywood movies?
I guess that it is the collapse of wave packet speaking (transition from Quantum world to Classical world: E. Schrödinger Cat). BH out, WH remain similarly as W.Ritz in the classical electrodynamics.
juan_rod:” My original question consisted of a general and or limited understanding of Quantum physics and the curvature of space-time. now you have introduced electrodynamics, how is this relevant to the properties of a BH?”
You received the identical answer to your original question from Marcus and me.But nobody know the ultimate truth. Let me formulate our answer in my own words:
The classical A. Einstein local field theory of gravitational interactions is not complete ( It can’t be wrong, it based on universally valid and firmly established experimental result that the inertial mass is identical to the gravitation mass. It has enormous predictive power, it was verified and confirmed by all available experiments. In addition, it is most beautiful theory ever formulated by human mind). However, our answer was: the Cartan’s torsion should be added (see Marcus in the “Einstein was wrong, and should be Cartanized!” session and F.W. Hehl et al, Rev. Mod. Phys., 48, 393 (1976) for example). They wrote:”Not least among this evidence is the demonstration that the U(4) theory arises as a local gauge theory for the Poincare group in space-time”. That I also know with certainty from completely different consideration (the structure of the tensor products in QM). Compare with A. Einstein (1915), today we have experimental evidence that in addition to the long range interactions transparent in the Classical world, two short range interactions are hidden classically and transparent in the Quantum world: weak and strong. All four are called the fundamental interactions. It is generally accepted that no other fundamental interactions exist. All fundamental interactions have the same origin: presence of phases in the QM description of system states. It allows to formulate a principal postulate of the physics: Principle of Local Gauge Invariance (E. Schrödinger, H. Weyl, Y. Aharonov, D. Bohm and ultimately C.N. Yang and R.L. Mills; for review see L. O’Raifeartaigh “ The Daving of Gauge Theory”, Prinston Univ. Press (1997). Using that postulate the phenomenological U(2) theory of electroweak interactions was formulated ( S. Weinberg et al). It has unquestionable experimental confirmation. In addition, the identical approach allows to formulate the preliminary version of the strong interactions (QCD). It also has substantial experimental support.
All that I consider as elements of the relativistic quantum field theory. The consistent formulation of that theory is still open problem. I do not believe that the formulation of QG may be obtained before, however, every attempt is legitimate. This is the way the physical knowledge is acquired.
For the described reasons I consider our debate about BH very interesting but at present status of the theory groundless. I have no required background in gravitation (I did not work in that area of scientific research, only read sporadically experimental and theoretical papers). In past I was deeply impressed by Y. Zeldovich presentation, he demonstrated time oscillations in classical world which I associate with the quantum behaviour. For all these reasons I did not accept Marcus statement “everything that has been observed about BH so far is simply consistent with classic Gen Rel”. But frankly, I have no idea. For sure, the complete classical as well as quantum gravitation theory must be in compliance with all physical knowledge obtained during last 450 years and not in contradiction with it.
If what I said still seems to you complicated, next time try to ask more simple questions.
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