# Does GR have Background?

1. Feb 14, 2012

### waterfall

In the Physics World article "Loop Quantum Gravity" by Carlo Rovelli, he mentioned that:

"General relativity is not about physics on curved spacetimes, asymptotic space–times, or connections between theories defined over different backgrounds. It is the discovery that
there is no background; no space–time.The challenge for the physicists of the 21st century is to complete the scientific revolution that was started by general relativity and quantum theory.
For this we must understand quantum field theory in the absence of a background space–time. Loop quantum is the most resolute attempt to address this problem."

I thought General Relativity had Background and mass/stress/energy just curve the spacetime background. But Rovelli mentioned above there was no background, no space-time. What is he talking about?

2. Feb 14, 2012

### elfmotat

The Minkowski metric isn't a background, it's just a particular solution of the field equations. It's no more fundamental than any other metric in GR.

Last edited: Feb 14, 2012
3. Feb 14, 2012

### Bill_K

Rovelli is talking about his Loop Quantum Gravity ideas, clearly not standard General Relativity which has a curved spacetime background as you describe it.

4. Feb 14, 2012

### waterfall

This is werid, Even if he is working on LQG, he should still refer to standard usage. For example. can he refer to an apple as a banana, so how could he refer to GR as having no background. Is he trying to redefine it.

5. Feb 14, 2012

### tom.stoer

It's rather simple.

A picture where you have 'ripples' of spacetime on top of a given backround is misleading in GR; the idea is familiar from weak field gravitational waves, but in general it does not make much sense; how do you get the Schwarzschild solution from a 'deformed' Minkowski metric? The picture becomes seriously wrong when you try to define a canonical formalism quantum gravity.

In classical GR the picture of a backgrund spacetime is misleading and useless, but strictly speaking not wrong.

6. Feb 14, 2012

### waterfall

So you agreed with Rovelli that General Relativity "is the discovery that there is no background; no space–time." Who else agree with these two men. So it means there is no space-time. And if there is no space-time, there is no General Relativity either.

7. Feb 14, 2012

### elfmotat

I think you're confusing "no background spacetime" with "no spacetime," though (judging by the above excerpt) you're not entirely to blame.

An example of a background spacetime would be the weak field approximation to the metric:

$$g_{\mu \nu }=\eta_{\mu \nu }+h_{\mu \nu }$$

In this case, the Minkowski metric ($\eta_{\mu \nu }$, flat spacetime) is the background.

8. Feb 15, 2012

### harrylin

Good question; that remark is in direct conflict with Einstein's explanations. GR is a field theory with space-time description and in the absence of a background you have no field either. No background -> no field -> no GR.

9. Feb 15, 2012

### Naty1

Looks to me like post #2 and likely #5 are correct.....at least I THINK I understand their meaning.....but the terminology describing 'background' and utilized in posts here IS confusing because it apparently has different meanings to different people.

I find this utterly confusing: I think he means GR is "not about physics with a fixed background of space time".....or maybe "GR is about physics IN curved spacetime"....not taking place against a previously selected background. Hence post #2.

GR is background independent unlike for example string theory, where extra dimensions must be manually CHOSEN. These are inputs to the formalism, not derived from the formalism as
in GR. This is fundamentally why we lack 'unification'.

So in post #5:
IS MISLEADING because no background is GIVEN....none is selected....again in the context
of post #2.

Here is how Lee Smolin describes the situation in THE TROUBLE WITH PHYSICS,
in the chapter, 'The World as Geometry':

Smolin goes on to describe how Kaluza-Klein extra dimension [and later string theory]:

[I still wonder why is this tiny dimensional change can 'stop time' why nobody reversed
the process to initiate a big bang....to begin time...that kind of miniscule perturbation seems more aligned with vacuum fluctuations that 'everything coming from nothing'...]

Last edited: Feb 15, 2012
10. Feb 15, 2012

### Naty1

Here are some further insights...again Lee Smolin from THE TROUBLE WITH PHYSICS ,, 2007,

11. Feb 16, 2012

### Passionflower

What I think Rovelli is trying to say is that:

You can have a background with test objects in GR, but once we do physics with objects that play an integral role in 'shaping' spacetime there is no longer a physics on a background but the physics and the background are the same thing.

12. Feb 17, 2012

### waterfall

Even Lee Smolin has same definition as Rovelli as when Smolin said in "Trouble With Physics":

"To say that the laws of physics are background independent means that the geometry of space is not fixed but evolves. Space and time emerge from the laws rather than providing an arena in which things happen."

Isn't it that in General Relativity space and time were simply curved by the laws or mass/stress/energy? What is Smolin talking about that space and time emerge from the laws?

Are these Loop Quantum Gravity Theorists trying to redefine classical GR? But some of you support them. What is the consensus about this?

13. Feb 17, 2012

### atyy

Classical GR is background independent. This is a traditional way of saying that GR has no prior geometry. In special relativity there is a prior geometry of flat spacetime. It is prior geometry because no matter how much matter you put on it, the spacetime is still flat. In GR, you cannot specify your geometry first then put matter as you wish, because matter curves spacetime. Nor can you put matter first, because there is no meaning to "where" without spacetime. So you must put matter and geometry on at the same time, so the geometry is not prior to the matter. This is the sense in which GR has no prior geometry.

However, if one restricts to spacetimes which can be covered by harmonic coordinates, then GR does have an alternative formulation as a spin 2 field on flat prior background. Rovelli and Smolin are claiming that the "no prior geometry" view is better for generalization to quantum gravity than the spin 2 field view. This seems a matter of taste, unless there is experimental evidence showing that spacetime in our universe cannot be covered by harmonic coordinates.

Last edited: Feb 17, 2012
14. Feb 17, 2012

### waterfall

What' harmonic coordinates? Is our GR not covered by harmonic coordinates? And when you mentioned "GR does have an alternative formulation as a spin 2 field on flat prior background" are you talking literally where gravity is a spin 2 field meaning gravity is field based and not really geometry? But there is still the flat geometry thing which signifies SR. Why not just use the original Euclidean Newtonian spacetime and add a field not just spin 2 but includes SR field as well?

In String Theory. The 6 dimensional "Calabi-Yau spaces" is the background of the Strings, but somehow the Strings themselves recover classical GR. Why did the String Theorists accept this formulation since the idea of strings in Calabi-Yau spaces are not really a background independent idea? Why did they ignore the basic idea of GR of BI?

I'm rereading Smolin "Trouble With Physics" and trying to understand the contexts from all point of views.

15. Feb 17, 2012

### atyy

In GR you can use any coordinate system you want. Harmonic coordinates are a particular choice of coordinates.

16. Feb 17, 2012

### waterfall

So our world can be described completely by this particular choice of coordinates called Harmonic coordinates hence making possible the spin 2 field or even combo spin 2, SR field on Euclidean physical space?

17. Feb 17, 2012

### waterfall

Here you are talking as if GR were already 100% proven. It's just a model and one can discard it and replace with another one in the future. Unless you are saying that this model is definite just like how Triangle obeys Pythagorean Theorem in Euclidean? But in Euclidean, we are not talking about time intermixing with space. Also note the time in SR and GR is just imaginary. So sometimes when we think of GR a lot. We assume this is automatically how the world works. My point is that. In the end, gravity can still be field based and not just geometry with geometry only as a result of symmetry of certain mathematical feature. This means a field based gravity can have more and richer degrees of freedom perhaps like anti-gravity which can't be allowed in GR, any objections?

Does this harmonic coordinates have blackholes and other dynamics in it or allowed? Because it seems you are saying that it contraints the field based approach of gravity. But this is not a priori or the argument totally sound.

18. Feb 17, 2012

### Passionflower

Who says so?

It is unusual if it does not but in GR matter does not necessarily have to be attractive.

19. Feb 17, 2012

### waterfall

How do you model negative curvature in GR such that an object with gravity shielding can just float in air without propulsion?

20. Feb 18, 2012

### atyy

I'm unsure of this point, but I think that harmonic coordinates include the event horizon of a black hole, as well as the expanding universe. Some references that discuss this are:
Cook, Initial Data for Numerical Relativity, section 3.3.2
Weinberg, Gravitation and Cosmology, section 8.1 - 8.3