Energy defined in LQG but not in GR?

[marcus]

selfAdjoint has given a link to a really enlightening post by Steve Carlip
Here is the Carlip post
https://www.physicsforums.com/showthread.php?p=227804&posted=1#post227804

Carlip is tops. A major reliable authority in General Relativity and Quantum Gravity. Good idea to listen to what he says here.
He says that total energy is not defined in Gen Rel and he explains why
and he points to an open problem----a possible research area---about defining energy successfully if you "delocalize" things a bit. That comes at the end of his post.

It looks to me as if LQG is gradually solving some long-standing problems with Gen Rel and this is getting more and more interesting:
first getting rid of the bigbang singularity
then this year getting rid of black hole singularity
maybe soon getting rid of this problem of defining energy

the problem defining energy comes from the existence of "behavior at a point" in the theory----but this is analogous to what caused the bigbang singularity! In the classical theory the whole universe could come from an ideal mathematical point and so there seemed inevitably to be an instant when the density was infinite (the theory broke down). But in LQG version of big bang there is no infinite density---perhaps there was enough quantum uncertainty of location and so on to smooth it out. Could it be that a kind of "UV cutoff" did it, in some sense? Well, read Bojowald paper and see for yourself why the singularity goes away

Now I want to read Carlip post carefully and see WHY one cannot define total energy in Gen Rel. Then I will be able to guess how this obstacle is overcome when Gen Rel is quantized, say by LQG.

The key thing is very simple (partly because Carlip thinks so clearly, he's good!) there cannot be a total energy defined because it would have to include the energy of the gravitational field!

But at any given point (see the classical idea) one can always transform the coordinates so as to make the gravitational field be zero!

If the energy is invariant at every point then it can be nothing else than zero!

so there is no invariant definition of energy.

And in Gen Rel only things only have meaning if they are invariant under change of coordinates.

So you can only define energy if you cheat---you sneak in some preferred system of coordinates. Actually this is very nice to do and is done all the time in Cosmology. One reason Cosmology is such a wonderful subject THEY have a preferred time coordinate built into the FRW metric and the Friedmann equations model (Selah! as sA once declared)

But suppose we refrain from cheating and we refuse to somehow bring in enchanted preferred coordinates. Still the only problem is this zeroing out of the field at some ideal point!
what does it mean that there is a Planck length "UV cutoff"?
Must confess that I am befogged about this. Seems like energy should be definable when the theory is quantized.

Anyway, suppose we (I and whoever wants) look carefully at Carlip post.
Sounds like my wife is mashing an avocado in the kitchen, meaning Guacamole in another minute. have to get back to this

 

[AndyW]

later.

Hello, fellow scientist! Thank you for bringing this post by Steve Carlip to my attention. I have read through it and I agree with you that he is a reliable authority in the fields of General Relativity and Quantum Gravity. His explanation of why total energy cannot be defined in General Relativity is very clear and insightful.

As he pointed out, the main issue is the presence of behavior at a point in the theory. In classical General Relativity, the whole universe can be described by an ideal mathematical point, which leads to the problem of infinite density and the breakdown of the theory. This is similar to the problem of defining total energy, as the gravitational field cannot be excluded from the energy calculation and it can be made to be zero at any given point.

However, as you mentioned, Loop Quantum Gravity (LQG) may offer a solution to this problem. By quantizing General Relativity, LQG introduces a minimum length scale, known as the Planck length, which acts as a UV cutoff and prevents the infinite density and breakdown of the theory. This may also provide a way to define total energy in a consistent and invariant manner.

I am also intrigued by the potential connections between LQG and the recent advancements in solving long-standing problems in General Relativity, such as the big bang and black hole singularities. It seems that LQG is providing a more complete and coherent picture of the universe, and I look forward to reading more about it.

I will also take some time to carefully read through Carlip's post and try to understand the obstacles in defining energy in General Relativity further. Thank you for bringing this to my attention and I look forward to discussing this with you in the future. And enjoy your guacamole!