Exploring the Relationship between QFT, GR, and Backreaction in Curved Spacetime

[star apple]

I know we do not have a version of QFT (?) in which we can dynamically solve for the QFT and the background spacetime at once. What we can do is where if we come up with a QFT whose expectation value of the stress-energy tensor doesn't match the fixed background spacetime geometry via the Einstein Field Equation, we go back and try again taking or taking *back reaction* into account.

The question I’d like to ask is. Is this normal due to simply incomplete QFT tool.. or is it really necessary to quantize spacetime--or at least to build a quantum theory of something whose classical limit looks like spacetime?

In our daily life. We think Schroedinger Equation is enough in our biochemistry and we walk visualizing Galilean space. Sometimes we may think of QFT a bit as we navigate in minkowski spacetime. But I want to get used to think in terms of QFT in curved spacetime as this is the more complete mode. Therefore I’d like to know if the backreaction thing described above can exist by its own (meaning can be complete itself) without quantizing spacetime or create something where the classical limit looks like spacetime.

 

[star apple]

In other words, if something is approximate.. does it always mean there is another more complete theory lurking around.. like in our QFT using perturbation approximation.. does it mean it's a sign of incomplete theory? Isn't there anything in physics in which approximation is the final thing and nothing more to it? In regards QFT and General Relativity.. I guess the incompatibility is more than having to take backreaction into account.. or more about the infinities.. how is this related to the problem of backreaction.. are they separate problems?

 

[star apple]

Let me rephrase my question so it makes more sense.

Bee said that http://backreaction.blogspot.com/2017/10/space-may-not-be-as-immaterial-as-we.html

"Physicists have gathered evidence that space-time can behave like a fluid. Mathematical evidence, that is, but still evidence. If this relation isn’t a coincidence, then space-time – like a fluid – may have substructure...
<bypassing several paragraphs later>
"If space-time is made of smaller things, this could solve a major problem: How to describe the quantum behavior of space time. Unlike all the other interactions we know of, gravity is a non-quantum theory. This means it doesn’t fit together with the quantum theories that physicists use for elementary particles. All attempts to quantize gravity so-far have either failed or remained unconfirmed speculations. That space itself isn’t fundamental but made of other things is one way to approach the problem."

Of course spacetime being not fundamental makes more sense that its being fundamental. It's like a stone age man asking if a pixel in a computer screen is infinitely small.

But my question is. If spacetime was not fundamental and made up of smaller things. Would the back reaction approximation used by QFT in curved spacetime still valid?

(A Yes or No answer is enough.. lol.. thanks)

 

[bapowell]

Small nit, but this statement makes no sense: "Mathematical evidence, that is, but still evidence." I can come up with mathematical "evidence" for anything. Scientific evidence is a whole other matter.

 

[star apple]

Small nit, but this statement makes no sense: "Mathematical evidence, that is, but still evidence." I can come up with mathematical "evidence" for anything. Scientific evidence is a whole other matter.

Thanks for pointing that out. Maybe she meant mathematicaly consistent.