# B Covariant Quantum Fields

1. Feb 10, 2017

### mieral

I just read Carlo Rovelli new book "Reality is Not What It Seems: The Journey to Quantum Gravity" in one sitting. I'd like to know about the following:

"Fields that live on themselves, without the need of a spacetime to serve as a substratum, as a support, and which are capable by themselves of generating spacetime, are called "covariant quantum fields." The substance of which the world is made has been radically simplified in recent years. The world, particles, light, energy, space, and time - all of this is nothing but the manifestation of a single type of entity: covariant quantum fields."

Are all quantum gravity theories based on covariant quantum fields where the fields don't live on spacetime but created space and time?

2. Feb 10, 2017

### julian

In classical GR, the resolution of Einstein's hole argument implies that physical entities are located with respect to one another only and not with respect to space-time. In GR the "space-time" manifold is a mathematical construct devoid of physical meaning. Quoting Rovelli's book "Quantum Gravity", in particular the part on classical general relativity: "The world is made up of fields. Physically, these do not live on spacetime. They live, so to say, on one another. No more fields on spacetime, just fields on fields."

Rovelli would argue the quantum theory should not be based on notions devoid of physical meaning in the classical theory.

Last edited: Feb 10, 2017
3. Feb 10, 2017

### julian

I wrote up Einstein's hole argument a while back. In fact I was doing a search for it earlier on today but the thread goes back so many years it doesn't seem to exist anymore. I'll write it up again tomorrow. It doesn't require an extensive knowleadge of GR, but it would be good if you understand how to combine the metric tensor function in space-time $x-$coordinates, $g_{\mu \nu} (x)$, together with an infintesimal coordinate separation $dx^\mu$ in order to obtain the proper time $ds$ interval:

$ds^2 = \sum_{\mu , \nu} g_{\mu \nu} (x) dx^\mu dx^\nu$

which describes a particular space-time geometry.

Last edited: Feb 10, 2017
4. Feb 10, 2017

### MathematicalPhysicist

I think Rovelli is confused between what is reality and what does the maths represent?

Fields are defined as real or complex (I think you can extend it to hypercomplex, quarternions, etc; but these aren't necessarily mathematical number fields) functions from some mathematical space to another; in the context of calculus 3 if you will, we have real fields as functions from $\mathbb{R}^n$ to $\mathbb{R}^m$.

So if we take Max Tegmark's metaphysical stance, then fields are still defined on some "space", just it's not called spacetime (which is a 4-dim Pseudo Euclidean space), and not the confusing idea of "Fields living on themselves", whatever that means...

5. Feb 12, 2017

### haushofer

I'm also curious what exactly is meand by such fields.

6. Feb 12, 2017

### MathematicalPhysicist

Never shall I read pop sci books, I haven't read a single pop sci book since I entered university (I tried reading Barrow's book on "nothing", but got distracted by my demanding studies.

If someone really wants to know how things are done in science then there is no other way but reading the technical literature; otherwise it's just reading mambo jambo for all my account.

7. Feb 12, 2017

### mieral

But if as Max Tegmark wrote in the Mathematical Universe which I also happened to read. What if the software that created this interactive simulation was written or used the language of General Relativity and Quantum Mechanics as well as Loop Quantum Gravity. Then classicality and conventional space is all illusion. What is wrong with thinking in terms of GR, QM and LQG when trying to think of our world.

In this case. The map is really the territory.. because it is all map in the software or programme.. there is no real world or physical objects are also just effects or illusions.. so how can you justify to retain the word "space"?

8. Feb 13, 2017

No.