The WLC/SC "Something From Nothing" Cosmology Thread

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_Philo Sofee
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Re: The WLC/SC "Something From Nothing" Cosmology Thread

Post by _Philo Sofee »

I'm getting Rovelli's book for Christmas DrW! Thanks for recommending it!
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_Physics Guy
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Re: The WLC/SC "Something From Nothing" Cosmology Thread

Post by _Physics Guy »

That diagram is a little weird.

"Covariant" has two meanings. One is narrowly technical in a way that isn't very important: tensor fields can be either covariant, or contravariant, or mixtures of both. If you're familiar with the "chain rule" of calculus then the difference between covariance (in this sense) and contravariance is easy to state; otherwise it's pretty meaningless. In neither case is it anything big or deep. Just two different ways of transforming, and they can be mapped onto each other by contraction with the metric tensor.

The other meaning of "covariant" is a substantial idea.

In relativity, a quantity is invariant if it does not change at all when the reference frame changes. An equation is covariant if it equates two things which both change when the reference frame changes, but which both change in just the same way. The equation itself thus remains valid in every frame, and in the same form. That's covariance, and it is a basic principle of physics now that all fundamental laws of nature should be covariant equations. Once you think about it, the principle is not so much deep as obvious.

So "covariant quantum field theory" is an important concept: the theory is covariant in the sense that its field equations are covariant equations. But "covariant quantum fields" are not important concepts. Fields (as opposed to equations) can only be covariant in the first sense I mentioned, and every covariant field can be mapped onto a contravariant one by contraction with the metric tensor. So insisting on covariant fields, as opposed to contravariant ones, would merely be a quirky notational preference: literally, a preference for writing subscripts rather than superscripts.

So where Rovelli's diagram shows that Einstein's 1915 contribution was to unite "spacetime" and "fields" into "covariant fields", that's a bizarre use of language that makes it look as though Rovelli's understanding has reached a limit. Einstein introduced a new way for equations to be covariant, by redefining the way in which things should change when the reference frame changes. He didn't invent the principle of covariance. We might credit him with launching (Einstein-ian-ly) covariant field theory, though this is not obviously fair because Einstein's whole line of thinking on this point began from the fact that Maxwell's equations were already fully covariant. Einstein's contribution was uniquely enormous, but saying that he introduced "covariant fields" is not the right way to say anything true.

Quantum field theory is simply the quantum mechanics of fields, like the electric and magnetic fields. It is true that quantum field theory unifies particles and fields: it shows how to define a field operator for every kind of particle, and how to identify particles with quantized excitations of fields. So that part of Rovelli's diagram is okay. Further down, though, it gets weird again.

Covariant quantum field theory has been used extensively since it was developed, for the electromagnetic field, by P.A.M. Dirac in the 1930's. It is not something which will only come with quantum gravity. It's an awesome and enormous subject and it has already been here for decades. No sensible theory of quantum gravity, however, is yet understood. All significant attempts at such a theory have begun by trying, in one way or another, to go beyond quantum field theory. So Rovelli's final diagram line, about quantum gravity introducing "covariant quantum fields", still doesn't make sense even if we generously interpret "covariant quantum fields" as meaning "covariant theory of quantum fields".

I don't know how much good there may be in the rest of Rovelli's book—and I'm afraid I'm not going to read it. Judging from that diagram, though, I'd say that he's only going to be reliable up to a point. Past that point, he may start to babble.

Frankly, I don't think there are any books about quantum gravity that are really worth a lay person reading. The first requirement for a theory to make sense to a lay person is that it makes sense at all. No quantum gravity theories currently do. None is ready for prime time yet, or even close. I'd suggest waiting till you hear on the news about the Nobel prize for quantum gravity before buying anyone's book on the subject. If you really want to read startling speculations asserted with problems glossed over, try some theology. I've heard there's yummy green Jello with that.

Relativistic quantum field theory, though, is much better understood. Feynman's little book "QED" is probably a great place to start.
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Re: The WLC/SC "Something From Nothing" Cosmology Thread

Post by _subgenius »

Fence Sitter wrote:
Okay, we can't explain how gravity works perfectly, so what? It isn't evidence that ANY GOD EXIST.

But, this also does not eliminate the possibility for ANY GOD EXIST.
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