Charge conjugation in quantum gravity

[Joker93]

TL;DR Summary

What is charge conjugation in a theory that includes quantum gravity, if the "charge" associated with gravitational interactions is the mass?

The charge associated with gravitational interactions is the mass. In the Standard Model, charge conjugation is the "flippin" of all kinds of charges (electric, color, etc). So, if we were to, say, incorporate quantum gravity in a beyond the Standard Model theory, what would the full charge conjugation operation include? Would it also include flipping the mass' sign? If so, what would that mean if we assume that negative mass doesn't exist (we haven't measured such a thing yet)?

If that isn't the case, then what would you say is the most general definition of charge conjugation, assuming that we have a theory with more than one kinds of charge (such as electric+color)? This should, of course, be consistent with when we call a particle its own antiparticle; the most general definition I've found, a particle is its own antiparticle if after flipping all the charges, we get the same result.

 

[Vanadium 50]

Summary:: The charge associated with gravitational interactions is the mass.

Not in GR.

The rest of your message kinds of builds on this.

 

[Joker93]

Not in GR.

The rest of your message kinds of builds on this.

So what is charge in GR then?

 

[Vanadium 50]

The stress-energy tensor.

 

[Joker93]

The stress-energy tensor.

That makes so much sense (from GR) that I feel stupid. So, what is charge conjugation in this case then?

 

[Vanadium 50]

Why do you think "charge conjugation" has any meaning at all here? What about, I dunno, the First Germanic Sound Shift?

 

[ohwilleke]

That makes so much sense (from GR) that I feel stupid. So, what is charge conjugation in this case then?

More seriously, some quantum gravity theories are "chiral" (i.e. have parity dependent aspects), such as this one (which I picked more or less at random from a list of search results for published chiral quantum gravity papers).

This is so even though classical GR itself is not chiral and no observable scale gravitational phenomena are chiral.

Quantum gravity theorists explore chiral theories because you get equations and formulas that seem more likely to be viable to calculate with and to fit into a larger unified theory or larger scheme in some circumstances.

For example, some quantum gravity theorists have explored chiral theories of quantum gravity in pursuit of a unification of the weak force and quantum gravity through complementary SU(2) groups, such as Roger Penrose's work in formulating quantum gravity in terms of twistors and spinors, or in order to explore interfaces between quantum gravity and non-commutative geometry (which, non-obviously, overlaps with Penrose's work).

In chiral quantum gravity theories, a parity or helicity flip of a particle with mass or energy would be somewhat analogous to charge conjugation (maintaining CPT symmetry) which has never been observed to be violated in nature, since the charge in CPT symmetry is specifically electromagnetic charge and not a more generalized concept.

But, unlike the color charge and electromagnetic charge of the strong force and the electromagnetic force, respectively, in which anti-particles of particles with ordinary charge have corresponding anti-charges of the same magnitude but the opposite direction, the stress-energy tensor contributions of gravity do not have negative mass-energy counterparts in conventional GR or in most theoretical classical and quantum variations on GR.

In particular, antimatter in the form of anti-particles in the Standard Model do not have negative mass, nor are their kinetic energies any different from the kinetic energies of ordinary particles.

For example, the mass of a positron is the same as the mass of an electron.

There are theoretical variations of GR which allow for the possibility negative masses and negative energies, but they aren't popular and don't have much motivation from observation (the main motivation is as one possible way to explain for the phenomena most commonly attributed to the cosmological constant and/or cosmological inflation).

The reason for this difference between the strong force and electroweak forces on one hand, and gravity on the other, is basically because in GR, mass-energy always attracts other mass-energy sources, while the strong force and electromagnetic force can be attractive or repulsive. As Fermilab explains, this feature of gravity is also why, unlike the spin-1 carrier bosons of the electromagnetic force, the weak force, and the strong force, the hypothetical carrier boson of gravity in quantum gravity, the graviton, is a spin-2 carrier boson.

 

[Joker93]

Why do you think "charge conjugation" has any meaning at all here? What about, I dunno, the First Germanic Sound Shift?

I can't seem to tell if you're being sarcastic or just using good old fashioned humor!
In any case, me not knowing if charge conjugation has a meaning in GR might actually be the essence of my question at the end of the day. I do suspect -maybe naively- that there should be some analogue to it in GR (since it exists in every other field theory I've personally studied), so I do think that a properly explained answer would be more fruitful here.
Thanks.

 

[Demystifier]

If that isn't the case, then what would you say is the most general definition of charge conjugation

Loosely speaking, charge conjugation is the transformation of the field $\phi\to\phi^*$. The vector current such as $\phi^*(\partial_{\mu}\phi)-(\partial_{\mu}\phi^*)\phi$ changes sign under such a transformation, but in gravity we have a tensor "current" such as $(\partial_{\mu}\phi^*)(\partial_{\nu}\phi)$ which does not change sign.

 

[Vanadium 50]

You came into this thread insisting that charge conjugation coupled with gravity gave you some kind of negative mass. Then you were told that the source of GR isn't mass, but the stress-energy tensor. The whole basis of your question has had the rug pulled out from it.

It's kind of like "What is the melting point of blue?" "Blue isn't a material. It doesn't have a melting point." "But if it did, what would it be?"

 

[Joker93]

You came into this thread insisting that charge conjugation coupled with gravity gave you some kind of negative mass. Then you were told that the source of GR isn't mass, but the stress-energy tensor. The whole basis of your question has had the rug pulled out from it.

It's kind of like "What is the melting point of blue?" "Blue isn't a material. It doesn't have a melting point." "But if it did, what would it be?"

I didn't insist on anything. I just wrote what I thought was true and admitted to the fact that it might be a naive thought. But, ok, sure, what's your point then?
I don't see anything productive from this. The conversation has shifted to the meaning of charge conjugation in gravity, which is actually the essence of my question.
I'm thankful that you have given this thread your time by answering, but I don't appreciate your previous sarcasm and whatever this is.

 

[Joker93]

Loosely speaking, charge conjugation is the transformation of the field $\phi\to\phi^*$. The vector current such as $\phi^*(\partial_{\mu}\phi)-(\partial_{\mu}\phi^*)\phi$ changes sign under such a transformation, but in gravity we have a tensor "current" such as $(\partial_{\mu}\phi^*)(\partial_{\nu}\phi)$ which does not change sign.

I see. So, for a gravitational field, is the transformation the same?

 

[Demystifier]

So, for a gravitational field, is the transformation the same?

Yep.