Which are the Higgs implications for GR?

[Tubbythin]

Yep. That's why one of the discovery searches was "higgs to gamma gamma"---higgs decaying to two photons---which is made possible by a virtual-particle intermediary which is both massive (so it couples to higgs) and charged (so it couples to photons).

It must be two (or more) virtual particles then to conserve charge?

 

[Wowbagger]

Because if those particles have mass, then according to the SM they should interact with the Higgs field.

What I wrote was sorta implied by some of the "explanations" I was reading. Clearly some of them aren't very good ones.

 

[alexi_drago]

Don't know if this question makes any sense but does the effect of the higgs field work with or against gravity? Is acceleration due to force of gravity opposed by the higgs field or is the force of gravity exerted through interactions with the higgs field?

 

[Fredrik]

What are the Higgs implications for GR?

I'd say "none", since GR is a classical theory and the Higgs particle is part of a quantum theory. The only way that new information about quantum phenomena can have an impact on GR research is by suggesting what sort of solutions of Einstein's equation we should consider interesting. The Higgs particle doesn't even do that. It's only needed to resolve some difficulties in a quantum theory of interacting particles.

The SM is fully compatible with GR, which is a classical theory of gravity. The problem comes when one tries to quantize GR - but that's a problem pretty much intrinsic to gravity, and one we don't know how to solve even without the SM.

I think this is a bit inaccurate. You're probably thinking of it this way because it's so obvious to you that a classical theory can't be in complete agreement with a quantum theory that it's not even worth calling it an "incompatibility".

I agree of course that the significant incompatibility is that it's crazy hard to define a quantum theory of gravity.

 

[Vorpal]

You could have a have quantized fields of the standard model on a classical spacetime background. So there is no incompatibility in the sense of logical inconsistency, even though there may be an incompatibility in some looser sense of physical principles.

 

[Cuddles]

1. Why is it that photons do not interact with the Higgs field? That is, what is the mechanism which causes other particles to interact with the Higgs, thus creating mass, whereas photons lack this mechanism?

See my post here. The Higgs mechanism is a fundamental part of symmetry breaking of the electroweak force. Above the critical energy, all electroweak gauge particles are massless. Below the critical energy, the standard model without the Higgs mechanism would predict that they remain massless. With the Higgs mechanism added you get extra symmetry breaking that results in a variety of gauge bosons with different masses - photons, W^+/- and Z. There isn't a mechanism added that the photon lacks, the mechanism added is a fundamental part of what makes a photon a photon.

2. How does gravity fit into the Higgs? If the Higgs is responsible for giving particles mass, and gravitational forces act upon mass, is there some kind of tie in or connection between the Higgs field and gravity fields? (I'm particularly interested in this one)

No. The standard model still says nothing whatsoever about gravity when the Higgs mechanism is added to it.

3. What about dark energy? The Higgs field apparently penetrates all of the universe, because we observe all particles in the universe, no matter their location, to have mass (say, via gravitational interaction). And apparently dark energy, whatever it is, also permeates all of the universe; is there a connection between the two?

No. All fields penetrate all of the universe, there's nothing special about the Higgs field there. Dark energy is one area the standard model struggles with, and the Higgs doesn't help it there. Or at least, it hasn't so far.

4. Can the discovery of the Higgs help in the search for dark matter particles? Since we know dark matter interacts gravitationally, then it must have mass, and if it must have mass there should be some kind of relationship to the Higgs field.

The standard model completely fails where dark matter is concerned. It just doesn't predict it exists at all.

Ultimately the answer to all these questions is likely the same thing - the Higgs mechanism does not only exist as part of the standard model. The SM predicts a very specific Higgs particle, and it's entirely possible, likely even, that the one we've seen is not, in fact, the particle predicted by the SM. It's therefore hopeful that whatever theory the new particle does fit will also do better at explaining all these other points as well. Especially since they're a large part of the reason all the alternative theories exist in the first place.

 

[sol invictus]

So, is the main trick of the Higgs the symmetry breaking thing that I read about but find hard to understand?

Right.

The SM is fully compatible with GR, which is a classical theory of gravity. The problem comes when one tries to quantize GR - but that's a problem pretty much intrinsic to gravity, and one we don't know how to solve even without the SM.

I think this is a bit inaccurate. You're probably thinking of it this way because it's so obvious to you that a classical theory can't be in complete agreement with a quantum theory that it's not even worth calling it an "incompatibility".

I agree of course that the significant incompatibility is that it's crazy hard to define a quantum theory of gravity.

As Vorpal says, there's absolutely no problem coupling quantum field theory to classical general relativity in the sense of putting a QFT on a (fixed) curved background. That's a completely standard thing to do, and it's as well defined as QFT on flat spacetime, if not more so in some cases.

If there's a problem, it comes from the back-reaction of quantum fluctuations on the geometry. The divergent vacuum energy of QFT is the first of such problems (that's the cosmological constant problem), but it's trivial to fix by adding a counterterm (a bare cosmological constant that cancels the divergence). However other divergences may not be so easily fixed. There's a difference of opinion on that among experts.

 

[Fredrik]

You could have a have quantized fields of the standard model on a classical spacetime background. So there is no incompatibility in the sense of logical inconsistency, even though there may be an incompatibility in some looser sense of physical principles.

As Vorpal says, there's absolutely no problem coupling quantum field theory to classical general relativity in the sense of putting a QFT on a (fixed) curved background. That's a completely standard thing to do, and it's as well defined as QFT on flat spacetime, if not more so in some cases.

If there's a problem, it comes from the back-reaction of quantum fluctuations on the geometry. The divergent vacuum energy of QFT is the first of such problems (that's the cosmological constant problem), but it's trivial to fix by adding a counterterm (a bare cosmological constant that cancels the divergence). However other divergences may not be so easily fixed. There's a difference of opinion on that among experts.

I don't have any objections to what you're saying here (and I'm not sure why you think I would). We just seem to have different ideas about what it would mean for a theory of physics to be "fully compatible" with another. I'm not sure what I would want that to mean, but I definitely wouldn't say that a theory that says that matter behaves "quantum mechanically" is fully compatible with a theory that says that matter behaves "classically".

 

[sol invictus]

I don't have any objections to what you're saying here (and I'm not sure why you think I would). We just seem to have different ideas about what it would mean for a theory of physics to be "fully compatible" with another. I'm not sure what I would want that to mean, but I definitely wouldn't say that a theory that says that matter behaves "quantum mechanically" is fully compatible with a theory that says that matter behaves "classically".

But that's just it - GR doesn't say anything at all about how matter behaves, apart from the fact that it says that gravity acts on it (and it says that gravity acts on all forms of energy in a completely universal way, regardless of the nature or composition of that energy). So at least a priori there's nothing in consistent about quantum matter coupled to classical GR.

Remember - classical GR is a theory of geometry, while the SM is a theory of particles and field that exist on some (possible curved or dynamical) geometry.

 

[Roboramma]

Remember - classical GR is a theory of geometry, while the SM is a theory of particles and field that exist on some (possible curved or dynamical) geometry.

I thought the main, or at least one, issue was that QM doesn't work on an infinitely divisible continuum as it leads to infinities, but GR treats space as though it were an infinitely divisible continuum.

I don't know anything about this, however.

 

[sol invictus]

I thought the main, or at least one, issue was that QM doesn't work on an infinitely divisible continuum as it leads to infinities, but GR treats space as though it were an infinitely divisible continuum.

I don't know anything about this, however.

QM in general, and quantum field theory in particular, works just fine on an infinitely divisible continuum. That's not a problem.

The problem comes when you try to quantize the spacetime metric - when you try to make the geometry quantum. That leads to divergences that no one knows how to handle properly.

 

[Fredrik]

But that's just it - GR doesn't say anything at all about how matter behaves, apart from the fact that it says that gravity acts on it (and it says that gravity acts on all forms of energy in a completely universal way, regardless of the nature or composition of that energy).

Let's talk about SR for a minute, to keep things simpler. Minkowski spacetime defines a framework in which we can define both classical and quantum theories of matter. I guess some people would refer to that framework as "SR", while others would reserve that term for the set of theories of classical point particles and fields on Minkowski spacetime. If "SR" refers to the framework, then SR doesn't say anything about how matter behaves. If it refers to the set of all classical theories in that framework, then it does.

Similarly, each metric obtained by solving Einstein's equation defines a framework in which both classical and quantum theories of matter can be defined. I guess this is why you're saying that GR doesn't say anything about how matter behaves.

My problem with this is that a solution to Einstein's equation isn't a metric g, but a pair (g,T), where T is a stress-energy tensor of classical matter. So there is always classical matter involved when we're doing something that I can consider "GR".

 

[Vorpal]

STR has never been about the movement of classical point particles except as an incidental implication when applied to them: even in its genesis in 1905, it was explicitly a statement about laws of physics in general. Technically so is GTR.

But for the thrust of your concern, I'm don't know. At least, it's not obvious that it's self-inconsistent to just proceed perturbatively around a classical solution. Regularivation be willing, you might make [latex]$\langle T_{\mu\nu}\rangle$[/latex] or whatever, though I'm sure I don't understand even a fraction of the difficulties in applying this.

 

[sol invictus]

My problem with this is that a solution to Einstein's equation isn't a metric g, but a pair (g,T), where T is a stress-energy tensor of classical matter. So there is always classical matter involved when we're doing something that I can consider "GR".

It's a pair (g, T), where T is a stress-tensor. No one said T has to be a classical stress-tensor. For instance as Vorpal suggests, you can try to use the vacuum expectation value of the quantum stress tensor. That approach is problematic for a variety of reasons; nevertheless, some experts (myself not included) believe it to be consistent.

What can certainly be consistent is to use a fixed or predetermined metric g that does not depend on dynamical T, and then quantize the fields. That can still be a solution to Einstein's equations in a certain limit, and regardless it is quantum field theory in curved spacetime.