Calculating Quark Gravity in Proton and Antiproton: Equations and Formula

[Rade]

I know it would be a small force, but what is the equation to calculate the gravity between the three quarks in the proton (uud), and then the antiproton ?

 

[jtbell]

I don't think it's possible to answer this question (yet), since we don't have a generally-accepted quantum theory of gravity, nor the experimental means to test such a prediction.

 

[selfAdjoint]

Even the quantum gravity theories we have, whether stringy or other, don't allow full bore standard model particles cat the phenomenal calculation level yet. So far anything like that is still pretty close to handwaving.

 

[Rade]

I don't think it's possible to answer this question (yet), since we don't have a generally-accepted quantum theory of gravity, nor the experimental means to test such a prediction.

Is this not then a good example of what Einstein was talking about--that QM theory is limited, since it cannot explain the most simple many-body (e.g., 3 quarks within a nucleon) gravity interaction ?

 

[selfAdjoint]

Is this not then a good example of what Einstein was talking about--that QM theory is limited, since it cannot explain the most simple many-body (e.g., 3 quarks within a nucleon) gravity interaction ?

No it's not. Einstein's objection to quantum theory ws at a much deeper level than mere contingency about gravitational interactions. Note that General Relativity can't answer this question either. The awkwardness that GR and QM aren't easily mated is an equal opportunity embarrasment.

 

[Physics Monkey]

Hi Rade,

I would just like to add something to the good responses so far.

With the assumption that the gravitational interaction remains unmodified down to 10^-15 meters, one can estimate the gravitational energy of, say, a proton. A simple estimate would be $$E_G \sim G \frac{M^2_p}{R_p},$$ where $$M_p$$ is the proton's mass, and $$R_p$$ is some measure of the proton's radius (~ 10^-15 meters). Plugging in the numbers you find that $$E_G \sim 10^{-30}$$ eV; a ridiculously tiny result. It is numbers like this that demonstrate the utter irrelevance of gravity for Standard Model physics.

Assuming, of course, that gravity remains unmodified down to scales of 10^-15 meters. The best experiments have only tested Newton's law at distances of the order of microns, so we're talking about a huge extrapolation. One might take the success of the Standard Model as strong circumstantial evidence that gravity is indeed unimportant at the scales under discussion. Nevertheless, there are many mysteries remaining and we never know what lies beyond. Many more recent theories, often involving extra dimensions, do predict that gravity should be modified at length scales relevant to present particle physics. There is also relativity to worry about, and I don't mean just the lack of a full theory of quantum gravity. These are just a very few of the possible problems this estimate could face.

Still, we shouldn't shortchange the theory too much. With our assumptions in place, naive as they may be, we can talk about the gravitational energy of quarks and we can predict that it is completely irrelevant.

 

[Rade]

... Still, we shouldn't shortchange the theory too much. With our assumptions in place, naive as they may be, we can talk about the gravitational energy of quarks and we can predict that it is completely irrelevant.

Yes, thank you for your response. How exciting if we do find that gravity has new properties at distances less than 10^-15 meters. Yet, should we not at least in theory (via QM) be able to derive the equations that I look for in the OP--I care not if the answer says the force is not significant, I look for the mathematics that appears to not exist (anywhere !). I find it fascinating that such a simple question as presented in OP stumps exact mathematical answer via theory of QM (and, as explained by Selfadjoint, GR as well). It almost seems like we travel along the incorrect paradigm as to topic of gravity at quantum scale--perhaps not out-of-box thinking needed, but a new box.