Why proton's so lite?(Wilczek nobel talk)

[marcus]

In Wilczek nobel acceptance talk
http://arxiv.org/hep-ph/0502113
on page 21

right under equation (2)
the interesting question is posed
"Why is the proton so light?"

It is a Quantum Gravity question, because he is comparing proton to the Planck mass-----the QG scale. In a quantum theory of gravity combining special rel (|c| = 1) and ordinary quantum mechanics (|hbar| =1) with the classical theory of gravity, general relativity (|8piG| = 1) there is a natural scale for any type of physical quantity and you could phrase what he is asking as:

"why is the proton only a quintillionth of the natural QG mass unit?"

By quintillionth I mean the 10^-18 that you see in Wilczek's equation (2).

It's nice that, having apparently chosen to have only two equations in the whole Nobel acceptance talk he made one of them this: the proton mass is a quintillionth of QG natural mass.

The other equation in his talk, equation (1), is what he calls a "modern embodiment of the ancients' elusive, mystical 'Music of the Spheres'".
That part is on page 14.

It is a nicely crafted talk for general audience---intuitive and evocative.

And he answers the question about lightness posed on page 21:

"...The proton’s mass is set by the scale at which the strong coupling, evolved down from its primary value at the Planck energy, comes to be of order unity. It is then that it becomes worthwhile to cancel off the growing color fields of quarks, absorbing the cost of quantum localization energy. In this way, we find, quantitatively, that the tiny value of the proton mass in Planck units arises from the fact that the basic unit of color coupling strength, g, is of order 1/2 at the Planck scale! ..."

 

[nightcleaner]

ok, this is interesting. i havnt read that far yet. So do I understand that the Planck mass as we have it now is not a fundamental unit, but can be broken down , perhaps multidimensionally, into smaller base units of about sqrt Planck Mass?
nc

 

[marcus]

ok, this is interesting. i havnt read that far yet. So do I understand that the Planck mass as we have it now is not a fundamental unit, but can be broken down , perhaps multidimensionally, into smaller base units of about sqrt Planck Mass?
nc

I am glad you are interested by Wilczek's talk. I am too.
I don't think that is what he is saying.
But I will let someone else answer who knows more about the other parts of the talk.

To the extent of my knowledge the Planck mass IS fundamental and is not broken down into smaller base units of mass.

the PROTON mass is the one that can be analyzed into smaller pieces. a proton is made of two U-quark and one D-quark
so its mass can be analyzed in terms of constituent pieces and the energy of their motion inside the proton and their confinement (lot of stuff here that's out of my ken but anyway he seems to think the proton mass can be explained in terms of what it is made of)

the reason he compares proton mass to Planck mass is because there is nothing anyone knows of that is more fundamental to compare it to.
so, one can say I guess that SO FAR it is fundamental

BTW in case anyone else is reading this and was wondering, in equation (2) the m_p stands for the proton mass

 

[Stingray]

It is interesting that the proton's mass can be understood, but this does not, as he's claiming, explain the feebleness of gravity. Gravity is still extremely weak if you look at the gravitational interactions between electrons, and their masses have nothing to do with the strong coupling parameter as far as I know.

By the way, does anyone else get a little disturbed by all the "numerology" that particle physicists use? The last time Wilczek gave a colloquium here, he went on and on about how strange it was that why certain quantities were "big" or "small." Those kinds of things have never seemed problematic to me.

 

[Haelfix]

Its not numerology, there's a very specific physical reason why he's quoting the scales he's talking about. This is what's known as the hierarchy problem.

Loosely speaking (very loosely actually), field theories are valid only up to a certain energy scale. Usually the point where they stop or start making sense is when some symmetry is spontaneously broken. One of the problems with the standard model as currently formulated, is there is a huge gap between the last time this happens (the electro weak symmetry breaking scale) and whatever comes next (say the Planck regime). In principle a lot of the values we cherish and measure could undergo quantum corrections, as no symmetry protects them.. The measure of just how bad this could go wrong, is given by the order of magnitude difference in the scales. Its hence very hard to believe that this is the entire story.

Now, the Planck regime is an assumption of a regime where new physics emerges. By dimensional analysis it is precisely the place where gravity becomes comparable in strength to the other interactions. Its best if you don't think of it as a precise 'number', but rather a general order of magnitude place where stuff becomes important. At least, that's how particle physicists think of it.

Keep in mind, there could be other scales of importance, like say the grand unification scale (where the strong force decouples from the electro weak force) before the Planck scale. But that's additional info not found in the sm.

 

[Haelfix]

Btw, Stingray I don't know how good your QFT is, so i'll give you another example of an unnatural ratio.

Namely, the difference between the mass of the electron and the mass of say a neutrino.

If you look at the naive theory, a neutrino mass term after electroweak symmetry is going to acquire a higgs vev, naturally you would expect whatever mass comes out is going to be say within an order or two of magnitude of this mass scale. The physics is said to be 'set' by this value. The problem is the mass is measured to be much, much lighter than that. So we put in by hand some suppression factor. It turns out there is a neat mechanism to generate this suppression naturally (without some weirdness happening at late orders in perturbation series), but if we assume that doesn't happen we are a bit at a loss to explain how such a huge ratio could exist with the tools we currently possess.

 

[Chronos]

Good observations on the relationship between particle energies and the realms where spontaneous symmetry breaking occurs. In that sense, the Planck mass is very much fundamental - it is in the GUT energy realm.

 

[marcus]

Wilczek active in Quantum Gravity

It looks to me as if Wilczek is making an excursion into QG research
He and Sean Robinson just post this
http://arxiv.org/abs/gr-qc/0502074
A Relationship Between Hawking Radiation and Gravitational Anomalies
5 pages, 1 figure

"We show that in order to avoid a breakdown of general covariance at the quantum level the total flux in each outgoing partial wave of a quantum field in a black hole background must be equal to that of a 1+1 dimensional blackbody at the Hawking temperature."

this is just my impression but it sounds like he has gotten interested in QG and is probing for soft spots. for example here is an exerpt

---exerpt from introduction---

Hawking radiation from black holes is one of the most striking effects that is known, or at least widely agreed, to arise from the combination of quantum mechanics and general relativity. Hawking radiation originates upon quantization of matter in a background spacetime that contains an event horizon—for example, a black hole.

One finds that the occupation number spectrum of quantum field modes in the vacuum state is that ofa blackbody at a fixed temperature given by the surface gravity of the horizon.

The literature contains several derivations of Hawking radiation, each with strengths and weaknesses. Hawking’s original derivation[1, 2] is very direct and physical, but it relies on hypothetical properties of modes that undergo extreme blueshifts, and specifically assumes that their interactions with matter can be ignored.

Derivations based on Euclidean quantum gravity are quick and elegant, but the formalism lacks a secure microscopic foundation[3].

Derivations based on string theory have a logically consistent foundation, but they only apply to special solutions in unrealistic world models, and they do not explain the simplicity and generality of the results inferred from the other methods[4, 5].

In all these approaches, the Hawking radiation appears as a rather special and isolated phenomenon. Here we discuss another approach, which ties its existence to the cancellation of gravitational anomalies...
---end quote---

 

[Chronos]

I think Wilczek is on shaky ground classifying Hawking radiation as a special case phenomenon. Hawking radiation is virtually demanded by the laws of thermodynamics.

 

[marcus]

I think Wilczek is on shaky ground classifying Hawking radiation as a special case phenomenon. Hawking radiation is virtually demanded by the laws of thermodynamics.

I think you may not have understood what he said. He is critical of models which MAKE IT SEEM a special case phenomenon.
I do not see Wilczek on shaky ground at all. If, on reflection, you still do then I am curious to know your reasoning and wish you would explain, Chronos.

BTW Wilczek also has expressed skepticism about extra dimensions, as I learned from a poster at Not Even Wrong today.
An unnamed poster said: "...see for example the panel debate on extra
dimensions at the Kavli conference on
http://www.phys.cwru.edu/events/cerca_video_archive.php
See the session on gravity and in particular the
panel debate on extra dimensions (in that panel
wilczek argues against extra dimensions.)
See also http://mitworld.mit.edu/video/204/
and in particular his answer to scott hughes question about extra dimensions..."

the Kavli conference was 11 October 2003, so if you go to that link and scroll down to that date you get a panel talking about extradimensions with Wilczek on the panel. I have not listened to it so I cannot vouch that he expresses doubt about extraD, but so we are told.

the MIT talk is 13May2004
and is called "the origin of mass and the feebleness of gravity"
and the extraD bit is supposed to be in the questions at the end. but the
talk should be very interesting. same topic as the series of articles called "scaling mount Planck" in Physics Today.

 

[marcus]

Chronos let me repeat this to make something clear by example

Derivations based on string theory have a logically consistent foundation, but they only apply to special solutions in unrealistic world models, and they do not explain the simplicity and generality of the results inferred from the other methods[4, 5].
...

Here Wilczek is saying that the fact that stringy derivations of hawkingradiation only apply to special solutions is a problem for string.
He is not saying (as you appear to suggest) that hawkingradiation is some kind of "special case phenomenon". He believes that it should be explained in a simple and general way and therefore a theory which can only handle it using a complicated or contrived or unrealistic (his word) model must be at fault.
I think you have the misconception that Wilczek is saying that hawkingradiation is a "special case phenomenon" and that he is therefore on shaky ground when he is, in fact, saying the opposite. It is not "special case" and therefore he is disatisfied with theories that can only give contrived or unrealistic explanations.
BTW he didnt mention LQG, I suppose because LQG does not at least at present give a derivation of hawkingradiation. But if it did, and if the derivation was far-fetched unrealistic or "special case" then this would be a fault of LQG, in Wilczek's estimation, I should expect. His condemnation of such theories is not limited to stringy type but is across the board.