Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Wednesday, November 28, 2007

Mass Gap Again

Speaking of particle masses, let us recall the famous Mass Gap problem.

I am curious about something. As Distler pointed out in June, in a post discussing Witten's new $Z(q)$, which is polynomial in the $J$ invariant, Witten emphasized in his talk [on 2+1D gravity] that the gauge theory approach is wrong. Does this mean that the Mass Gap problem needs to be rephrased? After all, the official statement begins with the words: prove that for any compact simple gauge group G, a non-trivial quantum Yang-Mills theory exists. Why would we care about this nonsensical question if it's the wrong question? Surely the Mass Gap of interest is the physical one.

By the way, the Hoehn paper mentioned in Distler's post looks like an interesting application of lattices and codes.

7 Comments:

Blogger CarlBrannen said...

The mass gap problem is so deeply intertwined with the "old physics" that I think it is impossible to translate it into new physics.

They begin with a perfectly symmetric vacuum, and then break the symmetry. Schwinger's approach, and the density matrix approach, is to treat the vacuum as a mathematical convenience. Instead, I think that Nature is what Nature is, and if our symmetric models of Her do not match, it is our models that are broken, not Nature.

The Koide mass formula is a good example of this. The assumption of a perfect symmetry only operates at the limit of very high energies. Koide's formula works instead at zero energy, which is what makes it fairly well ignored by the old folks.

November 28, 2007 10:12 AM  
Blogger Kea said...

Yes, it seems that any reasonable alternative description of the problem ought to include the physically relevant mass operators, Koide relations etc. Heh, since they changed the rules after the Perelman incident, web publications qualify for adjudication. Maybe you could build a hostel near the mountains with the money.

November 28, 2007 10:19 AM  
Blogger CarlBrannen said...

Kea, if you follow the Perelman analogy, wouldn't we have to, uh, turn down the prize? I think it's better to keep our eyes on the problems rather than any rewards.

It does make sense that new physics would be published using the internet rather than on, what is that stuff called? You know, chemically processed pulpwood? You know, the stuff that is controlled by the old folks. (They say the nouns go first.)

I think that mass gap problem will melt away as an unsolved mathematics problem with no known physical applications. Sort of like an epicicyle problem after Newton.

November 28, 2007 12:37 PM  
Blogger Kea said...

I feel I can talk freely and lightheartedly about rewards precisely because I have zero expectations of ever receiving any. And BTW, I was not recommending following Perelman's turn down.

November 28, 2007 12:41 PM  
Blogger Matti Pitkanen said...

Strange that mass gap problem has been classified as a purely mathematical problem.

The notion of mass is all but well-understood in physics. There are too many open conceptual questions. Are inertial and gravitational masses one and same thing? Are elementary particles massless and receive their masses via Higgs mechanism and/or some other mechanism.

I think that many of us agree that gauge theories are only phenomenological descriptions working below length scale cutoff. Cutoff is very rough representation of finite measurement resolution and this is what we should mathematize (you can guess how I would continue...;-).

For these reasons giving to the mass gap problem and Riemann hypothesis same status is strange.


I often find fun from the fact that my life work is completely worthless unless it is printed on paper blessed by highly respected authories. If this does not demonstrate that physics is a belief system very much analogous to organized religion then what?!

November 28, 2007 4:50 PM  
Blogger L. Riofrio said...

Unfortunately I am quite far from those mountains. Hopefully I can find out more about Witten's idea firsthand.

November 29, 2007 12:49 AM  
Blogger Kea said...

Hopefully I can find out more about Witten's idea firsthand.

Excellent, Louise. Please report back after your visit.

November 29, 2007 7:47 AM  

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