Arivero: Quantum Area & Time Bounds in Relativistic QM

[marcus]

http://arxiv.org/abs/gr-qc/0603123
Some bounds extracted from a quantum of area
Alejandro Rivero
10 pages, no figures
"Asking very elementary relativistic quantum mechanics to meet quantums of area and time, it is possible to observe at a general level: a) the seesaw bound for the mass of neutrinos, and b) the need of a gauge group at energies below Planck mass."

 

[Chronos]

A nice paper by arivero. Simple and concise.

 

[arivero]

I will expand on it in physcomments.org in a couple hours (now I volunteered to watch an exam)

 

[josh1]

A nice paper by arivero. Simple and concise.

Hi Chronos,

So what's it about?

 

[selfAdjoint]

So what's it about?

Well, if the abstract that Marcus posted didn't tell you enough, maybe this quote from the start of the paper will:

Having the seesaw mechanism as an explicit realization, a general lower bound on the mass of neutrinos has been traditionally derived from Planck mass (see e.g. R.E. Schrock mini-review on neutrinos for [2]) so that $$m_ ≈ am^2 e_w/ ¯M_P$$ , with $$me_w$$ the electroweak scale, $$¯M_P$$ a generic new physics scale whose maximum value is Planck mass, and a a dimensionless constant, probably a Yukawian coupling.

Now it is obvious that any argument asking an electroweak force $$GF_m^2$$ to be of order $$am_/ ¯M_P$$ will serve to obtain this bound. The latter quotient can be argued as a quotient of energies or as a quotient of wavelengths. It seems interesting to remark that we can derive this condition from the existence of a quantum of area, asking that the measurement of area swept by any orbiting particle must be at least such quantum and assuming this quantum to be directly related to Planck’s area. The example reshapes in some way our view of symmetry breaking at the Planck scale, as it happens that below this mass scale gravity becomes too weak to be able to sustain this quantum and it needs to be supplemented by other forces: lectromagnetism, strong or electroweak forces. In the case of neutrinos only electroweak interaction is available, and this imposes a bound to neutrino mass.

 

[josh1]

Sorry SelfAdjoint, but that really doesn't help. Can you explain it in a way that even a dummy like myself can understand? Thanks.

 

[marcus]

Sorry SelfAdjoint, but that really doesn't help. Can you explain it in a way that even a dummy like myself can understand? Thanks.

That's a strange post---it has such modesty! The josh voice is certainly different from one I remember from months or years back---the jeff voice---and you Josh1 are surely a new person although you say many of the same things I've noticed and sometimes have a similar message. But jeff would never have said "even a dummy like myself" even joking. He was obviously OBVIOUSLY no dummy. And neither, clearly, are you Josh1.
things change, maybe even get better in some cases, and also PLUS ÇA PLUS C'EST as the French say.

In any case, you and I are in the same boat regarding this paper. I posted it without comment because

1. I am proud of Alejandro's work in general----setting up physicscomments and contributing to discussions various places

2. Several people like Hans DeVries discuss stuff like this with Alejandro

3. I want to give Alejandro and maybe Hans a chance to have this paper noticed and discussed without Alejandro having to push it himself and come here and say "hey look, I just posted this"

So I put notice of this paper without comment, and people who understand it better, or else Alejandro himself, can talk about it if they want.

 

[arivero]

Well, I have just resumed some of the lateral discussions in a pair of old threads, because some details were interesting to be kept somewhere else, beyon physicsforums and sci.physics.research. There was a old hand waving argument related to the SeeSaw mechanism: basically that the scales of Planck and Higgs can be used to generated a third one, and that this one can put a lower bound to neutrino mass. Of course this argument was just theoretist play before oscillation of neutrinos, but now it has become relevant. The SeeSaw mechanism makes it concrete, but it was typically argued from renormalization group point of view. In the note I was just pointing out that the possibility of using other arguments to combine Planck scale and electroweak scale, and then getting neutrino bounds. It is not rare because, as I said and selfadjoint has quoted, it was very general.

The paper has ten pages but three-four of them are appendixes and digressions to do mental note of other details.

As I told, more in physcomments. But I am still here hearing :-)

 

[Chronos]

It was a very nice paper, arivero. I have always appreciated your insights. You raise several interesting points worthy of discussion.

 

[hossi]

Hi there, just back from a conference, must have missed the paper. Since I found myself mentioned in footnote 8, some remarks about the 'general discussion' in case anybody is interested:

I don't really know what to make out of these arguments. It seems to me mostly like playing around with constants. E.g. to make the conclusion with the neutrinos it takes a bound state of two neutrinos, I guess a neutrino and an anti-neutrino with Z_0 exchange.

However, the mass which enters the calculation is not one of the neutrino-masses, but the 'effective' mass of the 'central-force-problem'. I.e. m= m_1*m_2/(m_1+m_2). Inserting this and (thats an additional assumption) m_1>>m_2, you see that you get a lower bound on the smaller mass.

That is

a) not very helpful since we would prefere to know why the mass of the (left handed) neutrinos are small (so we would want an upper bound) and

b) it does not say anything about where the heavier mass (of the potential right handed neutrino) is, so it is not a derivation of any see-saw mechanism.

That was the reason for the Remark 1: maybe it would bring more insight to start from the see-saw scales and turn the argumentation around.



B.

 

[Chronos]

But, hossi, would you not agree that is a very well grounded approach to the question? I think his paper was elegant and well phrased. I admit prejudice; arivero has greatly impressed me with his excellent posts here.

 

[arivero]

I don't really know what to make out of these arguments. It seems to me mostly like playing around with constants.

A way to take them is that any theory should have these orbiting solutions in the appropiate limit so they are general arguments. But yes, the big difference is that real seesaw is a concrete recipe to build masses via a majorana term and this is more as the generic argument now disappeared from the Review of Particle Properties.

E.g. to make the conclusion with the neutrinos it takes a bound state of two neutrinos, I guess a neutrino and an anti-neutrino with Z_0 exchange.

However, the mass which enters the calculation is not one of the neutrino-masses, but the 'effective' mass of the 'central-force-problem'. I.e. m= m_1*m_2/(m_1+m_2). Inserting this and (thats an additional assumption) m_1>>m_2, you see that you get a lower bound on the smaller mass.

Well two neutrino masses, having an effective mass m/2, is the worst case (think on correction factors 1+m/M); for m_1>>m_2 the effective mas aproaches m_2 which again should be the neutrino one because it is the smaller mass. A secondary problem is to consider if the area is to be considered the one swept by the line from one particle to another or the one taking the center of mass as center, but this is also worked out in classical mechanics. Everything joined, it can amount to "order unity" corrections, I do not worried more about there because I was not calculating the exact constant of the Z0 coupling between two neutrinos, so I was already having a "order unity" discrepance around. If I even find a time to work out the "exact" (Born approximation or so) orbit force for a pair of neutrinos, then I will correct also the effective mass terms (I will do it surely in a near future because I was interested on the relativistic orbit of a top quark around a central higgs field (because the coupling is very funny,
y_t = 0.991 \pm 0.013) and techically it is much of the same problem. ). Of course at the end we have the nuissance of lack of evident relativistic invariance of a central force field, this was the motivation to go to field theory a hundred years ago.

 

[hossi]

But, hossi, would you not agree that is a very well grounded approach to the question? I think his paper was elegant and well phrased. I admit prejudice; arivero has greatly impressed me with his excellent posts here.

Hi Chronos,

as I pointed out before the approach does not lead to a see-saw mechanism, and it does not explain the smallness of neutrino-masses. I honestly don't know what to make out of an approach that builds up on areas swept out by quantum-particles, in whatever interpretation. Any interaction that can bind the particles together is quantum field theory and not quantum mechanics, this quantum field theoretical interaction has to be described. And it's more than a coupling constant.

A way to take them is that any theory should have these orbiting solutions in the appropiate limit so they are general arguments.

Maybe it's possible to straighten out the argument, I don't know, but from what it written in the paper, it's not clear to me whether it makes sense on a deeper level than just relating constants to each other.



B.

 

[Chronos]

I'm not arguing against your point, hossi, merely focusing upon the point I believe arrivero raised. IMO, introducing a coupling constant may not be a bad idea. Any time you introduce a constant, you risk an objection on ad hoc grounds. I'm not sold on arrivero's concept, but, I think it deserves consideration.

 

[arivero]

Hmm it seems that Sabine is right to be worried about the neutrino part of the argument. Two years ago de Leo and Rotelli tryed to calculate in the context of Dirac equation a neutrino binding via Z0 and they found that while their analytical aproximation was favouring such binding the numerical calculation implied some wrong step in the analytic, and no bound state was found. This is because the high mass of the Z0 generates a very short ranged yukawa potential; when the range of yukawa potential is greater than compton length of the orbiting particle then a bound state can be expected to be found just as a perturbation of the coulombian solution, but it is not the case here.

While I was not aware of this article I loopsided it by suggesting that at least during a short interval I could consider the orbit as coulombian and charge the mass quotient to the coupling constant; I did not justifyed it. Without it, the argumentation of my article complicates a lot because I should go to study area law in generic scattering, unbound, solutions.

The italo-brazilian article was http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+j+PHRVA%2CD69%2C034006&FORMAT=www&SEQUENCE= and a followup was promised, but it has not appeared, so it seems they have not got to stablish a bound state.