Unveiling the Origin of Matter: A Geometric Unification in 4D Gravity

[marcus]

http://arxiv.org/gr-qc/0607014

An idea of where matter comes from

"...The first goal of this paper is to show that matter can arise in the most natural way in this formalism by introducing the simplest possible term breaking the gauge symmetry of the theory in a localized way. The gauge degrees of freedom are then promoted to dynamical degree of freedom, and as we will show, reproduce the dynamics of a relativistic particle coupled to gravity. This realizes explicitly in four dimension the idea that matter (relativistic particles) can arise as a charged (under SO(4, 1)) topological gravitational defect.

This strategy, well known in three dimensions, gives a new perspective where matter and gravity are geometrically unified [6] and was the key ingredient in the recent construction of the effective action of matter fields coupled to quantum three dimensional gravity [7]..."

It worked in 3D, and we were waiting to see if they could pull it off in 4D.

 

[selfAdjoint]

the idea that matter (relativistic particles) can arise as a charged (under SO(4, 1)) topological gravitational defect.

Humm, I suppose. I kinda liked the idea that matter arose as a front betwee different diffeomorphic systems on the spacetime manifold. Maybe both?

 

[marcus]

Humm, I suppose. I kinda liked the idea that matter arose as a front between different diffeomorphic systems on the spacetime manifold. Maybe both?

I have nothing intelligent to say about that, sounds like torsten-helge

I was never much enamored of their scheme, but it was nice to have them discussing it here at PF.

I am willing to give Freidel's idea a go. He has done a thorough preparation in 3D and now seems to be touching the next rung.
Basically I am just posting because I want to try out my new sig!

 

[Chronos]

I like that approach, and agree it is reminiscent of Torsten-Helge. This is a very exciting idea [albeit, I tend to be easily excited]. Matter could naturally arise as a potential difference in a scalar field - not unlike rain droplets forming from water vaper when air masses of different temperatures collide. By 'freezing' into existence when the field becomes locally out of whack, matter provides a mechanism to smooth out inflation. This is a seductive way to explain fine tuning problems in cosmology.

 

[garrett]

Here's another way of looking at what's in this paper:

Start with the Dirac action for a spinor field coupled to gravity. Make the ansatz that a classical solution exists for which this spinor field is concentrated as a delta function along a worldline. This isn't so hard, since you can just take a rest solution and boost it to the desired velocity along the worldline. Plug that into the Dirac action and the remaining piece is just this funny looking current, with the boost in it explicitly, multiplying the gravitational (gauge) field.

I do like doing things like this, so I like the paper. But I don't think it quite qualifies as achieving the stated goal of getting the matter part from gravity. To do that, you'd really want to get the Dirac action out of gravity first, as dynamics for the gauge freedom, then plug in a solution as I described above.

Of course, I may be a little biased, since this is what I did in my last couple of papers. ;)

 

[selfAdjoint]

Here's another way of looking at what's in this paper:

Start with the Dirac action for a spinor field coupled to gravity. Make the ansatz that a classical solution exists for which this spinor field is concentrated as a delta function along a worldline. This isn't so hard, since you can just take a rest solution and boost it to the desired velocity along the worldline. Plug that into the Dirac action and the remaining piece is just this funny looking current, with the boost in it explicitly, multiplying the gravitational (gauge) field.

I do like doing things like this, so I like the paper. But I don't think it quite qualifies as achieving the stated goal of getting the matter part from gravity. To do that, you'd really want to get the Dirac action out of gravity first, as dynamics for the gauge freedom, then plug in a solution as I described above.

Of course, I may be a little biased, since this is what I did in my last couple of papers. ;)

Funny, this sounds a bit like what Barut did. He wanted to get the Lamb Shift, etc., out of "the internal structure of the electron" contra QED. So He represented this internal structure as a current, integrated from a straight EM potential as
$\bar{\psi}A_{\mu} \psi$, then took the Fourier transform of this to throw it into the momentum form and plugged that into the Dirac equation (maybe he could have done it at the action level?). Is this a standard physicist technique?

 

[marcus]

Hey Garrett! You can have your Sig back any time. Just ask. I was afraid you wouldn't use it, so I adopted it myself.
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interesting remark on page 9----equation (3.13)

In Planck terms (if I understand correctly), the mass squared of the particle turns out to be proportional, via a Casimir quantity, to the cosmological constant Lambda.
So if one could discover why Lambda is so small, it would also address the question of why particle masses are so small compared with the Planck mass.

This looks intriguing, but I cannot make the orders of magnitude come out right. Anybody else have the same problem?

Maybe this mass is unrealistically small, much smaller than the neutrino mass...

 

[CarlB]

This looks intriguing, but I cannot make the orders of magnitude come out right. Anybody else have the same problem?

Suppose I have two particles and they happen to be fundamental particles and their masses happen to be equal to the Plank mass, call it "M". Suppose that the two particles have an attraction to each other. They get near each other, and they bind together. What should the order of magnitude of the binding energy be? Probably something around the Plank mass, call it M'.

So what is the mass of the bound state? M + M - M'. If M' is approximately equal to 2M, then you have two Plank mass particles combining to give a bound state that has a small mass.

If the mass you get out of that wasn't small enough, then maybe you need another level of binding. In any case, so long as your binding energies are far stronger than perturbation theory will allow you to compute, there is the possibility that the bound state will weigh less than any of the masses of the unbound subparticles.

I forget who came up with this idea, but I think it dates to the 1950s. No one has figured out a way to get it to work.

Carl

 

[SdogV]

The "Heim-Droscher Space" of 8 dimensions seems to follow from Heims Theory where particle masses ere predicted bears on these questions.

 

[Mike2]

Perhaps matter is defined as every possible path it could take. If we calculate the path integral from one point to the same point, adding up every possible path a particle could take to get to where it started at all times, wouldn't that leave us with the characteristics of particle that do not depend on travelling, but only those particle characteristics inherent to the particle itself?

It would seem according to the Path Integral formulation that we don't know where a particle is located until it interacts with other particles. So a lone particle could be anywhere, and space is defined as where the particle might be. Or a particle might be defined as every possible path through space.