Recent content by Marty4691

Thanks for your time and feedback. M.

I'll try and walk you through the 6D thing again. I probably wasn't very clear the first time. We can start with Dirac. When he formulated his equation he needed 4 matrices that anticommuted. Later he commuted each of his gamma matrices with all the others and ended up with 10 matrices which he...

Because the gamma matrices are 6D.

Yes, I get that. My point is that the Lagrangian density appears to live in a 6D mathematical space and we don't seem to know much about that space. If you don't want to take the dimensions of the Lagrangian as the dimensions of the SM, that's fine.

If you don't think the gamma matrices are fundamental enough to specify the dimension of the SM Lagrangian density, I guess that's your call. Like I said, the consensus is that the whole 6D thing is just a mathematical convenience and nobody should lose sleep over it... That said, the gamma...

Dirac realized that his gamma matrices were the minimum generators of a (+++--) space : P. A. M. Dirac, J. Math. Phys. 4, 901 (1963) For the weak force they added another gamma matrix which like the others was required to anticommute giving the minimum generators of SL(4,R) which it turns out...

So, here's the thing. The SM uses a six dimensional mathematical space to crunch probabilities. That is, one with three space dimensions and three time dimensions. That's a fact. Now, the consensus is that it is just a convenient tool. The argument goes something like this. The electron in the...

It's the coherence of the mixed state that's the issue, not the individual mass eigenstates. The three mass eigenstates are treated as particles, but nothing holds them together. They're just assumed to remain together to maintain coherence of the mixed state. But the universe is full of fields...

The SM seems to side-step the issue. A basic assumption in the neutrino sector is that the mass eigenstates maintain coherence over very large distances. But no rigorous justification is given for this assumption. How mass eigenstates do this still seems to be an open question...

I'm not advocating the preon models, but I was just wondering if you considered neutrinos as "composite" particles. They appear to be a mixed states of three mass eigenstates. So, a "composite" of three particles even if the particles aren't observable...

Before I forget, PFers might be interested to know that SO(3,3) space-time has two classes of spin one-half particle. One class of particles has spin angular momentum, as usual. The other class of "particles" has spin angular energy and the following two properties: (1) They are either...

Nice macroscopic example. I guess I would argue that we may not understand causality at the quantum scale. Take spin angular momentum. We know from Noether's theorem that it is associated with space rotations, but we are told that there is no actual physical rotation in space, it's an internal...

So, it turns out that fresh_42 was right: mathematically, there is a conserved quantity due to invariance under time rotations (https://doi.org/10.3390/sym12050817). This quantity has the same units of measure as the Planck constant. For lack of a better name, perhaps we can refer to it as...

Thanks bobob.

Thanks jedishrfu. Just to be clear: O(3,3) space is a mathematical space and the linked article makes no claims about the physics in O(3,3). As mentioned above the mathematical properties and relationships of some group theory algebras in O(3,3) overlap with the mathematical properties and...