The Higgs and a Gravitational Field Assumption

[Mystery111]

The search for a new theory which will acount for why mass appears in systems will be on it's way I predict. There are a few contending theories already, such as technocolor theory.

 

What stops us from believing that potential energy is a contributor of mass to systems? The Higgs Field acts mathematically like a potential energy being added to a system. To understand this, one should realize that mass only appears in a system when the ground state oscillator moves away from the ground state as a flucuation in the Mexican Hat Potential in broken Galilean symmetry.

 

The mathematical abstraction of this interaction is given by the Higgs Field [math]\phi[/math] and the mass term which is conventionally given as [math]f[/math] in the potential energy diagrams. In effect, it costs potential energy to make matter. The way this mathematically enters the equation is by an interaction term given as:

 

 

[math]g_Y \bar{\psi} \psi = g_Y \psi_{L}^{\dagger} \phi \psi_{R} + g_Y \psi_{R}^{\dagger} \psi_L \phi^{\dagger} =g_Y f (\psi_{L}^{\dagger}\psi_R + \psi_{R}^{\dagger} \psi_L) + g_Y H (\psi_{L}^{\dagger}\psi_R + \psi_{R}^{\dagger} \psi_L)[/math]

 

The dynamical aspect of the equations is that a Higgs Boson can come along and decay into an electron-positron pair, there are other ways to veiw this above, but this is generally the easiest way to view it, in my opinion. The Higgs Boson becomes a particle as a mechanical reason to why systems may obtain a mass. But what if a particle is not required, what if mass is a phenomenon of a local event in the internal structure of a particle but still arising as provided from a potential? Then we must say that the massless system [math]f=0[/math] at the ground state [math]\phi=0[/math] is locally disconnected from interaction with the potential [math]\phi[/math] - it isn't until the fluctuation moves away from the ground state will the system be locally interactive/(or connected)* to the system in question.

 

We attribute mass of a system to the gravitational field. Not only are gravitational effects present in mass (but also massless energy) there is also curvature. Perhaps a particle like a photon will somehow be locally effected by some kind of coupling to a gravitational field when it moves away from the potential - this would mean there is an intrinsic change with how it dynamically interacts with the local gravitational field giving rise to inertia, or inertia-like behaviour. I don't think this would alter the math very much. You'd simply change the Higgs potential [math]f^2\phi[/math] term for the gravitational potential term [math]M^2 \phi[/math], and the Higgs Boson itself would change from being a physical particle mediator to simply the particle in question being fed energy from the gravitational potential.

 

Does any object to such a statement?

 

 

 

*(Note this is not the usual gamma connection of general relativity)

[Mystery111]

There are other ways to view the potential mathematically. You can have

 

[math]V= \frac{-\mu^2}{2} + \frac{\lambda \phi^4}{4}[/math]

 

Differentiation gives

 

[math]V= -\mu^2 + \lambda \phi^3[/math]

 

Rearranging gives

 

[math]\phi^2 = \frac{\mu^2}{\lambda}[/math]

 

then if this is simply the ground state then this is just [math]f^2[/math] which has dimensions of mass

 

[math]f^2 = \frac{\mu^2}{\lambda}[/math]

 

which raises a problem in my conjecture above. It was the same problem that the Higgs Boson faced. [math]f^2[/math] was a very small number in theory, it would only account for some of the observable mass and energy in the universe, because [math]f^2[/math] may be just a small portion of what we deal with. The theory was that this mass term could be represented in much more massive terms, this would be the unseen stuff we speculate permeating spacetime.

Edited November 3, 2011 by Mystery111