      # Hierarchy Problem: Search For The Mass Formula

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### #1 Dubbelosix

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Posted 04 August 2018 - 08:17 PM

https://consciousnes...erarchy-Problem

In my blog, I explain how to unite the idea's of Weinberg and those with successful mass formula that attempt to explain the particle masses of the standard model.

### #2 Dubbelosix

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Posted 05 August 2018 - 01:30 AM

We stated that

$\frac{m}{m_e} = nk [\frac{\sqrt{G}m}{2 e}]^n = nk [\sqrt{\frac{H_0 \hbar^2}{mc}}\frac{1}{2 e}]^n= nk [\sqrt{\frac{H_0}{mc}}\frac{\hbar}{2 e}]^n$

$\frac{m \mu_B}{e^2} = \frac{\hbar}{2e}$

in which

$\mu_B = \frac{e \hbar}{2m}$

is the Bohr magneton.

Since this term arises $\frac{\hbar}{2e}$ then we can even speculate it in the following form as:

$\frac{m}{m_e} = nk [\frac{\sqrt{G}m}{2 e}]^n = nk [\sqrt{\frac{H_0 \hbar^2}{mc}}\frac{1}{2 e}]^n= nk [\sqrt{\frac{H_0}{mc}}\frac{m \mu_B}{e^2} ]^n$

It's only theoretical looking for alternative ways to write something, but sometimes messing around like this can be intuitive.

Edited by Dubbelosix, 10 August 2018 - 04:48 PM.

### #3 Dubbelosix

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Posted 08 August 2018 - 03:55 PM

Just a small thing as well I came across again, also, totally theoretical whether it true within nature, but if a mass formula did depend on the parameter $H_0$ then maybe these other dynamics and interpretations will show a new line of investigation?

$H_l = \frac{c \sqrt{1 - \frac{v^2}{c^2}}}{2r_{HS}} \frac{1}{1 - \frac{v^2}{c^2}} = \frac{c}{2r_{HS}}\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = H_t$

The Hubble sphere radius is defined as

$r_{HR} = \frac{c}{H_0}$

and you will notice that, so the transverse Hubble parameter being equal to the logitudinal Hubble parameter (directions in time) is dynamically linked with the present day value which had notation $H_0$.

Edited by Dubbelosix, 08 August 2018 - 03:56 PM.

### #4 Dubbelosix

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Posted 09 August 2018 - 08:37 PM

### #5 Dubbelosix

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Posted 16 August 2018 - 12:48 AM

Just a small thing as well I came across again, also, totally theoretical whether it true within nature, but if a mass formula did depend on the parameter $H_0$ then maybe these other dynamics and interpretations will show a new line of investigation?

$H_l = \frac{c \sqrt{1 - \frac{v^2}{c^2}}}{2r_{HS}} \frac{1}{1 - \frac{v^2}{c^2}} = \frac{c}{2r_{HS}}\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = H_t$

The Hubble sphere radius is defined as

$r_{HR} = \frac{c}{H_0}$

and you will notice that, so the transverse Hubble parameter being equal to the logitudinal Hubble parameter (directions in time) is dynamically linked with the present day value which had notation $H_0$.

Feynman took the idea of the electromagnetic mass as a real thing. In fact, the presence of a charge experimentally-showed from early on that it was much harder to push a charged object than an uncharged one. It was also noticed by early pioneers that charge made a particle slightly heavier.

The only exception that early scientists found was between the proton and neutron, but Feynman explained these where more complicated objects in which the net charge is zero for a neutron (but) it does possess a charge distribution that was certainly not zero. There are additional electromagnetic contributions to the mass, such as the magnetic moment.

If say, we assume the gravitational field plays itself a role in the determination of the mass (just as quantization of the gravitational potential will lead to creation and annihilation operators), then it might be related to early curvature in which particle production can occur. Though this next part is not so much a problem, it must be noted as well that there is no separation of the wave when matter is present as shown through de Broglies theory but cases in which longitudinal waves are zero are cases reserved for a system moving at the speed of light.

The gravitational field for both longitudinal and transverse masses are:

$\Gamma_L = \frac{1}{2} \gamma^3 \frac{\partial g_{00}}{\partial x}$

$\Gamma_T = \frac{1}{2} \gamma \frac{\partial g_{00}}{\partial y}$

$\Gamma_T = \frac{1}{2} \gamma \frac{\partial g_{00}}{\partial z}$

There is also the interesting fact that gravitational waves are themselves manifestly transverse. How this translates into the transverse properties of the mass is uncertain but it seems any gravitational waves in a theory like this would come out of this would be cases in which Lorentz contraction goes to zero (ie. Longitudinal effects are neglected). But in what relation to the transverse and longitudinal mass remains unclear to me.

The gravitational four-force is

$F_{\mu} = \Gamma^{\lambda}_{\mu \nu} u^{\mu}p^{\nu}$

Which has units of energy over length. You could argue that transverve and longitudinal mass are out-dated, and in a sense, it is. Because while they were still used by Einstein during the production of his first few papers, he later dropped this for the ‘’relativistic mass.’’ They are still handy to know and in the formula involving the Hubble parameter that I derived, may reveal interesting effects on the production of particles in early cosmology that dictate their masses.

Edited by Dubbelosix, 16 August 2018 - 01:01 AM.

### #6 Dubbelosix

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Posted 16 August 2018 - 01:19 AM

Those connections of the gravitational field (the Christoffel symbols) are loosely equivalent to a force term. From Einstein electrodynamics of moving bodies, the force exerted in a particle is given in terms of the transverse and longitudinal masses as

$\frac{m}{(1 - \frac{v^2}{c^2})^{\frac{3}{2}}} \frac{d^2 x}{dt^2} = e\mathbf{E}_x$

$\frac{m}{(1 - \frac{v^2}{c^2})} \frac{d^2 y}{dt^2} = e\mathbf{E}_y$

$\frac{m}{(1 - \frac{v^2}{c^2})} \frac{d^2 z}{dt^2} = e\mathbf{E}_z$

The mass is explicitly defined as a force in this equation, divided by the respective acceleration $\frac{F}{a}$. In such cases, it is advantageous, according to Planck, to define such a force not as $m(\frac{dv}{dt})$ but instead as $\frac{d(mv)}{dt}$ to allow mass to vary. But what do we mean when we say mass is manifested from a force divided by acceleration? Do we interpret mass then as some force exerted on the system? We know that weight itself is an effect of a ''force'' on the system. There are so many kinds of different assumptions on mass but the one that is largely accepted is an interaction from a Higgs boson. I always wondered why the gravitational field would not provide mass to systems - In that way, there is no ''true'' quantization but instead every particle in the standard model becomes a gravitational fluctuation. But it's hard to persuade a world now of an alternative to a Higgs mechanism when we think we have already detected it.

Edited by Dubbelosix, 16 August 2018 - 02:31 AM.

### #7 Dubbelosix

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Posted 16 August 2018 - 01:23 AM

It's not so hard to think that a gravitational field could assume the mass of a particle when ~

1) Under weak equivalence, there is no difference between the measure of inertia and the measure of gravitational mass

2) That inertia over here is affected by mass out there, a concept of Machian relativity - in that sense, the force exerted on the particle manifested as mass is experienced as a contribution of the gravitational bodies in the universe (but I tend to think there is more to the story here).

Edited by Dubbelosix, 16 August 2018 - 02:51 AM.

### #8 Dubbelosix

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Posted 16 August 2018 - 04:26 AM

Even an argument due to symmetry within our theories, would lead to the gravitational field determining the mass of a particle, just as the electromagnetic field generates the photon - the only real difference is the gravitational force, under weak equivalence and strong equivalence is a pseudo force. It is not mediated by a particle per se. Gravity is though, contributed by every particle, so there is no one such particle which contributes to gravity in the universe. Trying to argue for some gravitational understanding of the mass would be at odds with what most scientists will tend to think, concerning the Higgs particle and the Higgs mechanism - physicists even think we have probably detected the HIggs which led to big news at the time over the globe.

It has been a common theme of my work exploring mass as a property of charge. And electromagnetic charges are also expected to contribute to the total mass of a system, which in relativity is simplified under the relativistic mass formula. In a similar symmetry/analogy an electron only possesses a charge [because it is moving through] an electromagnetic field. Therefore the mass would arise as a charge $\sqrt{G}m$ because it has a motion through the gravitational field.

In a way we would have to argue that mass depends on a gravitational field strength $\phi$, which for determining masses, we assume was an early phenomenon in the expansion of the universe that depended on the Hubble parameter in some way, according to the approach by Weinberg. For a mass to depend on field strength would look like:

$\Box \phi = \rho$

This was in fact an equation predicted by Nordstrom in his first approach to a theory of gravity. It wasn't considered logical and today we might understand this by stating that the mass does not vary proportional to the gravitational field strength (ie. the mass of an electron near the surface of the Earth is the same as an electron in the space lab).

Of course, we can hypothesise it is possible early cosmology allowed some exotic type of physics in which temporarily particles did in fact depend on the field strength of gravity - in which case the particle masses would be determined as the gravitational field varied with expansion. It may be for instance, a matter of gravitational particle production - a real concept in which the quantization of a gravitational field will lead to a production of particles, and may happen in an irreversible way as well.

It’s not enough to say that the gravitational charge of a system is generated by moving through a gravitational field, the gravitational field is not a property any different to the geometry of spacetime itself, so the source of the generation of the mass akin to electron charge in an electromagnetic field, is spacetime itself!

Motion through a vacuum does not mean a motion through nothing - the vacuum is not Newtonian but quantum mechanical in nature. The vacuum is a durable, dynamic sheet that has it’s own properties. Even at the most fundamental level we expect there to be fluctuations in accordance to predictions of quantum mechanics; though these particles are off-shell, the word virtual should not be taken to mean they are not real.

I can actually think of a situation in which motion through a vacuum (could in principle) explain the effect of mass by a motion of the raw form of energy we call photons. This actually goes back to a model proposed to good accuracy that the electron can be modelled as a bound photon. In this sense, the motion of a photon is caught up in itself and mass is a measure of this motion - it mirrors what Dirac believed the electron to be, which was simply a photon moving in a zig zag path through space, a motion that became known to be zitterbewegung.

This ‘’zitter motion’’ was first predicted by Schrodinger from his own solutions to his famous equation which bears his own name. DeBroglie also implemented zitter motion into his own theory - it presented itself as an internal ‘’clock’’ given to matter - you cannot describe a passage of time without a sense of matter and treating them as clocks is a reasonable and logical approach. Though zitter motion has not been detected yet fundamentally (since the motion of the photon must be at very small scales, it has at least been analogously recreated twice:

‘’For the hydrogen atom, the zitterbewegung produces the Darwin term which plays the role in the fine structure as a small correction of the energy level of the s-orbitals. Zitterbewegung of a free relativistic particle has never been observed. However, it has been simulated twice. First, with a trapped ion, by putting it in an environment such that the non-relativistic Schrödinger equation for the ion has the same mathematical form as the Dirac equation (although the physical situation is different). ‘’

Wiki

So in a strange way, a concept rooted from theoretical physics could explain the mass of a system as a motion through the vacuum: It’s just that in this model, the motion is specified as a bound path or a zitter motion of a photon. It obeys the notion that mass has an energy, it also agrees to why antiparticles will decay with matter into photon energy for all kinds of particles.

Edited by Dubbelosix, 16 August 2018 - 04:31 AM.