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Two Of My Blog Posts On The Role Of The Planck Constants And Possible Couplings At Femtometer Range


Dubbelosix

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Over a hundred years ago, Planck introduced his famous units of length, mass and time [see Sivaram, What is special about the Planck mass?] and these units have played a very large role in both cosmology and that which studies the small, quantum mechanics. It is generally believed that the Planck relationship with mass underlines something fundamental about a quantization of mass. It may do, but it doesn’t seem to relate to any particles we know of in the standard model - in fact the Planck mass may only refer to objects known as Planck particles, a type of micro-black hole.

 

The fundamental units of length, mass and time are all related by three fundamental constants: Plancks reduced constant ћ, c the speed of light and G and do not depend upon masses associated with any particle like the electron or proton or corresponding Compton lengths. The Planck mass, for instance, seems to be a very basic unit of mass being 10^19 times the proton mass! Naturally this leads to an energy 10^19 GeV (see Sivaram) and at this scale the gravitational coupling strength corresponds to the dimensionless quantity Gm²/ћc ~ 1 and becomes strong compared to the electromagnetic fine structure e²/ћc ~ 1/137. An example that exists in literature, is the gravitational attraction between two protons becomes Gm(1)m(2)/ћc ~ 10^-38 in which m(1) and m(2) are the proton masses.

 

The problem with considering this though, that this is something that can be applied to all particles, should we not be able to detect large curvatures associated to the required curvature at such distances?

 

Interestingly, P^−4 propagators can be described entirely in terms of their spacetime curvature which gives rise to speculation whether gravity is a direct alternative to the strong binding force and indeed, that quark duality or confinement itself arises from spacetime geometry (see Abdus Salams work on strong gravity). Consider that in such a case, the strong force phenomenon would be indistinguishable to strong gravity. Such a model where curvature plays the role of the strong force was explored in depth by a number of authors, with the idea originating with Abdus Salam, though I am skeptical of the model he chose. Though who am I, he's a nobel prize winner right?
 
 For such a model to work, the scale in which the curvature needs to be measured would be the femtometer range - at this scale, gravity can be of magnitude 137 times stronger then electromagnetism matching the strength of the strong force or in length of interaction 10^-15 m which is roughly the size of a nucleus, so it is much smaller than anything we are capable of observing - we take pictures of atoms, not with photons but with electron microscopes because the electron wavelength is capable of being 100,000 times shorter than a photons wavelength so they are capable of taking pictures of some of the smallest things in existence. For such model to work, we will need to look for studies which describe a non-Newtonian gravity arising in the femtometer range, in fact, such approaches appear to have been explored before:

 

Nuclear constraints on non-Newtonian gravity at femtometer scale

Jun Xu1, Bao-An Li1,2, Lie-Wen Chen3,4 and Hao Zheng3

Published 7 February 2013 • 2013 IOP Publishing Ltd

 

Before we even discuss the quantization of mass that must be required in quantum theory, we must first discusss, what is mass anyway?

 

The physicist has thought about mass in a number of different ways. To Einstein, the mass was a measure of the energy content of a system (in fact it is impossible to separate the two). In a crude way, you could say energy is a type of diffused mass while mass is a type of concentrated energy. When we created a context of field theory, is was discovered that mass itself came into existence from a process of symmetry breaking of fields. On a technical level, mass was seen to be the deviation of a ground state goldstone boson into a higher energy state in a Mexican hat potential. There is also reason to think mass itself is partly electromagnetic in nature. Even though many articles have claimed that electromagnetic theories of mass have been ruled out, it was frequently taught by Feynman that the appearance of a charge seems to make a particle slightly heavier.

 

The two particles that did not share this property was the proton and neutron values - he goes on to say though that while the charge is zero for a neutron, the charge distribution is not zero! Feynmann says, it is only its nert charge which is zero and so calculating its electromagnetic mass is a fair bit more complicated. There are other electromagnetic energies to take into account as well, Feynman mentioned that there exists the non-zero magnetic moment. Feynman has stated that the neutron sometimes looks like a proton with a negative π-meson charge cloud surrounding it. As far as we can tell the muon differs only slightly from an electron - it acts very similar to an electron and because of this it has no nulcear forces and interacts with the electromagnetic field. Some have gone as far to say Muons are just heavier electrons! Feynman has stated that ''whoever explains the electron with have to deal with the muon. The reason why is because their behaviour is indistinguishable and so the mass ought to come out the same.''

 

I tend to think about mass content similar to Einstein, I do not believe there is anything wrong in thinking about mass as an energy content, since experimentally, this appears to be a given fact. E = Mc² can be understood intuitively as a measure of how much energy you can obtain from the system; The magnitude of the energy that can be taken from a system depends on the conversion factor c² - the reason why this acts as a conversion factor is because it is massive number, the speed of light squared. The mass can be small, but when the coefficient c² acts on this, we get back a lot of energy E.

 

So in all respects, there appears to be good reasons to think particles confine energy to create a phenomenon of mass. Questions of symmetry breaking are really only good for questions during the electroweak symmetry breaking phase. There appears there could indications there are internal dynamics going on inside the particle to explain the confinement of the energy. There is already experimental indication that everything in nature consists of confined photon energy. The special cases of gamma-gamma reduction from particle-antiparticle interaction is a fundamental situation where they are reduced back the energy in which they consist of which are two gamma ray photons. At least two papers that have been written in literature has taken this idea seriously, that all forms of matter are confined trajectory paths of internal dynamics of photons. Taking that into ‘’knot theory’’ a variety of particles could arise with the given masses of the Heirarchy problem.

 

Matti Pitkannen has explored a condition in which the effective Planck constant can have spectral properties in which I noted that would have implication for the Heirarchy problem related to a fundamental relation to the square of the mass (in natural units of G = c = 1):

 

[math]\hbar_{eff} = n \hbar = M^2[/math]

 

Some immediate applications which come to mind, is the Klein Gorden solutions and the neutrino mass squared term. Matti explained this was in fact the most obvious application (so it appears he was well aware of this suggestion). When you apply relativity to this, a change in mass implies

 

[math]\Delta M = \frac{\Delta E}{c^2}[/math]

 

This would calculate the energy differences of the squared mass terms

 

[math] \hbar_{eff} = n\hbar \rightarrow \Delta M^ 2 = \frac{\Delta E^2}{c^4}[/math]

 

These mass differences may need adjustable parameters to explain how the Hierarchy manifests, but I suspect them to be something which requires Matti’s definition of different spectral properties of the Planck constant - I also suspect electromagnetic contributions to rest mass must be taken seriously - in which case, transversal and longitudinal will be useful equations to develop those idea’s

 

[math]M_L = \frac{M_0}{( \sqrt{1 - \frac{v^2}{c^2}})^3}[/math]

 

[math]M_T = \frac{M_0}{(\sqrt{1 - \frac{v^2}{c^2}})}[/math]

 

(see wiki entry on mass-energy equivelance). I will be investigating what kind of spectral properties could be calculated - it’s not unusual to think spectral properties exist - we know of the famous Zeeman interaction which also measures quantized spectral properties of light emission in the presence of a magnetostatic field.

Edited by Dubbelosix
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