Emerging Time, Inflation And Planck Quantum-Cosmology

[Lucious]

To show how time emerged when matter is considered, we begin with an equation which is in the strong gravity range using the gravitational fine structure and a timeless action:

 

 

 

[math]\alpha_G \cdot \hbar = \int p_{\gamma} \cdot q[/math]

 

 

[math]\int \hbar\ dr_s = \lambda \int [m_{\gamma} v \cdot q][/math]

 

 

We know this because of Maurapitus' principle

 

 

[math]\int mv\ ds = \int p \cdot q[/math]

 

 

[math]ds = cdt[/math]

 

 

You can find an energy

 

 

[math]\int E = \int p \cdot \dot{q}[/math]

 

 

Our generalized coordinate [math]\dot{q}[/math] has absorbed the time term. You find the clock to matter by distributing a frequency

 

 

[math]\int \hbar\ dr_s = \lambda \int [mv \cdot q][/math]

 

 

The mass term requires a coefficient: [math](\frac{c^2}{\hbar})[/math] to become a frequency term itself. This would imply a relativistic change in the wavelength [math]\lambda_2 - \lambda_1 = \Delta \lambda[/math] since frequency and wavelength are related

 

 

[math]\nu = \frac{c}{\lambda}[/math]

 

 

[math]\lambda = \frac{c}{\nu}[/math]

 

 

distributing the coefficient we have (including a factor of 2 as true zitter term)

 

 

[math]\int d r_s\hbar\ (\frac{c^2}{\hbar}) = \lambda \int [2m(\frac{c^2}{\hbar})v \cdot q][/math]

 

 

This gives time to matter! The equation simplifies to

 

 

[math]\int c^2 \ dr_s = \lambda \int [2m(\frac{c^2}{\hbar})v \cdot q][/math]

 

 

[math]\int c^2 r_s = \mu[/math]

 

 

In the Planck sceme and using strong gravity [math]G_s[/math] we have

 

 

[math]\int c^2 \ dr_s = \lambda \int [2m(\frac{c^2}{\hbar})v \cdot q][/math]

 

 

Multiply by [math]\frac{G}{c^2}[/math] gives

 

 

[math]G_s dr_s = \int c^2 \ dr_s \frac{G_s}{c^2}= \lambda \int [2m_P(\frac{c^2}{\hbar})v \cdot q]\frac{\ell}{m_P}[/math]

 

 

multiply through by [math]m^2[/math] and cancel out the length

 

 

[math]\hbar c = \lambda \int [2m_P(\frac{c^2}{\hbar})v \cdot q]G_s m =  \lambda \int [2m_P(\frac{c^2}{\hbar})v \cdot q]\mu[/math]

 

 

Knowing the Weyl quantization relationship [math]\hbar c =Gm^2[/math] means we have the charge.

 

 For a strongly bound photon in the high gravity range would move in a circulatory motion, this is of course zitter motion.

                                                             

Indeed, a photon trapped in a minimized proper change in time given by the equation

 

[math]\lambda(\gamma_L|_{\delta [t_1,t_2]}) = \Delta t_0[/math]

 

 

Where [math]\gamma_L[/math] be a Lipschitz-continuous function

 

 

[math]\lambda(\gamma_L|_{[t_1,t_2]}) = |t_2 - t_1|[/math]

 

 

In the proper frame, the phase of the orbital and rotation of the internal photon is

 

 

[math]\phi = \omega_P (\lambda(\gamma_L|_{\delta [t_1,t_2]}))[/math]

 

 

It's proper time must be described by the length of the confined photon

 

 

[math]\omega_P \ell_P(\gamma|_{\delta [t_1,t_2]}) = \omega \gamma(\lambda(\gamma_L|_{\delta [t_1,t_2]}) - \frac{v \cdot \ell_P}{c^2})[/math]

 

 

The phase is then related to the structure of gravity and the wavelength of the photon via

 

 

 

[math]\sqrt{\alpha_{G_s}} = \sqrt{\frac{Gm_{P}^{2}}{\hbar c}}[/math]

 

 

[math]= (\omega_P t_P) = 2 \pi f \gamma(\lambda(\gamma_L|_{\delta [t_1,t_2]}) - \frac{v \ell_P}{c^2})[/math]

 

 

And we have a connection to time as well within this fine structure in the beginning as well from our action equation we first presented.

 

 

 

 

 

ref 1. Hestenes, The zitter clock

 

ref 2. https://books.google.co.uk/books?id=XUKXYiGs8KcC&pg=PA140&lpg=PA140&dq=mass+squared+term+importance&source=bl&ots=jrvxv3oGya&sig=HYWB3eEUCgW-KR7iRcmcVKnfpck&hl=en&sa=X&ei=KZDKVOD_PMz3UqjzgYAK&ved=0CFMQ6AEwCA#v=onepage&q=mass%20squared%20term%20importance&f=false

Edited January 30, 2015 by Lucious