The Flux Of Time, A Modern Perspective Of Time Physics

[Aethelwulf]

 

 

[math]v_i=\frac{\delta d_i}{\delta t} = \sqrt{\frac{2(E-V)}{\sum_i M_i(\delta d_i)^2}} \delta d_i[/math]

 

 

I feel compelled to clear something up. Someone argued to me on another site that the equation is not time independent... yes, the time still appears on the left,but the important quantity is the right hand side expression of the equation.

 

Barbour in this sense, really did make time vanish and he was completely justified in doing so.

Edited July 20, 2012 by Aethelwulf

[Aethelwulf]

(The right hand side) sorry. Fixed it :)

[Aethelwulf]

Here's a very interesting paper about diffeomorphism invariance resultant from a timeless non-dynamical model and asks if time is really fundamental

 

I can't provide a link, but you can look it up yourself

 

''Is the Notion of Time Really Fundamental? - MDPI''

[Pmb]

Here's a very interesting paper about diffeomorphism invariance resultant from a timeless non-dynamical model and asks if time is really fundamental

 

I can't provide a link, but you can look it up yourself

 

''Is the Notion of Time Really Fundamental? - MDPI''

I couldn't find one that I could download and read.

 

I still don't think that the momentum conjugate to time makes any sense. Its the energy that is conjugate to the time. Sometimes the Hamiltonian coincides with the energy; but it is the energy that is primarily concerned.

[Aethelwulf]

I couldn't find one that I could download and read.

 

I still don't think that the momentum conjugate to time makes any sense. Its the energy that is conjugate to the time. Sometimes the Hamiltonian coincides with the energy; but it is the energy that is primarily concerned.

 

I was able to find a link after all http://www.mdpi.com/2073-8994/3/3/389

 

Anyway, as for the momentum conjugate to time, I know, the name is off-putting because as you said, time and energy are conjugates of each other. I can't really explain it more however than the quote I provided and by saying it is in physics literature.

[Pmb]

I was able to find a link after all http://www.mdpi.com/2073-8994/3/3/389

 

Anyway, as for the momentum conjugate to time, I know, the name is off-putting because as you said, time and energy are conjugates of each other. I can't really explain it more however than the quote I provided and by saying it is in physics literature.

That's a journal article which is not available to the public. Therefore I couldn't download it.

[Rade]

That's a journal article which is not available to the public. Therefore I couldn't download it.

See this slide presentation by Girelli on the topic:

 

http://fqxi.org/data/documents/Girelli%20Azores%20Talk.pdf

[Aethelwulf]

That's a journal article which is not available to the public. Therefore I couldn't download it.

 

There is actually another copy of the work you can search for on the web... I just can't link that specific one. It is in a PDF but I can't link it for some reason

 

[PDF]

Is the Notion of Time Really Fundamental? - MDPI

www.mdpi.com/2073-8994/3/3/389/pdfFile Format: PDF/Adobe Acrobat - Quick View

by F Girelli - 2011 - Cited by 16 - Related articles

www.mdpi.com/journal/symmetry. Article. Is the Notion of Time Really Fundamental? Florian Girelli 1,⋆, Stefano Liberati 2 and Lorenzo Sindoni 3. 1 School

[Rade]

There is actually another copy of the work you can search for on the web... I just can't link that specific one. It is in a PDF but I can't link it for some reason

Try this link:

 

http://fqxi.org/data/essay-contest-files/Girelli_timeessayfinal_1.pdf

[Aethelwulf]

Thank you Rade.

[Aethelwulf]

And so there are some reasons why a covariant form of

 

[math]\hbar \nabla^2\psi = \dot{m}\psi[/math]

 

would be more acceptable. For starters, let us write out the complete time-dependent form of the flow equation in a covariant form

 

[math](\hbar \Box - \dot{m})\psi = 0[/math]

 

Another way to write this is

 

[math](-\hbar \eta^{\mu \nu}\partial_{\mu} \partial_{\nu} - \dot{m})\psi = 0[/math]

 

Taking the effect of gravity into the equation, the equation would then take the form

 

[math](-\hbar g^{\mu \nu} \nabla_{\mu}\nabla_{\nu} - \dot{m})\psi = 0[/math]

 

The more complicated version of this but still equivalent is

 

[math]-\hbar(g^{\mu \nu} \partial_{\mu}\partial_{\nu} + g^{\mu \nu} \Gamma^{\rho}_{\mu \nu} \partial_{\rho})\psi = \dot{m}\psi[/math]

Edited August 3, 2012 by Aethelwulf

[Aethelwulf]

Now the reason why the Covariant form

 

[math](\hbar \Box - \dot{m})\psi = 0[/math]

 

Is perhaps the better approach, is because our previous form

 

[math](\hbar \nabla^2 - \dot{m})\psi = 0[/math]

 

Is not time independent - time appears as a derivative in [math]\dot{m}[/math]. Because of this, just for consistency, [math]\nabla^2[/math] might be better replaced with its time dependant cousin [math]\Box = \frac{1}{c^2}\frac{\partial^2}{\partial t^2} - \nabla^2[/math].

Edited August 3, 2012 by Aethelwulf