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Aug29-08, 09:38 AM
PF Gold
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P: 522
In the context of cosmology, the Friedmann-Acceleration equation highlights the need to understand the components that contribute to both the energy density [tex][\rho][/tex] and pressure [P]:

[1] [tex] \left(\frac {\ddot a}{a} \right) = - \frac {4 \pi G}{3} \left( \rho + \frac {3P}{c^2} \right) [/tex]

However, I was hoping somebody might be able to answer some questions, in part-2, about the relationship between [tex][\rho][/tex] and [P] specifically related to radiation. First some initial references with respect to mass [m]:

[2] Energy Density [tex]\rho = Energy/Volume [/tex]
[3] Pressure [tex]P = Force/Area [/tex]
[4] [tex]P = \omega \rho c^2[/tex]

On this basis, I can see how the units between [tex][\rho][/tex] and [P] are resolved, albeit that there is no explanation of [tex][\omega][/tex] other than it is a ‘weighted’ number with no units. If I expand [2] for matter as follows:

[5] [tex]\rho = mc^2/Volume [/tex] or
[6] [tex]m =\rho V/c^2[/tex]

As such, I have a relationship between [tex][\rho][/tex] and [m], but while [4] alludes to a corresponding relationship between [m] and [P], I must first define [tex][\omega][/tex]. This seems to be done on the basis that matter in the universe is so low its density can be treated on par with dust and, as such, has no pressure and so [tex][\omega=0][/tex].
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