Hi Pervect,(adsbygoogle = window.adsbygoogle || []).push({});

Since you deleted my last post, and gave me a3rdwarning, the Forum readers no may longer have a context for what this post is about. So I need to make it clear, in the interest of intellectual integrity, that I am confessing my errors and apologizing for misstating theacceptableviews about the Friedmann equation.

I have re-adjusted my interpretation of the following excerpt from Simon Singh's 2005 book, "Big Bang, The Origin of the Universe." Singh has a PhD in particle physics from Emmanuel College, Cambridge University and also studied at CERN, Geneva. He has been awarded the Kelvin Medal from the Institute of Physics in 2008, for his achievements in promoting Physics to the general public. Here is the excerpt:

"Friedmann explained howhis model of the universe could react to gravity in three possible ways, depending on how quickly the universe started expanding and how much matter it contained. The first possibility assumed that the average density of the universe was high, with lots of stars in a given volume. Lots of stars would mean a strong gravitational attraction, which would eventually pull all the stars back, halting the expansion and gradually causing a contraction of the universe until it collapsed completely. The second variation of Friedmann’s model assumed that the average density of stars was low, in which case the pull of gravity would never overcome the expansion of the universe, which would therefore continue to expand forever. The third variation considered a density between the two extremes, leading to a universe in which gravity would slow but never quit halt the expansion. Thus the universe would neither collapse to a point nor expand to infinity."

Finally, I appreciate that Singh DID NOT actually mean thatFriedman explained howhis model of the universe could react to gravity in three possible ways, depending on how quickly the universe started expanding and how much matter it contained.

What Singh must have really meant was that the 2nd Friedmann equation was derivedONLYfrom the Einstein Field Equations. His derivationcould not in any wayhave been influenced by the concept of "escape velocity", i.e., the concept that the expansion rate depended on how quickly the universe started expanding and how much matter it contained.

I note in passing the following statement in the Wikipedia article on the FLRW metric:

"[This FLRW] equation can be derived also from thermodynamical considerations and is equivalent to the first law of thermodynamics, assuming the universe expansion is an adiabatic process (which is implicitly assumed in the derivation of the Friedmann-Lemaître-Robertson-Walker metric).

Having re-adjusted my thinking, I now understand that Wikipedia should be interpreted as saying that the Friedmann equations were derivedONLYfrom the Einstein Field Equations, and not from the first law of thermodynamics. (The first law of thermodynamics of course says, in the context of an object launched from a gravitational mass, that what goes up, must come down, unless it has enough momentum to escape.) To attribute such a thought to Friedmann or Lemaitre would not only bewrong, but I would also be compelled to take 100% credit for Wikipedia's statement as my own personal theory. The honor would be great, but not worth the penalty. So I must renounce any such theory.

Finally, I ruefully mustrenouncethe unsubstantiated theory if one starts with the 2nd Friedmann equation and substitutes 3M/4PiR^3 for the mass density element, the two equations are functionally equal. Even if it were true (which I am not permitted to suggest here), one MUST ACCEPT that such equivalence is a COMPLETE COINCIDENCE. Surely it ispreposterousto suggest that, in deriving his equation from the Einstein Field Equations, Friedmann would have taken any notice of the first law of thermodynamics or its related concept of escape velocity.

I have one final statement to make. The Friedmann equation is unequivocally derived ONLY from the Einstein Field Equations. Any resemblence to the first law of thermodynamics or the escape velocity equation is acoincidence. I repeat it 3 times before bed each night.

Jon

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Friedmann recantation

Loading...

Similar Threads - Friedmann recantation | Date |
---|---|

B Help with understanding a Friedmann flat universe | Feb 7, 2018 |

Insights A Journey Into the Cosmos - FLRW Metric and The Friedmann Equation - Comments | Jan 12, 2018 |

Insights Coordinate Dependent Statements in an Expanding Universe - Comments | Jan 6, 2018 |

I Friedmann Equation - Positive Curvature | Dec 26, 2017 |

**Physics Forums - The Fusion of Science and Community**