For your further information bsengstock20, I can take you through the assumptions made by Hawking and Penrose in their 1970 paper and we can then see how their perfect mathematical proof actually says nothing meaningful about the universe.
The singularities of gravitational collapse and cosmology | Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
This is from the paperâs abstract.
The theorem applies if the following four physical assumptions are made:
(i) Einsteinâs equations hold (with zero or negative cosmological constant),
(ii) the energy density is nowhere less than minus each principal pressure nor less than minus the sum of the three principal pressures (the âenergy conditionâ),
(iii) there are no closed timelike curves,
(iv) every timelike or null geodesic enters a region where the curvature is not specially aligned with the geodesic. (This last condition would hold in any sufficiently general physically realistic model.)
Hawking and Penrose had to assume these four things, for the following reasons. First, because at the time of writing the value of the universeâs cosmological constant was unknown. That was rectified in 1998, but in such a way that it violated assumption number 1.
Second, because at the time of writing Alan Guth and Andrei Linde hadnât yet formulated the theorem of cosmic Inflation. They did this in 1979/80 and in doing so their theorem violated Hawking and Penroseâs second assumption. All three of the principal pressures (matter, energy and the Inflaton field) modelled in inflation theory are equal to minus the sum of the three principal pressures. Exactly the opposite of what is needed for the second assumption to hold. In a nutshell, the Singularity theorem is incompatible with Inflationary theorem from get go.
The status of the third and fourth assumptions made by Hawking and Penrose were unknown then and remain unknown to this day. They pertain to the very earliest moments of the universeâs existence and as such are forever closed off to investigation using any part of the electromagnetic spectrum. The Cosmic Microwave Background (CMB) is responsible for this. It forms an opaque âwallâ that cannot be penetrated by anything except gravitational waves. That is why the closest cosmologists can get to observing the Big Bang event itself is 380,000 years after it. Before that time the temperature, density and pressure of the CMB was too high for any light signals (of any frequency) to pass through it. Back in 2014 the BICEP2 science team claimed to have detected a B-mode polarization signal imprinted on the CMB, made by gravitational waves emanating from the Big Bang. But this result was later shown to be an artefact generated by interstellar dust. So, assumptions three and four of the H - P remain purely theoretical and supported by no observations, no data and no evidence.
So hereâs the score card for the Hawking - Penrose Singularity theorem.
Assumption # 1 - Falsified by the discovery of a small but positive cosmological constant in 1998.
Assumption # 2 - Incompatible with Inflation, which is confirmed by multiple lines of evidence.
Assumption # 3 - To date unconfirmed, due to the obscuring effects of interstellar dust.
Assumption # 4 - Ditto.
Thereâs another lesson to be learned from all of this bsengstock20.
A proof is only as good as the assumptions it is based upon.
If they are found to be faulty, are contradicted by empirical evidence or are untestable, then even if the proof is mathematically sound, it still fails.
Thank you,
Walter.