In 2009 the Hubble telescope measured Hubble's constant $H_0$ to be $74.2 \pm 3.6$ km/s/Mpc. Graham D obtains a value of $78.3$ km/s/Mpc, but I suspect this needs to be modified somewhat. Anyway, if we view $H_0$ as an angular frequency, then it corresponds to a characteristic energy of $E = \hbar H_0$.
For example, for $H_0 = 77.7 = 2.522 \times 10^{-18} s^{-1}$, the characteristic energy will be $E = 0.00166$ eV, using $\hbar = 4.1357 \times 10^{-15} / 2 \pi$ eVs. Traditionally, cosmologists turn $H_0$ into a current size for The Universe, given by $R = c / H_0$. This would be around $12.5$ billion light years for Graham D's value of $H_0$. But as Louise Riofrio likes to remind us, $R = ct$, and the speed of light was far larger in the early cosmic past. Measuring $H_{0}^{-1}$ is like measuring time. Since $H_0 = c / R$, we can say that $E = \hbar c /R$.
14 years ago
I looked at Graham D, and the changing light could also be a changing time.
ReplyDeleteUlla, that is the point of the changing $c$. Light speed helps us to define units.
ReplyDeleteThanx again for the linx!
ReplyDeleteYou are most welcome, Louise. Many people today know that the old cosmology is wrong, but the real $c$ change is still ahead.
ReplyDeleteHello Kea and everyone. Despite what I wrote and now write on the zooforum it was based upon addressing a public audience and getting basic science across in an interesting style as naive ideas evolved, ignoring any embarrassments that would occur as warts and all appeared and erupted. The members did appreciate this but as time progressed comments fell silent.
ReplyDeleteI'll address here all the comments that have appeared on Marni's site but not chronologically . I read through Louise's paper "GM=tC^3" this weekend and got a better impression of what you and Kea care about. I think Louise has it absolutely correct but with some caveats.
Newton knew the velocity of sound in rock and in water. Expressed in today's units the densest of rock transmitted sound at 55 microsec/ft and for water 190 microsec/ft. But not all average rocks are the same average density Specific Gravity(SG) 2.7 versus water SG 1. But some rocks are less dense, full of water filled porosity so he used the bulk density, the measured SG as SG^(1-f) where f is the fractional porosity.For other bulk properties such as how heat is transmitted for what we now call thermal conductivity the measured bulk property eg. for rock Kr and for water as Kw to give the bulk property Kb as the geometric product Kr^(1-f)*K^f
Newton tried this approach for sound velocity in air. He knew the velocity of sound in air varied so he devised an f factor called crassitude. It was totally wrong and he was vilified for it, but he didn't care. Nor did the protagonists realise the PVT relationships and what was to become thermodynamics.
They still use the time average relationship of sonic velocities as the Wyllie equation and empirical corrections to different rock types in sedimentary basins. Each basin has its own correction factor lol. At high porosity and permeabilty there is a small change of sonic velocity depending upon the rheological properties, many muds are thixotropic. Many years ago I derived a relativistic Whyllie type equation for phonon velocities in rocks that was never used subsequently!
Anyway Newton got his average rock density for the Earth as twice the above density but it still wasn't the correct value that his theory demanded ca. SG 5.5
He tried the approach to measure light speed. He knew it depended upon the bulk property of empty space. But he gave up after a short time. Why? He realised the velocity of light was greater than not only the Earth's gravitational escape velocity say 7 miles/second, where he just had a chance for a measurement to that of the solar escape velocity ca. 27 miles/second. Since he knew that all stars were just like our sun the less bright stars were farther away, the brightness diminishing by the inverse square law. He also knew from his law of cooling, where he could feel but not see the loss of warmth or phlogiston from a hot object ( don't actually touch it), that they would eventually cool after about 80,000 years; a long time in as a ratio since the divine creation ca. 5,500 years before. We attempt the same calculations ever since.
A light bulb is porous but not permeable. Most bulk properties have both factors. There are great voids and filamentous structures of galaxies with matter and dark matter. Over a great distances the homogeinity and isotropy structure average out, hopefully.
I posted in case there was a length glitch and I've now forgotten where I was (glum).
ReplyDeleteLouise's matter density agrees with Planck derived units and this would suggest we reside in a gigantic black hole. We have the same problem Newton had and infact ever since Einstein.
Weinberg's approach was that critical density, the 3H^2/(8*Pi*G)is derived from what we see out to substantial z , at a distance beyond which all local velocities are minimal relative to the Hubble flow. His critical density doesn't change much from the relativistic corrections. Also, Omegam is much less than Omega critical. For the Omega ratio =1 then the contributions for gravitational matter is 0.3 at best. Note that the used neutrino densities mass fraction 0.0003 are derived from Weinberg's approach when he used only two neutrino species that were massless. So like relic photons their wavelengths were stretched to negligeable energies, their original greater energies transferred to the gravitational field. However, neutrinos now have a rest mass, whose energy can become dominant after great elapsed time and expansion. For an Omega =1 condition as Louise develops, the universe expands, gravitation slows the expansion almost hovers but never stops and marks time before eventual collapse. A tiny fraction of Omega <1, eventual collapse; Omega>1 continued expansion.
H is imprecisely known ca. 5-10% error. The supernova standard candle data are the best we have and the best available after correction for dust and as Robert Kirschner points out we now have independent checks and tie ins with the distance to the larger Magellanic cloud at ca. 160,000 light years. The z value come from spectral wavelength shifts it doesn't give velocities of recession. Ho is imprecisely known and you can't really quote it to more than two figures.
Oops I reached the 4096 character limit so I've appended it on the galaxyzoo forum
Best Wishes Graham
Welcome to AP, Graham! We are very happy to see you here. Apologies for the delays in comment posting. By the way, it is entirely optional, but if you want to you can comment using inline latex between dollar signs.
ReplyDeleteNeedless to say, each person here has their own research interests. But I think I am finally optimistic that we can all put together a picture that is not merely hopefully coherent, but manifestly coherent. Apologies also for my many ramblings and errors, but I do as Graham does and heed not the concerns of those who cannot listen.
Viva the $c$ change.
Sorry to ask again, but I am only a simpleminded biologist. If time is compressed it gives the redshift. How is mass changed by the compression?
ReplyDeleteIn Louise's cosmology the universal mass obeys $M = t$. This happens in Penrose's cosmology too, which is why the maths mumbo jumbo often says things like 'conformal boundary'. But which masses are you talking about? We have also previously discussed different possible rest mass scalings with cosmic time. And we have yet to properly understand the spectra.
ReplyDelete