On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson <[email protected]> wrote:
> > > On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote: > > The Scientific American article "Misconceptions About The Big Bang" by > Charles Lineweaver and Tamara Davis at > https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf > (distilled from their more technical review 'Expanding Confusion' at > https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. > 42-43, along with other common misconceptions: > > "Running to Stay Still > the idea of seeing faster-than-light galaxies may sound mystical, but it > is made possible by changes in the expansion rate. Imagine a light beam > that is farther than the Hubble distance of 14 billion light-years and > trying to travel in our direction. It is moving toward us at the speed of > light with respect to its local space, but its local space is receding from > us faster than the speed of light. Although the light beam is traveling > toward us at the maximum speed possible, it cannot keep up with the > stretching of space. It is a bit like a child trying to run the wrong way > on a moving sidewalk. Photons at the Hubble distance are like the Red Queen > and Alice, running as fast as they can just to stay in the same place. > > One might conclude that the light beyond the Hubble distance would never > reach us and that its source would be forever undetectable. But the Hubble > distance is not fixed, because the Hubble constant, on which it depends, > changes with time. In particular, the constant is proportional to the rate > of increase in the distance between two galaxies, divided by that distance. > (Any two galaxies can be used for this calculation.) In models of the > universe that fit the observational data, the > denominator increases faster than the numerator, so the Hubble constant > decreases. In this way, the Hubble distance gets larger. As it does, light > that was initially just outside the Hubble distance and receding from us > can come within the Hubble distance. The photons then find themselves in a > region of space that is receding slower than the speed of light. Thereafter > they can approach us. > > The galaxy they came from, though, may continue to recede superluminally. > Thus, we can observe light from galaxies that have always been and will > always be receding faster than the speed of light. Another way to put it is > that the Hubble distance is not fixed and does not mark the edge of the > observable universe. > > > *I don't think this is the consensus view, which is that the Hubble > constant IS constant, and galaxies beyond our event horizon will never be > seen, if the universe in their region is expanding faster than c. AG * > Davis and Lineweaver are just reviewing the current consensus view in that article and paper, not suggesting any new physics. In general relativity's cosmological solutions there is a time-dependent "Hubble parameter" whose value at any given cosmological time is called the "Hubble constant" at that time, but which can change over the long term (see the first paragraph of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html for example). Astrophysicist Ethan Siegel mentions in an article at https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that even in models that don't have accelerating expansion due to the cosmological constant, the Hubble constant still need not be constant in time. He explains this by looking at the first Friedmann equation governing an expanding universe, where a term equivalent to the definition of the Hubble constant is on the left side of the equality and the right side has terms for energy density, global curvature of space, and the cosmological constant. So, in an expanding universe that's spatially flat and has zero cosmological constant, if the energy density is changing as matter/energy becomes more spread out, the term equivalent to the Hubble constant must be changing as well. From the article: "Even if you had a flat Universe (which means you can eliminate the second term on the right-hand side) and a Universe without a cosmological constant (which would mean eliminating the third term on the right-hand side, too), you’d understand immediately that the Hubble “constant” cannot be a constant in time. ... In all cases except for a cosmological constant (i.e., dark energy, to the best of our understanding), the energy density changes as the Universe expands. If the energy density changes, that means the expansion rate changes, too. The Hubble constant is only a constant everywhere in space, as we measure it right now. It’s not a constant in the sense that it changes over time." Siegel has another article covering a lot of the same issues at https://www.forbes.com/sites/startswithabang/2018/06/29/surprise-the-hubble-constant-changes-over-time/ where he also mentions that it got the name "Hubble constant" because "for generations, the only distances we could measure were close enough that H appeared to be constant, and we've never updated this". > > What does mark the edge of observable space? Here again there has been > confusion. If space were not expanding, the most distant object we could > see would now be about 14 billion light-years away from us, the distance > light could have traveled in the 14 billion years since the big bang. But > because the universe is expanding, the space traversed by a photon expands > behind it during the voyage. Consequently, the current distance to the most > distant object we can see is about three times farther, or 46 billion > light-years." > > > *But within the observable universe, space is expanding at a rate less > than c. Correct? So the 46 BLY distance doesn't seem right. AG* > Galaxies within the observable universe can be receding faster than c, as mentioned in that Davis/Lineweaver quote earlier, and in their review paper at https://arxiv.org/pdf/astro-ph/0310808 in section 3.3. If this seems like an intuitive contradiction it may help to be more precise about how cosmologists define the term "observable universe": the radius of the observable universe is defined in terms of the *current* proper distance (see https://en.wikipedia.org/wiki/Comoving_and_proper_distances#Uses_of_the_proper_distance on the meaning of 'proper distance' in cosmology) of the most distant objects (at rest relative to the cosmic microwave background radiation) such that if they emitted light towards us at some point in the *past*, the light would have been able to reach us by now. This doesn't necessarily mean that if a galaxy in the observable universe emits light *today* that the light will ever be able to reach us. One way of visualizing this definition more easily is using the "comoving distance", which is equal to the proper distance at the current time but which is adjusted so that the comoving distance of all objects at rest relative to the CMBR is fixed, i.e. if a galaxy has a proper distance of 9 billion light years today then it had a comoving distance of 9 billion light years in the distant past, say a billion years after the Big Bang, even though its proper distance at that time was much smaller (the 'scale factor' in cosmological equations gives the proportionality between the proper distance to the comoving distance). If you have a graph of various galaxies plotted in terms of the comoving distance, then the size of the observable universe is just the maximum size of our past light cone on this graph--see the last two of the three graphs Fig. 1 on p. 3 of that Davis/Lineweaver paper at https://arxiv.org/pdf/astro-ph/0310808 where the lines labeled "light cone" show our current past light cone which defines the size of the observable universe (the third graph is visually simplest because they use a "conformal" time coordinate which has a varying relation to ordinary proper time, in such a way that all light ray worldlines are 45 degree angles just like in special relativity graphs--on that third graph the left axis shows the conformal time, the right axis shows the proper time). The two graphs with comoving distance also show that the maximum size of our past light cone is identical to the *current* size of our "particle horizon", which is just the future light cone of our location at a point arbitrarily near the Big Bang. So the observable universe can also be defined in terms of the particle horizon (i.e. the current distance to the furthest galaxy that could receive a light signal from our location emitted at some point in the past). And like I said above, one consequence of these definitions is that just because a galaxy is currently within the observable universe, that does not rule out the possibility that light emitted from the galaxy *today* will never be able to reach us. This is shown by the third conformal graph in Fig. 1, where the definition of conformal time is such that an infinite future proper time is only a finite interval of the conformal time, so the top of the graph shows the maximum distance any given light ray will reach at a proper time of infinity. This means we will never see any events outside our past light cone at infinity, which is labeled our "event horizon" on the graph. If you think of the vertical dotted lines on the graph as worldlines of particular galaxies, you can see there that some of them were at one point within our past "light cone" which has an apex at the current time, but their current location in spacetime (where their worldlines intersect with the horizontal 'now' line) is outside the "event horizon", our past light cone whose apex is at infinite future proper time. So, we will never receive light from those galaxies as they are today, but since we can receive light from them that they emitted in the distant past, their current location is considered part of the "observable universe". Jesse > > > > On Mon, Sep 16, 2024 at 12:53 AM Alan Grayson <[email protected]> wrote: > > It's claimed to be 46 billion LY, but its age is only measured as 13.8 > billion years. What I find puzzling about these numbers is that it seems > this would imply the rate of expansion must have been greater than c during > its lifetime. But AFAICT, the measured rate of expansion using Hubble's law > never exceeded light speed before it reached its present size. Can anyone > explain this apparent discrepancy? TY, AG > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/eb57d007-3a2d-45ff-9e99-78039ee01022n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/eb57d007-3a2d-45ff-9e99-78039ee01022n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/e0e2ee64-c917-4fd3-9d30-0183d9635da1n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/e0e2ee64-c917-4fd3-9d30-0183d9635da1n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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