On 9/11/2024 1:16 AM, Quentin Anciaux wrote:


Le mer. 11 sept. 2024, 10:08, Alan Grayson <[email protected]> a écrit :



    On Tuesday, September 10, 2024 at 3:50:08 PM UTC-6 Quentin Anciaux
    wrote:



        Le mar. 10 sept. 2024, 23:19, Alan Grayson
        <[email protected]> a écrit :



            On Tuesday, September 10, 2024 at 2:19:42 PM UTC-6 John
            Clark wrote:

                On Tue, Sep 10, 2024 at 3:57 PM Alan Grayson
                <[email protected]> wrote:


                        *>> Even if you ignore Dark Energy and
                        postulate that the Hubble constant really is
                        constant, every object a megaparsec away (3.26
                        million light-years) is moving away from us at
                        about 70 kilometers per second. So if you try
                        to look at objects a sufficiently large number
                        of megaparsec away you will fail to find any
                        because they are moving away from us faster
                        than the speed of light.*


                    >/That was in the past. At present, the universe is
                    expanding at about 70 km/sec./


                *Galaxies are receding from the Earth at 70 km/sec for
                EACH megaparsecdistant from Earth they are. The
                further from Earth they are, the faster they are
                moving away from us, so if they are far enough away
                they will be moving faster than the speed of light
                away from us. *
                *
                *

                    /> You're assuming the universe today is infinite,/


                *NO! I said IF the entire universe is infinite today
                then it was always infinite, and IF it was finite
                10^-35 seconds after the Big Bang then it's still
                finite today. I also said nobody knows if the entire
                universe is infinite or finite. *

                    *>*///Hubble's law applies to the past, not to the
                    future,/


                *What the hell?!*


            *How about an intelligent reply? Obviously, if the
            universe is infinite today, it was always infinite. But
            that's what I am questioning. For galaxies to fall out of
            view, they have to moving at greater than c. Now they
            aren't receding that fast. How will they start moving that
            fast? You're applying Hubble's law without thinking what
            it says. Just because a galaxy is now receding at less
            than c, how will continued expansion increase that speed
            to greater than c? AG *


        The farther they are the faster they are receding from you, so
        as they continue to get farther away they receed faster from
        you till the point they receed faster than c and go out of
        your horizon.

        Quentin


    Prove it, if you can. I see the separation distance increasing
    linearly as the radius of the sphere expands, so light can reach
    either galaxy, from either galaxy. AG


To address your point about the linear increase in distance, here's how distant galaxies can still recede faster than the speed of light, even with constant expansion:

1. Hubble’s Law:
Hubble’s Law shows that the recession velocity (v) of a galaxy depends on its distance (d) from us:
v = H0 * d
Where H0 is the expansion rate. This means that as the distance increases, the recession velocity increases proportionally.

No.  Note that v is just ddot = H*d  So it's a differential equation with solution d=c*exp(Ht) where c is the distance at time zero.

Brent


2. Linear increase in distance:
You're right that, with a constant expansion rate, the distance between two galaxies increases linearly with time. However, because recession velocity depends on distance, the farther apart two galaxies are, the faster they recede from each other. So, even if the distance grows linearly, the recession velocity grows proportionally with distance.


3. Hubble Distance:
The key point is the Hubble distance:
d_H = c / H0
At distances greater than this, the recession velocity exceeds the speed of light (c). This doesn't violate relativity, as it's the space between galaxies that expands faster than c, not the galaxies moving through space.


4. Analogy of the balloon:
Think of two points on the surface of an inflating balloon. As the balloon expands at a constant rate, the distance between the points increases linearly. However, if the points are far enough apart, they will move away from each other faster than a closer pair of points. Similarly, in the universe, even though the expansion rate is constant, galaxies farther apart recede faster due to their increasing distance.


5. Why light can’t reach us:
For galaxies beyond the Hubble distance, the space between us expands faster than light, meaning their light can never reach us. This is why galaxies eventually move out of our observable universe.



In summary, even with a linear increase in distance due to constant expansion, the recession velocity increases with distance, and for sufficiently distant galaxies, this velocity eventually exceeds c.

                *John* K Clark   See what's on my new list at
                Extropolis <https://groups.google.com/g/extropolis>

                hwt


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