1. Hubble's Law
Hubble's Law provides a linear relationship between the recession velocity
of a galaxy and its distance from us. The equation is:
v = H_0 \times d
Where:
is the recession velocity of the galaxy (the rate at which it moves away
from us due to the expansion of space),
is the galaxy’s distance from us,
is the Hubble constant (the current rate of expansion of the universe).
2. Speed of Light Threshold
To determine when a galaxy's recession velocity exceeds the speed of light
, we can rearrange Hubble's Law to find the critical distance at which this
occurs:
v = c \implies H_0 \times d = c
Solving for :
d = \frac{c}{H_0}
This distance, known as the Hubble distance, is the point beyond which
galaxies recede from us faster than the speed of light due to the expansion
of space. For a typical value of around 70 km/s/Mpc, this distance is
approximately 14 billion light-years.
3. Superluminal Recession Beyond the Hubble Distance
When a galaxy is located at a distance greater than the Hubble distance ,
its recession velocity exceeds the speed of light. However, this does not
violate special relativity because the galaxy isn't moving through space
faster than light—the space between us and the galaxy is expanding.
4. General Relativity and Expanding Space
The framework of general relativity allows for the expansion of space
itself, where two points in space can recede from each other faster than
the speed of light without breaking the laws of physics. The light emitted
by such galaxies can never reach us if the space between us continues to
expand faster than the light can travel.
Conclusion:
Mathematically, based on Hubble's Law, any object at a distance greater
than will recede faster than the speed of light due to the continuous
expansion of the universe. This superluminal recession is a natural
consequence of the geometry of expanding space and does not require any
change in the local speed of light.
This shows, geometrically and mathematically, that the distance between two
galaxies can increase faster than the speed of light if they are separated
by more than the Hubble distance. This is guaranteed by the continuous
nature of the expansion as described by Hubble’s Law.
Le mer. 11 sept. 2024, 09:42, 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 megaparsec
> distant 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
>
>
> *That's your claim, but, like I wrote, if say, the rate of expansion is
> fixed, the separation distance isn't increasing faster than c. It's just
> increasing. AG *
>
> * John* K Clark See what's on my new list at Extropolis
> <https://groups.google.com/g/extropolis>
>
> hwt
>
>
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