On Tuesday, January 14, 2020 at 3:37:22 PM UTC-7, Alan Grayson wrote:
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> On Tuesday, January 14, 2020 at 11:56:51 AM UTC-7, Alan Grayson wrote:
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>> On Tuesday, January 14, 2020 at 10:27:27 AM UTC-7, John Clark wrote:
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>>> On Tue, Jan 14, 2020 at 6:47 AM Alan Grayson <agrays...@gmail.com> 
>>> wrote:
>>>
>>>  
>>>
>>>> > >It is true for a de Sitter universe as a solution of the Einstein 
>>>>> equations. If the universe is spherical, it will eventually recontract, 
>>>>> and 
>>>>> light cannot get right round and back to its starting point before the 
>>>>> universe recontracts to a point. If the universe is expanding via dark 
>>>>> energy, even if spherical, light still cannot get round because of the 
>>>>> expansion. In other words, you can never see the back of your own head no 
>>>>> matter what the geometry of the universe!!!!!
>>>>> Bruce
>>>>>
>>>>>>
>>>> > *Since it's not a perfect sphere* [...]
>>>>
>>>
>>> Because we're talking about curved Spacetime and not curved space and 
>>> because non-Euclidean geometry must be used (due to that minus sign that 
>>> sneaks into Pythagoras formula if time is one of the dimensions) it's 
>>> misleading to call it a "sphere", it's even misleading to call it the 
>>> surface of a 4D sphere. What we really want to know is it the geometry of 
>>> the universe is open or closed.
>>>
>>
>> *Hypersphere; closed; if you believe it's age is finite. AG *
>>
>>>    
>>>
>>>> *> light never exactly returns to its starting point. That's just an 
>>>> approximation *
>>>>
>>>
>>> That's what happens in a de Sitter universe, its flat and open and you 
>>> get a de Sitter universe if the universe is not dominated by matter but by 
>>> the Cosmological Constant, which is probably Dark Energy.
>>>
>>
>> *Since it's not perfectly homogeneous, a beam of light can be bent, this 
>> way and that way, so it's unlikely to return exactly to its point of 
>> origin. You know, what we OBSERVE and MEASURE is an expanding universe, so 
>> an ad hoc insertion of an infinite spatial extent is suspect. AG*
>>
>
> *It's like a leaf on a tree. The leaf is our universe, closed and finite 
> in spatial extent. It's attached to what I've called "the substratum", 
> analogous to a tree, possibly infinite in spatial extent and having an 
> infinite past. Let's call it "the Tree of Life". Our universe is connected 
> to it, has been since the BB, which is why it's expanding, like a leaf 
> growing.  AG*
>

*A fruit tree is a better analogy, since most fruits are approximately 
spherical, as is our universe (hyper-spherical); observable and 
non-observable regions. It must be somehow connected to its source or 
origin, but how that connection manifests is currently above my pay grade. 
The problem with current models of a flat universe is that the infinity of 
spatial extent implied, seems like an ad hoc hypothesis, not organically 
connected with the rest of the theory. AG *

>
>> Already about 74% of the matter/energy in our universe is in the form of 
>>> Dark Energy, and as time progresses that percentage can only increase and 
>>> we'll get closer and closer to a pure de Sitter universe. That's because 
>>> the Cosmological Constant is a property of empty space, so as the 
>>> accelerating universe creates more space it also creates more Dark Energy, 
>>> however the total amount of matter (both regular and dark) remains fixed.  
>>> And in a de Sitter universe the distance between any 2 non-accelerating 
>>> points will, given enough time, eventually be moving apart faster than the 
>>> speed of light.
>>>  
>>>
>>>> *> **Let's forget it. These discussions are worthless.*
>>>>
>>>
>>> It appears you are not following your own advice.
>>>
>>> John K Clark 
>>>
>>

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