Flat and closed

twr

Oct 23, 2019
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I read in an article from space.com the following:
"In an open, flat universe, the photons, left undisturbed, would travel along their parallel courses without ever interacting."

I think that is not correct. The universe can be flat and closed nevertheless and the parallel course of photons wouldn't meet.

Think of a torus.

BG TWR
 
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Aug 14, 2020
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Flatness is simply a reductionist view of multi-dimensionality to 2-dimensionality.... then 1-dimensionality.... then 0-point dimensionality. Dimensionalities of balloon / ballooning in dimensionality. In which case the twain would either be always expanding apart from a point-position-entity, or always coming together to a point-position-entity, or third possibility, simultaneously both. In other words, there would be no such thing as being "left undisturbed."
 
I read in an article from space.com the following:
"In an open, flat universe, the photons, left undisturbed, would travel along their parallel courses without ever interacting."

I think that is not correct. The universe can be flat and closed nevertheless and the parallel course of photons wouldn't meet.

Think of a torus.

BG TWR
The article is saying that a flat or open universe has parallel lines staying parallel or diverging, respectively.

A closed model is one where “parallel” lines will eventually converge.
 
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I read in an article from space.com the following:
"In an open, flat universe, the photons, left undisturbed, would travel along their parallel courses without ever interacting."

I think that is not correct. The universe can be flat and closed nevertheless and the parallel course of photons wouldn't meet.

Think of a torus.

BG TWR
I don't think a torus could be considered flat. Although, as you point out, the 2 photons would remain parallel but they are still going round in warped space. I'm not sure whether the article you are referring to means 2 individual photons or a continuous beam. For individual photons they will never interact as you say, but beams will meet up with their source. Note they are only parallel when orbiting around the external centre and not when going round the short way, for want of better words.
 
The article is saying that a flat or open universe has parallel lines staying parallel or diverging, respectively.

A closed model is one where “parallel” lines will eventually converge.
Hasn't twr pointed out a closed and non-flat model where, at least in one direction, 2 parallel lines wont ever meet each other?
 
Aug 14, 2020
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Hasn't twr pointed out a closed and non-flat model where, at least in one direction, 2 parallel lines wont ever meet each other?
Can't happen. We are realizing where Newton's first law will never work given enough space and time, either in an open / an opening system, or in a closed / a closing system. Einstein's "steady state" universe only works as an ultimate net balance of forces, motions, changes, and exchanges. An ultimate net result '0' of energy with '1' left over. In point, to make a point, the Universe (U) at the speed of light (c=1 ((+/-)'300,000kps' -- inertial finite closed / closing systemic, local foreground relativity speaking) and/or 0 ('uncertainty' -- inertialess infinite open / opening systemic, non-local background QM speaking)). I do get wordy, but there are several dimensions involved, and all of them involved at once (all a multi-dimensionality to be kept inseparably in mind at once).
 
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A light-time frame is a single-sided flat 2-dimensional frame of light-time existing at the speed of light. Therefore it, light-time (light / time), can never be caught up to from the rear because it masslessly has no such thing as a rear. Observers and travelers will always deal in fronts regarding light. You might picture it this way, any rear to light-time you might conceive of would in fact be a light-time front mixed in coming from somewhere (light / times in and at "crossroads"). No rearward face / no existence rearward to front.

Now that I've made that as plain as I can, I will advance in dimensionality to higher, more 'multi'-dimensionality. An expanding universe. At 1,000 light-years the traveler witnesses an Earth, if he can witness an Earth, circa 1021 CE It matters not what direction out from Earth, it is the in-light expanded virtual surface of the Earth at 1,000 light years from Earth in any direction, and all directions, out from Earth. And so on the physic on out into the universe beyond the Milky Way, beyond Andromeda, beyond the local galactic cluster....

Is the picture stop action frozen in space-time? The dead center point of the focus is, but nothing else in the accelerating expansion of the ever increasing inclusion of light-time(s) periphery into the frame, at the ballooning surface flatness of the frame, is. The speed of light 'c' is quite busily geometrically squaring, so to speak. And its no naked singularity of "speed of light" based center point to the ballooning frame. The point of Earth being the center of the universe is only one center of an infinity of center points of accelerating expansions ('c' squaring's) of light-time frames. And there are light-time (space-time) "crossroads" throughout the entire system. All travelers, including all observers, all animations, pass through the "crossroads," the 'Multiverse'. They total up to -- they reduce to -- just one overall universality of crossroad, Stephen Hawking's "Grand Central Station" (and "Grand Central Clock") of Universe (U).
 
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Something may be misleading in my post #7 above. I took little explanatory account of gravity's distortions or the fact that every object in the universe, therefore the quanta dynamics-like boiling cauldron of the greater universe (u), and Universe (U), itself, is always in motion (always in animation). The graduating reductionist look to photo-like stillness, a nakedly singular mural, regarding the background universe(s) in no way reflects any of this.... well, not really. The actual motion and animation would only have grown greater, vaster, faster, and even seemingly hotter, the more into non-local background (from any local foreground) the universe gets in space-time. The reductions through horizons to photo-like stillness is a collapse in ever increasing mass complexity (regarding background) to ever increasing simplicity of picture (regarding foreground). Of course that distant mural, as distant mural, does have its own realization; its own dimensionality; its own reality; its own entity; its own crunch and bang and vacuum of physicality. No universe traveler would or could ever -- open systemically -- grasp it (it would be forever beyond his reach), in a far distantly fixed, redshifted always, horizon from him. Evolutionary universe would always be coming out (blueshifted) of that distantly maintaining horizon mural toward him as he tried to travel toward, traveling into, the revolutionary horizons (the revolutionary divides (relativity to relativity, to relativity,....), Now (t=0), to Now (t=0), to Now (t=0),.... an always one the same constant of Now (t=0), out of Infinity constant (t=1)).
-------------------------

It's a Multiverse Universe.
 
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