The Flatness Problem; solved?

[Gibsense]

Space is curved; time rotates at a position away from an observer.

Time runs perpendicular to space (curved in a closed universe) and therefore rotates at an increasing distance from an observer. The current practice of assuming time always runs parallel in the universe is an error.
Many posts on this forum allude to space curvature (eg hypersphere and the balloon). See post "Flatlander3D: Hypersphere to Flat Space"

Reading the book 'Sphereland' has prompted me to state the answer above explicitly even though this forum had already 'covered' the issue. So much so ( and Cat will appreciate this), that Cat's favourite analogy to illustrate the expansion of the universe (inflating a balloon) also serves as an analogy to illustrate space curvature (and hence time rotation)

This answer is obvious.
As illustrated in the book Sphereland we 3D people cannot visualise 4D space and therefore time rotation. And, like the King in 'Sphereland', we are ignorant of the curvature reality of the space we live in. The King in Lineland could only sense 'the line' and could not agree/visualise a line curved as this involves an extra dimension to his confinement in a line. Similarly, we cannot visualise (except mathematically) the additional dimension of 4D space.

The Dragon in the room then is the Curvature of the Universe. Some recent research suggests a 5% (?) bias of extra mass indicates the universe is closed and therefore 'curved'. Problem? What problem?

If space is curved; time rotates at a position away from the observer.

 

[Gibsense]

Problem? What problem?

Maybe I should add that although Relativity mathematically describes reality, I wonder if the insistence that time is the 4th dimension has misled us all. I personally am convinced that there is an embedding space of 4 dimensions and that time is a process occurring within those 4 dimensions and is NOT the 4th dimension.
Prove me wrong........

 

[CryptoCraig]

Space is curved; time rotates at a position away from an observer.

Time runs perpendicular to space (curved in a closed universe) and therefore rotates at an increasing distance from an observer. The current practice of assuming time always runs parallel in the universe is an error.

I agree 100%, time isn't parallel to space, it can't be. Time dilation should be proof to this.

An observer is really never experiencing the present moment. What an observer sees and hears is "delayed" by the speed of light and sound. This delay, in everyday life, is usually microseconds. When observing very large or distant objects or when observing at the atomic level, this delay can be significant.

If light can bend due to gravity, that should be a clue that the speed of light may have changed, causing the bend. If light bends around a large mass, why are the different wavelengths not separated, or are they? Is the difference in speed due to time being compressed/expanded where the light curved? Or is space compressed/expanded where the light curved?

Mass and speed will bend time. What else can bend/alter time?

 

[Atlan0001]

Your very observation of light from any distance whatsoever requires there be more than one vector dimension of light involved. Your very observation of anything at all from a distance, including detecting the gravity of the dark universe, requires the involvement of more than one vector dimensionality of light.

 

[Catastrophe]

Is there not something very wrong with a balloon analogy?

As the balloon expands, the "spot" on the surface expands. Ergo, a ruler expands, and a flatlander using the ruler would not measure expansion. The ruler would still show x cm..

As our "universe" "expands" we stay the same size, and thus appreciate expansion.

Cat

 

[Gibsense]

Is there not something very wrong with a balloon analogy?

As the balloon expands, the "spot" on the surface expands. Ergo, a ruler expands, and a flatlander using the ruler would not measure expansion. The ruler would still show x cm..

As our "universe" "expands" we stay the same size, and thus appreciate expansion.

The general consensus is that cosmic expansion has minimal effect in gravitationally bound areas; in other words, gravity counters expansion. Bill mentioned in another post the degree of expansion observed in the Solar System.

However, if you recognize that the vector for expansion is orthogonal to space, it becomes easy to explain. As illustrated in the sketch below, the expanding "force" affects the gravity well shape of space at right angles to that space. Because this expansion is orthogonal to space, the shape remains unchanged while the rest of the universe expands outward.

Understanding gravity as the curvature of space rather than as a force is essential. To illustrate this, consider the balloon analogy: the surface of a balloon can have various shapes and does not have to be a perfect sphere. Think of the oddly shaped balloons that maintain their form when inflated.

This logic can be extended to explain 'c' etc all in a big holistic idea but I'll not bore you with it now.[url=https://postimages.org/]share picture[/URL]

 

[Catastrophe]

The balloon analogy is based on a spherical balloon.

Even that is not a good analogy, because you have the neck sticking out, and there will be minor deviations in elasticity. No analogy is perfect.

A flatlander, by definition, is not able to discern another space dimension. Analogies are not meant to be infinitely variable to "prove" infinite imaginary situations. Analogies prove nothing; they provide inanimate "pegs" on which to "hang" selected ideas.

Cat

 

[Gibsense]

The balloon analogy is based on a spherical balloon.

Yes, that is so but why do you point this out? The diagram is a cross-section of course. A balloon with little ears maybe - it doesn't matter it's just to show that pressure applied evenly would result in a proportional increase allowing for ( as you point out) the balloon material may vary.

 

[Atlan0001]

The "Mandelbrot set" pointed out one fact I seem to be the only one to see. The Flatlander will observe and realize both infinite breadth and depth within the 1-2-dimensionality of Flatland. A realization that there is far more dimensionality to Flatland than previously realized . . . thus far, far, more dimensionality to 3-4-dimensionalty than we realize.

One (soliton bubble wave-like) example:
================

Tesseract - Wikipedia

en.wikipedia.org

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The very realization of soliton-gravitational waves....
================

Inverse-square law - Wikipedia

en.wikipedia.org

================

 

[Gibsense]

The "Mandelbrot set" pointed out one fact I seem to be the only one to see. The Flatlander will observe and realize both infinite breadth and depth within the 1-2-dimensionality of Flatland. A realization that there is far more dimensionality to Flatland than previously realized . . . thus far, far, more dimensionality to 3-4-dimensionalty than we realize.

One (soliton bubble wave-like) example:

Do you mean that the fractals just keep on going as if to hint at greater depths hence another dimension?

 

[Catastrophe]

The general consensus is that cosmic expansion has minimal effect in gravitationally bound areas; in other words, gravity counters expansion. Bill mentioned in another post the degree of expansion observed in the Solar System.

However, if you recognize that the vector for expansion is orthogonal to space, it becomes easy to explain. As illustrated in the sketch below, the expanding "force" affects the gravity well shape of space at right angles to that space. Because this expansion is orthogonal to space, the shape remains unchanged while the rest of the universe expands outward.

Understanding gravity as the curvature of space rather than as a force is essential. To illustrate this, consider the balloon analogy: the surface of a balloon can have various shapes and does not have to be a perfect sphere. Think of the oddly shaped balloons that maintain their form when inflated.

This logic can be extended to explain 'c' etc all in a big holistic idea but I'll not bore you with it now.[url=https://postimages.org/]share picture[/URL]

Gibsense, I was pointing out that, where the "inkspot observer" expands pro rata, then "he" will not observe the expansion because his ruler will expand similarly. Just to point out that analogies cannot be generalised too widely.

I have noticed another fault, or restriction. Over small expansions it appears OK, but, of course, if (using 2D flatland analogy) the inkspots approach 180 degrees apart, they would be moving parallel to each other, and eventually would start moving towards each other.

Another example of not following analogies too far. Of course, the analogy is worthwhile at smaller times/expansions, but will break down if pushed too far.

Of course, if you substituted an ellipse (or hyperbola) for the circle, the expansion would just approach to become constant at "infinity", or after "infinite" time.

Cat

 

[Gibsense]

Gibsense, I was pointing out that, where the "inkspot observer" expands pro rata, then "he" will not observe the expansion because his ruler will expand similarly. Just to point out that analogies cannot be generalised too widely.

I have noticed another fault, or restriction. Over small expansions it appears OK, but, of course, if (using 2D flatland analogy) the inkspots approach 180 degrees apart, they would be moving parallel to each other, and eventually would start moving towards each other.

Another example of not following analogies too far. Of course, the analogy is worthwhile at smaller times/expansions, but will break down if pushed too far.

Of course, if you substituted an ellipse (or hyperbola) for the circle, the expansion would just approach to become constant at "infinity", or after "infinite" time.

A person and his ruler do not get bigger;
They are part of the gravity well, as are the planet, sun, galaxy, and cluster. Yes, the sketch is still analogical but that is the point! Analogies exist as a way of understanding that which is only accessible by mathematics like imagining spacetime (a 4D object spatially modified i.e. length by width by height and not by x, but by 'c' or - if you prefer - 't').

The sketch is the best I can do and I believe it is valid - just 2 dimensions dropped.

I am having difficulty understanding the second paragraph regarding 180-degree parallel expansion. If you refer to the expansion of a sphere this cannot occur. Perhaps you are looking at the end trumpet shape of many illustrations to show an expanding universe that is flat (?)

The thing is that this does not show the universe as flat. It is a 5-dimensional drawing with 2 dimensions dropped. Each ring illustrates the universe at various times and also represent n-spheres so the final rings at the ends of the 'trumpet' are still spheres!

If expansion acceleration is real, then an infinite universe will happen in time (provided spacetime can stretch without the balloon bursting ! ). However, the universe may not be accelerating - there is doubt as I attempt to show.

Again you will need to help me understand the last paragraph. Guessing at your meaning, I should say that the surface of a ball (the sphere) is 2D. As it gets bigger there is no parallel expansion between dots.

I would expect the universe to be a slightly flattened sphere (although understanding his reasoning for Hawking ruling a perfect sphere out is beyond my pay grade) and a rough surface (covered in gravity wells). I suspect you are trying to show a spherical universe as invalid

 

[Gibsense]

I misspoke. Spacetime is not 3D space x 'c'. It is a modified 3D space by the curvature of a hypersphere