Hi - "Space being thinner" = If one imagines travelling in an orbit 1000 miles above the Earth and comparing it to swimming in a river and then imagine travelling in an orbit 100,000 miles above the Earth where it would feel like swimming in air. The fabric of space is less dense. So to cover the same distance through that medium you would have to go a lot further in geometrical terms. Note the orbital distances drawn on paper are geometrical distances that assume that the fabric of space is uniformly dense. This should also explain why C = 2πR doesn't work in an environment such as we are discussing. Thanks for your reply Hartman352
I understand the idea of varying densities and that atmospheric density is inversely proportional to altitude.
However, one can't simply say "space" alone, because it is called "space-time". When Einstein concocted his general theory of relativity, one of the great advances was to recognize that space and time were combined into a single entity: spacetime. Another was that the presence of matter and energy curved the very fabric of this spacetime, and that curved spacetime, in turn, dictated how matter moved.
If you’ve ever seen a picture of a bent, two-dimensional grid with masses sitting on it representing space, you’ll know this type of illustration is extremely common. It appears to depict the "fabric of space" as being curved by the presence of mass, and therefore, any other particle traveling along this fabric will have its path bent towards this gravitational source. The larger the mass and the closer you get to it, the larger the curvature, and therefore, the larger the observable bending.
It appears as though a mass somehow gets pulled “down” onto the fabric, and then the other particles traveling through that space are pulled “down” by some unseen, mysterious force as well. Additionally, the grid lines curve away from, rather than towards, the mass, which also can’t be right, especially if gravity is attractive.
The spacetime curvature around any massive object is determined by the combination of mass and distance from the center-of-mass. However, this two-dimensional grid-like depiction of spacetime isn’t necessarily the most accurate way to perceive it. (T. PYLE/CALTECH/MIT/LIGO LAB)
Gravity simply exists, while the equations that describe General Relativity are geometric in nature. The idea that mass-and-energy curves space is correct, even though this naive visualization is wrong when applied to real world space-time.
Greywolf says, "Swimming 1 mile through crude oil = the same as swimming 20 miles in air."
I think you have confused matter density and energy usage as opposed to matter density and distance. While the energy expended by swimming a mile through oil will be greater than swimming through distilled water or spring water, you should use apples to apples, etc., by using the same distance in each case when discussing the energy expended through actions carried out in different densities.
When speaking of distance in space-time, I don't see where simple geometry would not apply. But regardless of what fluid density one swims in or through, the set distances covered will, in each case, be the same.
Concentric orbital rings around a black hole of a million Solar masses, outside of the Schwarzchild radius, will still equate to C = 2πR, regardless of the amount of infalling matter which must be plowed through while navigating a particular circumference.
The effect that such matter density encountered will have is to increase the time the distance is travelled, thus determining speed, not distance. Speed = Distance/Time, and it's iterations (Speed is directly Proportional to Distance and Inversely proportional to Time. Distance = Speed X Time, and
Time = Distance / Speed) –
which tell us how slow or fast an object, and we, move. (See: https://testbook.com/learn/maths-speed-time-and-distance/
Thus, the distance travelled divided by the time taken to cover the distance equals the speed of travel. Matter density within that latter distance will affect the time needed to travel a particular distance, not increase the absolute distance.