Originally posted by convectBecause space time is curved in higher dimensions. According to Einsteins General Theory of Relativity matter bends spacetime. When light bends around a star (a well known and observed fact), it still travels in a straight line, however since space is bent, it can meet up with another light beam that took the other way around the star. There is a sphere around a black hole on which light can travel in a perfect circle whilst simultaneously traveling in a straight line.
Wait...how can light or a moving body with no forces acting on it move in a circle?
Also the universe as a whole is like a 4 dimensional sphere in that if you keep traveling in one direction you will eventually get back to where you started (a circle).
Originally posted by twhiteheadBut isn't that the same as a force acting on it?
Because space time is curved in higher dimensions. According to Einsteins General Theory of Relativity matter bends spacetime. When light bends around a star (a well known and observed fact), it still travels in a straight line, however since space is bent, it can meet up with another light beam that took the other way around the star. There is a sphere a ...[text shortened]... ou keep traveling in one direction you will eventually get back to where you started (a circle).
Originally posted by twhiteheadAnd has it been established that the Universe is in fact closed, and not open? I.e., if you go far enough in one direction you come back to where you started?
Because space time is curved in higher dimensions. According to Einsteins General Theory of Relativity matter bends spacetime. When light bends around a star (a well known and observed fact), it still travels in a straight line, however since space is bent, it can meet up with another light beam that took the other way around the star. There is a sphere a ...[text shortened]... ou keep traveling in one direction you will eventually get back to where you started (a circle).
I deal daily in Newtonian physics, and the only tensors I ever encounter are stress-energy tensors which don't transform coordinate systems nor have curvature or Riemannian metrics or whatever, so pardom my ignorance.
Originally posted by Andrew HamiltonA 3d balloon would logically require 3d space to expand into. Why would a 4d "balloon " universe not require 4d space to expand into?
Oh -I see, I had somehow totally misread what you said there -I must have been trying to read it way too fast I guess -my apologies 🙂
The balloon in this hypothetical experiment will be completely contained within a small part of our universe and would be 3-dimensional with negligible 4-dimensional curvature + the space itself within it will not ...[text shortened]... t forget all the analogies thrown at you and study the properties of 4-dimensional geometry. 🙂
Originally posted by twhiteheadYou are in fact changing the definition of straight simply due to
A straight line: A line, which within the dimensions that it is being discussed, is one dimensional. In mathematical terms it would be defined as x=a where a is constant, and x is a given axis.
A circle is defined as being a straight line when using the polar co-ordinates in two dimensions ie r=a where a is constant and r is the radius. So circles are ...[text shortened]... of diverging lines later converging.
If you have better definitions, then please let us know.
perspective, straight is still straight and circles are still circles, and
looks can be deceiving. Latitude and longitude are still references
that circle the globe, I understand you position, I am still in
disagreement with you. We can create a flat map of the earth and
the latitude and longitude could appear to be straight lines on it
too; however, reality they are never straight lines they reference
the circle the planet.
Kelly
Originally posted by twhiteheadThis is where we differ, if it is bending it is no longer straight.
Because space time is curved in higher dimensions. According to Einsteins General Theory of Relativity matter bends spacetime. When light bends around a star (a well known and observed fact), it still travels in a straight line, however since space is bent, it can meet up with another light beam that took the other way around the star. There is a sphere a ...[text shortened]... ou keep traveling in one direction you will eventually get back to where you started (a circle).
Kelly
Originally posted by twhiteheadYou are wrong, if it forces something to bend it is acting upon it. It is
No it isn't. There are some subtle differences which have been tested and Einsteins predictions are what is observed.
no dfferent than a ship at sea that is setup to run a straight course,
but is throw off course,because either the water or the wind causes it to
go off by altering its course.
Kelly
Originally posted by twhiteheadDo this, find a globe lay a yard stick across on top of it does the
You are yet to provide a definition of a straight line. By my definition it is still a straight line.
yard stick remain straight? Wrap a tape measure around it, did the
tape measure bend?
Define straight again and tell me did the globe change anything?
Kelly
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Originally posted by knightmeisterin this context -correct -it wouldn’t require any 4-dimensional space to expand into in THIS context. You are still visualising it 3-dimensionally but at the same time not realising that visualisation is wrong.
A 3d balloon would logically require 3d space to expand into. Why would a 4d "balloon " universe not require 4d space to expand into?
You cannot visualise in 4-dimentions and some of the properties of typical 3-dimensional space do not apply to 4-dimensions in this context -so you have to think outside the box if you are ever to understand what the physicists understand.