Evenstar wrote:My big problem isn't Halloween... I've been viewing a couple Great Courses on the universe that, although both are over 10 years old now, describe a 'spatially flat' universe one minute but acknowledge too that one (Hubble Telescope) can see off in every direction some 13+ billion light years and still find galaxies (~14 billion light years still being the 'big bang'). I am clearly missing on how tens of billions of galaxies in every direction in a 3-dimensional universe can be described as 'spatially flat'?!
I have never tried putting all this into words before and doing so should actually help but it hasn't yet. One thing also involved that I cannot grasp is how in this spatially flat 3-dimensional universe spacetime curves. I would love to KISS.
Okay...go for it. Somewhere I figure that if I read enough different descriptions of my topic all will click into place... Please--no math. And if the curvature of spacetime can be left out of spatially flat that would be terrific. Also...pointing me favorite links to resolve this rather than writing it all out here is logical. Perhaps I'll try googling this one more time too but dare to post anyway. Thanks.
If you don't like math, then I should be the perfect person to explain it to you, because I am math-allergic, too. (And at least I
hope that I will be able to explain it to you.)
The way I understand curved spacetime, it means that spacetime can be thought of as an "elastic sheet", and any massive object which is "resting on this sheet" will make bumps in it. The illustration at left shows the Earth in curved spacetime.
Another thing to remember about curved spacetime is that more massive objects will make bigger bumps.
This illustration suggests that the Earth is not inside the Sun's "bump", or gravity well, but that is certainly not true. Anything that orbits the Sun is
inside the Sun's gravity well, otherwise it wouldn't orbit it.
In black holes, a lot of mass is concentrated in a small or perhaps zero volume. Therefore a black hole is thought to
punch a hole right through spacetime. Einstein's theory of relativity can't explain how deep that hole would be.
So there are bumps and gravity wells in spacetime, and likely even holes. But that doesn't necessarily mean that spacetime considered as an entirety is curved.
I believe you can think of "curved but flat space" as a road with potholes in it. The potholes represent the numerous gravity wells in spacetime. Yet the road itself may well be "flat". The road doesn't necessarily go "uphill" or downhill". For all its potholes, it may well be sort of "flat".
That's how I think of it.
Ann
[quote="Evenstar"]My big problem isn't Halloween... I've been viewing a couple Great Courses on the universe that, although both are over 10 years old now, describe a 'spatially flat' universe one minute but acknowledge too that one (Hubble Telescope) can see off in every direction some 13+ billion light years and still find galaxies (~14 billion light years still being the 'big bang'). I am clearly missing on how tens of billions of galaxies in every direction in a 3-dimensional universe can be described as 'spatially flat'?!
I have never tried putting all this into words before and doing so should actually help but it hasn't yet. One thing also involved that I cannot grasp is how in this spatially flat 3-dimensional universe spacetime curves. I would love to KISS.
Okay...go for it. Somewhere I figure that if I read enough different descriptions of my topic all will click into place... Please--no math. And if the curvature of spacetime can be left out of spatially flat that would be terrific. Also...pointing me favorite links to resolve this rather than writing it all out here is logical. Perhaps I'll try googling this one more time too but dare to post anyway. Thanks.[/quote]
If you don't like math, then I should be the perfect person to explain it to you, because I am math-allergic, too. (And at least I [i]hope[/i] that I will be able to explain it to you.)
[float=left][img]http://i.stack.imgur.com/3vGJJ.png[/img][c][size=75]The Earth in curved spacetime. Source:
http://physics.stackexchange.com/questions/3009/how-exactly-does-curved-space-time-describe-the-force-of-gravity[/size][/c][/float]The way I understand curved spacetime, it means that spacetime can be thought of as an "elastic sheet", and any massive object which is "resting on this sheet" will make bumps in it. The illustration at left shows the Earth in curved spacetime.
Another thing to remember about curved spacetime is that more massive objects will make bigger bumps. [url=https://scienceisbrilliant.files.wordpress.com/2013/10/space-time1.gif]This illustration[/url] suggests that the Earth is not inside the Sun's "bump", or gravity well, but that is certainly not true. Anything that orbits the Sun is [url=https://s-media-cache-ak0.pinimg.com/564x/75/c4/96/75c496a4aabe5589fe8c70cdbef725d9.jpg]inside the Sun's gravity well[/url], otherwise it wouldn't orbit it.
In black holes, a lot of mass is concentrated in a small or perhaps zero volume. Therefore a black hole is thought to [url=http://ichef.bbci.co.uk/wwfeatures/wm/live/624_351/images/live/p0/2r/z7/p02rz7lq.jpg]punch a hole right through spacetime.[/url] Einstein's theory of relativity can't explain how deep that hole would be.
So there are bumps and gravity wells in spacetime, and likely even holes. But that doesn't necessarily mean that spacetime considered as an entirety is curved.
[float=right][img2]http://blogsdir.cms.rrcdn.com/91/files/2013/11/bar-roads.jpg[/img2][c][size=85]Road with potholes. Source:
http://www.equipmentworld.com/potholes-cost-drivers-more-than-700-annually-in-five-cities-with-roughest-roads/[/size][/c][/float] I believe you can think of "curved but flat space" as a road with potholes in it. The potholes represent the numerous gravity wells in spacetime. Yet the road itself may well be "flat". The road doesn't necessarily go "uphill" or downhill". For all its potholes, it may well be sort of "flat".
That's how I think of it.
Ann