Genady

I don't think we can't know that. We don't know yet. Chances are that quantum gravity theory will let us know.

I think it boils down to this: 3a+2b=1 a2>b Show that a3>1/64

I disagree. If one follows the development, one can see that all these grand cosmological theories come from experiment and observation processed by human mind.

Ai, robots, computers, automobiles, dishwashers, typewriters, bicycles, steam engines have equal effect on definition of life.

My tank is larger than your tank.

My tank: Bonaire National Marine Park - Stinapa Bonaire

I do not do any other forums. Never did. I am not even sure what it means. I guess it relates to home aquariums. My aquarium is too big to keep at home. Fortunately, it takes care of itself pretty well. It has a lot of fish, naturally.

I don't know for sure, but I very much doubt it. Everyone here, including Dutch, have Bonaire resident cards.

Why would I care who invented XYZ? I am sure that person has a name. I am also quite sure I don't know that person. The most importantly, I don't know what XYZ is except it has something to do with corals. I know something about corals.

Yes. Even if it is copied and pasted from the magazine.

Cool. But don't come all at once. Bonaire’s laid-back beauty might blow you away. The food will, too. - The Boston Globe

That is what we see on a starry sky. We see one picture that includes stars as they were just several years ago and stars as they were thousands of years ago, all at once. Another example is multiple images of a galaxy created by its light going around a massive object by different routes. As these routes are of different lengths, we see at once the galaxy as it was at different times in the past.

I've never heard of this. Can I read an abstract?

Maybe, to keep focus, threads should be limited to, say, 63 or 127 replies. If members want to continue a discussion beyond that, somebody will start a new thread with a clear formulation of the issue from scratch.

Looks like 55 kg and 110 kg are masses of the skaters rather than of the walls. Look at them, one is thin, and the other is not.

Right. The only issue is that I don't have any idea what we are discussing now and why. Yes, cylinder is flat. A cone is flat everywhere except the very tip. A bagel is not flat except along the very top and the very bottom. Etc.

Agreed. This detour was just a little exchange between @sethoflagos and me and should've been over with the @Markus Hanke's post above. However, some posters have picked up some comments as if they were standalone statements and have used them to educate the audience in an unrelated material.

You are correct. The discussion here is in terms of Riemann curvature, which is relevant for discussions on GR, usually. You are correct again. The mathematical treatment can be found in textbooks on differential geometry that include discussion on the spacetime of GR. Also, in bits and pieces, in articles on Internet. PS. The Riemann curvature is of course tensor rather than a matrix.

Yes, size and time. I think, this is the correct answer. I don't know. I don't know that theory well enough. To my very limited understanding, no. My answer to this is, Yes.

If the scale factor in FLRW metric is a constant, the space cannot expand or contract.

Yes, so? It is not a spacetime. The metric signature is different.

It goes like this. For the 3+1 dimensional spacetime to be flat, i.e., to have a vanishing curvature it has to be Minkowski, i.e., to allow coordinates in which the metric is Minkowski. For a spacetime with FLRW metric to allow this, the scale factor needs to be constant. Thus, with a non-constant scale factor, the spacetime with FLRW metric is not flat. We can keep one dimension, namely time, constant and consider the 3D slice separately. This 3D space can be Euclidean, hence flat.

I think that the issues has been already resolved, multiple times, e.g.,

The point of the above discussion was that even with k=0 precisely, the spacetime is not flat although the space is flat.

I am not sure about the smallest Plank; I've asked some questions about it for clarification in another thread but have never got a reply. Regardless, even in one splitting moment infinite number of universes may appear.