Genady

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.

Yes, and I understand (although disagree) that there is. Moreover, some divisions create infinite numbers of the universes at one splitting point.

Yes, but there is infinite number of points on that finite line where the universes split.

A lack of definition is not a 'big problem.' Most of the concepts we use in life, science and even many in math lack definitions. For another example, AI recognizes faces, cars, molecules, etc. without definitions. Only when we understand something really well, we can come up with a good definition for it.

No, we are not.

Yes, it is extremely close to flat spatially, but the discussion here is about flatness of spacetime, and the spacetime of our universe is not flat.

Because expanding (or contracting) spacetime is not a flat spacetime.

A flat spacetime would be Minkowski spacetime. A homogenous isotropic universe is not.

On these scales the universe seems pretty flat spatially, as I understand, and this has no relation to the time translation symmetry, does it?

Thanks. I think I understand you.

Could you describe a bit of what you mean by this, please?

Einstein was invited to a dinner where he was asked by a hostess to "be so kind as to explain to my guests in a few words, just what is relativity theory." He said he was reminded of a walk he one day had with his blind friend. The day was hot and he turned to the blind friend and said, "I wish I had a glass of milk." "Glass," replied the blind friend, "I know what that is. But what do you mean by milk ?" "Why, milk is a white fluid," explained Einstein. "Now fluid, I know what that is," said the blind man. "but what is white ?" "Oh, white is the color of a swan's feathers." "Feathers, now I know what they are, but what is a swan ?" "A swan is a bird with a crooked neck." "Neck, I know what that is, but what do you mean by crooked ?" At this point Einstein said he lost his patience. He seized his blind friend's arm and pulled it straight. "There, now your arm is straight," he said. Then he bent the blind friend's arm at the elbow. "Now it is crooked." "Ah," said the blind friend. "Now I know what milk is."

Thank you for mentioning it. This reminded me about the question I wanted to ask for some time: Is Planck time the shortest time only in combination of GR with QM? In other words, it is the shortest neither in the standard QM nor in the standard GR, but only if GR is extrapolated to very small distances? If so, how certain it is as there is no established theory of quantum gravity? Another question: If tP is a short interval measurable in some rest frame, wouldn't we be able to measure a shorter part of it if we move fast enough relative to that frame, because of the time dilation? (I.e., tP in the rest frame will become γtP in our frame which is >tP)

I don't think so. Let's take Schrödinger equation, for example. It relates time derivative d/dt and spatial derivative d/dx. Thus, it assumes that time interval and distance can be infinitesimally small together.

There is no finite limit to how small a time interval between events can be (in QM, SM, SR, and GR.)

My professors and textbooks in classes on evolution have never mentioned anything like this. What does it mean?

Yes, we could, and no, it would not. We also could, and do, work in natural units with c=1, in which case there is no multiplication nor division by c, and units of length and time are the same.

If a mutation occurs in a cell of tissue A during early development, soon after it differentiated from cells of other tissues, wouldn't most or all of its daughter cells, which could be most or all of the tissue A cells, carry this mutation and thus have DNA different from DNA in other tissues?

Exactly! +1 So, what is the difference that makes "curious minds" so unhappy with time, and not with space, that they feel a need to do something about it, up to and including, to eliminate it completely from the picture? It doesn't seem to be in our visual sensations, per @iNow's explanation above. BTW there is a good answer to Carl Sagan's question, It flows past events. Anyway. I think that the difference is numerical, namely in the speed of light which is a very big number, and which separates our perception of time from that of space. As we turn or walk, we observe spatial changes in the environment. On the other hand, it seems that whatever we do, time keeps flowing all by itself. But in fact, it is an optical illusion caused by the speed of light being so different from our everyday speeds. If speed of light were, say, 5mi/h, as soon as we started walking, we would observe temporal changes in the environment. And then, I think, the mystery of time would be no more. Or, at least, it would be no more mysterious than space.

We set up experiments in classical physics as well. And the outcomes of those experiments depend on our setup. This is not special for QM. The detector does not need to have a mind to affect the outcome.

It will happen the same way if an observer is nowhere. For example, you can videotape the experiment and throw the tape away. The results will be the same. It is the fact of measurement rather than that of observing that makes the difference.

It does not. This is misunderstanding. In QM, mind does not change an expected outcome. Nor any other outcome.

The above quote demonstrates that time is a difficult concept. It does not however describe time as being a more difficult concept than space. More to the point, Carl Sagan emphasizes difficulties of the physics of time, while @swansont emphasizes biology of our senses: If I understand it correctly, it means that the time concept is more difficult because it is not visual. I am curious, if blind persons think that space is more 'mysterious' concept than time?

Thus, this reads, "A collective human recognition of limitations declares that god does not have a gambling problem with dice games." Is it correct?