Genady

PS. When I said, and what I meant was removing the r-dot term of the equation for approximation. (@joigus)

Sorry, @joigus for not making myself clear. I do not suggest adding gravitational and kinematical effects as I know that all is already there in the equation. What I did was not something common-sensical but rather something algebraical, by simply substituting expression for (r-dot)/c = v/c in the second equation above, instead of approximating it by 0, as you did in your approximation. Is there a mistake in my algebra? I'd like to know.

Thank you, @joigus for the clarity. This calculation shows - both formally and intuitively - how the proper time behaves if we consider only the gravitational time dilation. I am just not convinced that we can ignore the kinematical time dilation of the free-falling from infinity observer C. That is because for such an observer, (v/c)2 = (1-rs/r)2(rs/r) Substituting it in the second equation above gives, I believe, dτC= (1-rs/r)dt rather than dτC= (1-rs/(2r))dt making τC smaller than in the calculation above.

The quoted post was the @AlexanderSamualDunnett's greatest contribution to the total well-being rating of all beings...

What is it?

What @Mordred said, plus the better picture is them being squeezed all together into one crazy soup of elementary particles rather than torn apart. Good night to both of you.

No, they don't get smaller. Yes, it is. The explosion occurs into the space. In expansion, the entire space is expanding.

Phew lol

Yes, I am. I understand that this is what you've referred to in: I don't know. There are many inflationary models on the market. I am referring to the standard Big Bang model, LCDM, and to the expansion which we observe.

It was not clear. In this case, I've asked wrong questions. In this case: I don't know anything about M. Kaku, but I've read several books and have heard several presentations of R. Dawkins. I think that AI's imitation of R. Dawkins is OK in words used, but completely wrong in content. I think, his response would be very different, sharp and short.

Why is it unlikely?

Are there mysteries there?

Which mysteries?

We don't have much air traffic here. Only about 2 jets a day. I am sure there was no jet on that line that day. I certainly would've noticed otherwise. Moreover, the "trail" stays in place without going anywhere for a couple of minutes while the wind blows, and the clouds move.

Could be, especially since there is in fact another island in that direction, not far behind the horizon, about 50 miles away. However, the data don't support it. The camera is pointing to the West, the sunset. The prevailing wind is from the North-East, the trade wind. The wind blows from the West only during one short period in September called, wind reversal. I didn't observe this phenomenon during a wind reversal.

This phenomenon can be observed on the island where I live at sunset. From time to time, not often, maybe a few times a year. This image holds for a couple of minutes and then fades and dissipates. I think I know the answer, but I might be wrong. Pix from my porch:

Normally, yes. But this OPer was not serious and was not really interested and has been banned. So, now we're free to discuss the question in any context. I consider a proton to be a "bag" of two positive and one negative charges. At a small enough distance, the electron would induce the proton to be more positive in the electron direction and more negative in the opposite direction. Increasing the attraction as a result. Perhaps, at a small enough distance electron and neutron also attract, by a similar mechanism. Your thoughts?

Me too. Still?

Maybe at some very small distances?

No. They can only affect a mindset, but they cannot "make" a specific mindset as there are other factors affecting it.

You are absolutely right. It is, however, not what the OP question was about. It depends on the initial conditions.

Expansion of space is a purely gravitational effect. When I walk away from the computer the distance between me and the computer increases. It has nothing to do with the space expansion. Matter is not continuously created in the space expansion.

Because they move in this case under their electrostatic repulsion, not under their gravity.

No, they would not.

So, we're talking about a bunch of ionized hydrogen atoms. Yes, they will repel each other electrostatically, and the group will fly apart. They will move in space. It will be the same space as before. Change in their configuration will change a configuration of their gravitational field.