Genady

Does a phenomenon become 'emergent' after we find a way to describe how it emerges? If a condition for a phenomenon to be emergent is to "be described without knowing or needing from what they exactly emerge", and the evolution of a wave function is a phenomenon that is "described without knowing or needing from what they exactly emerge", how come that this phenomenon does not qualify as being emergent?

Do 'regularity' and 'existence and uniqueness' mean the same?

Does a qualification of being 'emergent' apply to a phenomenon or to an equation describing it?

Schrödinger equation describes the phenomenon of a wave function evolution without knowing or needing from what it exactly emerges. Does it make this phenomenon an emergent one?

Which regularity makes differential geometry effective in describing GR?

Aren't there two different concepts: one is 'probability', the other - 'probability density'?

Twenty seven years ago, our Marine Park started a long-term "experiment" in coral development, albeit inadvertently. They installed concrete mooring blocks, 1m x 1m x 1m, along the town shoreline for yachts and boats to moor. Coral colonies began inhabiting the block faces. Years later, I’ve noticed that this intriguing growth is not randomly uniform but instead follows patterns, some quite puzzling. Here is one of them. There are two lines of the moorings between South and North ends of the downtown boulevard. One line consists of a dozen moorings constructed from three blocks each and is located about 50m from shore, just near the reef drop-off. Another line consists of a dozen moorings constructed from two blocks each and is located on the sand-flat, half way between the reef drop-off and the shore. I've compared exposed vertical faces of the blocks near the drop-off and those of the blocks near the shore. Where would one expect to find more corals? Wouldn’t corals prefer to grow near the reef and away from the town shoreline with all its polluted water and sewage runoff? The corals provided surprises. More coral colonies grew on the faces of the blocks close to the shore than on those close to the reef. Only 12% of the faces of the off-shore blocks are covered with live corals, like here: Twice as much, 25%, of the close-to-shore block faces are covered with live corals, like here: What is going on? Are shore effects good for the corals? Are some off-shore effects bad for them? What factors are responsible? Any ideas? Questions? More info?

Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Step 1.5: = (28)2 + 28*38 + (38)2 Step 2: = (28)2 + 2*28*38 + (38)2 - 28*38 Step 2.5: = (28 + 38)2 - (24*34)2 Step 3: = (28 + 38 + 24*34)(28 + 38 - 24*34) = 8113*5521

Sure. The photons would change the particle's momentum, but not the observation. They would do so also if not observed.

Observations do not change the physical behavior of particles. They behave just the way they behave.

Thank you for the detailed answer. As a synopsis, classical GR doesn't lead to a "start of time". Quantum GR might, albeit not necessarily.

Shh. Nothing moves faster than light. Mass or not.

Ignoring particles and staying with geometry for now. As we go back in time, the three spatial dimensions of spacetime collapse, but the temporal dimension survives. So, at the BB the 4D spacetime geometry is replaced by 1D time geometry (there are no many choices for geometry in 1D.)

Einstein is not an idiot. Einstein is not, period. Just like that famous parrot: 'E's not pinin'! 'E's passed on! This parrot is no more! He has ceased to be! 'E's expired and gone to meet 'is maker! 'E's a stiff! Bereft of life, 'e rests in peace! If you hadn't nailed 'im to the perch 'e'd be pushing up the daisies! 'Is metabolic processes are now 'istory! 'E's off the twig! 'E's kicked the bucket, 'e's shuffled off 'is mortal coil, run down the curtain and joined the bleedin' choir invisible!! THIS IS AN EX-PARROT!!

But the second part in Dark Energy is Energy. That is what goes into that formula, Masha.

If I'm allowed to speculate here, I could imagine that in that hot dense particle soup, before Higgs and before symmetry breaking, all particles were massless. Thus, time was "frozen", like the time of a photon is.

Yes, space has mass. Substitute a dark energy for E in E=mc2 and you get the space mass. PS. As my math teacher used to say, "For my every question he has his every answer."

Why is it often said that "time itself started with the Big Bang"? If you take the scale factor in the Friedmann–Lemaître–Robertson–Walker metric to zero, then the spatial component goes to zero, but not the temporal one. In other words, space contracts, but nothing happens to time. Or, in the words of A. Zee, "In our current description, space is created at the Big Bang, but not time." (Zee, A. Einstein Gravity in a Nutshell: p. 787). So, any idea from where the notion of beginning of time in BB comes from?

Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Step 1.5: = (28)2 + 28*38 + (38)2 Step 2: = (28)2 + 2*28*38 + (38)2 - 28*38 Step 2.5: = (28 + 38)2 - (24*34)2

Yes, the third one. There is one more after that. Thanks a lot. Right. Or by endlessly repeated (esp. in a pop-science) reference to "mathematical beauty".

This is all correct. The overlap between Mathematics and Physics is far from being complete. Especially, from the Mathematics perspective (I might be just a bit biased ). Mathematics is much-much larger than the part used in Physics. The OP, however, was why there is such an overlap at all and quite a big and essential one, from the Physics perspective.

On the other hand, sometimes these numbers turn out to be not requiring any theoretical basis. For example, Kepler worked hard to find a geometrical principle explaining why Solar System has five planets. Of course, it turned out that there are more than five, but moreover, it turned out that this number as well as the planets' given orbits, are just an incidental consequences of the Solar system evolution.

The highly successful Standard Model has about two dozens of such numbers that need to be just put in by hand. One of the criteria for a good theory Beyond Standard Model is to have fewer of those.

Yes, this is one direction of thought. For example, see the reference here: I don't like this direction of thinking. I rather think in the opposite direction, similar to Penrose and to this: In other words, it is not math that corresponds to the physical world, but rather physical theories that correspond to math. Physical theories, to be good theories, need precision, rigor, clear concepts, they need to be free of human prejudices, psychology, vague language, etc. Math has exactly these attributes. Physical laws are described mathematically by necessity. To this argument (which is Penrose's one, not mine) I add a bit of biology. For example, humans, like all other mammals, have an area of the brain responsible for computing a "mental map" of the surroundings. It evolved because it gives obvious advantages to the organism. And of course it computes specifically 3D maps. Why would it do any other kind? We never needed to deal with any other kind. Thus, we are good in visualizing in 3D. Now, studying phenomena beyond our immediate experience, we stumbled upon other kinds. We cannot use our visual imagination and intuition, and our everyday language, to describe them. Mathematics is the only available tool.

May I reply point by point? Starting with the last point? Thank you. I didn't mean it as an offence. I didn't mean to shut you up. Please, continue commenting and explaining. Am I obligated to reply? That is what I think is not always necessary, is it? May I reply only on comments that are of interest to me? Somebody else might be interested and reply on other comments. In my opinion, discussions, unlike arguments, don't have to end in agreement or disagreement. They can just give a food for further thought.