MigL

What does that mean ?? You've been here long enough to know that there is no common now.

I'm confused; are CPU68 and CPU29000 the same person ? And, if so, what caused him to lose faith in Motorola processors of 40-50 years ago, in favor of AMD RISC processors of 30 years ago.

The unitarity condition of Quantum theory dictates that the time evolution of a quantum state, as per the Schrodinger equation, is represented by a unitary operator. This implies the total probability of all possible outcomes must always sum to 1, meaning probability is preserved in time, and information is conserved. Everything that goes into a Black hole is/has information; when the BH evaporates through Hawking Radiation, that information is randomized as thermal radiation, and the ability to follow the time evolution of the information vanishes. That is a problem/paradox according to Quantum theory

Space is a 'concept' to which we apply an ever changing ( as our understanding of its properties increases ) definition to. Bold move, re-opening a closed thread. I hope you bring more to the table this time around, or it will quickly follow the same fate.

Anyone can come up with WAGs. Provide a mechanism; then we can talk.

Way to go, INow 👍 Were you out there stumping ?

How do you know space-time curves ??? The model we have, GR, implies that curved space-time geometry ( a mathematical construct ) acts exactly the same as Gravity. If I have a map made of flexible material, and I pull up the area where a mountain is shown, it 'acts' the same as the real mountain. But the real mountain is not made of flexible material, nor is it 2dimensional, nor can you hold it in your hand, nor ...

This has already been answered by several members, myself included; pity you don't read, or understand, replies. At an early time ( before inflation ) the whole universe was in causal contact, which means information could be exchanged by all parts to establish isotropy and homogeneity throughout the universe. Symmetry breaks ( which would also lead to inflation as drops from false zero-point energy ) that resulted in Grand Unified Force breaking up into the current interactions, also established current global and gauge symmetries responsible for the laws we observe. This is current theory. Granted it doesn't explain the absence of magnetic monopoles at the 'edges' of symmetry break domains, nor does it point to insights about dark matter/dark energy, but it explain a lot of observations and makes quite a few valid predictions, so none of us are ready to discard current theory because you don't understand it and think it doesn't provide any 'answers'.

The word that 'triggers' suspicion of AI usage for me is 'framework'. As in

If then the argument becomes that information is 'hidden' for some observers, but not all, to preserve QM's unitarity condition. Does this not, then, introduce the concept of 'preferred observer', and that Physical Laws may differ for different observers/different locations/different times ? IOW, 'fixing' the information paradox wrecks Physics. ( out of the frying pan, into the fire )

My bad again. In my original post, I should have said My apologies for the confusion. ( speed kills AND adds to confusion )

Given that this 'candle in the cave' is causal, it means we can detect/measure the effects it causes. But the 'candle' has, so far, avoided detection, and we are in the exact same position. All you are doing is giving it a different name.

Yeah. My bad. And I realize that it's not an accurate description, but every ( layman's ) pictorial representation of 'shells' shows higher energies further from the nucleus, such that total ionization is at infinite separation. So I thought my explanation appropriate for the 'level' of the discussion.

I don't have much to add to prime number sieve optimizations, but for others like myself, the following provides some interesting ibsights and historical background on the age old search for primes

Yes Ix-yI=Iy-xI and ???

Atoms are not charged; if they were they'd be ions. A Hydrogen atom has 1 electron ( 2S orbital ) and one proton in the nucleus, making it neutral. A Nitrogen atom has 7 electrons and 7 protons in the nucleus, making it neutral. Two of these electrons are in the inner 1S orbital, and 5 electrons are in the outer valence 2S orbital. The 2S orbital is 'happiest' when it is totally filled with 8 electrons, so when a Nitrogen atom comes across some Hydrogen atoms (given the right circumstances ) it 'steals the electrons of three Hydrogen atoms, forming NH3; while NH3 is still a neutral atom, its charge distribution is imbalanced, as the side of the tetrahedron with three Hydrogen atoms is predominantly triple positive ( 3 'bare' protons ), and the side with the Nitrogen atom now has 3 extra electrons, making it predominantly triple negative, and this imbalance of charge leads to Ammonia being a polar ( preferred charge direction ) molecule.

How about listing some of these implications so that we may discuss them without having to read the paper you linked ?

Don't like to get involved much in Religious discussions. If you substitute 'nations', 'governments', or even 'cultures' in the above post for the word 'religions', it would still be just as applicable. I would not fault the religion itself, but how it is interpreted/leveraged by some people. And, as it is a man-made concept, it cannot be static, but evolves with the times, as @joigus has suggested Hence differences between Old and New Testament, or even how the Church is struggling to stay relevant in modern times. I don't think many people have a need for Religion, just like many people have no need for nations, cultures or even governments; IF everything is working well. But when things go wrong, and there is suffering, people hope that their nation/government/culture will take care of them. ( even when that hope is an irrational belief, as in in America under D Trump ) That is what Religion provides; a crutch, or a hope, to get some people through their times of suffering. I'm not a believer, and I don't need a crutch, but I certainly don't fault those that do. I do fault those that leverage that suffering to take advantage of the sufferers, by blaming everything wrong on the 'heathens', much like the government of D Trump blames everything wrong with America on the immigrants ( which once made it great ).

Some resins are activated by amines, some by UV, some by oxidizers. IOW, air can be a self activator. The activator is an 'accelerant' that speeds up a slowly occurring chemical process.

Believe it or not, the Challenger part of the Mariana Trench, at a depth of 36000 ft. does support active life. "Life, uh, finds a way" Dr. Ian Malcolm ( Jeff Goldblum ) Jurassic Park 1993

I'm not sure the forum discussion process is suitable for that. I know you often try, but I think the best we can do is 'steer them' in the right direction. Thanks. I wasn't sure; my last Chemistry course was a long time ago ( Gr. 13 in 76/77 ).

I think you need a quick tutorial on the Lewis representation of bonds. Other than the first row of the Periodic table, which has a maximum of 2 electrons in its 1S orbital, all others contain up to 8 ( 2S, 2P, ... ), because the central Transition Metals can be disregarded ( their outer electrons are not valence, but rather conduction ). Atoms, whether free or bonded to others are 'happiest' when their lowest orbitals are full with 8 electrons, so sometimes they steal, or sometimes borrow, electrons from their bonded neighbor. Two dots, inline between neighboring atoms is equivalent to a line ( .. > - ). Four dots, where two are inline is equivalent to two lines ( :: > = ). And this can go to three lines or ( possibly ? ) to four. Sometimes this electron 'book-keeping does not take the protons in the nucleus into account, so when one of the pair 'steals' electrons from the other, you end up with 'excess' charge on opposite ends, and this ionic bond is polar ( as Studiot and KJW are discussing above ). A simple example would be water ( H2O ) where the electronegative Oxygen ( 6 protons ) now has 8 electrons due to uneven sharing, making its side negative, while leaving the Hydrogen sides with an excess positive charge. You know, your best resource for learning IS your teacher ( at least until you have enough foundational knowledge, discipline and confidence for self-learning ). If something is not explained to your satisfaction, keep asking questions; they owe you this knowledge.

Again, what does this mean ? I assume microcosm is in quotes because you are giving it a non-standard definition. You're going to supply a citation for this also ? I don't remember reading any Einstein where he says the geometric ( space-time ) field is a "substance'. Or are you assigning a non-standard definition to substance also. Energy, not being a substance, is a property of photons. As such, a pair of high energy photons ( gamma ) can give rise to a a couple of particles with the property of mass ( obeying conservation laws, of course ) with additional energy supplying the property of momentum to those particles. Clearly the energy of the photons is greater than that of the particles.

I don't know what that means. Re you considering entropy a form of un-useable energy ? While massless non-matter has no valid frame, it does have a 'travel' time of d/c.

No. If y is larger than x the relation is not satisfied.