MigL

Sure came in handy for I Newton.

As Joigus says, the gravity produced by a BH is no different than from any other equivalent mass. If expansion can overcome the gravity of galaxy clusters, it can similarly overcome the gravity of a BH composed of the masses of the equivalent number of stars in that galaxy cluster. There is no upper limit on BH size. There is only a limit to how much you can feed them. Once they 'eat' all close by mass via their accretion disc, they can't overcome farther out stable orbiting material, and stop growing. Direct collapse, however,without going through star lifetimes, is a totally different mechanism.

That is speculative. And not at all consistent with the accepted definition of a Closed Timelike Curve. https://en.wikipedia.org/wiki/Closed_timelike_curve

I don't understand. How exactly does your oscillator's worldline loop back to a previous co-ordinate ?

Again, this is not about the merits of the decision, rather, about who makes it. If the American people want abortion rights, put it into law. The 'Constitutionaity' is decided by the electorate. It should NOT be decided by unelected, unaccountable judges.

As far as I know, every CTC has to have some means of spacelike translation, and wormholes ( even if impossible to realise ) are one such means. ( otherwise, how could an object return to the same co-ordinates in space-time previously occupied ? ) Are there other ways to 'construct' a CTC ?

Don't know the author of that quote, INow ( although I should ), but it was W Churchill who said … "it has been said that democracy is the worst form of Government except for all those other forms" I imagine 'other forms' includes Government by unelected, unaccountable judges. ( Wouldn't an unelected, unaccountable President be a dictator ? So why do we put up with judges doing it ? ) And if you say W Churchill was the author of your quote also, I'm going to assume he was a very confused individual.

I only used abortion , and Roe vs. Wade, as one example where Democrats want a left-leaning Supreme Court to protect the abortion status quo, but there are many others. D Trump, for example, wants a Republican stacked ( right-leaning ) Supreme Court to rule on the ( un )Constitutionality of the Affordable Care Act. An Act which he's had 4 years to replace with 'something better' ( his words ), but he still has no plan to replace it with; he just wants to scrap the existing Act which a lot of Americans are happy with, and most want expanded coverage. There are many other issues decided by Supreme Court rulings ( elections, fracking, pipelines, etc. ) which get decided solely by the political leanings of the majority of the Supreme Court Judges. Should not the people have a say through elected representation, not unelected, unaccountable partisan judges ?

The 'effect' produced does not vary linearly with the 'cause ? For example, tapping someone on the head may produce a mild headache. Tapping someone a little harder would produce a bigger headache. That is the linear response part. If however, you bang someone on the head really hard … they die. That is the non-linear part ,because the effect produced diverges drastically. Tis can also be explained in terms of mathematical functions, but it isn't as interesting.

I really have a problem with the American Supreme Court, and the Canadian equivalent. It seems that the people we entrust with making laws, your Congress, and our Parliament, don't give a damn about passing just or complete laws, then, rely on a partisan and unelected Supreme court to 'interpret' those laws in their favor. It doesn't seem to matter which party is doing it ( they both do it ), D Trump wants a Republican leaning Supreme Court so he can get rid of the ACA and get a favorable election result from the E College, neither of which he can legally do as the laws are now interpreted. The Democrats on the other hand, want to have a Democrat leaning Supreme Court so as to protect Roe vs. Wade and legal abortion. If the American population supports legal abortion, and this is expressed through their votes and representatives in Government, why is subterfuge and stacking of courts with unelected ( and unaccountable ) judges required ? Why are not proper laws passed which resist varying interpretations, and that the people have a say in ? ( this could be re-pjrased as "Why are our elected representatives not doing thei rjobs properly ?" )

Heeeeeey ! So did Clint Eastwood in 'Gran Torino', but he turned out to be a stand up guy, in the end.

We had a few threads about this exact problem a few years back. I distinctly remember a thread where I was spectacularly wrong, but I can't find that one, just the thread about a charged ball in free fall from 2018.

This is the example I've always used... Bart and Lisa Simpson each have a wormhole generator, such that they can look through the wormhole and 'see' ( world line of zero length ) each other. Bart takes his wormhole generator and goes on a relativistic journey to another star, and returns, all the while looking at Lisa through the wormhole. His journey takes ten years, but when he gets back to Earth, 100 years have elapsed, and Lisa is long dead. So Bart steps through the wormhole and rejoins Lisa, whom he can still see, 90 years in the past. A lot of 'what ifs' and assumptions are involved, such as stable and predictable wormholes that can be 'linked', Relativistic ( close to c travel ), etc., but, current impossibilities aside, the 'mechanism' is there. As to whether it will ever be realizable, I doubt it very much also.

I think they are claiming that time travel is self-consistent, and paradoxes do not necessarily occur. And have come to this conclusion by looking at the 'general' case, not specific cases. And sorry if I gave the impression that it was your claim of a viable mechanism. I intended their claim was 'generous'.

Lesson to be learned … Dye your hair. ( nobody looks good with white hair, and the flies really show )

From my first post ( on Tuesday ), an acceleration involves a change of inertia. Even fundamental particles ( no internal structure ) will experience a change of inertia. Non-accelerating frames are called inertial frames, and accelerating frames are called non-inertial, as a consequence. Inertia is what resists forces that produce accelerations. And mass is what resists changes in inertia.

CTCs have 'provided a mechanism for time travel for quite some time, but they provide no answers for the causality breaking paradoxes that arise. I haven't looked at the paper, and probably wouldn't begin to understand it, but I assume it attempts to provide those answers. And saying CTCs provide a mechanism for time travel is being generous, there is still the problem of space-like translation via wormhole ( or some such device ) to achieve time travel. CTCs just move the goalposts of the problem from one ( current ) impossibility, to another ( current ) impossibility.

In a way we are limited by our own existence. Consider J DeLancie's words as 'Q', at the end of the last episode of Star Treck:TNG ... Q : You just don't get it, do you, Jean-Luc? The trial never ends. We wanted to see if you had the ability to expand your mind and your horizons. And for one brief moment, you did. Capt. Picard : When I realized the paradox. Q : Exactly. For that one fraction of a second, you were open to options you had never considered. *That* is the exploration that awaits you. Not mapping stars and studying nebulae, but charting the unknown possibilities of existence. Maybe in 400 years ...

That first clip of D Trump Jr. at rhe RNC sounds just like the villain in the WonderWoman:1984 trailer: " Welcome to the future. Life is good; but it can be better. And why shouldn't it be ? All you need is to want. Think about having everything you've always wanted... Now, I take what I want in return" Interesting looking movie. Lassos and rides the lightning, gorgeous legs, and a New Order soundtrack. Gotta see it if Covid ever lets up.

Well that settles it. I'm an agnostic atheist. ( I'm a science guy, we're never 100% sure of anything )

If it was a Catholic school, the priest/friars or nuns would have been able to tell the story of how the Bishop of Rome, Leo I, was sent out to meet Attila and negotiate a truce, thus sparing the sacking of Rome. ( not actually true, Attila was low on supplies, but the Catholic Church does like to take credit ) PS the way it's going, this will be off-topic split off also.

No library, no internet, and no other teachers who could reference Attila ? Must have really sucked !

Not exactly. Ideas are protected by 'free' speech. Inciting people to dangerous actions, is not. ( yelling "FIRE" in a theater incites a stampede and people get hurt )

Open up his textbook and say "This guy here on page 78" Then ask the teacher to take some remedial History courses.

I would think anybody does. M Pence wasn't too bad, but in his debate, D Trump came across as a guest on the Jerry Springer Show.