MigL

I live in a University town. The majority of kids are immigrants, who realize the value of education. Rich affluent kids, ( with no socially imposed barriers ) just want to go to College to party. There are certainly some barriers to education, but want and encouragement are big factors in getting one. The 5 year old black kid that MSC mentions, might have a chance at an education IF his dad was home to encourage him. If his dad was home, he might not be on his own most of the time, and might not have to drop out to get a job, or worse , join a gang. I was an immigrant child in 1968, and my parents worked day and night to make sure we kids got a University education. ( although now that I think about it, I could have become a plumber, and made a lot more money ) First generation immigrant kids work very hard to make sure they don't have to live the life their parents did. Second generation, not so much. Do you think its a coincidence that lately, Colleges and Universities are filled with Middle Eastern, North African, South Asian and east Asian students ? I'm not sure about the US, but in Canada, visible minorities make up over 30% of 1st year students. https://higheredstrategy.com/visible-minority-participation-in-university-studies/ A much higher percentage than is present in the general population.

You should have said that to begin with. There would have been a lot less confusion. Limits approach a limiting value; they never actually reach it.

The metric field is a mathematical construct. So are derivatives of it, and so is space-time. They are components of a mathematical ( geometric ) model. There is nothing to actually curve, although we do observe test particles following geodesic paths as IF there was.

Still not sure what exactly you mean by x cannot equal zero. Are you talking about limits ( as x -> 0 ) ?

Yes it does cut both ways; I never said it didn't. I've known plenty of people who had no 'barriers' to obtaining the best 'money is no object' education. Yet their 'everything should be handed to me' attitude allowed them to not even try, and they drop out halfway through 1st year University. There are many barriers to an education, or expanding our knowledge; the worst ones are of our own making.

Why is it always barriers imposed by, or the fault of society, when someone fails ? What part does personal responsibility play in this ? Markus Hanke taught himself GR ( and many other aspects of Physical Science ). It was not provided for him, but he wanted it and he got it. Barriers did not hinder him. You, yourself, have displayed a questioning attitude. One of the best ways to learn about things you know little about. Yet others come here with the attitude that what little knowledge they have , is all there is. They ask no questions, but make conjectures and proclaim results which more learned members quickly dismiss. And yet their attitude, not barriers, allows them to double down and insist they are right ( until they are banned ). A good attitude, and a willingness to learn, go a long way in these days of internet access and on-line courses.

I never had any use for anyone called Dave . Also, people who part their hair on the left. And mustaches … ( especially on women )

Don't think so. Lorentz and Poincare had no part in GR. ( but I could be wrong )

The model that we have, General Relativity, has a coordinate system whose 'curvature' is what we commonly call gravity. This agrees to a very high degree with observations and experiments made of the actual world around us. Do you really think that the concept we call space-time has an actual 'fabric' which can be curved ???

There are two long range forces, gravitational and electromagnetic, and two very short range forces, color and weak ( flavor ). As far as we know, Dark Matter interacts with all other matter, including itself, gravitationally, but does not interact via the Electromagnetic force at all ( or only extremely weakly ). That means we cannot detect it by electromagnetic means ( no visible, radio, infrared, uv, x-ray or even gamma emissions ), but its gravitational interactions with matter and itself, will produce 'falls' or orbits around its center of gravity. It could also be captured by BH event horizons when it intercepts them. Dark Matter particles may get very close to each other, or even collide, but, since they don't interact via the color force, they will not clump together like quarks in nucleons, or protons and neutrons n the nucleus due to residual. And since they don't interact electromagnetically, they won't clump like electrons and protons in atoms. So I see very little chance of being able to localize a large enough mass of Dark Matter that it would be able to collapse to a BH. One type of neutrino is being investigated as a candidate for Dark Matter, so there is the possibility that it also interacts via the weak ( flavor ) interaction, but again, this interaction does not produce bound states.

Again, this is not related to CTCs, and I fail to see how it relates to time travel. It is an off topic hijack. Start a new thread in Speculations. And be prepared to support it.

Thanks for the fuller explanation Janus. I was trying to keep it as simple as possible since all the above is explained in the Wiki link, and MSC didn't seem to fully understand it. And if yo look at the video in the link, it shows what I meant by 'wind up'.

If you look at the rotation of a typical galaxy and take into consideration the visible mass ( estimated star, gas and dust mass) distribution ( flattened spiral ), you would expect the outer spiral arms to be 'winding up'. IOW, just as the outer planets of the solar system take much longer than the inner planets to orbit, the outer parts of the spiral arms should be 'lagging' in their rotation about the center, but, what we actually see, is that galaxies rotate like a giant pinwheel, there is no lagging rotation at the outer extremities. This implies one of two possible things … 1 - Could the laws of Gravity ( Newton, GR ) be wrong at very large scales ? This is addressed by MOND ( Modified Newtonian Dynamics ), but MOND seems to work for galactic rotation and then reverts to good old gravity at even larger scales ( between galaxies and clusters ). It also has other issues which make it a non-starter ( Google MOND ). 2 - Could the rotation be affected by other factors of which we are currently unaware ? It turns out that a spherical mass distribution ( not just a flattened spiral mass ) would result in the observed rotation rates. But we don't detect any Electromagnetic radiation from this 'dark' mass, so it must mean that whatever mass is there doesn't interact electromagnetically, only gravitationally. Since option 2 is the more plausible, the search for this Dark Matter was begun, and is still ongoing. The indirect evidence for its existence is piling up ( Google Dark Matter ), from gravitational lensing to galaxy 'seeding', but still no viable model or direct evidence for it.

How exactly ??? I suggest reading the link provided ... "The rotational/orbital speeds of galaxies/stars do not follow the rules found in other orbital systems such as stars/planets and planets/moons that have most of their mass at the centre." https://en.wikipedia.org/wiki/Galaxy_rotation_curve

And I though Zap and his YouTube friend had done a good job of explaining. OK, one more time... The Earth is orbiting the Sun at a radial distance of 150 million km. We now start compressing the Sun. When it is half its current size, the Earth still feels the same gravitational attraction and remains in orbit at 150 Mkm. When it is one tenth of its current size, the Earth still orbits at 150 Mkm, and feels the same gravity. When it is 1/1000 of its current size, the Sun still has the same mass, and the Earth is still orbiting at the same radius of 150 Mkm, so it still feels the same gravity. However, when the Sun is compressed past its Schwarzschild radius, 2GMsun/c^2 , or about 6 km across, it is enclosed by an event horizon, which means that, for the mass of the sun, a 3 km radial separation requires an escape velocity faster than the speed of light. https://en.wikipedia.org/wiki/Schwarzschild_radius IOW, the event horizon goes black because no light can reach us any longer. Yet the Earth is still happily orbiting at 150 Mkm, and feeling the same gravity. So, to recap, if our Sun was a Black Hole, at the current distance from the sun we would feel exactly the same gravity as we currently do. If we were to move closer to the Sun, since as a Black Hole it is vastly smaller, we would feel an increase in gravity, until we get to about 3 km radial separation, at which point no force in the universe could keep us from falling into the event horizon ( its gravity would be THAT strong ). Yes, mass is directly proportional to Schwarzschild radius, but I'm not sure I follow or understand the rest of your questions. Please re-phrase or clarify.

Wouldn't account for the anomalies in galactic rotations https://en.wikipedia.org/wiki/Galaxy_rotation_curve

What's really sad is that, centuries later, you still don't understand it. Maybe you should have some humble pie with your Thanksgiving dinner; ask proper questions and stop being so derisive.

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 ?