 black hole. Our Milky Way, with a black hole of a mere 4 million solar masses, is a relative wimp; the most massive black holes among the nearby galaxies are several billion times more massive than the Sun (as we saw for M87). Moreover, the larger the elliptical galaxy (or the bulge of the spiral galaxy), the more massive the black hole will be; the mass of the black hole is typically about 1/500 of the mass of the bulge of stars in which it sits.
This is covered in more detail in Chapter 16 of Welcome to the Universe. Buy the book.
Newton would say that if you took two masses and set them at rest in interstellar space, they would start accelerating toward each other because of their gravitational attraction, and they would eventually hit each other. Newton would say this is because they exert forces on each other at a distance, and these forces pull them together. Einstein says that the two masses cause the spacetime around them to be curved. In that curved geometry, the two particles simply travel on the straightest possible trajectories they can, which brings them together.
This is covered in more detail in Chapter 19 of Welcome to the Universe. Buy the book.
Suppose I got an enormous trash compactor and crushed Earth to a smaller size, wadding it up like a ball of paper and crushing it into a smaller radius. What would happen to the escape velocity? Earth’s mass would be the same, but its radius would be smaller, making the escape velocity from its surface rise. Eventually, if I crushed Earth to small enough size, the escape velocity would become equal to the velocity of light c. … Einstein showed that nothing can travel faster than the speed of light—if you crush Earth to a radius inside its Schwarzschild radius, it’s never going to re-emerge: it forms a black hole. We call it a “black hole,” because no light from inside it can ever get out. The mass will continue to collapse to still smaller size, where gravity will pull it together even more strongly, increasing the escape velocity even more. Inside the Schwarzschild radius, gravity wins over all other forces, and the mass collapses to a point, a singularity of infinite curvature at the center. … If you were to venture inside the Schwarzschild radius, could you ever get back outside? No. You would have to travel faster than light to do so, and Einstein showed that was impossible.
This is covered in more detail in Chapter 20 of Welcome to the Universe. Buy the book.
Time begins at the Big Bang—a singularity of infinite curvature is there. … What happened before the Big Bang? This question makes no sense in the context of general relativity, because time and space were created at the Big Bang. It’s like asking what is south of the South Pole. If you go farther and farther south, you will eventually get to the South Pole. But you can’t go farther south than the South Pole. Likewise, if you go farther and farther back in time, you will eventually get to the Big Bang. That’s when time and space were created, so that’s the earliest you can go. Aristotle liked a universe that was infinitely old, because you would not have to ask how it got started; if it had a beginning, a first cause, then you would have to explain what caused the first cause, he worried. Einstein and Newton liked infinitely old universes also. But Friedmann’s universe started with a Big Bang at a finite time in the past, when both space and time were created.
This is covered in more detail in Chapter 22 of Welcome to the Universe. Buy the book.
How can one get an infinite number of universes each ultimately infinite in size, from just a finite beginning? De Sitter spacetime looks like a trumpet with its mouth opening upward. … This remarkable spacetime geometry, in which inflation continues forever and the space becomes infinitely big, allows creation of an infinite number of infinite bubble universes in an ever-inflating sea. … Inflation seems inevitably to produce a multiverse of universes. Just how sure are scientists of this? Once Sir Martin Rees (the Astronomer Royal) was asked at a conference how sure he was that we lived in a multiverse. He said he wouldn’t be willing to bet his life on it, but he would go so far as to bet the life of his dog. Linde rose to say that since he had spent decades of his life working on the multiverse idea, he had proven that he would bet his life on it. Nobel Laureate Steven Weinberg said he would be willing to bet Linde’s life on it, and Martin Rees’s dog’s!
This is covered in more detail in Chapter 23 of Welcome to the Universe. Buy the book.
If we look around, we can see the universe showing us what we should be doing. We live on a tiny speck in a vast universe. The universe tells us: spread out and increase your habitat to improve your survival prospects. We live on a planet littered with the bones of extinct species, and the age of our species is tiny relative to that of the universe as a whole. We should spread out before we die out. We have a space program only about half a century old that is capable of sending us to other planets. We should make the wisest possible use of it before it is gone. Will we venture out, or turn our backs on the universe?
This is covered in more detail in Chapter 24 of Welcome to the Universe. Buy the book.
Welcome to the Universe is a personal guided tour of the cosmos by three of today’s leading astrophysicists. Inspired by the enormously popular introductory astronomy course that Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott taught together at Princeton, this book covers it all—from planets, stars, and galaxies to black holes, wormholes, and time travel.
Welcome to the Universe: The Problem Book features more than one hundred problems and exercises used in the original course, ideal for anyone who wants to deepen their understanding of the original material and to learn to think like an astrophysicist. Whether you're a student or teacher, citizen scientist or science enthusiast, your guided tour of the cosmos just got even more hands-on with this essential companion book.
Michael A. Strauss is professor of astrophysics at Princeton University.
© 2016 by Princeton University Press. All rights reserved.
If you are interested in learning more about Princeton University Press’s science titles, sign up here.Now of course we can still make simple looking statements like ‘God must be worshipped.’ But what it means is I’ll subject all of them to thorough critique. Specifically, I will refuse to conceive of those sentences in unitarian terms. Instead I will ensure that the Subject of that sentence can refer to each Person of the trinity and to the triune life as a whole. And I will think hard about how these explicitly trinitarian considerations affect the truth of the proposition. In other words I will resolve to conceive of both the Subject and the verb in these sentences in explicitly trinitarian terms.
But does this really make a fundamental difference to ‘simple God-talk’?
Or think about the concept of ‘God’s monarchy’ – i.e. that God exercises a singular rule. As a simple (functionally unitarian) concept this would lead us to think of God’s rule in ways fundamentally opposed to a trinitarian understanding. Trinity doesn’t mean there are three thrones and it doesn’t mean that the Lamb is off-centre on the throne. It means that the Father rules through (and only though) His Spirit-anointed Son (cf Psalm 2). Yet without this trinitarian dynamic being explicit, the triune God’s monarchy will be misunderstood.
Or again, think about this contentious statement: ‘God is unoriginate.’ It was a favourite of Arius – what do we make of it? It seems completely logical. It seems to be guarding against things we want to guard against. Surely full divinity cannot be predicated of anything that has an origin outside itself. Right? We can’t have divinity that depends on anything outside itself can we?? Well, on this understanding we look at the Son Who has His eternal origin in the Father, and we conclude that the Son is less than fully God. That’s the very logic Arius used and it’s just why Athanasius got so picky and said that Arius should not name God from creation and call Him unoriginate but name Him from His Son and call Him Father. In other words – unless from the outset you define God’s nature with the Father-Son reciprocity in mind you won’t be able later to call Jesus God – not fully God.
The problem is that it has begun in functionally unitarian ‘God-talk’ and it simply cannot be rescued by trinitarian nuance. That’s not the direction of travel. We can’t go from functional unitarianism to trinitarian discussion as though we’re moving from the synopsis to the novel. The comparison is more like two competing treatises.
When we talk trinity we talk about basic things – fundamental, bedrock things. We don’t simply uncover extra depths when we lay bare the perichoretic life of God. Actually we discover an essential logic that requires articulation according to this trinitarian dynamic.
i’ve always wondered about ‘Ancient of Days’ too. In the song there’s no mention of the Son of Man and actually everything that’s said of the Son of Man in Daniel 7 is ascribed to the Ancient of Days in the song!
Bish- I have thought about that song quite a bit. Being as the chorus is