“That space and time are replaced by spacetime immediately tells us how a field, be it electromagnetic or gravitational, varies in time once we know how it varies in space.”

*In*“On Gravity: A Brief Tour of a Weighty Subject” by Anthony Zee

“Einstein says the space-time is curved and that objects take the path of least distance in getting from one point in to another in space-time. The curvature of space-time tells the apple, the stone, and the cannonball to follow the same path from the top of the tower to the ground.”

*In*“On Gravity: A Brief Tour of a Weighty Subject” by Anthony Zee

“Gravity curves space-time. That’s it.”

*In*“On Gravity: A Brief Tour of a Weighty Subject” by Anthony Zee

On August 17, 2017 two neutron stars collide (Zee references this in his book).

Let me hypothesize: consider a particle on the surface of one of the neutron stars belonging to a pair, about 10 km from the centre. It's being pulled downwards by an enormous gravitational force - about a hundred billion times stronger than gravity on the Earth's surface (if I calculated it right). But if the particle is going really, really fast (for example, close to the speed of light) it's still able to escape the star and not get pulled back in. That's fundamentally no different to achieving escape velocity from the Earth or the Sun, it's just much bigger numbers. Imagine that star instantly collapsed into a black hole. The particle 10 km from the centre would continue being pulled in the same direction by the same amount of mass, with exactly the same gravitational force as before. It could therefore escape just as easily as it could escape from the neutron star. As far as that particle is concerned, there's nothing magical about the black hole; it's just a big nearby mass. With two neutron stars colliding, I think their combined mass will produce a black hole with an event horizon radius of maybe 7 km, which is even smaller than the original stars. By definition, anything closer than 7 km to the centre would be unable to escape even if it travelled at the speed of light. But anything further away can still escape by going fast enough. The collision process will presumably accelerate some particles to huge speeds, so they're far enough away and going fast to escape even after the black hole has formed.

Many stars form in pairs, triplets etc., and live like that throughout their life. This is even more true for stars more massive than our Sun (the really massive stars always seem to form as part of multiple systems). So when they pop their clogs and become neutron stars they can still be bound by gravity in the same system (not absolutely guaranteed, since they probably went bang first, which could provide enough energy to disrupt the system). Even if they turn into neutron stars at different times, there's a pretty good chance they'd be left orbiting each other at the end, and then eventually they will get closer very slowly over time (perhaps a bit quicker if they interact with another star system in passing). The keep radiating gravitational waves all through this until eventually the get close enough that the rate at which they emit energy becomes significant (i.e., starts to equal the gravitational potential energy they each feel from the other). As you continue to spit out that energy the rate at which the orbit tightens will increase dramatically until you get the final merger. (For the record the Earth also emits gravitational waves as it orbits the Sun. Fortunately for us, it only emits about as much power as a light bulb...)

This is all great, and to think one man postulated it: Einstein.

However, I’ve been sharing lots of nonsense regarding the Standard Model, basically saying it’s got still massive holes in it. To wit:

1. Quantum physics does not join to the physics of large objects and after almost 100 years we still have not come close to doing so;

2. Black holes are infinite inside, over the Event Horizon. But infinity means we have no theory what is "beyond" the Event Horizon nor what happens to matter sucked into them, the math and theory break down;

4. It’s all fecking lies; it's the leprechauns and rainbows;

3. And most important of all ... Standard Model physics still cannot explain Bicycles, when ridden, stay upright.

My answer to the points above:

1. QM works fine with large objects. It works and is very necessary when matter becomes compressed such as in a star, white dwarf or neutron star; it’s also relevant due to the fact that quantum tunneling is involved in photosynthesis, for example, just read Jim Al-Khalili's book “The Coming Age of Quantum Biology”, which gives many other examples how QM is totally relevant when it comes to biological systems;

2. The infinity occurs at one point at the centre of the event horizon not just over it. So nothing is known about what happens at a singularity and it will never be known;

3. Seriously?

4. As for riding a bike, it involves balance. In the inner ear are a couple of tubes with fluid in which the brain uses to maintain balance. Stability comes from the angular momentum in the wheels. Try riding a bike slowly.

The amount of hard work and diligence put in so you can catch something as remote, esoteric and rare as this as it is actually happening (well, as soon the light reaches here, etc.) is almost if not more impressive as the event itself. We were banging rocks together to make sparks not so long ago, and now this...think about it, how do people manage to find and record this... the ingenuity and labour involved just floors me. Impressive. When people are still arguing the earth is flat and NASA use fish eye lenses, in the background quietly awesome events of nature are being observed and studied, in the hope of cleaning more doors of perception.

Most people don’t get what Gravity is: “Gravity” is the bending of space itself. So the light doesn't bend; it’s simply traveling in a straight line though bent space. If you throw a ball in forwards in the air, the arc is not gravity pulling on the ball, the arc is the ball travelling through bent space caused by gravity. So the ball actually moved in a straight line, it is in fact space that is bent by gravity, which is what we observe. The curve is the bending of space in front of you. Also the speed of light is fixed. It’s not the speed of light that is fixed but the max speed that a massless particle can move in a vacuum which is the speed limit. Light can’t go faster than this speed limit.

String theory predicts the existence of gravitons. The problem of detection of these bosons (nothing to do with the Higgs) would be their very low probability of interacting with any detector (i.e., their "cross-Section" is v. small).

The force of gravity at the scale of atoms is by unfathomable orders of magnitude smaller than the other 3 forces (its @1000 Trillion Trillion weaker than the Strong Nuclear Force that binds atoms!) &, could never be produced in a particle beam experiment such as LHC. In fact at the quantum level we would not know it even existed if not for at the scale of planets & stars etc. its effects become apparent. There is the possibility that the reason it is so weak is we are only affected by a small part of the force the rest being present in another dimension. String theory predicts this.

People wondered, what is out there, behind the horizon? Is it a cliff, do we topple from earth, when we reach it, is there another world, we know nothing about and some began to dream and set out to find out, what lie there.

I think the sense of purpose is the only thing keeping us from decadence. If we see ourselves integrated into a bigger picture, we feel a sense of duty. And now, that I think about it, maybe the state our world is in and our disinterest of meaning and purpose are coupled? It’s a consequence of Einstein’s field equations: ‘Space-time tells matter how to move; matter tells space-time how to curve.’ Any two things in orbit around each other will radiate energy away in the form of gravitational waves (it takes energy to squeeze and stretch the fabric of space). Ordinarily the amount is so utterly feeble as to be undetectable. It’s a different matter when two black holes are about to merge, however: two tiny objects each with many times more mass than the Sun spiral around each other thousands of times a second during their final death throes. That’s quite a blur that rips space and time to shreds in the vicinity. Once space-time has imploded all that is left on the outside is the bending and rippling of space. Nature is a good accountant and converts energy to different forms all the time. The energy used to bend space is deducted from the final mass of the black hole merger.

In the case of (almost?) any physical black holes the answer to 'how much energy lies outside the horizon' is surprisingly simple: all of it. The reason for this is reasonably easy to describe, if not to understand. Almost all black holes (and from now on I'm just going to say 'all') originate from some kind of collapse: a large star runs out of fuel and collapses and you get a black hole. Except you don't, quite. There are two ways of thinking about why: one is to say that, as stuff falls inwards, then, as seen from far away (by us, say) it gets more and more red-shifted and thus moves more and more slowly. And it never actually quite crosses the event horizon, because that's the point where the red-shift becomes infinite and it just stops. Another (which I find easier) is to remember that the event horizon is always in the future for anyone outside it. And that means anyone: there are no observers outside the horizon for whom it is in the past, and thus no observers outside the horizon ever observe anything crossing it, and this includes the initial collapse. These statements are actually equivalent, of course. So a 'black hole' formed from a collapse event is not, in fact, quite a black hole, because nothing has ever -- and nothing ever will -- cross the horizon (and in fact there is no horizon) from the perspective of an observer far from the event. Everything is 'frozen' just as the thing forms. So that sounds like I'm saying that black holes don't exist, and I kind of am saying that. However it turns out that this makes no practical difference: it's easy to show (it's basically Newton's shell theorem) that the gravitational field of one of these collapse objects is identical to a BH's, and it's almost as easy to show that these objects are really black (no information reaches you from in-falling matter) and so on: they are in every detectable respect the same as actual Black Holes, which is why it is safe to treat them as such.

There is one important way (or a way which may be important) that they are different: because the collapse is essentially frozen, there is no singularity yet from the perspective of an outside observer (i.e., us). But these almost-Black-Holes do have Hawking radiation, and so they (very, very slowly, and in practice not at all until the universe has cooled a very long way from where it is now) lose mass as thermal radiation. So eventually, over ludicrously long time-scales, they will evaporate. And this means that there never will be a singularity!

**Bottom-line**: Zee’s book give us is a middle approach to the concept of gravity. As an introductory text it’s invaluable. His explanation of the principle of least action is also masterful. Zee is absolutely right that it's interesting (no doubt) and useful (again, no doubt). All modern physics is based on this principle, from Relativity to Quantum Mechanics to String Theory. Although this doesn't necessarily "prove" it's correct, it shows how it is actually used (likewise we never really “proved” that Newton's Laws are equivalent to Hamilton's Principle). I studied and passed my classical mechanics exams and can apply the Lagrangian and Hamiltonian formulations for solving simple problems like Harmonic oscillator, planetary motion, etc. Most writers make the situation too difficult at a very early stage of their explanation by introducing the subtle concepts of virtual work, d'Alembert’s principle, generalized coordinates, etc., making it very difficult to follow. Zee is a great teacher, given me the feeling of how the analytical formulation treats mechanical systems from a deeper level of reasoning. Susskind's explanation of the principle of least action is also pretty good, but Zee’s is better. I hate it when theoretical physicists start using the so-called hand-waving approach. Zee avoids this trap magnificently.

NB: How do they know which bit of sky a gravitational wave came from, you that is asking at the back? By having multiple detectors separated by thousands of miles, and at different angles to one another: the separation of the detectors is such that the arrival time of the gravitational wave at each detector is slightly but measurably different (in the order of milliseconds). The orientation of the arms of the detectors, and the differing amounts each arm is "squeezed", gives an idea of the direction of travel of the wave. The gravitational waves were there for millions of years, as long as the spiraled around each other. It's just that in the final moments before their collision the waves got strong enough to detect. The direction the gravitational waves came from can be determined roughly from the slight differences in timings of their arrival in those 3 or 4 gravitational wave observatories we currently have around the globe. I think astronomers started looking into that that direction optically only after the collision (and the gamma ray burst) already happened, so all they could see was the after-glow. But that after-glow is the important part of the light that contains all the chemical information! The physics of detecting the gravitational waves is fairly standard stuff. The interferometer is a hundred years old in principle. What makes LIGO so sensitive is the accuracy and detail of its engineering, and the engineered systems to eliminate noise. The theory underpinning the waves themselves isn’t new, it has been extensively studied for decades. So once the confirmation of their existence was achieved, pretty much everything else was in place. This latest event has confirmed that their speed of propagation corresponds to the theory as well.