How Elastic is Space (Spacetime)? | LIGO & Gravitational Waves

[bland]

TL;DR

The Sun magically and instantaneously is vaporised and dispersed by vandals from an alien civilisation. Eight minutes later when that information reaches the Earth, what precisely happens.

Now that gravitational waves are more famous because of LIGO, it got me to thinking about what we (lay people) are usually told would happen, which is that the Earth will continue in a straight line at a tangent to its orbit at that moment that information arrives eight minutes later. Which is good enough to get the idea across that that is trying to be gotten across.

However I'm trying to picture it which is difficult because we're used to having a two dimensional image, like the bowling ball on the trampoline. So I'm thinking it will be a wavefront that hits the Earth but what is the size of this wavefront, it would start off at the size off the Sun I suppose (maying I suppose incorrectly), but what exactly would happen when it hits, would there be other following ripples or is the Sun not massive enough to do that.

Specifically I'm thinking as the Earth careens off on a tangent would it also be bobbing up and down as other following ripples engulf it, and if so by how much.

 

[Ibix]

It's impossible to describe the Sun vanishing in GR. Doing so violates local conservation of energy, which is built into the Einstein Field Equations - so although you can pose the question, you cannot get an answer. The Sun can explode or move away, but it cannot just vanish.

The fact that you do see answers suggests to me that some sources are effectively crossing their fingers behind their back and answering related questions, probably that gravitational waves propagate at $c$. Applying that result to the idea of the Sun vanishing is, however, nonsense.

 

[bland]

It's impossible to describe the Sun vanishing in GR. Doing so violates local conservation of energy, which is built into the Einstein Field Equations - so although you can pose the question, you cannot get an answer. The Sun can explode or move away, but it cannot just vanish.

OK well I pose the same question but replace 'vanish' with explode into finely dispersed particles. I was under the impression that we could postulate impossible things in thought experiments in order to understand some other point.

Sort of like Einstein's weighing a box as a photon escapes through timed hole, and the box moves up a bit in the gravitation field because the weight of the box is now less. I mean all that is impossible as well as silly, but that's not the point.

Or would it be better to say that by 'vanish' I meant vanish from the spot where it was, by being instantly transported elsewhere in the universe using some unknown technology. Am I then allowed to ask how spacetime reacts to this sudden disappearance, and my question still remains, what is the size of the disturbance in spacetime when it finally reaches the Earth, and does the Earth then continue in a straight line or bob around as well.

In fact for what I want to know it might be better to postulate a billion Sun mass black hole with the Earth orbiting it at some distance and then this super massive black hole is similarly 'vanished' by transporting it elsewhere, that would give a much bigger disturbance to work through.

Can you understand what I'm wanting to know? Is it an unreasonable question.

 

[Ibix]

I was under the impression that we could postulate impossible things in thought experiments in order to understand some other point

Depends what you mean by "impossible". Rockets capable of accelerating at millions of gravities and pilots not turning into strawberry jam in the process is fine. Situations that the theory explicitly says cannot happen can't teach you anything. It's a bit like asking what's north of the north pole - superficially a reasonable question, but nonsense when you try to answer it.

OK well I pose the same question but replace 'vanish' with explode into finely dispersed particles.

Nothing happens until the expanding cloud reaches Earth, for the general relativistic equivalent of the Shell Theorem. Once the particles start to flow past Earth it gets complicated, and a detailed answer depends on what the particles are - light, ordinary matter, or a mix. But generally you'll find that the "gravitational attraction" will fall and the Earth will spiral outwards - more so because the particles would presumably push it outwards.

Or would it be better to say that by 'vanish' I meant vanish from the spot where it was, by being instantly transported elsewhere in the universe using some unknown technology. Am I then allowed to ask how spacetime reacts to this sudden disappearance

No, because again this violates local conservation of energy: there is a small region of space containing a chunk of star (i.e., some mass and energy), which then doesn't contain anything. But the contents didn't flow through the boundary of the region - they've just gone, and mass and energy in that small region is not conserved. The Einstein Field Equations cannot be solved in this case, so there is no answer.

Can you understand what I'm wanting to know? Is it an unreasonable question

I understand what you are asking - you want to know how spacetime reacts to a chunk of matter suddenly disappearing. Unfortunately the question cannot be answered - the situation is forbidden by the laws of physics as we know them. That makes it a "what's north of the north pole" question, one that is self-contradictory and no answer is possible.

 

[PeterDonis]

I was under the impression that we could postulate impossible things in thought experiments in order to understand some other point.

No, you can't. You can postulate things that are possible--consistent with the laws of physics--but not technically feasible given our current or expected future technology. You cannot postulate things that are impossible--inconsistent with the laws of physics. The sun vanishing is the latter.

Sort of like Einstein's weighing a box as a photon escapes through timed hole, and the box moves up a bit in the gravitation field because the weight of the box is now less. I mean all that is impossible

No, it isn't. It's all consistent with the laws of physics. It's just not technically feasible given our current or expected future technology.

Or would it be better to say that by 'vanish' I meant vanish from the spot where it was, by being instantly transported elsewhere in the universe using some unknown technology.

No, this is also inconsistent with the laws of physics.

In fact for what I want to know it might be better to postulate a billion Sun mass black hole with the Earth orbiting it at some distance and then this super massive black hole is similarly 'vanished' by transporting it elsewhere

Inconsistent with the laws of physics.

 

[PeterDonis]

I pose the same question but replace 'vanish' with explode into finely dispersed particles.

This version is consistent with the laws of physics, and @Ibix described what those laws say about this scenario.

 

[David Lewis]

The Sun magically and instantaneously is vaporized and dispersed by vandals from an alien civilization. Eight minutes later when that information reaches the Earth, what precisely happens?

If memory serves, Faraday presented the Sun magically disappears thought experiment to help people understand the lines of force concept. The Sun affects space surrounding the Earth in such a way that it pulls the Earth toward the Sun. So if you took the Sun away, the Earth would still feel the force for a short time. General Relativity was 60 years in the future.

 

[PeterDonis]

If memory serves, Faraday presented the Sun magically disappears thought experiment to help people understand the lines of force concept.

That doesn't mean it's a valid thought experiment in the context of GR.

In fact, it's not even a valid thought experiment in the context of electromagnetism if you actually work it out. EM has charge conservation, so a charged object, which would need to be present to be a source of lines of force, can't just disappear, since that would violate conservation of charge. So it's just as invalid to think about how the disappearance of a charged object would affect other charged objects, as it is to think about how the disappearance of an object with mass would affect other objects with mass.