B Can we see 2 black holes orbiting each other?

[Ibix]

so if at t=t1 we have 2 dustclouds resulting in 1 singularity while I change the initial conditions at t=t2 then at t=t2 also the singularity is removed.

Again, how are you going to make a change when you only have tools that obey deterministic laws? The behaviour of the stuff you plan to use was already determined at t1, so the outcome was never going to be what you (erroneously) predicted at t1.

 

[HansH]

The thing is, how do you change the initial conditions?

in reality you need to move matter and energy around. But the only available stuff is already in the world and, if the world is deterministic, the "change" is already baked in.

at a small scale I assume that is what we are doing constantly. for example when I drive in a car I constantly move matter and energy around. so the fact that we cannot do that at a large scale is probaly not because it is not possible but because we as humans simply don't have sufficient options available. in theory we could make a large hydrogen bom and blow away a dustcloud I assume.

Or suppose there is a collapsed star that is just 1 kg away from further collapsing into a black hole. then I could send a rocket of at least 1kg to that structure making it become a black hole. so then the final situation of ending up in a singularity of not depends on my decision at t=t1 to change the initial conditions of the collapsed star by sending a rocket to that collapsed star.

 

[Ibix]

at a small scale I assume that is what we are doing constantly. for example when I drive in a car I constantly move matter and energy around.

Sure. And if you do that in a deterministic universe, that's always what was going to happen, whatever you thought before you did it.

in theory we could make a large hydrogen bom and blow away a dustcloud I assume.

Sure. And if you do that in a deterministic universe, that's always what was going to happen, whatever you thought before you did it.

I could send a rocket of at least 1kg to that structure making it become a black hole. so then the final situation of ending up in a singularity of not depends on my decision at t=t1 to change the initial conditions of the collapsed star by sending a rocket to that collapsed star.

Sure. And if you do that in a deterministic universe, that's always what was going to happen, whatever you thought before you did it.

 

[Ibix]

To put it another way, your mental model that doesn't include you sending a rocket to add the 1kg is not an accurate model. You didn't include your rocket in it. So you didn't change the initial conditions - you simply had the wrong ones.

 

[HansH]

To put it another way, your mental model that doesn't include you sending a rocket to add the 1kg is not an accurate model. You didn't include your rocket in it. So you didn't change the initial conditions - you simply had the wrong ones.

don't you think initial conditions also include mass being at a specific location at a specific time. if the rocket is here with me on earth it is too far away from the collapsed star to make it ever a black hole. but If I decide to send my rocket to that collapsed star it will for sure pass the critical limit I suppose. so keeping the rochet on earth or sending it to the star are 2 different initial conditions because the lead to a different result.

 

[Ibix]

but If I decide to send my rocket to that collapsed star it will for sure pass the critical limit I suppose. so keeping the rochet on earth or sending it to the star are 2 different initial conditions because the lead to a different result.

So you can have two different models of the star, one with the rocket and one without. Sure. But that is not a model of the universe, which includes the rocket and includes you. A larger model includes you and the rocket, and in a deterministic universe the outcome of your choice is already determined by the initial conditions before you start thinking about building a rocket. That's what deterministic means.

You are free to consider a model that is not deterministic, but that is not GR. However, the singularities you asked about are a feature of the mathematics of GR (and since we don't have a non-deterministic theory of gravity we cannot say anything about any possible singularities in such a theory), so you are either stuck with determinism or you asked a poor question.

 

[HansH]

so you are either stuck with determinism or you asked a poor question.

I am not sure what you mean with poor question, but for me it is not a poor question if it leads to a better insignt. for me the insignt dat GR requires a deterministic universe with a consequence that there is no free wil (because even your thinking is predetrmined by initial conditions) was new for me, and probably also new for a lot of people. I think you can use that story in court when you have rubbed a bank, because it means that there was nothing you could to to prevent it anyway.

 

[Hill]

Back to physics. There is only one possible outcome - the black holes either merge or not. If they merge, there is one singularity. If they don't, there are two. Looks clear to me.

 

[Nugatory]

for me the insignt dat GR requires a deterministic universe with a consequence that there is no free wil (because even your thinking is predetrmined by initial conditions)

This would be a more impressive insight if it didn’t apply just as well (or badly, depending on your philosophical preferences) to all of classical physics since the beginning of the discipline. The possibility that the universe might not be deterministic didn’t arise until early in the twentieth century with quantum mechanics.

 

[ersmith]

Stepping back for a moment from the argument about determinism, the original question talked about the "geometrical position" of a singularity, and of singularities orbiting each other. This makes me think that perhaps the OP is conflating the GR singularity and the Newtonian center of mass. This is an easy mistake to make. From far away we can indeed model black holes as point masses governed by Newtonian gravity. This approximation breaks down badly when you approach the event horizon. In any case, the "singularity" is the place in spacetime (not just space) where the mathematics ceases to produce sensible answers. This is *not* the same as "the center of the black hole". It's not even clear to me that the latter phrase is well defined.

 

[Vanadium 50]

I never said I dont like it.

No, you just listed the things you didn't like about it.

Complaining about determinism is a philosophical argument, not a scientific one.

because if you want to make steps you should think outside the box.

And b efore you lecture us on doing that, don't you think you should learn where the box is?

 

[HansH]

No, you just listed the things you didn't like about it.

Complaining about determinism is a philosophical argument, not a scientific one.

And b efore you lecture us on doing that, don't you think you should learn where the box is?

first of all I am not complaining (which sounds to me as a negative attitude). complaining about things while complaining cannot change them is stupid. But instead I am trying to understand things.
When determinism starts to have impact on the validity of GR (as it was concluded not be be compatible with a non deterministic universe) it for sure is a scientific one I assume.

I learned from this topic that the box is in this case general relativity requiring a deterministic universe. With thinking outside the box I also do not refer to myself, (so probably you misunderstood that) but to the way progress can be made in general so also for physics. your remark gives me a bit the impression of betittling, which also does not sound as a very positive attitide, sorry.

 

[PeterDonis]

GR seems to be deterministic

Not "seems to be", is.

when the initial conditions are given

If the initial conditions aren't given, you don't have a well-defined solution, so you can't say anything whatever about what happens.

do you agree if I change the set of initial conditions that the result could be that we get a different future moment in time witout a singularity?

Meaning, if you specify a different set of initial conditions? Sure. You can specify initial conditions that don't lead to a spacetime with a singularity in it. But you can't arbitrarily "change" them once you've specified them. You can't take your original scenario, with initial conditions that lead to a singularity, and then say, well, in the middle somewhere I'm going to change it so the singularity doesn't form.

 

[PeterDonis]

When determinism starts to have impact on the validity of GR

This is word salad. GR is a deterministic theory. It has also been tested to be valid within a very wide domain. So whatever you are thinking of here, it's wrong.

As I have already said, GR is not a complete theory. So the fact that GR, as a theory, is deterministic, does not mean everything in the actual universe is deterministic, or that if we find any evidence of non-determinism, it must mean GR is wrong.

In any case, as I have also already said, all of this is irrelevant to the discussion in this thread. This thread is in the relativity forum, so GR is the theory we are using here. If you don't want to accept that, then this thread will be closed as there is no point in further discussion.

 

[PeterDonis]

as it was concluded not be be compatible with a non deterministic universe

Nobody has concluded any such thing. There could be non-determinism in the universe, just not within the domains in which GR has been tested. For example, there could be non-determinism in your brain when you make a decision. GR is not a theory of biology or neuroscience, and it says nothing whatever about whether your brain is deterministic. But it does say, for example, that no amount of non-determinism in your brain is going to save you if you jump off a cliff.

 

[PeterDonis]

in a deterministic universe the outcome of your choice is already determined by the initial conditions before you start thinking about building a rocket.

One has to be careful here. As I have pointed out, GR is not a theory of biology or neuroscience, and it doesn't claim that the processes in your brain when you make a choice are deterministic.

What it does claim, however, is that the spacetime where the rocket stays on Earth, and the spacetime where the rocket flies to the star, are different spacetimes, since what the rocket does makes a difference to the final configuration of the star. So any specification of initial conditions has to include the specification of what the rocket does. (So "initial" conditions might be a misnomer, but that's the term that is commonly used.)

 

[HansH]

Nobody has concluded any such thing.

Ithink it was concluded in #36: 'You are free to consider a model that is not deterministic, but that is not GR'

 

[PeterDonis]

Ithink it was concluded in #36: 'You are free to consider a model that is not deterministic, but that is not GR'

Yes, but that's not the same as the claim you made that I responded to.

 

[HansH]

One has to be careful here. As I have pointed out, GR is not a theory of biology or neuroscience, and it doesn't claim that the processes in your brain when you make a choice are deterministic.

What it does claim, however, is that the spacetime where the rocket stays on Earth, and the spacetime where the rocket flies to the star, are different spacetimes, since what the rocket does makes a difference to the final configuration of the star. So any specification of initial conditions has to include the specification of what the rocket does. (So "initial" conditions might be a misnomer, but that's the term that is commonly used.)

my point is that in more earth like situations, movements can be influenced and still possible to fully calculate, for example if I have a pendulum with a mass and a length and an initial amplitude I can calculate the position as function of time, even when at t=t1 my mind decides to shorten the length of the wire by a factor 0.5.
so as result of my decision at t=t1 the result at t=10 years from now also changes, which is perfectly ok.

so I would asume that I can do the samen thing for the rocket shooting to the star en be able to calculate the situation of the black hole and its future if the theory is correct. so the situation of having a singularity or not should then be a function of my minds decision at t=t1.

 

[PeterDonis]

in more earth like situations

...we are not describing the whole universe, just a tiny subset of it, so there is no pretense of capturing all of the relevant conditions. So it's perfectly normal to just impose external interventions that your model doesn't capture.

the situation of having a singularity or not should then be a function of my minds decision at t=t1.

If you're going to just model the isolated system that either collapses to a black hole or not, then you could sort of (see below) treat it like the above, and just impose the external condition of you either deciding to launch the rocket, or not.

However, GR is also used to model the entire universe, where there is no such thing as "external interventions"; and more generally, a GR solution even for an isolated system, according to the theory, is supposed to be determined by initial and/or boundary conditions. So you would have to include the outcome of your decision whether or not to fire the rocket in those initial/boundary conditions, meaning that the case where you decide to fire the rocket, and the case where you don't, are two different models according to GR. There is no way to include in the GR model whatever things affect the processes in your brain that makes that decision; as I said, GR is not a theory of biology or neuroscience, and it simply does not model things like your brain processes.

 

[HansH]

Thanks, that helps. of course the discussion should not concern a connection between the brain and GR. I only used it to be able to generate a way to introduce a change at t=t1 to make the system remains as a collapsed star of further contract to form a black hole. so lets not talk about biology or neuroscience.

basically I started the thread to hope to get some better understanding how the situation evolves starting at the moment that the critical mass is reached and the process of collapsing is started. and especially how that evolves further down into the black hole and further into time. and for 2 merging black holes I was also wondering how that process evolves. Not sure if that can be explained a bit high level (the trouserlegs example was already such explanation) without the need to go into all details which would require a few years of university study first to get that theory digested.

 

[PeterDonis]

I started the thread to hope to get some better understanding how the situation evolves starting at the moment that the critical mass is reached and the process of collapsing is started. and especially how that evolves further down into the black hole and further into time. and for 2 merging black holes I was also wondering how that process evolves. Not sure if that can be explained a bit high level (the trouserlegs example was already such explanation)

As far as the merger goes, yes, the trouser legs is the best simple illustration that can be given at the "B" level.

As far as the original collapse process that formed the holes, it's not a question of "critical mass" exactly (though mass limits do play a role--see below), it's a question of what can hold the original object up against its own gravity to prevent collapse. What that thing is, and how it works, depends on the kind of object. Roughly speaking, there are four categories:

(1) Planets and similar objects, which are held up by ordinary atoms resisting compression. They can stay in such a state indefinitely. However, such objects can only have masses small enough that fusion reactions are not triggered inside them; if they get large enough for fusion reactions to start, they become...

(2) Stars, which are held up by thermal pressure of hot gas, heated by fusion reactions in their cores. They can only stay in such a state as long as the fusion reactions continue; once fusion reactions stop, they collapse into one of the two further categories below.

(3) White dwarfs, which are held up by electron degeneracy pressure. They can stay in such a state indefinitely as long as they don't accrete enough mass to put them over the Chandrasekhar limit of about 1.4 solar masses. If they go over that limit, they collapse, possibly into...

(4) Neutron stars, which are held up by neutron degeneracy pressure. (There are speculations that there might be other states of strongly interacting matter inside at least some neutron stars, such as strange quark matter, so "quark degeneracy pressure" might be a better general term, but that's not important for our discussion here.) They can stay in such a state indefinitely as long as they don't accrete enough mass to put them over the maximum mass limit for neutron stars, which is somewhere around 3 solar masses.

Objects that collapse into black holes generally start out as stars which are too massive to collapse into white dwarfs or neutron stars.

 

[HansH]

Thanks for these further overview. Of course it is good to know these 4 options. (for me this was not really new but good to have the overview)
For me at the moment I am really interested in the collaps process or merger process itself and If I can understand that a a high level, so it is sufficient to know that there is at least a method to let it collapse to be triggered by a simple press on the button and neglecting all the rest of the universe around that is not domanant for starting the process, which I represented by the rocket example.

one thing I am not certain about is the question if it is possible to represent this process of collapsing in a causal way, so suppose I press my button at t=t1 (for the ease of the example assuming then at t=t1 the collapsing process starts so the rocket is already very close when it is launched) how does it then progress go forward looking to the trouser example: does it then start at the part of the shoes (assuming they are close to the event horizon) and then wind up in time? and especially how does time flow from the shoes to above because spacetime falls inwards faster than the speed of light. imagining how that works is already a point on its own (ok probably this is also not the best way to describe but the best way I can think if at for the moment ) but at least it hopefully shows the point I am thinking about.

 

[PeterDonis]

For me at the moment I am really interested in the collaps process or merger process itself and If I can understand that a a high level, so it is sufficient to know that there is at least a method to let it collapse to be triggered by a simple press on the button

It's not that simple, since there is no way to, for example, accrete a significant amount of mass onto a white dwarf or a neutron star just by pressing a button (unless you also have a star's worth of mass lying around in a bin that your button releases). Nor is there a way to stop fusion reactions in a star's core just by pressing a button.

and neglecting all the rest of the universe around that is not domanant for starting the process

The collapse can be modeled as an isolated system, yes; the rest of the universe doesn't affect it appreciably.

if it is possible to represent this process of collapsing in a causal way

Of course. What normally causes the collapse, as I said, is something like fusion reactions stopping in a star's core, or a white dwarf or neutron star accreting enough mass to put it over the applicable maximum mass limit. These are causal processes. They aren't as simple as someone pressing a button, but that's true of most of the causal processes in our universe.

how does time flow

"Time flow" is not a good way of thinking about this. You have a spacetime geometry. That geometry is produced from some set of initial conditions, but thinking of that as "time flowing" is too simple.

For example, the "trousers" is a spacetime viewpoint. Yes, the "upward" direction (from shoes towards waist) is, more or less, the "future" direction of time, but, for example, mass falling inward doesn't go straight upwards in such a diagram, but it is still moving on future directed timelike worldlines. The collapse part would be down at the shoes, yes (below the shoes would be the object before it collapses), so the collapse is "in the past" with respect to the black holes that get formed, and those formation processes are in turn "in the past" of the merger (where the legs of the trousers meet). But that notion of "in the past" (basically, "towards the bottom of the diagram") is very general and leaves out a lot of important factors. It's the best that can be done at a "B" level, but it's still very, very heuristic.

spacetime falls inwards faster than the speed of light

No, in the viewpoint you refer to here, which is different from the "trousers" viewpoint, space flows inward around a black hole (it only flows inward "faster than light" inside the horizon). But you can't mix this viewpoint with the "trousers" viewpoint. They're different heuristic pictures, and both of them leave out a lot. In particular, the "space flowing inward" viewpoint can't handle black hole mergers at all (and isn't very well equipped even to handle the collapse of a single object to form a black hole).

 

[HansH]

Is there any graphical representation or animation available somewhere that gives an idea of how this process of merger or collapsing star to a black hole evolves in spacetime?

 

[PeterDonis]

evolves in spacetime?

Nothing "evolves in spacetime". Spacetime is a 4-dimensional geometric object that already contains the entire history of the system. So a spacetime representation does not show anything "changing" or "evolving".

As far as animations go, you might try Andrew Hamilton's home page:

https://jila.colorado.edu/~ajsh/

He has done a variety of simulations of various black hole scenarios. The basic idea of all of them is to pick an observer with a particular worldline in the spacetime, and show how things look to that observer as a function of their proper time along the worldline. He also has some spacetime diagrams.

 

[HansH]

Nothing "evolves in spacetime". Spacetime is a 4-dimensional geometric object that already contains the entire history of the system.

Yes of course, thinking about that I realize that there is indeed nothing to evolve as time is already in. But I also ralize that then the rocket that I decide to launch at a certain time can not be included in this system in this way, other than assuming the launched rocket is part of the 4-dimensional geometric object so the launching moment is on beforehand defined in the structure itself.

Basically this does not have to be a problem, as the effect of the launch moment is still fully visible in the 4D object.

so I could calculate the resulting spacetime as function of the launching moment. That actually adds an additional dimension to the structure which is all posible launching moments. Normally if you add a dimension to some structure all matrices, tensors etc then also get additional dimensions. However as you can probably see the 5th dimension as fully independent here (simply includes all possible spacetimes as function of the launching moment), I assume it doesn't give extra complications. (it does not make sense for example to look at the derivative of the launching moment having an effect on something else)

 

[PeterDonis]

the rocket that I decide to launch at a certain time can not be included in this system in this way

Sure it can. See below.

other than assuming the launched rocket is part of the 4-dimensional geometric object so the launching moment is on beforehand defined in the structure itself.

I'm not sure what you mean here, but as I said before, the case where the rocket is launched, and the case where the rocket is not launched, are two different spacetimes--two different 4-dimensional geometries. You can't have a single solution that includes both possibilities, because the spacetime geometries are different. But you don't need to have a single solution that includes both possibilities. You can just have two solutions.

I could calculate the resulting spacetime as function of the launching moment. That actually adds an additional dimension to the structure which is all posible launching moments.

No. If you change the "launching moment", you again change the spacetime geometry. It won't change whether a singularity is present (since if the rocket is launched, by your assumptions, a singularity will be present), but it will change other things about the geometry, because the spacetime geometry includes relationships like "when on Earth's clock the rocket gets launched". If you change when on Earth's clock the rocket gets launched, you change the spacetime geometry. So you don't have one "structure" with an additional "dimension" to represent the possible launching moments. You have as many different "structures" (spacetime geometries) as you have launching moments.

the 5th dimension

There isn't one. See above.

You are verging on personal speculation at this point. I would strongly suggest taking some time to work through a GR textbook to see how spacetime models are actually constructed.