B Spagettification and a singularity

[PeterDonis]

Will even a proton get ripped apart? Or maybe even quarks (when there are preons inside it)?

The classical model in GR that we are using here doesn't include any quantum structure of matter, so it's not really possible to answer this question. We would need a theory of quantum gravity. Such a theory might well eliminate the singularity, though.

 

[HansH]

Will even a proton get ripped apart? Or maybe even quarks (when there are preons inside it)?

probably a different topic but hope this can be answered with a single yes or no: according to quantum mechanics smal things cannot have an exact position. so the term 'ripping apart' says something about position in relation to a strong gravitational field. Is there anything known about theory that predict to expect a particle or subatomic particle at a certain position in case of strong gravity? or is that just the gap in the theory so far we need a quantum gravity theory for?

 

[PeterDonis]

according to quantum mechanics smal things cannot have an exact position

Yes, that's why I cautioned in my post just now that we are using a classical GR model in this thread and can't really answer questions about quantum objects and how they behave near the singularity. We would need a theory of quantum gravity to do that.

is that just the gap in the theory so far we need a quantum gravity theory for?

Yes. See above.

 

[HansH]

ok then still one question about this quantum gravity: suppose we would have such theory. Then it probably result in the effect that the mass in the singularity spreads out to a certain distance according to some statistical propabilty function. So then you could assign a kind of effective size to that singularity so then time would not stop as curvature does not really get infinite, as then the singularity is replaced by a volume with an effective mass distribution so preventing finite mass in an infinite small area. Is that the direction modern science thinks into?

 

[BoraxZ]

Then it probably result in the effect that the mass in the singularity spreads out to a certain distance according to some statistical propabilty function.

Particles are spread out spatially on the line r=0. Only in the angular directions they get crammed.

I think in the classical picture point-like particles are themselves tiny black holes. If you smear these over space... I don't know what happens

This question is not answerable. Please do not clutter the thread with pointless questions.

Okay. Let me ask it differently. Doesn't each position in space have an imaginary clock running on that position (while both position and time are relative, i.e , there are no absolute clocks ticking)? I mean, it's spaceTIME. Or can we only say how fast that clock is running, like a pendulum, without actually keeping time, while particles arriving in that position (of in the hole) have an actual age? If so, is the hole made up of particles for which different proper times have elapsed (the "youngest", if not photons, having an age of about the time it took from the big bang to the formation of the hole)?

 

[PeterDonis]

suppose we would have such theory.

That doesn't help at all in answering questions unless we know what the theory says. Which of course we don't. So your questions in this post are not answerable.

 

[PeterDonis]

I think in the classical picture point-like particles are themselves tiny black holes.

This is speculation. Please do not clutter the thread with speculation.

 

[PeterDonis]

Doesn't each position in space have an imaginary clock running on that position (while both position and time are relative, i.e , there are no absolute clocks ticking)?

No.

 

[BoraxZ]

No.

So the clocks run only on timelike (massive) particles, while the spacetime they are in determines how fast their clocks tick? Can we say then that spacetime is filled with pendulums (and measure sticks), showing the pace of time (and spatial metric, as opposed to clocks and odometers)?
Or better maybe, with a metric...

Space has no age. Even not in the space-age.

 

[Ibix]

Doesn't each position in space have an imaginary clock running on that position (while both position and time are relative, i.e , there are no absolute clocks ticking)?

No. You can lay out an array of clocks if you like, but this involves you making a choice about how to zero them, which is equivalent to you choosing a definition of space. Notionally we can do this, and it's often the methodology for associating the abstract numbers of a coordinate system with measurable things in a spacetime. But something you choose can't be a natural property of spacetime.

 

[HansH]

No.

He means the singularity, which is a moment of time.

I know, so which moment in time are we talking about then? or is it the moment in time that the singularity was formed from a collapsing star? But then what about particles falling in later? I assume they cannot fall towards an earlier moment in time.

 

[Ibix]

I know, so which moment in time are we talking about then? or is it the moment in time that the singularity was formed from a collapsing star? But then what about particles falling in later? I assume they cannot fall towards an earlier moment in time.

All timelike paths that cross the horizon terminate on the singularity. It is the future once you've crossed the horizon, and that's the moment in time we're talking about. It's always in your future wherever and whenever you are, but once you cross the horizon there's no part of your future that doesn't include the singularity.

 

[HansH]

Yes that was also what I think, but then how can you speak about 1 moment in time, because I assume it is then all moments in time as set by the history of all particles fallen into the black hole and starting withe the moment in tim that the singularity was formed.

 

[Ibix]

Yes that was also what I think, but then how can you speak about 1 moment in time, because I assume it is then all moments in time as set by the history of all particles fallen into the black hole and starting withe the moment in tim that the singularity was formed.

The singularity is a spacelike line, and calling it "a moment in time" is a reasonable description. But spacetime inside a black hole is extremely curved. Fundamentally this goes back to something I said on the first page, that the direction of decreasing $r$ is timelike inside the horizon but spacelike outside. Trying to work out "when" the singularity is from outside the hole doesn't really make sense.

 

[Ibix]

You can work out the minimum proper time it would take you to get to the singularity from any event, but that depends on your available delta v and can be arbitrarily small given arbitrarily large acceleration. And you can work out the maximum proper time to get to the singularity, but again it depends on your available delta v and can be infinite.

Once you've crossed the horizon, though, you have a maximum of 15$\mu$s per solar mass of black hole before you reach the singularity.

 

[PeterDonis]

You seem to want to define a time coordinate such that the singularity is assigned one.

It's easy to assign individual points on the singularity a time coordinate. But it might not be the same time coordinate for all points on the singularity.

It is not clear to me whether any coordinate system exists that has the required properties -- spanning all of a black hole space-time and having a monotone increasing time coordinate.

Kruskal coordinates have both of these properties. However, they assign a different time coordinate to different points on the singularity. I'm not aware of any chart that has all three properties--the two you mention here, and assigning the same time coordinate to all points on the singularity.

 

[PeterDonis]

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[PeterDonis]

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