How can space know how to curve

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Discussion Overview

The discussion centers around the concept of how space curves in relation to black holes, particularly questioning the mechanisms behind this curvature and the implications of information loss associated with black holes. Participants explore theoretical aspects of general relativity (GR) and the nature of gravity, as well as the terminology used to describe spatial curvature.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Duordi questions how space can "know" how to curve around a black hole, given that no information escapes from it.
  • Some participants reference previous discussions and external resources related to gravity and black holes.
  • There is a claim that nothing actually enters a black hole, with some arguing that it is all "frozen in time" outside the event horizon.
  • Another viewpoint suggests that while things can fall into a black hole, their effects cannot influence the outside world, as gravity felt outside originates from the object's past history.
  • Participants discuss the implications of Einstein's GR equations, with one suggesting that space does not "know" anything but behaves according to these equations.
  • There is a debate about the terminology of "curving" versus "bending" space, with some suggesting "curving" is more scientifically accepted.
  • Participants discuss the solvability of Einstein's equations, with some asserting that they are non-linear and typically require numerical methods, while others argue that there are many known exact solutions.
  • One participant compares the complexity of GR equations to challenges in neuroscience, suggesting that both fields face difficulties with non-linear models.
  • There is a humorous exchange regarding the phrase "margarine can fool mother nature," which is not directly related to the main topic but adds a light-hearted element to the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of black holes and the implications of GR equations, indicating that multiple competing perspectives remain. The discussion does not reach a consensus on the understanding of space curvature or the terminology used.

Contextual Notes

Some claims about the nature of black holes and the behavior of space may depend on specific interpretations of GR and the definitions of terms like "curving" and "bending." The discussion also highlights the complexity of solving Einstein's equations, which may not have universally agreed-upon methods or solutions.

duordi
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How can space know how to curve from a black hole.
My understanding is that the no information can escape a black hole
so how can space know how much to curve?

Duordi
 
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Thanks for the reference.
There was some interesting discussion.

So technically nothing actually goes inside a black hole it is all frozen in time outside the black hole.

Duordi
 
"Nature cannot be fooled."

Margarine can fool mother nature.
 
So technically nothing actually goes inside a black hole it is all frozen in time outside the black hole

Technically, something does go into a black hole, and whatever that is does not come out. Sometimes a chair is just a chair.
 
so how can space know how much to curve?

Space doesn't "know" anything, it just does what it does, and what it does is curve or bend asccording to Einsteins GR equations. That is a first principal concept, not up for analysis unless you want to challenge the foundations.
 
DiracPool said:
Space doesn't "know" anything ... what it does is curve or bend according to Einsteins GR equations...

Isn't that putting the cart before the horse? :wink:
 
duordi said:
So technically nothing actually goes inside a black hole it is all frozen in time outside the black hole.

No. Things can fall into the black hole; it's just that nothing that happens inside the black hole's horizon can affect anything outside. So the gravity you feel outside the hole can't come from inside the hole; it comes from somewhere else. (As I noted in my posts in that thread, it actually comes from the past history of the object that collapsed to form the hole.)
 
Isn't that putting the cart before the horse?

What do you mean by that? First of all, Einsteins GR equations are non-linear, and therefore are only solvable via numerical integration, with perhaps the exception of the shperical Schwarchild thinga-ma-bobber.
 
  • #10
DiracPool said:
What do you mean by that? First of all, Einsteins GR equations are non-linear, and therefore are only solvable via numerical integration, with perhaps the exception of the shperical Schwarchild thinga-ma-bobber.

I meant Einstein's equations describe how space curves, rather than space curving to keep in line with Einstein's equations. Just joking! :smile:

BTW, question to anyone who may know the answer - is space 'bending' a scientific term (as opposed to 'curving')?
 
  • #11
BTW, question to anyone who may know the answer - is space 'bending' a scientific term (as opposed to 'curving')?

What's the diff? Sounds like the same thing to me.
 
  • #12
arindamsinha said:
is space 'bending' a scientific term (as opposed to 'curving')?

"Curving" is the term I usually see in papers (or popular books and articles) written by scientists; "bending" seems to be a more colloquial term used by laypeople.
 
  • #13
DiracPool said:
First of all, Einsteins GR equations are non-linear, and therefore are only solvable via numerical integration, with perhaps the exception of the shperical Schwarchild thinga-ma-bobber.

This is not correct. There are many exact, analytical solutions known to the Einstein Field Equation:

http://en.wikipedia.org/wiki/Exact_solutions_in_general_relativity#Types_of_exact_solution

Nonlinear differential equations are harder to solve than linear ones, but "harder" is certainly not the same as "impossible".
 
  • #14
This is not correct. There are many exact, analytical solutions known to the Einstein Field Equation:

Ok, so maybe there are more exact solutions than the Schwartzchild one, but, in fact, Einstein's field equations are notorious for being intractable analytically, for exactly the reason I mentioned, the non-linearlity of the differential equations. In neuroscience, we have the same problem with Freeman's KV model which couples thousands of non-linear ODE's to model the solutions. Impossible to solve even the simplest scenarios analytically.
 
  • #15
DiracPool said:
Ok, so maybe there are more exact solutions than the Schwartzchild one, but, in fact, Einstein's field equations are notorious for being intractable analytically, for exactly the reason I mentioned, the non-linearlity of the differential equations.

This is true, but it's not as extreme as it appears to be in neuroscience by your report:

DiracPool said:
Impossible to solve even the simplest scenarios analytically.

The exact solutions listed on the page I linked to include "simple scenarios" that are pivotal in our understanding of the universe:

(1) The black hole solutions (generalized Kerr-Newman, which includes Schwarzschild as a special case but also includes rotating and charged holes);

(2) The FRW solutions, which are central in cosmology.

It is true that for more complicated cases, which lack the symmetry of the above classes of solutions, we use numerical simulations; but the exact solutions above have given a lot of insight into the key factors involved. So analytical solutions, idealized as they are, are extremely important in GR.
 
  • #16
It is true that for more complicated cases, which lack the symmetry of the above classes of solutions, we use numerical simulations; but the exact solutions above have given a lot of insight into the key factors involved. So analytical solutions, idealized as they are, are extremely important in GR.

Point taken. You still haven't addressed my assertion that margarine can fool mother nature, though...
 
  • #17
DiracPool said:
You still haven't addressed my assertion that margarine can fool mother nature, though...

You're right, I haven't. :wink: I think I'm a counterexample; at least, I am if "margarine" is broadly interpreted to mean "butter substitute". Those haven't helped me lose any weight.
 
  • #18
I think I'm a counterexample; at least, I am if "margarine" is broadly interpreted to mean "butter substitute". Those haven't helped me lose any weight.

I still can't believe it's not butter..
 

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