Trouble with Infinity: Understanding Density at a Point

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Discussion Overview

The discussion revolves around the concept of infinite density at a point, particularly in the context of matter and singularities in black holes. Participants explore theoretical implications, the nature of matter, and the limitations of classical general relativity (GR) in describing such phenomena.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question how tangible matter can possess infinite density, suggesting a need for clarity on what "matter" is and its behavior at microscopic levels.
  • Others argue that singularities in black holes are not physical locations within the universe but rather mathematical constructs, with classical GR potentially breaking down before reaching them.
  • A participant raises the idea that "infinity" is not a number at a point, but rather a limit that approaches infinity as one nears a point, leaving the value at that point undefined.
  • Another perspective suggests that density could be viewed along a different axis, relating to energy/mass in an infinitely small space, while still adhering to thermodynamic principles.
  • One participant proposes that point particles like leptons and quarks could be considered to have infinite density, questioning the definitions of density and the implications of mathematical models that lead to undefined results.

Areas of Agreement / Disagreement

Participants express various viewpoints on the nature of infinite density and singularities, with no consensus reached on the interpretations or implications of these concepts. The discussion remains unresolved regarding the physical versus mathematical nature of singularities and the definition of density.

Contextual Notes

Limitations include the dependence on definitions of matter and density, as well as the unresolved nature of how classical GR applies to singularities and the implications of infinite density.

ChrisisC
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How is it possible that there is a infinite amount of density at a point? I understand how number can be infinite but how does something tangible like matter reach infinity?
 
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What do you think "matter" is? It is not some esoteric substance. It is made up of components that on a (sub)microscopic level behave according to the predictions of quantum mechanics.

Only on larger scales does the "intuitive" approach of a continuum make sense.
 
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Orodruin said:
What do you think "matter" is? It is not some esoteric substance. It is made up of components that on a (sub)microscopic level behave according to the predictions om quantum mechanics.

Only on larger scales does the "intuitive" approach of a continuum make sense.

okay, then how is it possible that infinite particles are in one spot in the universe, say at a singularity in a black hole? I'm having trouble comprehending how a never ending amount of particles can fit into a finite area. Wouldn't this area run out of space to fit the particles?
 
ChrisisC said:
okay, then how is it possible that infinite particles are in one spot in the universe, say at a singularity in a black hole?
They are not. In the case of standard classical GR, the singularity is (1) not "somewhere" - it is in the future of all observers - and (2) not a part of the universe.

It is also highly likely that classical GR breaks down before you reach the singularity.
 
Orodruin said:
They are not. In the case of standard classical GR, the singularity is (1) not "somewhere" - it is in the future of all observers - and (2) not a part of the universe.

It is also highly likely that classical GR breaks down before you reach the singularity.

So it's a mathematical entity not a physical one?
 
Orodruin said:
They are not. In the case of standard classical GR, the singularity is (1) not "somewhere" - it is in the future of all observers - and (2) not a part of the universe.

It is also highly likely that classical GR breaks down before you reach the singularity.

also, what do you mean by in the future?
 
ChrisisC said:
also, what do you mean by in the future?
If it was part of the universe, it would be more like a moment in time than a place in space. That "moment in time" would be in the future of all observers.
 
"How is it possible that there is a infinite amount of density at a point? I understand how number can be infinite but how does something tangible like matter reach infinity?"
'Infinity' is not a number at a point. A limit is 'infinite' if the number increases without limit as a point is approached,
but the value at the point is undefined.
 
Also, a different perspective: it exists along a different axis per se, more of a time measure than anything. Since it is a finite amount of energy / mass in a given infinitely small space, although the curvature of spacetime would be undefined, it would still exist within regular reasonable standards of Thermodynamics.
 
  • #10
Leptons and quarks are usually considered to be point particles, so you could perhaps consider them to have infinite density. But we humans invented the term density to be the ratio of mass to volume, so why shouldn't density be infinite? Any time we define a quantity as a ratio, we risk having infinities or undefined results. This isn't really a problem with Nature, but our choice of mathematical model.

For example, we could consider the neutron to have an infinite mass to charge ratio. How could Nature allow such an aberration? It didn't. We did.
 
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