Trouble with Infinity: Understanding Density at a Point

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In summary, the concept of infinite density at a point is often used in mathematical models, but it does not necessarily reflect the physical reality of matter. Matter is made up of components that behave according to quantum mechanics, and the concept of a continuum only makes sense on larger scales. The singularity in a black hole, which is often described as having infinite density, is not a physical entity but rather a mathematical concept. Additionally, classical GR may break down before reaching the singularity. The concept of density itself is a human invention and can lead to undefined or infinite results when used as a ratio. Overall, the idea of infinite density at a point does not accurately reflect the complexity of matter in our universe.
  • #1
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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  • #2
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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  • #3
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?
 
  • #4
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.
 
  • #5
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?
 
  • #6
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?
 
  • #7
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.
 
  • #8
"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.
 
  • #9
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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1. What is the concept of density at a point?

Density at a point refers to the amount of mass or substance present in a specific location or point in space. It is a measure of how tightly packed the particles of a substance are at that particular point.

2. How does density at a point relate to infinity?

Density at a point can help us understand the concept of infinity by showing us how a finite amount of matter or energy can be distributed over an infinite space. It also highlights the idea that as the volume of a space approaches infinity, the density at a point within that space approaches zero.

3. Why is understanding density at a point important?

Understanding density at a point is important in many scientific fields, such as physics, chemistry, and astronomy. It allows us to describe and quantify the distribution of matter and energy in space, and helps us make predictions about the behavior of various substances and systems.

4. Can density at a point be measured directly?

No, density at a point cannot be measured directly as it is a theoretical concept. However, it can be calculated by measuring the mass and volume of a substance and dividing the two. This gives us an average density over a given volume, which can then be used to estimate the density at a specific point within that volume.

5. How does density at a point differ from density in a volume?

Density at a point is a measure of the amount of matter or energy at a single point in space, while density in a volume is a measure of the amount of matter or energy contained within a specific volume. Density at a point is more precise and can vary greatly within a larger volume, while density in a volume gives a more general idea of the distribution of matter or energy within that volume.

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