I am having trouble understanding why, according to the Big Bang Theory, density at the point of singularity is infinite.

Here is my train of thought.

 

Volume at point of singularity = 0

Density = Mass / Volume

Density at point of singularity = Mass / 0

Density is undefined.

 

I don't understand why density is infinite at the point of singularity if the simple calculation above yields an answer that is undefined. Are my calculations incorrect?

The answer to this would be: science doesn't know. The only way we got the idea of the universe before the big bang being a singularity that was infinitesimally small, yet infinitesimally dense was by "rewinding," so to speak, the expansion of the universe from now to 14 billion years ago. The outcome? A singularity. In a singularity, physics seem to just... Break down. Our equations have never worked to understand a singularity. So that's just it, we don't know.

 

-Arch

Edited October 17, 201312 yr by Archimedes

I am having trouble understanding why, according to the Big Bang Theory, density at the point of singularity is infinite.

Here is my train of thought.

 

Volume at point of singularity = 0

Density = Mass / Volume

Density at point of singularity = Mass / 0

Density is undefined.

 

I don't understand why density is infinite at the point of singularity if the simple calculation above yields an answer that is undefined. Are my calculations incorrect?

Two points.

 

First, the big bang theory doesn't extend all the way back to time 0; our understanding of physics breaks down before then.

 

But, for the math you mention, you need to use the concept of "limits" to find out what happens when the volume is zero because, as you say, you can't divide by zero. Limits are usually covered in introductory calculus class, I think but you can get an informal idea by just considering what happens as the volume approaches zero: the density increases ... without limit. By making the volume smaller, you can make the density as large as you like.

 

The fact that this eventually ends up dividing by zero is pretty much what "singularity" means: a place where the math is undefined.

The answer to this would be: science doesn't know. The only way we got the idea of the universe before the big bang being a singularity that was infinitesimally small, yet infinitesimally dense was by "rewinding," so to speak, the expansion of the universe from now to 14 billion years ago. The outcome? A singularity. In a singularity, physics seem to just... Break down. Our equations have never worked to understand a singularity. So that's just it, we don't know.

 

-Arch

 

Two points.

 

First, the big bang theory doesn't extend all the way back to time 0; our understanding of physics breaks down before then.

 

But, for the math you mention, you need to use the concept of "limits" to find out what happens when the volume is zero because, as you say, you can't divide by zero. Limits are usually covered in introductory calculus class, I think but you can get an informal idea by just considering what happens as the volume approaches zero: the density increases ... without limit. By making the volume smaller, you can make the density as large as you like.

 

The fact that this eventually ends up dividing by zero is pretty much what "singularity" means: a place where the math is undefined.

 

Thanks for the informative replies! I never thought of using the concept of limits, but that actually makes the whole concept of a singularity easier to understand for me.