I still don't understand singularities

[MathJakob]

I still don't understand singularities!

I'm sorry for anyone bored of reading the threads I've made so far but either I simply do not understand it or I'm imagining the singularity totally wrong. If I'm chosing my words correctly, at the centre of a black hole is a dimensionless point of infinite density. The thing I have issues understanding is how an object can have infinite density and still exist.

So if we took a billiard ball and compressed it over and over again, it's diametre would approach 0 and it's density would approach infinite. The thing is once it's diametre reaches 0, you don't actually have an object anymore.

No matter how tiny incredibly small something is, it MUST have a diametre of some length... Regardless whether we can measure it or not... right?

I just don't see how you can take an object of some mass, compress it so much that it's diametre is reduced to absolute 0.

Obviously I'm in no position to question anyone as I barely understand anything about physics but I know the equations say this is how it is, but there is a chance the equations could just be wrong? I know we can't observe black holes so all we have to go on are the equations but has there ever been a case where something has been thought to be true because of equations but later upon observation it was proved that the equations were wrong?

Sorry if I'm not making sense.

 

[jedishrfu]

Our math and physical theories are by definition approximations of nature, very good approximations but still approximations. As a result, singularities creep in as we assume point-like particles or in the case of black holes matter collapsing into itself with nothing stopping the collapse which implies a singularity. Whether nature works this way in a black hole, we can't say for sure only that our mathematical understanding of black holes matches up with our experimental evidence.

As far as theories being worng, that is the nature of science each new theory must explain the past and current evidence that the prior theory failed to explain in order to be accepted as the new theory.

Look at how relativity replaced classical physics when the Michelson-Morley experiment failed to show evidence of an aether for light to travel through or how quantum mechanics replaced classical EM theory or radiating charges when the evidence showed electrons orbiting the nucleus did not fall into the nucleus of the atom.

In many cases, it can be showed that using various constraints the new theory can replicate the results predicted by the old theory as in relativity when velocities are very small relative to light speed that relativistic velocity addition becomes simple classical velocity addition.

 

[phinds]

We talk about the black hole "singularity" as a point because that's what the math extrapolates to, not because anyone really believes in a point with zero dimensions but finite mass (and thus infinite density). When a theory of quantum gravity is developed it is believed that the black hole singularity will be better understood and will make more sense. For now, as jedishrfu said, the math makes verifiable predictions (other than at the singularity) and so is useful, AND it's all we have so far particularly since we cannot do any tests on the singularity in a black hole.

 

[Chronos]

You are in good company with the many scientists who dislike the infinities that naively appear in GR. A proper theory of quantum gravity would solve these issues.

 

[martinbn]

I would recommend Geroch's paper.

What is a singularity in general relativity?

 

[Naty1]

I just don't see how you can take an object of some mass, compress it so much that it's diametre is reduced to absolute 0.

A bit of skepticism is usually appropriate. Otherwise you probably end up taking some pretty silly advice, for example.

It turns out that [theoretical] math has both misled us, describing phenomena not observed in this universe, but has also made incredible predictions for which experiments were designed and observations confirmed the prediction. Sometimes there is a range of applicability and another where predictions go awry. Like Newtonian physics not being so good at high relitive velocities and GR [this case] apparently not being so good at extremes of spacetime curvature.


Richard Feynman referenced stuff like this and I think the trick is knowing which situations apply:

“Do not keep saying to yourself, if you can possible avoid it, "But how can it be like that?" because you will go 'down the drain', into a blind alley from which nobody has escaped. Nobody knows how it can be like that.

"A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist."