Exploring the Limits: Planck Units and the Singularity of Black Holes

[BernieM]

Do Planck units apply inside of black holes? Are they modified? Or are they irrelevant? If some Planck units remain unchanged and applicable in black holes, which ones would those be?

 

[Nabeshin]

Do Planck units apply inside of black holes? Are they modified? Or are they irrelevant? If some Planck units remain unchanged and applicable in black holes, which ones would those be?

Not sure what you mean, Planck units are just that, just a specific choice of units. The question is equivalent to asking if the mks or cgs unit system still applies within a black hole, which of course it does.

 

[BernieM]

Planck length is the length at which quantum indeterminacy becomes absolute, for example. I don't think that is analogous to other conventional systems of measurement. But rather than debate that, perhaps I can explain further the reason for the question. If the radius of a black hole = 0 then gravity is infinite and physics breaks down in essence. But is it actually possible for something that begins by posessing properties of size, mass, energy, etc., to actually attain a size of ZERO? And if it can not become ZERO in size then the radius of the black hole can never have a radius of zero and no actual breakdown in physics occurs. Well I hope this helps to understand my real question then.

 

[SHISHKABOB]

black holes definitely have a non-zero radius, I'm not sure what you're trying to get at

 

[Steely Dan]

Planck length is the length at which quantum indeterminacy becomes absolute, for example. I don't think that is analogous to other conventional systems of measurement.

The Planck length (or any other Planck unit) is simply defined as the collection of fundamental constants (speed of light, gravitational constant, fine structure constant, etc.) put together in the right combination to yield a quantity with dimension of length. It does indeed have physical meaning too, but the Planck length would only change inside a black hole if either $G$, $c$ or $\hbar$ changed inside a black hole.

But rather than debate that, perhaps I can explain further the reason for the question. If the radius of a black hole = 0 then gravity is infinite and physics breaks down in essence. But is it actually possible for something that begins by posessing properties of size, mass, energy, etc., to actually attain a size of ZERO? And if it can not become ZERO in size then the radius of the black hole can never have a radius of zero and no actual breakdown in physics occurs. Well I hope this helps to understand my real question then.

One possible meaning of the Planck length is that it is the smallest meaningful length scale, so that any object would at least have the size of the Planck length. This would preclude a black hole from having a size of zero. But this is far from a settled question.

 

[Chronos]

I assume you are talking about the singularity as opposed to the event horizon. I'm not sure the Planck length is relevant, but, the Planck density may be. At 10^93 gm/cm^3 it is really big, but, not infinite.

 

[BernieM]

Yes, I was not specific but I was referring to the singularity. I guess the problem I am having is that given that not even 'empty space' is ever truly empty, r could never = 0 as long as there is "something" there.

 

[Dickfore]

Planck length is the length at which quantum indeterminacy becomes absolute, for example.

No, Planck length is defined as:
$$L_p \equiv \sqrt{\frac{G \hbar}{c^3}}$$

Period! So, which one of these constants do you suspect to change within a black hole?

 

[BernieM]

G. That's the problem if r=0 then G=$\infty$ or at least that's how I understand the dilemma of why physics breaks down in the singularity.

 

[Nabeshin]

G. That's the problem if r=0 then G=$\infty$ or at least that's how I understand the dilemma of why physics breaks down in the singularity.

This is a terrible way to try to understand it. In Einstein's theory, the constant G is the constant G, end of discussion. It never changes. Other theories of gravity might have a G that varies, but not GR. What happens at the singularity is the curvature of spacetime is predicted to be infinite: this is where we get a problem.