The Uncertainty Principle and Quantum Singularities

[Enola Straight]

It is a cornerstone of Quantum mechanics that you cannot know both the momentum and position of a particle.

What if the "particle" is a quantum singularity?

Can the UP be applied to Black Holes or the Big Bang singularity?

[Kuroneko]

The problem with this question is that it is far from clear just what a 'quantum singularity' would be. For something like a black hole singularity, nothing ever observes it--worse, any incoming energy from an attempt to observe it will be infinitely blue-shifted, perturbing the area around the singularity to such a degree that any supposed information present there will be rendered into noise. It's hard to see how meaningful uncertainty in measurement would be when referring to something one never actually measures; ordinary loopholes to direct measurement like quantum entanglement do not seem to apply. The Big Bang singularity is quite literally everywhere, so it is even less clear as to what "uncertainty in position" means in that situation.

[Wyrm]

Whew! I knew that how the uncertainty principle squares away with a quantum singularity was one of those Really Hard questions in physics, but Kuroneko has explained why. Thank you!

Why haven't you been titled "Great Sage Equal to Heaven" yet?

[Azrael]

In 1991, stephen hawking lost a bet with his collegues "on a technicality" that naked singularities could not exist. A supercomputer simulation showed that they can.

Wouldn't this be a paradox? Singularities have event horizons because of their strong gravitation, so how can singularities be naked and posses this strong gravitational field? If we were to observe this 'naked singularity' would it not be subject to the Uncertainty Principal, or would some other mechanism come in to play to prevent us from looking at it?

[Dooey Jo]

Wouldn't this be a paradox? Singularities have event horizons because of their strong gravitation, so how can singularities be naked and posses this strong gravitational field?

Under very special circumstances, singularities without event horizons can arise. For example in certain charged black holes that have such properties that they'll probably never be formed in nature. The computer simulations also relied on very special circumstances to produce naked singularities. But simple Schwarzschild black holes will always have an event horizon.

If we were to observe this 'naked singularity' would it not be subject to the Uncertainty Principal, or would some other mechanism come in to play to prevent us from looking at it?

It is hoped that a more complete understanding of quantum gravity will bring insight into those questions, and hopefully show that naked singularities cannot exist in reality.

[Azrael]

Under very special circumstances, singularities without event horizons can arise. For example in certain charged black holes that have such properties that they'll probably never be formed in nature. The computer simulations also relied on very special circumstances to produce naked singularities. But simple Schwarzschild black holes will always have an event horizon.

Ahh, I knew it had to be some kind of special circumstance. It would appear that electromagnetic repusion for a charged mass is much greater than gravitation, so no duracell Black Holes in nature.

I guess we'll never know all there is to know about black holes until we get one to study for ourselfs, and that means either making one (HA!) or going to one that has formed in nature - both requiring technology centeries, if not millenia, ahead of what we have now.

[Kuroneko]

Naked singularities are a product of some special conditions under GTR; in loop quantum gravity, they do not seem to exist, nor other types such as black hole singularities. That's why I said it's not clear what a 'quantum singularity' would actually be--there is no proper theory that has such things in the first place. Just as the uncertainty principle prevents atoms from electromagnetic collapse, it might in prevent gravitational collapse as well. But lacking an established theory that handles such cases, it's just speculation.

[drachefly]

It is a cornerstone of Quantum mechanics that you cannot know both the momentum and position of a particle.

No, not exactly. The cornerstone is that the position and momentum operators do not commute; and as a consequence, particles do not simultaneously have momentum and position constrained with the product of their ranges less than Planck's constant.

In other words, you can measure the position of a particle and the momentum of a particle, but when you do, your error bars can't both approach zero: their product cannot be less than Planck's constant.

What if the "particle" is a quantum singularity? Can the UP be applied to Black Holes or the Big Bang singularity?

Yes, on all counts.

[Kuroneko]

Yes, on all counts.

More "probably, if they have quantum counterparts" than "yes". There is no satisfactory quantum description of black hole singularities in the first place, and some minor evidence that their singular nature is a result of classical physics only.

[drachefly]

That reads suspiciously like, "Yes, if they actually exist."

[Kuroneko]

That reads suspiciously like, "Yes, if they actually exist."

It does, except it's slightly weaker.