Quantum Mechanics & General Relativity: Explaining the Singularity

[nateHI]

I keep hearing that QM and GR don't play well together. For example, a singularity, a result of GR, is small enough for QM to apply but...it doesn't. I was hoping someone could explain exactly where the "equations fail." Unfortunately I'm so ignorant in this subject matter that I can't be more specific than that. I just know to ask that question because I heard Michio Kaku state that the equations fail on some TV show.

 

[mathman]

"Where" is hard to answer. If the volume is small enough so that both theories have to be used, the results are nonsense. For example total probabilities aren't 1.

 

[phinds]

I keep hearing that QM and GR don't play well together. For example, a singularity, a result of GR, is small enough for QM to apply but...it doesn't. I was hoping someone could explain exactly where the "equations fail." Unfortunately I'm so ignorant in this subject matter that I can't be more specific than that. I just know to ask that question because I heard Michio Kaku state that the equations fail on some TV show.

I'll be damned ... Kaku actually said something that's true. A rare moment.

The GR equations fail when you get to the singularity at the center of a black hole, in that they give an infinity (infinite density, 'cause all the mass goes to a point), which is not considered physically likely. The hope is that QM will eventually give a more accurate picture of whatever it is that happens at the center of the BH and the even further hope is that somehow this will be reconciled with GR so that the two theories (which are each in their own realm, amazingly good theories) will play nicely together.

 

[bhobba]

I keep hearing that QM and GR don't play well together. For example, a singularity, a result of GR, is small enough for QM to apply but...it doesn't. I was hoping someone could explain exactly where the "equations fail." Unfortunately I'm so ignorant in this subject matter that I can't be more specific than that. I just know to ask that question because I heard Michio Kaku state that the equations fail on some TV show.

The issue is a bit more subtle than that:
http://arxiv.org/pdf/1209.3511v1.pdf

Basically Quantum Gravity is perfectly valid up to a certain cut-off about the plank scale. But then again so is QED - it breaks down in the so called electroweak region where the electroweak theory takes over. In fact the modern view of renormalisation - which is the trick used to get finite answers in theories like QED - is to take a cutoff very seriously and such theories are only valid to a certain cutoff. Quantum gravity is no different.

The real issue is the interesting physics for QED occurs well below that cutoff - the interesting physics for Gravity is above the cutoff and physicists really want to peek behind it.

Thanks
Bill

 

[nateHI]

Thanks all for the replies and the link to the article. I'll try to wrap my head around it when I'm not busy with my regular studies.

-Nate