Quantum Mechanics & General Relativity: Explaining the Singularity

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Discussion Overview

The discussion revolves around the incompatibility of Quantum Mechanics (QM) and General Relativity (GR), particularly in the context of singularities, such as those found in black holes. Participants explore where the equations of these theories fail when applied together, highlighting the challenges of reconciling the two frameworks.

Discussion Character

  • Debate/contested
  • Exploratory
  • Technical explanation

Main Points Raised

  • Some participants note that QM and GR do not work well together at singularities, where both theories should apply but lead to nonsensical results, such as total probabilities not equaling 1.
  • One participant mentions that GR equations fail at the singularity of a black hole, resulting in infinite density, which is considered physically unlikely.
  • Another participant introduces the concept of Quantum Gravity, suggesting it is valid up to a certain cutoff, similar to how Quantum Electrodynamics (QED) breaks down at the electroweak scale.
  • There is a discussion about the limitations of current theories and the desire among physicists to understand the physics beyond the cutoff where interesting gravitational phenomena occur.

Areas of Agreement / Disagreement

Participants express various viewpoints on the nature of the failure of equations in QM and GR, indicating that multiple competing views remain regarding the specifics of these failures and the implications for understanding singularities.

Contextual Notes

Participants acknowledge the complexity of the issues involved, including the dependence on definitions and the unresolved nature of mathematical steps related to the theories discussed.

nateHI
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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.
 
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"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.
 
nateHI said:
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.
 
nateHI said:
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
 
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
 

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