Classical and Quantum "merging" question

[conway]

How often is division by zero found, when merging mathematical statements of classical and quantum representations? I know of at least one, that is black holes.

[ydoaPs]

I know of at least one, that is black holes.

Do tell.

[conway]

Well sir I can reference a documentary entitled "who's afraid of a big black hole". In which physicist Michio Kaku explains then when "merging" the mathematics of quantum black holes and classical black holes, that equations such as A/O arise.

[ydoaPs]

In which physicist Michio Kaku explains then when "merging" the mathematics of quantum black holes and classical black holes, that equations such as A/O arise.

Even if your recollection is correct, Kaku on TV is anything but a reliable source. He is notorious for spouting nonsense that he knows is false simply to make some $$$ from a TV spot.

[Mordred]

Lol his cosmology textbook isn't much clearer.

[conway]

Fair enough, do you suggest then that this is not the case. Further that this case never occurs. Or that if so , it is "dealt" with by other means of mathematics?

[Mordred]

http://www.amazon.com/Einsteins-Cosmos-Transformed-Understanding-Discoveries/dp/0393327000/ref=sr_1_2?s=books&ie=UTF8&qid=1435631627&sr=1-2&refinements=p_lbr_one_browse-bin%3AMichio+Kaku

[ydoaPs]

How often is division by zero found, when merging mathematical statements of classical and quantum representations? I know of at least one, that is black holes.

By the way, it's not even clear whether quantum gravity must have any issues with black holes. Loop QG, for instance, removes the singularity by showing that the BH collapse is a bounce and that the inner volume never even reaches the planck scale; it happens exceedingly quickly, but looks like it is static due to gravitational time dilation.

[conway]

So assuming the right information than there is no / by zero? Is there any other cases though?

[ajb]

Infinities, independent of if they arise from division by zero, are usually taken as a signal that you are trying to apply a theory to a situation that it does not hold; that is outside of the expected domain of validity. So with black holes, near the classical singularity we expect that quantum gravity effects cannot be ignored and so general relativity is not expected to be a 'good theory'. Other examples of this kind can be found in classical electrodynamics.

[conway]

I think I understand what you are suggesting here. But then if relativity is "not a good theory" at the quantum scale, then why? Say if then it was not, that time and space were so small that they can not be defined, but rather that a "perspective" change has occurred and any further defining, requires a measure from the new point of reference. I don't know.... say relative mathematics perhaps. What examples are there for electrodynamics?

[ajb]

But then if relativity is "not a good theory" at the quantum scale, then why?

We know why general relativity fails to submit to the same methods of quantisation as say electromagnetic theory. The problem is Newton's constant, it has the 'wrong' dimensions to allow a proper description in terms of Feynman diagrams. However, you can deal with quantum general relativity as an effective theory and discuss gravitons to one-loop.

 

Say if then it was not, that time and space were so small that they can not be defined, but rather that a "perspective" change has occurred and any further defining, requires a measure from the new point of reference. I don't know.... say relative mathematics perhaps.

It is quite possible that classical space-time as described by general relativity is an emergent or derived phenomena. However, without a full theory of quantum gravity it is hard to say much more.

 

What examples are there for electrodynamics?

The electron self-energy. Typically calculations using Feynman diagrams diverge, you need to regulate them and then renormalise. These methods do not work for general relativity.

[conway]

thanks ajb lots here to learn about.

[Sensei]

I think I understand what you are suggesting here. But then if relativity is "not a good theory" at the quantum scale, then why?

 

At quantum level there is used special relativity, instead of general relativity, with success.

For instance in particle collisions in particle detectors at CERN,

or unstable particle/isotope decay.

 

Here you have example with [math]\pi^+[/math], [math]\pi^0[/math] and anti-protons:

http://galileo.phys.virginia.edu/classes/252/particle_creation.html

Edited July 3, 2015 by Sensei