Equations that arise when General Relativity and Quantum Mechanics are merged.

[goodfellow]

I am a first year undergraduate who in my spare time is desperately trying to understand what happens when General Relativity and Quantum Mechanics are 'merged'.

Almost all of the searches I have done on the subject have turned up with
the same similar statements:

'General Relativity and Quantum Mechanics don't work together'
'The solutions to simple questions give nonsensical answers with infinities'

etc. etc. Just very simple statements aimed at the general public.

Yet for the rest of the searches, I run into relativity complicated journals
aimed at postgraduates such as this:

(http://iopscience.iop.org/0264-9381/19/13/312/pdf/0264-9381_19_13_312.pdf
free version: http://wenku.baidu.com/view/e0c576d86f1aff00bed51edf.html)

Which don't really help me at all.

I can't seem to find any journals or textbooks that give an example of these two theories being combined, and that shows the equations that lead to the infinity answers; a middle ground so to speak, between the general public and postgradutes.

Here is an example of what I'm trying to find:


Michio Kaku goes through the equations from 3:30 to 7:30 in that short
clip, unfortunately all the 'good stuff' is just left out.

Does anyone know where I could look to find a detailed run through of the
equations he is going through in those clips?

Any help would be much appreciated.

 

[DrewD]

I think the answer is going to be no, there aren't any good ways to learn general relativity and quantum mechanics easily. That being said, MIT OCW has a class on GR and black holes that was taught to MIT undergrads. I haven't seen all of it, but they go through Einstein's field equations slowly.

You say you're a first year undergrad? If I were you (and I was... well, not you, but in a similar situation) I would focus on learning as much math as possible and understanding (really understanding) the physics you are learning now.

Have you had vector calculus and linear algebra courses? Have you studied differential equations? Do you understand special relativity? Don't stop trying to learn what you are trying to learn, but if you don't build up the foundation, you will someday be able to say that you memorized einstein's equations, but you still won't understand it.

 

[goodfellow]

I think the answer is going to be no, there aren't any good ways to learn general relativity and quantum mechanics easily. That being said, MIT OCW has a class on GR and black holes that was taught to MIT undergrads. I haven't seen all of it, but they go through Einstein's field equations slowly.

You say you're a first year undergrad? If I were you (and I was... well, not you, but in a similar situation) I would focus on learning as much math as possible and understanding (really understanding) the physics you are learning now.

Have you had vector calculus and linear algebra courses? Have you studied differential equations? Do you understand special relativity? Don't stop trying to learn what you are trying to learn, but if you don't build up the foundation, you will someday be able to say that you memorized einstein's equations, but you still won't understand it.

Of course I will still carry on with the physics I am learning now, I just finished doing 5 hours of vector questions, I am just researching this in my spare time.

I understand special relativity (or the basics of it at least), differential equations, vector calculus and I have a tenatative grasp of the main ideas behind quantum mechanics.

General Relativity and Einstein's field equations is what I haven't gone over yet.

My question wasn't 'how can I learn quantum mechanics and general relativity easily', all I want to do is have a basic idea of what Michio Kaku is doing in that clip, and if there is any literature that covers it it.

I understand that it is encompassing all of General Relativity and Quantum Mechanics in some sense, but I doubt I need thoroughly understand all the ins and outs of both topics to follow what Michio is doing there.

 

[DrewD]

In that case, the best thing I know is the MIT OCW video and Stanford has a relativity series too. Michio Kaku is talking about the Einstein field equations first, and then the schwarzschild solution. I did a quick search to see if I could find anything online that might be helpful, but I can't find anything that doesn't require a lot of differential geometry.

When he talks about a singularity, you don't have to use general relativity at first to see what he's saying. The same thing would happen with Newtonian gravity if you assumed that mass can be compacted into a point. Gravity would become infinite at r=0 as well. The schwarzschild solution just shows that mass that has volume will collapse into a singularity if it reaches a certain density. Deriving the schwarzschild solution is the topic of a wikipedia article.
http://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution

 

[goodfellow]

In that case, the best thing I know is the MIT OCW video and Stanford has a relativity series too. Michio Kaku is talking about the Einstein field equations first, and then the schwarzschild solution. I did a quick search to see if I could find anything online that might be helpful, but I can't find anything that doesn't require a lot of differential geometry.

When he talks about a singularity, you don't have to use general relativity at first to see what he's saying. The same thing would happen with Newtonian gravity if you assumed that mass can be compacted into a point. Gravity would become infinite at r=0 as well. The schwarzschild solution just shows that mass that has volume will collapse into a singularity if it reaches a certain density. Deriving the schwarzschild solution is the topic of a wikipedia article.
http://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution

Thanks a lot for you rtime, I'll check these out.

 

[goodfellow]

So I've been able to find a few good journals on the schwarzschild solution and black holes that I should be able to digest given enough time,

But what is Michio doing at 6:45 to 7:30 in that youtube clip?

He says he is inserting the Einstein Lagrangian into the 'probability that gravity will move from one point to another point'?

 

[IsometricPion]

He is using a Feynman path integral to try to obtain the probability for a particle to move from one given point to another given point under the influence of gravity (and quantum uncertainty). He then transforms the integral from position space into momentum space and obtains an integral that diverges. I think his comment about obtaining an infinite number of infinities refers to the fact that, unlike in some other theories where one can "tame" the infinities, this way of dealing with gravity is not renormalizable. Generally it is thought that some modification of gravity at high energies is necessary. For an idea of the magnitude of the corrections a quantum gravity theory would produce one can consider gravity as an effective field theory, this paper (on page 15) indicates that within the solar system the corrections would be extremely small (they would probably only be significant near gravitational singularities).

 

[goodfellow]

Thank you for the info.