Is the Mass of Super-Massive Black Holes Factored into Dark Matter Calculations?

[Drakkith]

no actually i m not talking bout accretion disk but the matters which are present near event horizon in a SMBH they will also radiate due to compression and thus they might also get radiated....

I believe that matter is also considered part of the accretion disc. Until it falls inside the event horizon I think it's still part of the disc.

 

[Passionflower]

The incompatibility of GR with QM is one of the outstanding problems of our time. Two theories, both in their own rights, the most successfully-tested theories ever devised, are not compatible. To try to combine them, particularly when it comes to gravity at small scales, produces nonsensical results (infinities).

Producing infinities is nothing unusual in quantum theory, and mathematical methods have been devised to get rid of them.

So I think that does not exclude the possibility that we have not devised a mathematical method to get rid of those infinities if we try to combine GR and QM.

 

[twofish-quant]

The more intense the gravity, the more time slows down as compared to an outside observer. From our perspective, outside the black hole, the time needed for a star to collaps to a singularity would be infinite.

Time doesn't slow down. One way of thinking about what happens is that the pulses that you send out are Doppler shifted so that people at a far distance see the pulses arriving at further and further intervals.

What you would observe as you fell into a black hole I don't know.

Assuming it's large enough so that tidal forces don't matter, you wouldn't notice anything unusual.

 

[twofish-quant]

Producing infinities is nothing unusual in quantum theory, and mathematical methods have been devised to get rid of them.

And those methods totally fall apart when you do gravity.

The problem is that the way that you deal with infinities in QM is to basically expand things out into a power series. At each stage, as you add more terms, you rescale (i.e. renormalize) so that when you do the infinite series you end up with finite values.

(Actually, you sort of cheat, and figure out that all you need are the first few terms, and you sweep the rest under the rug.)

This doesn't work with gravity. The problem is that gravity produces gravity. If you work with EM and imagine two electrons exchanging a photon, there is a tiny correction as that photon generates more photons, but it's small enough so that you can sweep under the rug.

With gravity, this doesn't work, because gravity generates gravity which generates more gravity which generates more gravity, and soon you have infinities popping up all over the place.

This is a terribly oversimplified version of what happens, and corrections are appreciated if I got something wrong.

So I think that does not exclude the possibility that we have not devised a mathematical method to get rid of those infinities if we try to combine GR and QM.

Most people think that no such method exists, and the reason we have all sorts of infinities while the world works is that some point in the real world you can chop off the power series because the rules change.

 

[Passionflower]

Assuming it's large enough so that tidal forces don't matter, you wouldn't notice anything unusual.

Would we see the light of the stars behind the black hole? And if so what would the redshift show the closer we get to the singularity?

 

[Drakkith]

What do you mean by "gravity generates gravity"?

 

[twofish-quant]

What do you mean by "gravity generates gravity"?

This is quantum field theory massively simplified.

You have two electrons. You ask what happens if those two electrons exchange one photon. Then you ask what happens if the electrons exchange two photons. Then three. You end up with a nice series of Feynman diagrams which you add up.

This works because photons are not electrically charged so that photons don't generate more photons (easily, yes I know about loop corrections, I'm vastly oversimplifying here).

Now let's try the same thing with gravity. Suppose we have two electrons, we calculate what happens when it exchanges one "graviton" with each other. The problem is that "gravitons" have energy, which means that they have mass, which means that they generate gravity. Gravitons having energy and therefore mass will attract each other, which means that they you have to take into account "gravitons" exchanging "gravitons" with each other. And those particles have energy therefore mass and...

So rather than having one infinity that you can deal with, you have infinities all over the place. The more corrections you put in, the worse your situation is. That means that the mathematical approach you use for QED, just won't work with gravity.

The other thing is that people that are much smarter than I am are of the opinion that this problem is not just because the mathematical approach is wrong, but that there is something basically fundamental about GR that makes all of these infinities pop out.

 

[twofish-quant]

Would we see the light of the stars behind the black hole?

I have to think about that, but once you cross the event horizon, most of the stars would look normal. You can't see into a black hole, but you can see out of it.

And if so what would the redshift show the closer we get to the singularity?

Off the top of my head, you wouldn't see a redshift for the things going into the black hole.

I have to warn you that my general relativity is very basic. I'm not a black hole expert, and my knowledge comes from thinking about what happens when a supernova turns into a black hole, so I haven't thought much about what things look like inside a black hole.

 

[Passionflower]

So rather than having one infinity that you can deal with, you have infinities all over the place. The more corrections you put in, the worse your situation is. That means that the mathematical approach you use for QED, just won't work with gravity.

Yes the mathematical approach you use for QED does not work with gravity. But how does that imply that it is impossible for someone to devise a method that does work?

 

[DaveC426913]

Yes the mathematical approach you use for QED does not work with gravity. But how does that imply that it is impossible for someone to devise a method that does work?

The claim is not that is it "impossible" for someone to devise a method, the issue is that no one has.

i.e. with our current understanding of QM (which has been tested extensively and passed with flying colours) and our current understanding of GR (which has been tested extensively and passed with flying colours), we cannot reconcile the two.

As he said, they do not play well together.

 

[twofish-quant]

The claim is not that is it "impossible" for someone to devise a method, the issue is that no one has.

Most mathematical physicists that I know are of the opinion that it is in fact mathematically impossible to reconcile classical GR and quantum mechanics, and that the problems that people have using standard QM techniques on GR are not a "lack of trying" problem but rather a "this is mathematically impossible" problem.

I don't understand the math myself well enough to explain why they think this, but if someone else doesn't chime in, I'll dig into the papers and try to come up with a "why GR is non-renormalizable cartoon" post.

with our current understanding of QM (which has been tested extensively and passed with flying colours) and our current understanding of GR (which has been tested extensively and passed with flying colours), we cannot reconcile the two.

The problem is that if you combine the two, you get infinite series that diverge. The good/bad news is that they diverge at energies which we cannot observe, which means that you can try to deal with the problem by chopping the infinite series once the energies get too high.

This gives you string theory or loop quantum gravity.

So the consensus seems to be that the real theory looks like QM and looks like GR, but it isn't QM or GR.

 

[twofish-quant]

Yes the mathematical approach you use for QED does not work with gravity. But how does that imply that it is impossible for someone to devise a method that does work?

It doesn't. But there seems to be a strong consensus among mathematical physicists that GR is non-renormalizable, which is to say that there are so many infinities that pop out, that no mathematical method can get rid of the infinities. The solution is to come up with a theory that looks like GR but isn't (i.e. string theory).

Now, since I don't specialize in quantum gravity, I can't explain why the quantum gravity people think it can't be done. Hopefully someone that does understand the field better than I do can chime in, and if not, I'll go through the papers and try to come up with a cartoon explanation.

 

[twofish-quant]

Actually the wikipedia article explains the problem...

http://en.wikipedia.org/wiki/Quantum_gravity

To summarize in a cartoon way. You can get rid of an infinity by dividing it by an infinity and setting infinity/infinity to a finite number that we can observe. With QED, there are three infinities so that we can do that.

For gravity, it turns out that there are an infinite number of infinities. So if you try that trick it turns out that you have to set an infinite number of numbers to finite values, which we can't do since that requires an infinite number of observations. All of the work in quantum gravity has been to try to turn that infinite set of fudge factors to a finite set.

 

[DaveC426913]

Most mathematical physicists that I know are of the opinion that it is in fact mathematically impossible to reconcile classical GR and quantum mechanics, and that the problems that people have using standard QM techniques on GR are not a "lack of trying" problem but rather a "this is mathematically impossible" problem.

I didn't mean to suggest that it was a problem just waiting to be solved.

I think the implication is that our understanding of GR or QM or both is broken, and they won't be reconciled until we understand them better.

 

[twofish-quant]

One thing that I've found out is that things are easy if you don't know why they are hard.

The reason that passionfruit's questions are interesting to me is that I was asking the exact same question in 1989 when I was a junior physics major. I knew enough QM and GR so that it *seemed* really simple to mix the two, and so I spent the next two years learning enough basic quantum field theory and GR to try to mix the two.

I remember when as a first year graduate student, I finally understood enough to realize why the problem was so hard, and why the easy solution wouldn't work. It was an "anti-eureka" moment, and the first of many.

One huge disadvantage that I had was that I lived in the "dinosaur era" before the World Wide Web existed. That means no google, no paper databases, no discussion forums, no wikipedia. We had USENET and e-mail. The good news is that with all of these tools, it should be a lot quicker to get people to the "anti-eureka" moment.

Something that I find funny is the Eureka myth. People always talk about that brilliant flash of insight which let's you realize how things work. The funny thing is that people don't talk about the reverse situation. Sometimes you get hit by lightning and the brilliant flash of insight is that what you've been working on the last few years just won't work.

 

[vinayjain]

When it is said that gravity cause gravity is it like magnetic field produces magnetic field ?

Please clarify

 

[Drakkith]

When it is said that gravity cause gravity is it like magnetic field produces magnetic field ?

Please clarify

See post # 37 by Twofish.

 

[phinds]

Something that I find funny is the Eureka myth. People always talk about that brilliant flash of insight which let's you realize how things work. The funny thing is that people don't talk about the reverse situation. Sometimes you get hit by lightning and the brilliant flash of insight is that what you've been working on the last few years just won't work.

Perhaps it's just semantics, but to me that's STILL a Eureka moment. Granted, you haven't discovered how something DOES work, but you have discovered how something doesn't work and that's a step of knowledge. I guess my point is that when you discover a new piece of knowledge, that's a Eureka moment, even if the knowledge is the certainty that something WON'T work.