# Why are Quantum mechanics and General relativity incompatible?

1. Apr 3, 2012

### MagnusM

Why are Quantum mechanics and General relativity incompatible?
Probably some complicated mathematics going on? Right?

2. Apr 3, 2012

### mathman

Your guess is correct. When both need to be applied at the same time (for example inside a black hole), mathematical nonsense results.

3. Apr 3, 2012

### K^2

Actually, it's not that complicated. The most obvious incompatibility is principle of superposition. Basically, Quantum Mechanics requires that equations that describe the system are linear. QM completely breaks down without this assumption. On the other hand, the field equations from General Relativity are non-linear.

Linearized gravity, which is basically Newtonian Gravity with added gravitomagnetic effects, can be quantized with some success. It's not terribly practical, but it makes some predictions about gravitational waves and gravitons.

Alternatively, you can do some limited quantum mechanics in GR setting, so long as effects of QM don't alter gravity too much. Hawking Radiation relies on this, for example.

So there are ways to make them work together in some limited situations, but overall, the equations are incompatible, and so a better theory is needed. My bet would be on QM being wrong and working only as a small-scale approximation, with true field theory being non-linear, same as that of gravity. But that's just a stab in the dark, really. Of course, we'll keep using QM in all likelihood regardless, due to it's great utility, same as we keep using Newtonian Mechanics despite its limitations.

4. Apr 3, 2012

### castro94

to put it rather simple , general realtivity aplies and correctly predicts the action of "big objects " while quantum mechanics tries to explain the unpredictable behaivor of small paricle , particles that everything is made of.
you can`t have a set of rules for big objects and another for the small particles that they are made of .
to me the most important factor why they cant go togehter , is called the uncertanity principle , it states that small particles cant be acuratly meaured without interfering on the particles behaivor and thus altering the result of the measurment. small particles simple seem to be to random to unpredictable , in fact they cannot even be meausered without being altered , and you can surely figure that this is not the case for any " big object "
big objects made of small particles seems to behave different from the particles that they are made of , that is way the genral relativity and QM fails to "explain" things , when put together

5. Apr 3, 2012

### K^2

castro, quantum mechanics adequately explains all of the behaviors of "large objects" with gravity being the only exception.

6. Apr 3, 2012

### castro94

and gravity beeing a result of an objects effect on space time due to its mass , so if you cant predict the effects of spacetime on an object and viceversa , can you truly say that you have explained the objects behavior ?
i know that the problem is that quantum mechanics fails to quantized gravity , or explain for the particale that would act as "transport" .
and the point that i wanted to highlight was the fact that small particle acts " ramdomly " and unpredicteable. i know that the obsevation paradox is a tricky problem , to say the least ,and i cant se how i would eventually get a slotion , becuase you cant meauser without measuring ..... and i think that the same aplies for big objects as well , but its precissly their mass ,and their effects on spacetime that make them differ from particles, a person cant be at two place at the same time , simply because he weights to much ..
or maybe i got all this wrong ???

7. Apr 4, 2012

8. Apr 4, 2012

### Khashishi

In GR, the metric of spacetime depends on the stress-energy distribution. In QM, you never know the energy distribution exactly.

9. Apr 4, 2012

### K^2

That's exactly the sort of thing that Quantum Field Theory is designed to deal with. And for other fields it does.

10. Apr 4, 2012

### MagnusM

Thank you for the replies. Getting some (although little compared to everyone else) understanding now. Still, I have one question remaining.

Mathematical nonsense as in bizarre answers and something very different from reality?
Like gravity being predicted to be too weak or something like that?

11. Apr 4, 2012

### K^2

The assumptions are incompatible. And by assuming a contradiction, you can derive absolutely anything. So in principle, any result you'd like, you can get. Want it to be too high, it can be made too high. Want it to be too low, it can be made too low. Mathematics is completely broken at this point.

12. Apr 5, 2012

### Andy Resnick

K^2 is giving you some good information.

QM and GR are also incompatible on a conceptual level- QM, even QFT, uses spacetime as a background upon which fields are described- for example, fields are written as U(x,t). However, in GR, spacetime is itself a dynamical field.