# Why general relativity and quantum mechanics are incompatible?

Holocene
I hardly know anything about quantum mechanics. Why does it clash with general relativity?

## Answers and Replies

Tweek
It has to do with that theory of quantum mechanics and that electrons don't follow classical mechanics. Electrons remain in an unknown orbital path around a nucleus which doesn't follow the laws of classical electromagnetism. They are unpridictable.

The problem with general relativity is that quantum mechanics is inconsistent with singularities. There is also a problem with determining the gravitation field of a particle.
The particles location and velocity can't known with certainty. See Heisenberg uncertainty principle.

Holocene
ah, got it.

And thus Einstein's quote, "God does not play dice".

Some have claimed this quote is indication that Einstein believed in a god.

off-diagonal
ah, got it.

And thus Einstein's quote, "God does not play dice".

Some have claimed this quote is indication that Einstein believed in a god.

yes, he believed in God but his God is a rules that dominate everything in the universe.

lbrits
Unfortunately none of these answers are correct, so I'll attempt to answer it.

You're welcome to do quantum mechanics in the presence of gravity. Meaning, with a curved space, look at quantum mechanical particles, their wavefunctions, or if you're bold, quantum fields on curved spaces. Hawking radiation and the Unruh effect are both examples of this and it is quite successful.

The problem is that you might want to view the metric in GR as another "field" that lives on spacetime, "telling matter how to move...", etc. But quantum mechanics, or rather its big daddy quantum field theory says that you should quantize this field*. It turns out that while most studied fields are renormalizable (their quantum corrections can be controlled), the metric field is non-renormalizable (their quantum corrections require infinitely many parameters to be put in by hand). Unless you are given those parameters from another source (say, string theory), then the quantization procedure is hopeless.

* You might ask why we need to quantize the metric, if all we get are problems and experiments don't seem to require it. First, as was mentioned, is we don't know what happens to quantum mechanics at singularities. Is unitarity lost? Maybe if we quantize the metric then these issues will resolve themselves. The second reason is as follows: Suppose we do a double-slit experiment so that we end up with a wavefunction for a particle with several peaks in space. Now, every particle, no matter how small, gravitates, and exerts an influence on other particles through gravity. If we have a wavefunction telling us that the particle is in a superposition of being in many places, then how should we interpret the gravitational field that the particle sets up? Should the metric be in a superposition too? For things to be consistent, the answer is yes! Unfortunately, so far only the string theorists (ok, some semi-classical gravity people) have a model in which this can be done, but there are many problems.

Holocene
yes, he believed in God but his God is a rules that dominate everything in the universe.

Misunderstandings arise when different people harbor different definitions of what god is.

As someone said, "If you want to call god energy, then you can find god in a lump of coal".

bill nye scienceguy!
why shouldn't you be able to find god in a lump of coal?

lbrits
why shouldn't you be able to find god in a lump of coal?

Because coal was put on the Earth by the devil to test our faith.

ehj
lol =P

Bose
We know photon exist for sure but we don't know if graviton exist
If that's the case, do we need to quantize GR anymore?

lbrits
We know photon exist for sure but we don't know if graviton exist
If that's the case, do we need to quantize GR anymore?

Yes. See the last paragraph in my post.

ThomasT
... Suppose we do a double-slit experiment so that we end up with a wavefunction for a particle with several peaks in space. Now, every particle, no matter how small, gravitates, and exerts an influence on other particles through gravity. If we have a wavefunction telling us that the particle is in a superposition of being in many places, then how should we interpret the gravitational field that the particle sets up? Should the metric be in a superposition too? For things to be consistent, the answer is yes! Unfortunately, so far only the string theorists (ok, some semi-classical gravity people) have a model in which this can be done, but there are many problems.
How should we interpret the particle superposition? Instead of saying the wave function is telling us that the particle is in many places at once, what's wrong with saying it refers to the possible results of some measurement preparation and it assigns certain values (probabilities) to those possibilities?

lbrits
How should we interpret the particle superposition? Instead of saying the wave function is telling us that the particle is in many places at once, what's wrong with saying it refers to the possible results of some measurement preparation and it assigns certain values (probabilities) to those possibilities?

Well, that's what I meant when I said "many places at once", which is sort of short-hand for a more precise statement.

But unless you assign probabilities to gravitational the metric as well, most of your configurations (probable or improbable) will look inconsistent. In other words, there will be configurations that you could prepare that don't make sense (why is the gravitational well here if the particle is over there?)

phyti
I hardly know anything about quantum mechanics. Why does it clash with general relativity?

One significant difference, GR is defined in terms of continuous concepts, QM is defined in terms of discrete concepts.

Staff Emeritus
Science Advisor
Gold Member
QM is defined in terms of discrete concepts.
The mathematics of quantum mechanics is quite firmly in the realm of continuous mathematics... In what sense could you mean this?

yoda66
what happens to time in quantum mechanics?

peter0302
Here's one thing I don't understand, and it goes to lbrits's point that the metric must be quantized for things to be consistent.

Was Einstein not a believer in Mach's Principle, that space and time don't really exist in a vacuum (no pun intended :rofl:) but, rather, are defined by the existence of matter itself?

Why, then, would we have any difficulty NOT quantizing the metric and just treating it as a mathematical construct - sortof like the wave function itself - something which does not necessarily have physical meaning, but, rather, which merely emerges when we try to represent past and future particle interactions?

To answer lbrits's question of how we'd think of the gravity caused by a particle in a superpositioned state, can we not simply look at the particle as a massive blob spread out across its wavefunction, whose mass density varies exactly with its probability density? Will we not get correct results if we do that?