# I Why don't general relativity and quantum physics agree?

1. Oct 29, 2016

### victorhugo

I always hear that the two 'don't match' and disagree, but never in what...
Someone mind explaining?

2. Oct 29, 2016

### Simon Bridge

Caution: this is a bit hand-wavey, just to give a novice the gist.

Observe: in general relativity (basically the theory of gravity), time is another dimension of space: space-time is the stuff of the Universe that does things; while, in quantum mechanics, time is a special thingie that everything happens with respect to - in fact, space and time are a kind of environment for things to happen in. That would be a core disagreement right there. Do you need others?

There are a lot of articles and discussions online about this - have a look.
https://www.physicsforums.com/threa...eory-of-relativity-and-quantum-theory.588070/

3. Oct 29, 2016

### Staff: Mentor

Are you talking about special relativity or general relativity.

4. Oct 29, 2016

### Mister T

Usually that's pointed out in regard to gravity. Einstein's general theory of relativity is the most successful theory of gravity that we have, but it ignores quantum theory. Quantum field theory is the most successful theory we have of the other known interactions, but no one has been able to include gravity in that scheme.

In chemistry, for example, you're trying to figure out how atoms interact with each other. The dominant interaction is electromagnetic. Gravity is so weak there you can ignore it. But quantum theory is needed to understand most of it.

In astronomy, for example, you're trying to figure out how planets interact with the sun. The dominant force is gravity, and in some cases the gravitational interaction is so strong you need Einstein's theory of gravity.

But if you're trying to understand how black holes interact, gravity is so strong you need Einstein's theory of gravity, and at short enough distances quantum theory is needed. Thus we lack a complete understanding.

So each of the two theories have their limits of validity, but keep in mind that all theories have limits of validity.

Last edited: Oct 29, 2016
5. Oct 29, 2016

### dextercioby

Adding to the previous post, the only theory which doesn't have a limit of validity would be an utopic ToE, that is a "theory of everything". But even that would have the ultimate test to pass, i.e. to answer the two questions: 1. To make predictions (output), which are the input parameters? 2. If it's really a theory of everything, how could it explain/mathematically derive the values of the input parameters?

Bottom line: (human) knowledge is theoretically infinite and will never develop a "theory of everything". But until then, yes, it can try to (and it has already been doing that for the past 40 years) unify gravity with quantum theory.

6. Oct 29, 2016

### victorhugo

Interesting, thanks for your responses.

Something just popped into my mind: what is the formula for the de Broglie wavelength taking into account special relativity mass/time/length dilations?

eg m= m0 / [sqrt: 1- ( v^2/c^2) ]

since lambda= h/ mv

we can plug in the two formulas, couldn't we?

7. Oct 30, 2016

### Simon Bridge

Plug which formula into what... to what end?

The mass equation is no longer used - it's misleading. It is SR anyway, the formulas you want are for GR.
The deBroglie wavelength is a stepping-stone concept - don't read too much into it. It is not important for the unification of GR and QM.

8. Oct 30, 2016

### Staff: Mentor

You didn't exactly answer my question asking for clarification, but if you are indeed asking about special relativity then there is NO conflict between special relativity and quantum mechanics. The conflict that there used to be was resolved about 90 years ago.

9. Oct 30, 2016

### Mister T

The modern convention is that there is no need to include mass in that scheme, although it can be done. It's a matter of preference, not necessity. For example, in the situation you describe all would agree that the de Broglie wavelength is given by $\lambda=\frac{h}{p}$ where $p$ is the momentum. And that for massive (as opposed to massless) particles $p=\gamma mv$ where $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. Thus we have $$\lambda=\frac{h}{\gamma mv}.$$
Using the modern convention we would call $m$ the mass rather than call $\gamma m$ the mass.

Last edited: Oct 30, 2016
10. Nov 1, 2016

### victorhugo

Yes sorry, I forgot to address your question. I just meant whatever relativity people mean when they say it conflicts with quantum mechanics. It appears that it is General Relativity then!

11. Nov 1, 2016

### Staff: Mentor

Ok, I have edited your title and deleted some irrelevant posts.

12. Nov 1, 2016

### doggonemess

In astronomy, for example, you're trying to figure out how planets interact with the sun. The dominant force is gravity, and in some cases the gravitational interaction is so strong you need Einstein's theory of gravity.

But if you're trying to understand how black holes interact, gravity is so strong you need Einstein's theory of gravity, and at short enough distances quantum theory is needed. Thus we lack a complete understanding.

Gravity seems to be the key thing messing up the neatness of the mathematics. Stupid gravity - always dragging us down and holding back progress.

13. Nov 1, 2016

### ProfChuck

The following is a bit of an over simplification and is bound to draw some legitimate criticism but I think it will help to visualize the nature of the apparent conflict. General relativity views gravitation as a geometric phenomenon expressed as the curvature of space-time induced by the presence of energy or mass. Quantum gravity (as usually described by several incomplete theories) views gravitation as the effect produced by the exchange of particles, either real or virtual, in much the same way that magnetic and electric fields produce force that can be described by the exchange of photons or similar particles. This is essentially the difference between classical and quantum physics. These are two different ways to produce a conjecture about the underlying mechanisms of observable phenomena. The problem is that when applied to extreme conditions, such as the event horizon of a black hole there are differences that must be resolved. In the case of a black hole the classical model assumes that the preponderance of the mass of the structure lies within the event horizon. This poses no problem for classical relativity as the presence of mass behind an event horizon still produces space-time curvature. Quantum gravity, however, assumes that the observable mass of a black hole is dependent on the exchange of particles. It is not clear how this can occur without jeopardizing causality because these particles must cross the event horizon in such a way as to produce the same results as the classical model which can be verified buy observation. The odd part is that experimental evidence confirms the validity of both models of reality to an exceptional degree of accuracy. The Newtonian/Einsteinian mechanics model of the equivalence of inertial and gravitational mass has been measured to better than 14 significant figures. And the quantum mechanics predictions of the moment of the electron has been measured to even greater accuracy. These kinds of agreements between theory predictions and actual measurements force one to conclude that the models have a very useful relationship to the underlying reality. It also suggests that neither model is complete.

14. Nov 1, 2016

### Staff: Mentor

It's even more extreme than that. The classical (GR) model says (not "assumes"--it's derived from the Einstein Field Equation) that the black hole is vacuum inside. The mass that originally collapsed to form the hole reaches the singularity and disappears. But this conclusion does not play well with QM, because it violates unitarity.

This is not a problem for two reasons:

(1) Virtual particle exchange is not limited by the mass shell condition (heuristically, virtual particles have a nonzero amplitude to travel faster than light).

(2) The gravity you feel when you're outside a black hole doesn't come from inside the hole; it comes from the matter that originally collapsed to form the hole, while it was still outside the horizon. In other words, it comes from the stress-energy in your past light cone.

See here for more discussion:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html

15. Nov 1, 2016

### ProfChuck

I raised this question back in the early 80's at CalTech. (Google "The Ivie conundrum" For some reason it doesn't show up on Yahoo). It has been quoted and misquoted several times since then. I posed it as part of a testing criteria for the evaluation of quantum gravity theories. There are testable predictions from general relativity that describe the behavior of black holes so where the domains of classical and quantum physics overlap the two models should produce identical or at least similar results.

16. Nov 1, 2016

### Staff: Mentor

I agree. I'm simply pointing out that "virtual particles can't get out of a black hole" is not, IMO, a valid reason to doubt that this can be done.

17. Nov 1, 2016