[chris (OP)]

In Caroline Steel's article about the theoretical existence of a multiverse, she reminds us that Einstein's general relativity and quantum mechanics disagree about gravity. But she doesn't say how.

What is the fundamental disagreement between the two?

[puppypower]

GR defines gravity in terms of space-time, while quantum theory defines gravity in terms of particles and waves. Both are half of the gravity equation, since gravity impacts space-time, but gravity also generates pressure which impacts particle phases.

If you look at the sun, it defines a space-time well with the core of the sun, being the most contracted position in the space-time well. Relative to pressure, the core has the closest particle distances, due to pressure, and therefore parallel the distance in space-time. However, the frequencies of particle phases are the fastest; gamma, in the core, and not the slowest like in the space-time well. Time due to pressure is not paralleling the time in space-time.This implies there is an aspect of time, connected to pressure, that is different from the time in space-time, that goes in the opposite direction of the time within space-time.

This is expected, since gravity is an acceleration which has the units of d/t/t. Space-time is only d-t, therefore acceleration has extra units of time compared to space-time, which is reflected in the pressure; particle phases frequencies. This is dimensionally consistent. Classical gravity was well aware of the extra time connected to pressure through experiments. Einstein explained the d-t aspect of acceleration, as space-time.

Pressure is interesting because, pressure is force/area. All forces of nature can generate pressure and be impacted by pressure. Pressure is a unifying force, connected to time, that exists beyond GR and space-time. Only gravity can alter space-time per GR, but all the forces can participate in pressure via the extra dimension of time. This allows gravity to alter phases.

If you look at a quantum universe, only certain states or quanta are possible. There are gaps between quantum states. Electrons in the hydrogen atom have certain energy states, with gaps between. The extra time in acceleration, comes from the gaps.

One way to see this is with dice. In a continuous universe, where all states are possible, probability would be analogous to a dice with infinite sides. A quantum universe is more like a dice with finite sides, such as six sides. If side A needs to appear, before nuclear reaction Z can occur; universal evolution, the infinite sided dice will take infinite trows for side A to appear, while the six sided dice needs six throws; 1/6 versus 1/infinity. Quantum saves time, for Z to occur.

If we add this extra time, from the gaps, to a quantum universe, we can appear to defy the odds. In other words, if we throw a six sided dice one throw per second, and each side has a probability of 1/6, it will take on the average, six seconds  for each side to appear. If I throw three 6's in a row, this should take 18 seconds, but it only took 3 seconds. I saved time. When you need the improbable, you need use more of the time in the gap. Since there is conservation of time, then the same improbable situation will need to take even longer the next time. The odds will average out over time.

[evan_au]

Einstein's general relativity and quantum mechanics disagree about gravity. ... What is the fundamental disagreement between the two?

Quantum theory has to deal with infinities in a few places. It has a well-established process of "renormalization" that deals with the infinities, and still produces useful and accurate predictions.

However, renormalization does not work when applied to gravity, and you end up with infinities in many places, that yield no useful predictions.

So, for now, it is felt that general relativity provides good explanations in "low energy" environments like our solar system. But it remains suspect in the high-energy environment of the big bang, and in the vicinity of black hole singularities, where quantum effects may dominate.

For a fairly readable explanation, see: http://en.wikipedia.org/wiki/Quantum_gravity