What is the largest difference between Einsteins Therory of Relativity and Quantum Mechanics?

Question

What is the largest difference between Einsteins Therory of Relativity and Quantum Mechanics?

Answer 1

Einstein could never accept Quantum theory because Quantum theory demands the element of 'randomness' and Einstein believed there was an underlying 'order' to the universe that is denied by Quantum theory.

Answer 2

Einstein's Theory of Relativity is a model similar to Newton's Laws of Motion and the Law of Universal Gravitation, except that it is far more complex. However, Einstein's field equations show that given a particular configuration of a system in which forces other than gravity are neglected, there is a unique way in which it can evolve over time, which may be found by solving the equations (approximate solutions are usually needed, except in special cases, such as black holes.)

In Quantum Mechanics, the precursor to the modern Quantum Field Theory, on the other hand, there is always an uncertainty in the observables from Newton's and Einstein's theories. The statement of this uncertainty is the Heisenberg Uncertainty Principle - you cannot know both a particle's position and its momentum accurately at the same time, and the more accurately you know one, the less accurately you know the other. (This applies not only to particles but to every object in the Universe.) In fact, it is not even the case that the particle's position and momentum are hidden to us - the particle does not _have_ a position and momentum - only a "wave function" from which approximations to position and momentum can be computed.

Einstein's Theory of Relativity is an almost perfect model for gravitation. No observation has ever been made which contradicts the theory. However, it breaks down at the singularity of a black hole - it predicts that energy density is infinite at that point, and therefore cannot predict what occurs there. However, the parameter "h", fundamental to quantum mechanics and known as the Planck constant, does not appear in any of Einstein's equations of relativity. This shows that Einstein's equations do not take quantum effects into account. When quantum effects are taken into account, the density is probably not infinite at the singularity after all (but these effects operate only on very short length scales, such as the singularity, and interactions between subatomic particles.)

Quantum mechanics is an almost perfect model for the other three forces - electromagnetism, the weak interaction, and the strong interaction. The first two are described by Quantum Electrodynamics (QED), the third by Quantum Chromodynamics (QCD). The former, like relativity, has been excruciatingly verified and no contradictory evidence has ever been found. We do not fully understand how to use the latter, for certain mathematical reasons - the predictions that it does make, however, have been verified experimentally. However, all attempts so far to use quantum mechanics to describe gravitation have failed.

That is, the theories of General Relativity and Quantum Mechanics are incompatible, even though neither describes the Universe fully. Theoretical physicists eagerly seek a way to unite the two theories, to produce a Quantum Theory of Gravity. That is one of the major research goals today.