Why is the theory of relativity incompatible with quantum mechanics?

[sam1123]

I've always heard this well known phenomenon but I have never really understood in detail why it is so, can anyone help me out?

[EdEarl]

I think the word incompatible is misleading. QM describes very small scale things, and GR and SR describe very large scale things. They do not describe the same things differently. Thus, they are not incompatible.

[ACG52]

When the equations of relativity are merged with the equations of QM, the results are infinities. This is a sign that says, 'something's wrong'.

[xyzt]

I've always heard this well known phenomenon but I have never really understood in detail why it is so, can anyone help me out?

The statement is not correct, QM and SR are fully compatible and they have been unified in a theory known as QFT.

It is GR that hasn't been unified with QM, YET. Work is underway (see LQG, String Theory, etc).

[Royston]

I think the word incompatible is misleading. QM describes very small scale things, and GR and SR describe very large scale things. They do not describe the same things differently. Thus, they are not incompatible.

 

Except that you can make predictions in the macroscopic domain using QM (see Ehrenfest theorem) to a suitable classical limit. Besides, it's GR and QM that are incompatible. Quantum electrodynamics combines SR and QM.

 

EDIT: Cross posted with xyzt

Edited July 4, 2013 by Royston

[D H]

There's no problem between quantum mechanics and special relativity. That is what quantum electrodynamics (QED) is all about. Feynman was awarded the Nobel Prize in physics for his work on QED.

 

The problem is between quantum mechanics and general relativity. They aren't in conflict with one another. It truly is a matter of incompatibility. So far, that is.

[sam1123]

Ooh okay, so what aspects of QM and general relativity are incompatible? I'm not that experienced in advanced physics

[mathematic]

Ooh okay, so what aspects of QM and general relativity are incompatible? I'm not that experienced in advanced physics

There are places where they both must be used together - inside a black hole or the big bang. As others have noted, the predictions are physically nonsensical.

[ACG52]

GR deals with a smoothly curving space/time. On the quantum level, space/time is not smooth. When you try to combine the equations of GR and QM, you get infinities, which is a red flag that something is wrong.

[D H]

GR deals with a smoothly curving space/time. On the quantum level, space/time is not smooth.

Space and time are still smooth in QM. They take derivatives, compute integrals. That implicitly assumes a smooth manifold.

 

The problem is the stuff that fills space and time, not space and time themselves. Vacuums are no longer vacuums if you look at them very closely. Virtual particles pop in and out of existence. The closer one looks the frothier things get.

 

When you try to combine the equations of GR and QM, you get infinities, which is a red flag that something is wrong.

You get infinities in quantum mechanics, too. Things such as 1+2+4+8+... keep popping up. Physicists found that giving meaning to divergent series such as this had attracted the best minds in mathematics for over a century. That the answer to this apparently meaningless series is the even more meaningless -1/12 was a viewed as a bit of a problem.

 

Physicists don't just do math and develop theories. They experiment. Experimental results showed that this apparently nonsense answer to this apparently nonsense series was -1/12. That led to investigations into what is now called the renormalization group. This work let those mid 20th century physicists get past the infinities that plagued their work on quantum electrodynamics and quantum field theory.

 

One of the problems between GR and QM is that the renormalization tricks that worked so nicely in quantum field theory just don't work. The infinities won't budge.

 

An even bigger problem is that melding GR and QM represents two big huge steps taken at once. The first step is a Grand Unification Theory that somehow will show that the electroweak and strong interactions are different aspects of the same interaction. The next step is a Theory of Everything that somehow will show that this unified electromagnetic/weak/strong interaction and gravitation are different aspects of the same interaction. It took a lot of work to develop electroweak theory. Taking two big huge steps at once is perhaps overreaching.

 

An even bigger problem yet is experimental validation of a GUT or even worse, a TOE. The energy scales are absolutely phenomenal. Even if someone comes up with a mathematically sound theory, testing that this is what describes the universe is going to be a huge, huge challenge.

[IM Egdall]

Quantum mechanics (QM) and general relativity (GR) have fundamentally different views of reality:

 

For one thing, GR sees the world as deterministic. If you know an object's position and velocity (speed and direction), you can predict exactly where it was in the past and where it will be in the future (assuming nothing has disturbed it.)

 

But QM is probabilistic. The more accurately you know a particle's position, the less accurately you can know its velocity, and vice versa. This is the Uncertainty Principle. So you cannot not know exactly where the particle was in the past or where it will be in the future. The best you can do is calculate the probability of it being at a certain place at a certain time.