# Is GR harder than QM?

1. May 20, 2012

### robertjford80

Which is more difficult to understand general relativity or Quantum Mechanics. Neil de Grasse Tyson basically straight-up contradicted himself in a docu on Einstein. In the beginning he said, GR is so complex that only a few people can understand it. At the end he said GR is simple, profound and encompasses a lot of territory like any good theory should.

2. May 20, 2012

### ghwellsjr

Maybe he was quoting Einstein from the last sentence of the original new york times article announcing Einstein's successful test of GR.

3. May 21, 2012

### chill_factor

GR is mathematically much more challenging than quantum, for the same level of understanding.

Let's just put it this way: Chemists and engineers know quantum, how many people besides hardcore astrophysicists know GR?

4. May 21, 2012

### Sonderval

I think you could argue like this - it depends on what you mean by "simple"

The fundamental equation of QM, the Schrödinger eq., is linear. This makes it not too difficult to solve for a vast number of problems, either exactly or numerically.
The fundamental equation of GR is non-linear, so the number of solvable problems (especially analytically solvable) is rather small.
This hinders understanding because to build up an intuition it is always helpful to look at a lot of examples. Thus, from a mathematical, solve-the-equations point of view, QM is vastly more simple than GR.

On the other hand, on a very general level, GR only uses spacetime curvature, but apart from that it is a classical theory, so there is no trouble with things like probability amplitudes, collapse of the wavefunction and all the other stuff in QM. So from a conceptual point of view, GR is simpler.

5. May 21, 2012

### robertjford80

How about this question. How much of GR do you need to understand in order to work your way through the basics of cosmology? When I say work your way through the basics of cosmology, what I mean is, I'm only interested in reading scholarly articles and understanding them, I'm not interested in becoming a cosmologist or a physicist. I just want to know what physicists are talking about. So how hard is it to understand the gist of GR rather than being able to understand it to the point where you can make a contribution to cosmology or particle physics?

6. May 21, 2012

### dm4b

I think GR is harder, mathemtically speaking, than QM, but easier than QFT.

Maybe Tyson meant GR is conceptually simpler than QM in his last statement? I think it probably is easier than QM to understand conceptually.

7. May 21, 2012

### Staff: Mentor

If you look at a standard undergraduate physics curriculum, you will conclude that QM is much easier than GR. Classical mechanics, special relativity, and E&M make a reasonable first year; classical waves and QM fill a second year, but GR is a graduate-level or fourth-year course.

However as others have already pointed out, that's at least as much a reflection of the computational difficulty as the intrinsic difficulty of the concepts. You can do an awful lot of QM with some vector calculus, linear algebra, complex analysis, and differential equations, stuff that every physicist-in-training will pick up by their second undergraduate year. Differential geometry and the brutally non-linear math of GR.... Not so much.

From an intrinsic difficulty point of view, GR may be easier than QM. It's elegant, complete, and based on one big idea that, once grasped, makes everything clear. QM, however... Read some of the various interpretations, consider what's behind the slightly tongue-in-cheek advice to "shut up and calculate", and you might reasonably wonder whether it is even possible to understand QM in the way that GR is understandable.

Of course there is a significant aesthetic component in one's attitudes towards the two theories: De gustibus non est disputandum.

Last edited: May 21, 2012
8. May 22, 2012

### Haelfix

Typically students find statistical mechanics the most challenging, followed by quantum mechanics, followed by GR.

Obviously it depends greatly on the professor involved, but that tends to be what we see. Some of it is probably selection bias:

General Relativity is of very limited applicability in physics, and so typically you see students who really want to learn it, whereas in stat mech and quantum one finds engineering students and the like.

9. May 22, 2012

### Ken G

GR in cosmology usually comes with a spectacular simplification called "the cosmological principle", which allows the equations of the dynamics of the universe on the largest scales to depend on only one parameter (the age). This is a drastic simplification of the equations that would otherwise be partial differential equations in low symmetry, but are instead an ordinary differential equation in high symmetry. So it turns out that cosmology is the simplest possible application of GR that involves the full nonlinearity of the theory. Understanding that aspect of GR is rather simple, but observational tests of it usually involve breaking the global symmetry so get a lot more intricate.

10. May 22, 2012

### Fredrik

Staff Emeritus
The equations are much harder to solve, but the theorems are much easier. Because of this, it's much harder to understand the mathematical foundations of QM than the mathematical foundations of GR.

I agree with what you said, if you only had the "how to calculate" aspects of the mathematics in mind.

11. May 22, 2012

### robertjford80

how about this, GR only includes one overarching principle whereas QM is used to explain a lot of phenomena, so maybe the math for GR is harder but it takes less time than QM because there's only one principle.

12. May 23, 2012

### muppet

I guess it depends on what you really mean by "understand".

If you mean, "get a working knowledge of", then the comparative difficulty of the different maths involved clearly suggests QM as the easier, as people have talked at length about.

At a conceptual level, how easy QM is to understand is inversely proportional to the amount of time you spend thinking about "the collapse of the state vector". If you're willing to accept that as a given observational fact about the nature of the measurements we can make, then QM is really quite simple; if you can't, it's possible to spend the remainder of your life trying to fill in the conceptual gaps without ever thinking about anything as complicated as a helium atom.

By contrast, GR is generally regarded as having quite a logical structure. There aren't really any totally ad hoc postulates or ill-defined concepts. But the logic is really quite subtle, and just saying that something is understandable is not the same as saying that it's easy to understand

13. May 23, 2012

### George Jones

Staff Emeritus
In my opinion, students could find physics courses in general relativity easier than courses in quantum mechanics. I think that students become more familiar with quantum mechanics because they spend more time studying it.

For example, when I was a student, I:

saw bits of special relativity stuck here and there into a few courses;

did not have the opportunity to take any lecture courses in general relativity;

was required to take three semesters of quantum mechanics as an undergrad and two semesters of advanced quantum mechanics as a grad student;

was required to take two semesters of linear algebra, which gives the flavour of much of the mathematics of quantum mechanics;

was not required to take any maths courses that give the flavour of the mathematics used in general relativity.

Because of the importance and widespread applicability of quantum mechanics, my programme offered much more opportunity to learn quantum mechanics than to learn relativity.

If physics students spent as much time studying general relativity and its mathematical background (say 4 or 5 semesters) as they spend studying quantum mechanics and its mathematical background, then general relativity would be understood by possibly millions of people. I understand why students spend much less time studying relativity than they spend studying quantum theory, and I am not necessarily saying that students should spend more time studying relativity (see the post above by Haelfix), but I do think that this time difference is a big part of the reason that general relativity still has a bit of a reputation.

Fortunately, there are many more good technical books on general relativity (pedagogical, advanced, physical, mathematical, etc.) available now than were available 25 years ago.