# If gravity is geometry then why talk about

1. May 28, 2014

### Sineira

... gravitons and Higgs bosons to convey mass or make space curve?

And to make us fall towards a massive object space is then larger the closer we get?

2. May 28, 2014

### Matterwave

Both of these concepts arise from the other major branch of physics, quantum field theory, which describes the 3 other fundamental forces of nature. General relativity, which describes gravitation, indeed has no need for gravitons and Higgs bosons.

However, it is unsatisfactory to have two different (and conflicting) theories describing the universe. We would eventually like to combine the two theories into one complete theory. The graviton is a theoretical particle that would arise if we were able to turn general relativity into a quantum field theory (so far, we have been unable to do so).

The Higgs boson doesn't really have to do with gravitation. It just gives particles inertial mass. Since it deals with mass, it is (should be) somewhat related to gravitation, but it's not really tied with it currently since we do not have a quantum theory of gravity.

3. May 28, 2014

### dauto

Hard to answer your second question. What do you mean by "larger the closer we get"? Can you elaborate?

Last edited: May 28, 2014
4. May 28, 2014

### Sineira

If a tiny object with comparably negligible mass is going to move towards a large object I just imagined space should get larger and larger the closer we get to make it move?

Thinking about this for two objects I realise I really must imagine this incorrectly because if Earth curves space so that it's "bigger" closer to Earth and the Sun does the same, then why do they attract?
The two "gravitations" must act independently so there really isn't one space to curve?

5. May 28, 2014

### dauto

Almost nothing you said above makes any sense. It is impossible to understand GR as a theory of curved space. You must understand it as a theory of curved space-time. The object falling to earth is just following an inertial trajectory in space-time - That is the "straightest" trajectory you can find in a curved space known as a geodesic. When the four-dimensional spacetime is projected into the three-dimensional space the geodesic trajectory is projected into a space trajectory that can be interpreted as a falling object.

6. May 28, 2014

### Staff: Mentor

General Relativity is an advanced geometric theory that describes space-time curvature in terms of a "metric", which is a mathematical way of describing the geometric and causal structure of space-time. If you aren't familiar with these advanced mathematical concepts then I can guarantee you that you cannot imagine how space-time curvature works to create gravitation. There are many analogies out there to help people, such as the "bowling ball on a trampoline" analogy where the trampoline's surface represents space-time, but these are very, very basic analogies that often confuse people more than they help them.

If you want to learn about gravitation, then you need to learn about General Relativity and at least have some understanding of what the math means.

7. May 28, 2014

### Sineira

I'm just trying to understand.
I will study GR, is there a specific book or similar you can recommend more than others?
I do know a bit of math and I'm willing to put in the effort.

8. May 28, 2014

### dauto

Well, you gotta walk first before you can run. How well do you know special relativity?

9. May 29, 2014

### Sineira

Oh I would say 5 on a scale of 10, whatever that means.

10. May 29, 2014

### Matterwave

What exactly is your math background? "A bit of math" is quite vague. General relativity, in order to understand it in all its mathematical beauty, requires differential geometry (the geometry of curved spaces). But if you just want to get a taste of what General Relativity is like, you can also learn about it phenomenologically from a math-light perspective, or you can look at it from a historical perspective as well.

If your background is strong, you can't really go wrong with Misner, Thorne and Wheeler's Gravitation. It is massive, and quite complete (at least as far as its age will allow), but is basically good for a graduate physics level course in general relativity (it does, however, develop special relativity in its opening chapters). This would NOT be my first recommendation for the subject, but more as a reference for when you get more acquainted with GR.

Bernrd Schutz's A First Course in General Relativity is perhaps a better introductory text, but it still assumes a physics and math background. It's probably at the level of a senior undergraduate or beginning graduate course. If Schutz is not clicking with you, you might try Hartle's Gravity, an Introduction to Einstein's General Relativity.

It's hard for me to recommend a more "easy" book than those though, since I learned GR formally by taking graduate courses in it. The only other book that I might recommend is Lillian R Lieber's The Einstein Theory of Relativity. It's quite a unique book, and an easy read. The math is understandable from a high school math background, and she really does develop tensor calculus! The problem with this book though, is it is quite outdated, and looks at general relativity from a much older mathematical perspective (more tensor calculus than differential geometry). As a first book, though, it might not be bad.

11. May 29, 2014

### Sineira

Thanks Matterwave, much appreciated!

I have an MSc EE and I passed whatever passes as math for that. I see I need to learn quite a bit here still.
I have Ray D'Inverno's book "Introducing Einstein's Relativity" and I'll start with that. Only got to chapter one last time :-)

Looking into these other books now.

12. May 29, 2014

### Matterwave

D'Inverno actually read Lieber's book when he was young. That should tell you how old that book is lol. I've read some of D'Inverno's book. It's viewpoint is also a little outdated. It still uses the "old" language of contravariant versus covariant tensors and defines them based on the transformation properties of their components. The newer language would just call them all tensors, and view tensors as multi-linear maps of vectors and one-forms into real numbers (accomplished in the old point of view via contraction).

This is not necessarily a bad thing. It might be easier to learn it this way at first. But it's a little less geometrical, and be forewarned that it is a little outdated in its language (I suspect due to D'Inverno's liking for Lieber's approach).